2001-2002 Undergraduate Calendar  Programs
	2001-2002 UNDERGRADUATE CALENDAR
	Carleton University

Mathematics and Statistics

(Science)

4302 Herzberg Building

Telephone: 520-2155

Undergraduate Adviser: 520-2150

WWW address: www.math.carleton.ca

Academic Administration

Director, A.B. Mingarelli

Associate Director, E.J. Norminton

Director, Institute for Graduate Studies and Research in Mathematics and Statistics, S. Melkonian

Adviser for Undergraduate Studies, K. Small

Co-operative Education Program Adviser, S. Mills

Teaching Staff

Professors Emeriti

M. Csörgö, B.A. (Budapest), M.A. (McGill), Ph.D. (McGill), F.R.S.C. • D.A. Dawson, B.Sc., M.Sc. (McGill), Ph.D. (Massachusetts Institute of Technology), F.R.S.C. • V.Dlab, R.N.Dr. (Charles), C.Sc. (Charles), Ph.D. (Khartoum), D.Sc. (Charles), F.R.S.C. • M.S. Macphail, B.A. (Queen's), M.A. (McGill), D.Phil. (Oxford), D.Sc. (Carleton), F.R.S.C. •J.N.K. Rao, B.A. (Andhra), M.A. (Bombay), Ph.D. (Iowa State), F.R.S.C.

Professors

J.D. Dixon, M.Sc. (Melbourne), Ph.D. (McGill) • Cyril W.L. Garner, B.Sc. (New Brunswick), M.A., Ph.D. (Toronto), F.T.I.C.A. • Angelo B. Mingarelli, B.Sc. (Loyola College), M.Sc., Ph.D. (Toronto) • J.N. Pandey, M.Sc. (Banaras Hindu), Ph.D. (New York) • Luis Ribes, Licenciado en Matematics (Madrid), M.A., Ph.D. (Rochester), Doctor en Ciencias (Madrid) • Kenneth Stuart Williams, B.Sc. (Birmingham), M.A., Ph.D. (Toronto), D.Sc. (Birmingham)

Associate Professors

Yuly Billig, Ph.D. (Moscow State) Amitava Bose, B.Sc., M.Sc. (McGill), Ph.D. (Carleton) • Patrick J. Farrell, B.Eng., M.Eng., M.B.A., Ph.D. (McGill) Che-Kao Fong, B.Sc. (Chinese University of Hong Kong), M.Sc., Ph.D.(Toronto) • Zhicheng Gao, B.A. (Nanjing), Ph.D. (California at San Diego) • Roger Herz-Fischler, B.Sc. (Polytechnic Institute of Brooklyn), M.A., Ph.D. (Oregon) • L.E. May, B.Sc., M.Phil. (London), Ph.D. (North Carolina State) • Sam Melkonian, B.Sc., M.Sc., Ph.D. (McGill) • Shirley Mills, B.Sc., M.Sc. (Manitoba), Ph.D. (Alberta) • Majid Mojirsheibani, B.Sc., M.Sc., Ph.D. (Toronto) M.J. Moore, B.Sc., Ph.D. (Birmingham) • Brian C. Mortimer, B.Sc. (Carleton), M.Sc. (Alberta), Ph.D. (London) • Edward J. Norminton, M.A. (Western Ontario), Ph.D. (Toronto) • John C. Poland, M.Sc., Ph.D. (McGill) • Irwin S. Pressman, B.Sc. (Manitoba), M.B.A. (Toronto), Ph.D. (Cornell) • Barbara Szyszkowicz, B.Sc., M.Sc. (Wroclow), Ph.D. (Carleton) Yiqiang Zhao, B.Eng. (Nanjing), M.S., Ph.D. (Saskatchewan)

Assistant Professors

Wojciech Jaworski, M.Sc., Ph.D. (Torun), Ph.D. (Queen’s)• Daniel Panario, M.Sc. (Sao Paulo), Ph.D. (Toronto) Konstantin Rybnikov, M.Sc. (Moscow State), Ph.D. (Queen’s)

Instructors

A. Alaca, B.A., B.Sc. (Karadeniz Technical), M.Sc. (New Brunswick), Ph.D. (Carleton) S. Alaca, B.Sc. (Karadeniz Technical), M.Sc. (New Brunswick), Ph.D. (Carleton) E. Devdariani, B.Sc., M.Sc. (Moscow State), Ph.D. (Queen’s) S. Dubé, B.Sc., M.Sc. (Carleton) A. Monadi, B.Sc., M.Sc. (Mashad), Ph.D. (Carleton) • A. Woodside, B.Sc. (Waterloo), M.Sc. (Carleton)

Distinguished Research Professors

M. Csörgö • D.A. Dawson • V. Dlab • E.O. Kreyszig, M.Sc., D.Sc. (Darmstadt)• M. Rahman, B.A. (Cambridge), B.Sc. (Dacca), M.A. (Cambridge), M.Sc. (Dacca), Ph.D. (New Brunswick) • J.N.K. Rao A.K.Md.E. Saleh, B.Sc., M.Sc. (Dhaka), M.A., Ph.D. (Western Ontario)

Adjunct Research Professors

M. Chacron D. Krewski (Health Canada) • I.A. Manji• P. Révész (Academy of Sciences, Hungary) • A.B. Singh (Research Triangle Institute)

Adjunct Professors

J.E. Graham • K. Hardy • P. Mandl • L.D. Nel • B.M. Puttaswamaiah

Sessional Lecturers

J. Chalmers • A. Galan-Benhin * I. Ganadry * K. Ghanbari * A. Mashaie * M. Lunney * K. Zhao

Programs in Mathematics and Statistics

The School of Mathematics and Statistics offers a wide variety of programs ranging from those giving a strong training in the theoretical aspects of mathematics and statistics to those which emphasize applications to industry and government.

The School offers both Honours and Major programs leading to the B.Math. degree. A co-operative education option is also available with the honours programs, allowing qualified honours students to complement their academic studies with practical experience in the workplace.

The following is a list and short description of the programs which are available:

Mathematics B.Math.(Honours and Major)

The Major programs are generally less theoretical than the Honours programs which may form an excellent introduction to graduate studies. The main areas of concentration are: algebra, analysis, topology, applied mathematics (classical and modern), statistics and probability.

Computer Mathematics B.Math.(Honours and Major)

The programs in computer mathematics are designed to provide a student with a background of computer-related mathematical ideas together with a firm base of computer science. These programs are of interest to students who are preparing for careers in government, industry, management, or systems analysis.

The Honours Computer Mathematics program also includes an Information Technology stream.

Statistics B.Math.(Honours and Major)

The Honours program is designed primarily for a student who wishes to prepare for a career as a professional statistician. The Major program in Statistics provides the academic groundwork for employment opportunities at the junior methodologist level, in a variety of statistics-related fields.

Computer Statistics B.Math.(Honours)

The Honours program in Computer Statistics is designed to provide students with a broad background in three complementary disciplines — computing, statistics, and mathematics — as preparation for careers in informatics (the collection, management, and analysis of information).

Computer Science and Mathematics B.Math.(Honours)

The Combined Honours program in Computer Science and Mathematics is a limited-enrolment program resembling the Bachelor of Computer Science program, placing equal emphasis on computer science and mathematics. There are two options available for concentration, namely:

Computing Theory and Numerical Methods

Statistics and Computing

Mathematics and Economics B.Math.(Honours)
Statistics and Economics B.Math.(Honours)

The Combined Honours programs in Mathematics and Economics, or in Statistics and Economics, provide students with a strong blend of courses in these modern disciplines.

Mathematics and Physics B.Sc.(Double Honours)

This program, which requires a minimum of 21.5 credits, is intended for students with a very strong background and interests in both mathematics and physics.

Combined B.Math./M.Sc. in Mathematics, or in Statistics

This program is designed as a "fast-track" to enable exceptional students to graduate in four years, with both a B.Math. and an M.Sc.

Admission Requirements

Bachelor of Mathematics (Honours) Programs offered by the School of Mathematics and Statistics

First Year (Honours Programs)

1. The OSSD including six OACs with an average of 75 percent or better, or equivalent, including a core consisting of an OAC in calculus and an OAC in algebra and geometry. An average of 65 percent or better is required over the two core OACs; or

2. The successful completion of 5.0 credits approved for a Qualifying-University year program with a GPA of 8.0 or better, including the core of: 0.5 credit in calculus and 0.5 credit in algebra.

Mathematics 69.007* and 69.017* must be successfully completed with a GPA over the two courses of 5.0 or better.

The combined B.Math./M.Sc. program in Mathematics, or in Statistics has a higher admission requirement than that stated above (see p. 332).

The Co-operative Education options have a higher admission requirement than those stated above.

Students presenting credits for one or more repeated subjects or courses may not be admitted directly into an Honours program except on the recommendation of the School. Applicants should note that meeting the minimum requirements stated above does not guarantee admission to the B.Math. programs. Students presenting OAC (or equivalent) averages lower than those stated above might be admissible on an individual basis after consideration of whether there are special circumstances which would permit their admission.

Advanced Standing (Honours Programs)

1. An in-course student wishing to enter an Honours program must apply to the Undergraduate Adviser, or the Associate Director, through the Registrarial Services office for the Faculty of Science.

2. For entry to an Honours program after the completion of First year, a student must have a GPA of 5.0 or better in the Honours subject(s), an overall GPA of 4.0 or better and the recommendation of the School. A student beginning the final 10.0 credits towards an Honours degree must present a GPA of 6.0 or better in the Honours subject(s), an overall GPA of 5.0 or better and the recommendation of the School. A student beginning the final 5.0 credits towards an Honours degree must present a GPA of 6.5 or better in the Honours subject or in each Honours subject and a GPA of 5.0 or better overall, as calculated for graduation.

3. Students applying for admission to a B.Math.(Honours) program at Carleton after having obtained a degree from Carleton or another university shall meet the same criteria as specified above.

4. No student may be admitted to a B.Math.(Honours) program without satisfying the requirements for entry to the corresponding Major program.

5. Students in the final year of a Major degree program wishing to be considered for entry to an Honours program must apply to the Registrarial Services office for the Faculty of Science to have their names withdrawn from the graduation list before March 1 of that year. If subsequently the student is not accepted for an Honours program, the student must reapply for graduation.

Applicants from outside the province of Ontario must present acceptable equivalent certificates generally required for admission to universities in their own provinces or countries. Applicants should note that meeting the minimum requirements stated above does not guarantee admission to the B.Math. programs.

Students presenting OAC (or equivalent) averages lower than those stated above might be admissible on an individual basis after consideration of whether there are special circumstances which would permit their admission.

Bachelor of Mathematics (Major) Programs offered by the School of Mathematics and Statistics

First Year (Major Programs)

1. The OSSD including six OACs with an average of 70 percent or better, or equivalent, including a core consisting of an OAC in calculus and an OAC in algebra and geometry. An average of 65 percent or better is required over the two core OACs. Students presenting an average of 65 to 69 percent over the six OACs may be considered on an individual basis; or

2. The successful completion of 5.0 credits approved for a Qualifying-University year program with a GPA of 7.0 or better, including the core of: 0.5 credit in calculus and 0.5 credit in algebra. Mathematics 69.007* and 69.017* must be successfully completed with a GPA over the two courses of 5.0 or better.

Advanced Standing (Major Programs)

1. In order to be admitted to Second year, a student must have completed the equivalent of a First-year B.Math. program with the required academic standing.

2. Applications for admission to Third year will be evaluated on their merits, and advanced standing granted for studies undertaken elsewhere when these are recognized as the equivalent of subjects offered at Carleton University.

3. Students not admitted to a degree program but taking courses at Carleton University as Special students may, on transfer to a B.Math. program, receive credit for not more than 7.0 credits, 4.0 of which must meet the First-year promotion requirements.

Program Requirements

Mathematics B.Math.(Honours)

This program requires a total of 20.0 credits with a minimum of 11.0 credits in Mathematics.

The First Year course pattern and the Statistics course requirement is outlined below.

1. Mathematics 69.102, 69.112 with an average grade of C+ or better [see also note (ii) below];

2. Mathematics 70.200, 70.210, 70.244*, 70.259*, 70.265*;

3. Mathematics 70.301*, 70.307*, 70.316*, 70.318*, and at least one of 70.302* or 70.308* (it is strongly recommended that Mathematics 70.301* be taken in the Third year);

4. 1.0 credit in Mathematics (70 series) at the 300-level or above;

5.Mathematics 70.495*, and 1.5 credits in Mathematics (70 series) at the 400-level or above;

6. Breadth Requirement: At least 4.0 credits outside the School of Mathematics and Statistics and the School of Computer Science, including: at least 1.0 credit from the College of Natural Sciences, and at least 2.0 arts or social science credits. Of these 4.0 credits, at least 1.0 credit must be at the 200-level or above.

In this program, the remaining 5.0 credits may be chosen from any department/school, including Mathematics and Statistics, subject only to the restriction that of the total of 20.0 credits, not more than 7.0 may be below the 200-level.

Students wishing to specialize in Applied Analysis may, with permission of the School, replace items 3, 4, and 5 in the Mathematics degree requirements by:

3. Mathematics 70.302*, 70.307*, 70.308*, 70.346*, 70.356*, and 1.0 credit from Mathematics 69.381*, 69.384*, 69.386*, and Honours courses in Mathematics (70 series) at the 300-level or above;

4. Mathematics 70.495*, 70.470*, at least one of 70.471*, 70.472*, and 0.5 additional credit in Mathematics at the 400-level.

Students wishing to specialize in Stochastics may, with permission of the School, replace items 3, 4, and 5 in the Mathematics degree requirements by:

3. Mathematics 70.301*, 70.308*, 70.356*, 70.358*, 70.359*, and one of 70.355*, 69.381*;

4. Mathematics 70.451*, and 0.5 credit selected from the range 70.450* to 70.459*; Mathematics 70.495*, and 1.0 credit in Mathematics at the 400-level or above.

Students specializing in Applied Analysis or Stochastics are encouraged to include at least 1.5 credits in Computer Science in their program.

Notes:

Prospective Honours students should note that the courses Mathematics 69.102, 69.112, 70.200 and 70.210 provide more than just the basic mathematical techniques; they also provide training in rigorous mathematical thinking and, as such, are basic to the Honours Mathematics program.

Students may be admitted to an Honours program in Mathematics after successful completion of First Year with:

• a GPA of 7.0 or better on all half credits offered from: Mathematics 69.107*, 69.207*; 69.117*, 69.217*; and
• a weighted GPA of 6.0 or better on all credits offered from:

Mathematics 69.102, 69.107*, 69.207*; 69.112, 69.117*, 69.217*.

Students offering Mathematics 69.107* must then take Mathematics 69.207*, and students offering Mathematics 69.117* must then take Mathematics 69.217*.

(iii) In certain cases the School may permit a student to replace a course at the Fourth-year level by a graduate course.

Computer Mathematics B.Math.(Honours)

This program requires a total of 20.0 credits; this includes a minimum of 14.0 credits in Mathematics and Computer Science in the main program, or 13.5 credits in Mathematics and Computer Science in the Information Technology stream.

Students may also be admitted to the Information Technology stream of this program after completing the B.Math.(Major) [or the former B.Sc.(Major) or the B.A.(Pass)] program in Computer Mathematics, provided that Faculty of Science requirements concerning Honours standing have been maintained. Students with Honours standing from their B.Math.(Major) [or the former B.Sc.(Major) or the former B.A.(Pass)] program in Computer Mathematics would require 5.0 additional credits in the Information Technology stream of this honours program: 3.5 credits in Mathematics and Computer Science [ 6, 7, 8 below], and 1.5 credits of options [from 10].

The First Year course pattern and the Statistics course requirement are given in detail below.

Computer Mathematics:

1. Mathematics 69.102, 69.112 with an average grade of C+ or better [see also note (ii) below];

2. Computer Science 95.142*, 95.145*, 95.146*, 95.242*, 95.244*;

3. Mathematics 70.200, 70.210, 70.244*, 70.259*, 70.265*;

4. Mathematics 69.384*, 70.301*;

5. Mathematics 70.316* and 70.318*; or Mathematics 70.385* and 69.381*;

6. 1.0 credit from Mathematics 69.375*, 69.381*, 69.382*, 69.386*, 69.387*, 69.389* and courses in the range 70.302* and above;

7. Mathematics 70.356* or 70.358*;

8. Mathematics 70.486*, and one of 70.482* or 70.483*;

9. Mathematics 70.495*, and an additional 0.5 credit from Mathematics 70.481*, 70.482*, 70.483*, 70.485*, 70.488*, or an approved 0.5 credit at the graduate level (70.580 series);

10. an additional 0.5 credit in Computer Science at the 200-level or above;

11. Breadth Requirement: At least 4.0 credits outside the School of Mathematics and Statistics and the School of Computer Science, including: at least 1.0 credit from the College of Natural Sciences, and at least 2.0 arts or social science credits. Of these 4.0 credits, at least 1.0 credit must be at the 200-level or above.

In this program, the remaining 2.0 credits may be chosen from any department/school, including Mathematics and Statistics, subject only to the restriction that of the total of 20.0 credits, not more than 7.0 may be below the 200-level.

Computer Mathematics - Information Technology stream:

1. Mathematics 69.102 (or 69.107* and 69.207*), and Mathematics 69.112 (or 69.117* and 69.217*) [for the GPA requirements over these courses, please see the Notes, item (ii) below];

2. Computer Science

95.142*, 95.145*, 95.146*, 95.242*, 95.244*;

3. Mathematics 69.208*, 69.257*, 69.265*; and 69.218* or 69.311*;

4. Mathematics 69.384*, 70.385*; at least one of Mathematics 69.381* or 69.386*; and 1.0 additional credit in Mathematics at the 300-level (excluding 69.352*);

5. an additional 0.5 credit in Computer Science (95-series) at the 200-level or above [and 95.305* or 95.304* are highly recommended]; and an additional 0.5 credit in Mathematics or Computer Science at the 200-level or above;

6. Mathematics 70.495*; and 1.0 additional credit in Mathematics and Statistics, 400-level or above;

7. 1.0 credit in Computer Science (95-series) at the 300-level or above;

8. 1.0 credit in Mathematics and Statistics at the 300-level or above;

9. Breadth Requirement: At least 4.0 credits outside the School of Mathematics and Statistics and the School of Computer Science, including: at least 1.0 credit from the College of Natural Sciences, and at least 2.0 arts or social science credits. Of these 4.0 credits, at least 1.0 credit must be at the 200-level or above.

In this program-stream, the remaining 2.5 credits may be chosen from any department/school, including Mathematics and Statistics, subject only to the restriction that of the total of 20.0 credits, not more than 7.0 may be below the 200-level.

Notes:

Prospective Honours students should note that the courses Mathematics 69.102, 69.112, 70.200 and 70.210 provide more than just the basic mathematical techniques, since they also provide training in rigorous mathematical thinking.

(ii) Students may be admitted to an Honours program in Computer Mathematics after successful completion of First Year with:

• a GPA of 7.0 or better on all half credits offered from: Mathematics 69.107*, 69.207*; 69.117*, 69.217*; and
• a weighted GPA of 6.0 or better on all credits offered from:
• Mathematics 69.102, 69.107*, 69.207*; 69.112, 69.117*, 69.217*.

Students offering Mathematics 69.107* must then take Mathematics 69.207*, and students offering Mathematics 69.117* must then take Mathematics 69.217*.

(iii) In certain cases the School may permit a student to replace a course at the Fourth-year level by a graduate course.

(iv) Business 42.142*, 42.242* and Computer Science 95.101* may not count for credit in this program, even as free electives.

Computer Statistics B.Math.(Honours)

This program is designed to provide students with a broad background in computing, statistics and mathematics, in preparation for careers in informatics - the collection, management and analysis of information (e.g., data mining and knowledge discovery in databases). This program requires a total of 20.0 credits, including a minimum of 13.5 credits in Mathematics and Computer Science (8.5 in Mathematics and 4.5 in Computer Science, plus an Honours project).

The First Year course pattern and the Statistics course requirement are given elsewhere in this section.

1. Mathematics 69.102 (or 69.107* and 69.207*), and Mathematics 69.112 (or 69.117* and 69.217*) [for the GPA requirements over these courses, please see the Notes, item (ii) below];

2. Computer Science 95.142*, 95.145*, 95.146*, 95.242*, 95.244*; one additional credit in Computer Science, 200-level or above (95.203*, 95.304* and 95.305* are recommended);

3. Mathematics 70.265* (or 69.265*) and 70.259* (may be replaced by 69.257* and 69.259*, with a minimum grade of B in each); 70.358* and 70.359* (may be replaced by 69.358* and 69.359*, with a minimum grade of B in each); 70.355*, 70.356*;

4. Mathematics 69.208*; 69.384* ; 69.386*; one of 69.218* or 69.311*;

5. Mathematics 70.495* (Honours Project);

6. 1.5 credits from Mathematics 70.450* - 70.459*;

7. 1.0 credit in Computer Science at the 300-level or above;

8. Breadth Requirement: At least 4.0 credits outside the School of Mathematics and Statistics and the School of Computer Science, including: at least 1.0 credit from the College of Natural Sciences, and at least 2.0 arts or social science credits. Of these 4.0 credits, at least 1.0 credit must be at the 200-level or above.

In this program, the remaining 2.5 credits may be chosen from any department/school, including Mathematics and Statistics, subject only to the restriction that of the total of 20.0 credits, not more than 7.0 may be below the 200-level.

Notes:

Prospective Honours students should note that the courses Mathematics 69.102, 69.112, 70.200 and 70.210 provide more than just the basic mathematical techniques, since they also provide training in rigorous mathematical thinking.

(ii) Students may be admitted to an Honours program in Computer Statistics after successful completion of First Year with:

• a GPA of 7.0 or better on all half credits offered from: Mathematics 69.107*, 69.207*; 69.117*, 69.217*; and
• a weighted GPA of 6.0 or better on all credits offered from:
• Mathematics 69.102, 69.107*, 69.207*; 69.112, 69.117*, 69.217*.

Students offering Mathematics 69.107* must then take Mathematics 69.207*, and students offering Mathematics 69.117* must then take Mathematics 69.217*.

(iii) In certain cases the School may permit a student to replace a course at the Fourth-year level by a graduate course.

(iv) Business 42.142*, 42.242* and Computer Science 95.101* may not count for credit in this program, even as free electives.

Statistics B.Math.(Honours)

This program is designed for students wishing to pursue careers as professional statisticians.

The program requires a total of 20.0 credits, with a minimum of 11.0 credits in Mathematics and Statistics.

The First Year course pattern and the Statistics course requirement are given elsewhere in this section.

1. Mathematics 69.102, 69.112 with an average grade of C+ or better [see also note (ii) below];

2. Computer Science 95.105*, 95.106*;

3. Mathematics 70.200, 70.210, 70.244*, 70.259*, 70.265* (Mathematics 70.210 may be deferred until Third year, and may be replaced by Mathematics 69.317*, plus 0.5 credit from: Honours Mathematics at the 300-level or above, and Mathematics 69.375*, 69.381*, 69.387*, 69.389*);

4. Mathematics 70.355*, 70.356*, 70.358*, 70.359*, 69.386*, and an additional 0.5 credit in Mathematics (70-series) at the 300-level or above;

5. Mathematics 70.450*, 70.495*, and 1.5 credits from the range Mathematics 70.451* to 70.459*;

6. Breadth Requirement: At least 4.0 credits outside the School of Mathematics and Statistics and the School of Computer Science, including: at least 1.0 credit from the College of Natural Sciences, and at least 2.0 arts or social science credits. Of these 4.0 credits, at least 1.0 credit must be at the 200-level or above.

In this program, the remaining 4.0 credits may be chosen from any department/school, including Mathematics and Statistics, subject only to the restriction that of the total of 20.0 credits, not more than 7.0 may be below the 200-level.

Notes:

Prospective Honours students should note that the courses Mathematics 69.102, 69.112, 70.200 and 70.210 provide more than just the basic mathematical techniques; they also provide training in rigorous mathematical thinking and, as such, are basic to the Honours Statistics program.

(ii) Students may be admitted to an Honours program in Statistics after successful completion of First Year with:

• a GPA of 7.0 or better on all half credits offered from: Mathematics 69.107*, 69.207*; 69.117*, 69.217*; and
• a weighted GPA of 6.0 or better on all credits offered from:
• Mathematics 69.102, 69.107*, 69.207*; 69.112, 69.117*, 69.217*.

Students offering Mathematics 69.107* must then take Mathematics 69.207*, and students offering Mathematics 69.117* must then take Mathematics 69.217*.

(iii) In certain cases the School may permit a student to replace a course at the Fourth-year level by a graduate course.

(iv) Students considering a career in actuarial science are advised to include Mathematics 69.381* in their programs.

Combined Honours Programs

Computer Science and Mathematics B.Math.(Honours)

This program is administered by a committee with representatives from the School of Computer Science and the School of Mathematics and Statistics.

Enrolment in this program is limited. Applicants should note that meeting the minimum published requirements for admission to this program does not imply automatic acceptance.

This program requires a total of 20.0 credits, with a minimum of 15.0 credits in Computer Science and Mathematics, placing equal emphasis on both these disciplines. Students may choose one of two options which serve as areas of concentration. All course selections must be approved both by the School of Mathematics and Statistics and the School of Computer Science

The First Year course pattern is given elsewhere in this section.

1. Mathematics 69.102, 69.117*; Computer Science 95.142*, 95.145*, 95.146*;

Note: Students who wish to keep open the choice of other Honours programs in Mathematics and Statistics are advised to take Mathematics 69.112 instead of 69.117* (and 69.217*).

2. Mathematics 70.200, 69.217*; Computer Science 95.203*, 95.242*, . 95.244*, and 95.304*;

3. Mathematics 70.210; Computer Science 95.300*, 95.305*, 95.384*, 95.385*; Mathematics 70.495* or Computer Science 95.495*.

4. Breadth Requirement: At least 4.0 credits outside the School of Mathematics and Statistics and the School of Computer Science, including: at least 1.0 credit from the College of Natural Sciences, and at least 2.0 arts or social science credits. Of these 4.0 credits, at least 1.0 credit must be at the 200-level or above.

5. 1.0 free option credit, subject only to the requirement that of the total of 20.0 credits, not more than 7.0 may be below the 200-level.

Candidates must also satisfy one of the following option requirements, each of which contains a total of 5.0 credits in Computer Science and Mathematics.

Option: Computing Theory and Numerical Methods (CTNM)

6. Mathematics 70.244*, 70.265*;

7. Mathematics 69.381*, 69.386* and one of Mathematics 70.301*, 70.302*, 70.307*, 70.308*;

8. Computer Science 95.484*, and 1.0 credit from Mathematics 70.481*, 70.482*, 70.483*, 70.485*, 70.486*, 70.488*;

9. 1.0 additional credit in Computer Science at the 300-level or above.

Option: Statistics and Computing (STC)

6. Mathematics 70.244*, 70.259*, 70.265*;

7. Mathematics 70.358*, 70.359* and at least one of 70.355*, 70.356*;

8. 1.0 credit in Mathematics from the range Mathematics 70.450* to 70.459*;

9. 1.0 credit in Computer Science at the 400-level.

Continuation in the Program:

To continue in the program, a student must:

(a) by the end of August each year, have gained at least 0.5 credit in the past 12 months towards the degree requirements, and

(b) have accumulated a GPA of 6.5 or better in each of Computer Science and Mathematics, and a GPA of 5.0 or better overall. (GPAs are to include any failing grades that have not yet been replaced by a passing grade in the same or a substitute course.)

Failure to comply with these standards requires withdrawal from the program.

Note: Some courses offered by the School of Business and the Department of Systems and Computer Engineering may be taken for credit as Computer Science courses in this program. For a complete list of these courses see the School of Computer Science entry: Other Relevant Courses Offered, p.195.

Mathematics and Economics B.Math.(Honours)

This program requires a total of 20.0 credits, including 6.0 credits in Economics and 9.0 credits in Mathematics and Statistics.

The First Year course pattern and the Statistics course requirement are given elsewhere in this section..

First Year:

1. Mathematics 69.102, 69.112 (or their equivalents);

2. Economics 43.100;

3. Computer Science 95.105*, 95.106*;

4. 1.0 credit free option.

Second Year:

1. Mathematics 70.200, 70.210, 70.244*, 70.265*, 70.259* (one of 70.210 or 70.244* may be delayed to Third Year);

2. Economics 43.202*, 43.203*, 43.212*, 43.213*.

Third Year:

1. Mathematics 70.301*, 70.358*, 70.359*, at least one of 70.302* or 70.308*;

2. Economics 43.420*, 43.421*;

3. 1.5 credits of options.

Fourth Year:

1. an additional 0.5 credit in mathematics at the 300- or 400-level;

2. 1.0 additional credit in mathematics at the 400-level;

3. Economics 43.490 (or 43.498), and 1.0 additional credit in Economics at the 400-level;

4. 1.5 credits of options.

Notes: (a) Students in this program may not count Economics 43.240* for academic credit (even as a free option);

(b) Students in this program are required to include a credit from the College of Natural Sciences in their course requirements.

Statistics and Economics B.Math.(Honours)

This program requires a total of 20.0 credits, including 6.0 credits in Economics and 8.5 or 9.0 credits in Mathematics and Statistics.

The First Year course pattern and the Statistics course requirement are given elsewhere in this section.

First Year:

1. Mathematics 69.102, 69.112 (or their equivalents);

2. Economics 43.100;

3. Computer Science 95.105*, 95.106*;

4. 1.0 credit free option.

Second Year:

1. Mathematics 70.200, 70.244*, 70.265*, 70.259*, and 69.317* (or 70.210);

2. Economics 43.202*, 43.203*, 43.212*, 43.213*.

Third Year:

1. Mathematics 70.355*, 70.356*, 70.358*, 70.359*;

2. Economics 43.420*, 43.421*;

3. 2.0 credits of options.

Fourth Year:

1. Mathematics 70.452*, 70.453*, and 0.5 credit from: 70.450*, 70.451*, 70.456* - 70.459*, 70.495*;

2. Economics 43.490 (or 43.498) and 1.0 credit in Economics at the 400-level;

3. 1.5 credits of options (or only 1.0 credit, if 70.210 was taken instead of 69.317*).

Notes: (a) Students in this program may not count Economics 43.240* for academic credit (even as a free option);

(b) Students in this program are required to include a credit from the College of Natural Sciences in their course requirements.

Mathematics and Physics B.Sc.(Double Honours)

This program consists of 21.5 credits, of which 16.5 or 17.0 credits are in Mathematics, Physics, and Engineering Physics. Entrance after First year and continuation in the program at the end of First year requires: successful completion of First year with a GPA of 9.0 or better over the courses Mathematics 69.102 and 69.112 (or their equivalents), and a GPA of 9.0 or better over the courses Physics 75.101* and 75.102*; or permission of the School of Mathematics and Statistics, and the Department of Physics.

Students entering the program directly from High School are required to present a minimum average of 75% in OAC Physics, Calculus, and Algebra and Geometry. For students seeking admission to this program who have already completed Physics 75.103* and 75.104*, consideration will be given to crediting these in place of Physics 75.101* and 75.102*.

First Year

Mathematics 69.102, 69.112;

Physics 75.101*, 75.102*;

1.0 credit in an experimental science: Biology 61.103* and 61.104*, or Chemistry 65.100, or Geology 67.105, or 67.106* and one of 67.107* or 67.108*;

0.5 credit in Computer Science: 95.105* or 95.107*;

0.5 credit arts or social science elective.

Second Year

Mathematics 70.200, 70.210, 70.244*, 70.265*, and 69.375*;

Physics 75.222*, 75.264*, 75.382*;

0.5 credit in Computer Science.

Third Year

Mathematics 70.301*, 70.302*, 70.307*, 70.316*;

Physics 75.307*, 75.366*, 75.371*, and 75.449*;

Engineering 97.315* and 97.399*;

0.5 credit arts or social science elective.

Fourth Year

1.0 credit in Mathematics at the 400-level or above (highly recommended: Mathematics 70.403*);

Physics 75.477*, 75.478*, and 1.0 additional credit in Physics at the 400-level or above;

Mathematics 70.495* or Physics 75.497* or 75.498*, and 0.5 credit Free Elective; or Physics 75.499;

1.0 credit arts or social science elective;

0.5 credit Free Elective.

Note: the Co-operative Education Option is not normally available in this program.

Mathematics B.Math.(Major)

This program requires a total of 15.0 credits, with a minimum of 7.0 credits in Mathematics.

The First Year course pattern and the Statistics course requirement are given elsewhere in this section.

1. Mathematics 69.102, 69.112 with an average grade of C- or better [see also note (i) below];

2. Mathematics 69.208*, 69.218*, 69.244*, 69.257*;

3. 3.0 credits in Mathematics selected from: Mathematics 69.259* and Mathematics (69-series) at the 300-level, excluding 69.311* and 69.352*;

(With permission of the School, one or more of the courses in requirement 3 may be replaced by a course in the 70 series at the 300- or 400-level, provided that of the total of 3.0 credits, not more than 2.0 are in the same area.)

4. Breadth Requirement: At least 4.0 credits outside the School of Mathematics and Statistics and the School of Computer Science, including: at least 1.0 credit from the College of Natural Sciences, and at least 2.0 arts or social science credits. Of these 4.0 credits, at least 1.0 credit must be at the 200-level or above.

In this program, the remaining 4.0 credits may be chosen from any department/school, including Mathematics and Statistics, subject only to the restriction that of the total of 15.0 credits, not more than 7.0 may be below the 200-level.

Students wishing to specialize in Applied Analysis may, with the permission of the School, replace requirements 2 and 3 in the Mathematics degree requirements by:

2. Mathematics 69.208*, 69.244*, 69.257*;

3. Mathematics 69.307*, 69.375*, and one of Mathematics 69.344*, 69.381*, 69.386*, or Physics 75.381*;

4. 1.0 additional credit in Mathematics at the 300-level, excluding 69.311* and 69.352*;

5. 1.0 additional credit at the 200- or 300-level chosen from Mathematics or Computer Science.

Students specializing in Applied Analysis are encouraged to include at least 1.5 credits in Computer Science in their program.

Note:

Students may be admitted to a Major program in Mathematics after successful completion of First Year with:

(a) a GPA of 5.0 or better on all half credits offered from:

Mathematics 69.107*, 69.207*; 69.117*, 69.217*; and

(b) a weighted GPA of 4.0 or better on all credits offered from:

Mathematics 69.102, 69.107*, 69.207*; 69.112, 69.117*, 69.217*.

Students offering Mathematics 69.107* must then take Mathematics 69.207*, and students offering Mathematics 69.117* must then take Mathematics 69.217*.

Computer Mathematics B.Math.(Major)

This program requires a total of 15.0 credits, with a minimum of 10.0 credits in Mathematics and Computer Science.

The First Year course pattern and the Statistics course requirement are given  .

1. Mathematics 69.102 (or 69.107* and 69.207*), and Mathematics 69.112 (or 69.117* and 69.217*) [for the GPA requirements over these courses, please see the GPA statement in Note (i) below];

2. Computer Science 95.102*, 95.105*, 95.106*, 95.202*, 95.204*;

3. Mathematics 69.208*, 69.257*, 69.265*; 69.218* or 69.311*;

4. Mathematics 69.384*, 70.385*; at least one of Mathematics 69.381* or 69.386*; and 1.0 additional credit in Mathematics at the 300-level (excluding 69.352*);

5. an additional 0.5 credit in Computer Science (95-series) at the 200-level or above [and 95.305* or 95.304* are highly recommended], and an additional 0.5 credit in Mathematics or Computer Science at the 200-level or above;

6. Breadth Requirement: At least 4.0 credits outside the School of Mathematics and Statistics and the School of Computer Science, including: at least 1.0 credit from the College of Natural Sciences, and at least 2.0 arts or social science credits. Of these 4.0 credits, at least 1.0 credit must be at the 200-level or above.

7. The remaining 1.0 credit may be chosen from any department/school, including Mathematics and Statistics, subject only to the restriction that of the total of 15.0 credits, not more than 7.0 may be below the 200-level.

Notes:

Students may be admitted to a Major program in Computer Mathematics after successful completion of First Year with:

• a GPA of 5.0 or better on all half credits offered from:
• Mathematics 69.107*, 69.207*; 69.117*, 69.217*; and

(b) a weighted GPA of 4.0 or better on all credits offered from: Mathematics 69.102, 69.107*, 69.207*; 69.112, 69.117*, 69.217*.

Students offering Mathematics 69.107* must then take Mathematics 69.207*, and students offering Mathematics 69.117* must then take Mathematics 69.217*.

(ii) Business 42.142*, 42.242* and Computer Science 95.101* may not count for credit in this program, even as free electives.

Statistics B.Math.(Major)

This program requires a total of 15.0 credits, with a minimum of 6.0 credits in Mathematics and Statistics.

The First Year course pattern and the Statistics course requirement are given elsewhere in this section.

1. Mathematics 69.102, 69.112 with an average grade of C- or better [see also note (i) below];

2. Mathematics 69.208*, 69.257*, 69.259*;

3. Mathematics 69.353*, 69.354*, 69.357*, 69.358*, 69.359*;

4. 1.0 additional credit at the 200-level or above chosen in a relevant topic from courses offered by the Faculty of Science, the School of Computer Science or the Faculties of Arts and Social Sciences, or Public Affairs and Management. This credit is in addition to the Breadth Requirement in item 5.

5. Breadth Requirement: At least 4.0 credits outside the School of Mathematics and Statistics and the School of Computer Science, including: at least 1.0 credit from the College of Natural Sciences, and at least 2.0 arts or social science credits. Of these 4.0 credits, at least 1.0 credit must be at the 200-level or above.

In this program, the remaining 4.0 credits may be chosen from any department/school, including Mathematics and Statistics, subject only to the restriction that of the total of 15.0 credits, not more than 7.0 may be below the 200-level.

Notes:

Students may be admitted to a Major program in Statistics after successful completion of First Year with:

• a GPA of 5.0 or better on all half credits offered from:
• Mathematics 69.107*, 69.207*; 69.117*, 69.217*; and

(b) a weighted GPA of 4.0 or better on all credits offered from: Mathematics 69.102, 69.107*, 69.207*; 69.112, 69.117*, 69.217*.

Students offering Mathematics 69.107* must then take Mathematics 69.207*, and students offering Mathematics 69.117* must then take Mathematics 69.217*.

(ii) Students majoring in Statistics are urged to include at least 1.0 credit in Computer Science in their program. Students are advised to consult the School of Computer Science regarding the most appropriate courses.

(iii) Students considering a career in actuarial science are advised to include Mathematics 69.381* and 69.386* in their programs.

Combined B.Math./M.Sc. in Mathematics, or in Statistics

This program is designed as a "fast-track" to enable exceptional students to graduate in four years, with both a B.Math. and an M.Sc. degree. It requires a minimum of 9.5 credits in Mathematics and Statistics, and 5.5 other credits towards a B.Math.(Major) degree; and then, either 2.5 credits in graduate studies and a thesis, or 4.0 credits in graduate studies and Mathematics 70.495* (Honours Project), for the M.Sc. degree.

Entry to this program directly from an Ontario High School requires both of the following:

(i) an average of 90 percent or better on the OACs in Calculus and Algebra and Geometry; and

(ii) an average of 85 percent or better over six OACs.

Other applicants should consult the School.

Entry and continuation in the undergraduate portion of this program as well as entry to the graduate portion require minimum GPAs of 11.0 in Mathematics and Statistics, and 10.0 overall.

B.Math./M.Sc. in Mathematics:

The First Year course pattern is given elsewhere in this section.

Mathematics courses required for this program are:

First Year

1. Mathematics 69.102, 69.112.

Second Year

2. Mathematics 70.200, 70.210, 70.244* , 70.265*, and 0.5 credit (70-series) at the 300-level or above.

Third Year

3. Mathematics 70.301*, 70.307*, 70.316*, 70.318*, and at least one of 70.302* or 70.308*; in addition, 1.5 credits at the 400-level or above in Mathematics and Statistics.

The remaining 5.5 credits are as follows:

(i) Breadth Requirement: At least 4.0 credits outside the School of Mathematics and Statistics and the School of Computer Science, including: at least 1.0 credit from the College of Natural Sciences, and at least 2.0 arts or social science credits. Of these 4.0 credits, at least 1.0 credit must be at the 200-level or above.

(ii) 1.5 credits of Free Electives.

Before entry into the Fourth year of this program, students must: obtain a recommendation from the School of Mathematics and Statistics to continue, apply to transfer to the B.Math.(Major) program and apply to graduate with a B.Math.(Major) degree, by the end of January of their Third year, and submit an application for graduate studies to the School by mid-February.

 Fourth Year

4. (registration as a graduate student) Mathematics 70.495* and 4.0 credits in Mathematics and Statistics at the graduate level (1.0 credit of these may be in another department/school); or: an M.Sc. thesis and 2.5 credits in Mathematics and Statistics at the graduate level (1.0 credit of these may be in another department/school).

Please refer to the Graduate Calendar for specific graduate requirements.

Students wishing to specialize in Stochastics may, with the permission of the School, replace the Second Year requirement of 0.5 credit at the 300-level or above by Mathematics 70.259*, and replace item 3 above by: Mathematics 70.301*, 70.356*, 70.358*, 70.359*, and one of 70.302*, 70.307*, 70.308*; and at least 1.5 credits at the 400-level or above in Mathematics and Statistics.

B.Math./M.Sc. in Statistics:

The First Year course pattern is given on p. 333.

Mathematics courses required for this program are:

First Year

1. Mathematics 69.102, 69.112.

Second Year

2. Mathematics 70.200, 70.210, 70.244*, 70.259*, 70.265*.

Third Year

3. Mathematics 70.301*, 70.355*, 70.356*, 70.358*, 70.359* and at least 1.5 credits at the 400-level or above in Mathematics and Statistics.

The remaining 5.5 credits are as follows:

(i) Breadth Requirement: At least 4.0 credits outside the School of Mathematics and Statistics and the School of Computer Science, including: at least 1.0 credit from the College of Natural Sciences, and at least 2.0 arts or social science credits. Of these 4.0 credits, at least 1.0 credit must be at the 200-level or above.

(ii) 1.5 credits of Free Electives.

Before entry into the Fourth year of this program, students must: obtain a recommendation from the School of Mathematics and Statistics to continue, apply to transfer to the B.Math.(Major) program and apply to graduate with a B.Math.(Major) degree, by the end of January of their Third year, and submit an application for graduate studies to the School by mid-February.

Fourth Year

4. (registration as a graduate student) Mathematics 70.495* and 4.0 credits in Mathematics and Statistics at the graduate level (1.0 credit of these may be in another department/school); or: an M.Sc. thesis and 2.5 credits in Mathematics and Statistics at the graduate level (1.0 credit of these may be in another department/school).

Please refer to the Graduate Calendar for specific graduate requirements.

Minor in Mathematics, or in Statistics

Students registered in degree programs [excluding programs offered by the School of Mathematics and Statistics] may obtain a "Minor in Mathematics" or a "Minor in Statistics" designation on their transcript and diploma by completing the appropriate courses specified below, with a GPA of 4.0 or better over the required credits.

When applying to graduate, students who have successfully completed all requirements must inform their Registrarial Services Office if they wish to receive the "Minor in Mathematics" or the "Minor in Statistics" designation on their transcript and diploma.

Minor in Mathematics:

4.0 credits of mathematics courses required:

i) 0.5 credit from Mathematics 69.104*, 69.107*, or 69.109*, followed by 69.207*; or 1.0 credit: Mathematics 69.102;

ii) 0.5 credit from Mathematics 69.114*, 69.117*, or 69.119*, followed by 69.217*; or 1.0 credit: Mathematics 69.112;

iii) 1.0 credit in Mathematics at the 200-level or above;

iv) 1.0 credit in Mathematics at the 300-level or above

(of these 4.0 credits, 2.0 must be taken at Carleton University).

 Minor in Statistics:

4.0 credits of courses required:

i) 0.5 credit from Mathematics 69.104*, 69.107*, 69.109*, or 1.0 credit: Mathematics 69.102; and 0.5 credit from Mathematics 69.114*, 69.117*, 69.119*, or 1.0 credit: Mathematics 69.112;

ii) either (a) or (b):

(a) one of: Mathematics 69.257*, 69.266*, 69.352*; and one of: Mathematics 69.259*, 69.267*;

(b) Economics 43.220, or 1.0 credit of approved introductory statistics;

iii) Mathematics 69.353*, 69.354*, 69.357* ;

iv) 0.5 credit in an approved course in computer programming at the 100-level or above, i.e. Computer Science 95.105*, 95.107*, Business 42.142*, Engineering 91.166*

(of these 4.0 credits, 2.0 must be taken at Carleton University).

The Co-operative Education Option

General information on the Co-operative Education Option can be found in the Co-operative Education section.

Co-operative Education formally integrates the student's academic experience with work experience in the private and public sectors. Work opportunities, which are available on a competitive basis, are coordinated to complement the student's course work and interests. Practical work experience provides insights and opportunities for development which enhances what is learned in regular course work, and prepares individuals for fulfilling careers in the work place. Specific details of the Option are to be found in the Mathematics and Statistics Co-op Student Handbook.

Admission Requirements

Students are eligible to apply to enter the Co-operative Option in one of two ways:

(i) directly upon being accepted into the First year of any Honours program offered by the School of Mathematics and Statistics; or

(ii) after completion of 5.0 or more credits (at least 2.0 in Mathematics/Statistics) at Carleton in any Honours program offered by the School of Mathematics and Statistics.

In case (i), students must have received marks of 80 percent or better in each of OAC Calculus and OAC Algebra and Geometry (or equivalent).

In case (ii), students must have a GPA of 8.0 or more in the mathematics and statistics courses required in their program and an overall GPA of 6.5 or better in their Mathematics and Statistics Honours program.

In addition, only for students in the Honours Computer Mathematics program, for a regular (ie., not a preliminary) co-op work term placement, completion of at least one of Computer Science 95.202* or 95.204* or 95.242* or 95.244* is required for eligibility for placement.

In both cases (i) and (ii), students must:

a) have full time status in each academic term immediately preceding a work term; and

b) be eligible to work in Canada (for off-campus work placements).

Note that meeting the above requirements only establishes eligibility for admission to the program. Enrolment in the Co-operative Option is limited.

Application forms for admission to the Co-operative Option are available from the Co-op Office. Completed applications should be submitted to that office [deadlines for applications are stated under Co-operative Education Admission Requirements]. Admission decisions are based on GPA and other requirements being met by the end of the previous term.

Eligibility for Placement in the First Work Term of the Co-operative Option

To be eligible for placement in the first (regular) work term of the Co-operative Option, a student must meet the above requirements by the end of the term preceding the first job placement process.

The Preliminary Work Term

Students who have been accepted into the Co-operative Option in First year may be given the opportunity to take part in a preliminary work term at the end of their First year. To be eligible for placement in this preliminary work term, students must at the end of their first term of study:

a) have a cumulative GPA of 10.0 or better in Mathematics and Statistics, and 10.0 or better overall;

b) be registered as a full-time student;

c) be eligible to work in Canada (for off-campus placements);

d) only for students in Honours Computer Mathematics: have successfully completed at least one of Computer Science 95.102* or 95.105* or 95.142* or 95.145*.

The Work/Study Sequence

The normal pattern of work and study terms in the Co-operative Option is as follows:

 

Each student in the Co-operative Education Program will take at least four work terms. Variations in the above pattern may be requested.

If no suitable job placements can be made, students will revert to their Honours program.

Continuation in the Co-operative Option

During a work term, Co-op Option students will register in one of five Work Term courses: Mathematics 70.220*, 70.320*, 70.321*, 70.420* or 70.421*. The Work Term courses must be taken in addition to the number of credits required for an honours degree. Each Work Term course will be graded Sat or Uns, based on both the employer's evaluation and the student's Work Term Report.

Honours Project for Co-op Option Students

The normal term for registration in Mathematics 70.495* (Honours Project) is the fall term. Co-op students who are working in the fall term of their final year, may request that their registration in 70.495* be arranged for one of the other terms. Further details concerning the Honours Project [Mathematics 70.495*] are given on pages xx and xx.

Graduation Requirements

All work terms should normally be completed prior to starting the last academic term. In addition to satisfying the requirements of the Co-operative Option as described above, a student must have completed the required credits specified for one of the Mathematics and Statistics Honours programs and at least four work term courses graded "Satisfactory".

Students who successfully complete the Honours degree requirements and who have registered in and successfully completed at least four work term courses will receive a Co-operative Option degree designation on both their transcript and diploma.

Course Selection

Course Load

The normal course load for a full-time student in the School of Mathematics and Statistics, during the Fall/Winter session, is the equivalent of 5.0 credits.

Students may register for a maximum of 2.0 credits in the Summer session.

A student may exceed the normal course load in the Fall/Winter session only with the Registrar's permission, which may be granted if a C average is maintained overall and in the Major field, and if recommended by the School.

First Year Course Pattern

For students admitted to a program offered by the School of Mathematics and Statistics, the First-year program leading to the Bachelor of Mathematics degree consists of 5.0 credits, as follows:

(a) at least 1.0 credit in Mathematics (excluding 69.185*/95.185*);

(b) 1.0 credit from the College of Natural Sciences or from the School of Computer Science (excluding 95.101* and 95.185*/69.185*);

(c) 1.0 additional credit in Mathematics or from the College of Natural Sciences or the School of Computer Science (excluding 95.101* and 95.185*/69.185*);

(d) 2.0 additional elective credits (excluding Science 60.101*, 60.102*, 60.201*, Social Sciences 03.300*, and Computer Science 95.101*).

Note: Mathematics 69.185*/Computer Science 95.185* can only be counted as a half-credit "Free Elective" [eg., under item (d)] in Mathematics and Statistics programs.

In establishing their First-year program of courses, students should consult with the Undergraduate Adviser, or the Associate Director, of the School of Mathematics and Statistics.

It should be noted that, in Mathematics and Statistics, most of the advanced courses are given during the day only. Students are advised to consult the School as early as possible to arrange their programs.

 Statistics Course Requirement

Students in all non-combined programs offered by the School of Mathematics and Statistics must present at least 0.5 credit in statistics in order to graduate.

In the major programs, and in the Information Technology stream of Honours Computer Mathematics, Mathematics 69.257* is required.

In the honours programs in Mathematics, Computer Mathematics [excluding the Information Technology stream], Statistics, and Computer Statistics, Mathematics 70.259* is required.

It is recommended that, when possible, one of Mathematics 69.257* or 70.259* be taken early in the student's university program.

 Courses Approved for a First-Year B.Math. Program

Mathematics 69.102, 69.112; 69.107*, 69.117*, 69.207*, 69.217*; 69.257*, or any Mathematics course for which the student has the prerequisite.

Computer Science 95.102*, 95.104*, 95.105*, 95.106*, 95.107*, 95.108*, 95.142*, 95.145*, 95.146*

Science Courses

Biochemistry 63.220*

Biology 61.103*, 61.104*, 61.192*, 61.193*, 61.216*; or if 61.103* and 61.104* have been completed prior to First year, with permission, any two of: 61.201*, 61.202*, 61.214*, 61.220*

Chemistry 65.010, 65.100; or if 65.100 has been completed prior to First year, with permission: 65.211*, 65.212*, 65.223*, 65.224*, 65.226*, 65.227*, 65.228*, 65.232*, 65.233* or 65.280*

Geography 45.105

Geology 67.104*, 67.105, or 1.0 credit from 67.106*, 67.107*, and 67.108*; or if one of Geology 67.100 or 67.105 has been completed prior to First year, with permission, any two of: 67.223*, 67.225*, 67.228*, 67.231*, 67.236*, 67.238*, 67.241*, 67.242*, 67.243*, 67.281*, 67.282*, 67.285*, 67.383*

 Physics 75.101*, 75.102*, 75.107*, 75.108*, 75.190; or if one of 75.101* and 75.102* or 75.107* and 75.108* has been completed prior to First year, with permission, any two of: 75.211*, 75.222*, 75.223*, 75.224*, 75.235*, 75.236*, 75.262*, 75.264*, 75.291*, 75.292*

Arts and Social Science Courses

All courses offered by the Faculty of Arts and Social Sciences or the Faculty of Public Affairs and Management, with the exception of: (i) Social Sciences courses listed below; and (ii) those courses on the list "Courses excluded for credit …", below. Advanced courses in certain disciplines may be included if the prerequisite has been completed prior to First year.

Social Sciences Courses not Acceptable as Social Sciences Electives

Social Sciences courses are available in the Faculty of Arts and Social Sciences and the Faculty of Public Affairs and Management.

However, the following Social Sciences courses are not acceptable as Social Sciences electives.

Business 42.101*, 42.102*, 42.104*, 42.105*, 42.142*, 42.201*, 42.202*, 42.230*, 42.242*, 42.270*, 42.301*, 42.308*, 42.400*, 42.401*, 42.402*.

Economics 43.220, 43.240*, 43.404*, 43.405*, 43.476*, 43.477*.

Geography 45.105, 45.207*, 45.302*, 45.303*, 45.305*, 45.306*, 45.307*, 45.311*, 45.312*, 45.313*, 45.315*, 45.318*, 45.319*, 45.400*, 45.402*, 45.403*, 45.405*, 45.406*, 45.408*, 45.411* (Geology 67.415*), 45.413* (Engineering 81.303*, Geology 67.419*), 45.414*, 45.417* (Engineering 82.424*, Geology 67.424*), 45.418*.

Interdisciplinary Social Sciences 03.300*.

Psychology 49.200, 49.220*, 49.270*, 49.300, 49.320, 49.321*, 49.322*, 49.323*, 49.324*, 49.325*, 49.326*, 49.327*, 49.356*, 49.370, 49.372*, 49.380, 49.401*.

Sociology 53.370.

Courses Excluded for Credit in all Programs Offered by the School of Mathematics and Statistics

The following courses may not be counted for academic credit (even as free electives) in any program offered by the School of Mathematics and Statistics:

Economics 43.240*, 43.404*; Business 42.230*; Geography 45.206*, 45.303*; Political Science 47.270; Psychology 49.200, 49.300; Social Sciences 03.401*, 03.402*; Social Work 52.250, 52.351*, 52.352*; Sociology/Anthropology 53.203, 54.203, 53.370, 53.403*, 53.404*, 56.450*.

It is understood that a student who has successfully completed one or more of these courses prior to September 1, 1996 will retain credit for these courses.

Note regarding Economics 43.220:

Students registered in any Mathematics or Statistics undergraduate program may not count Economics 43.220 for credit.

Students who have already completed Economics 43.220, and who wish to enter a Mathematics or Statistics B.Math.(Major) program, may be exempted from taking Mathematics 69.257* and 69.259* only with permission of the School of Mathematics and Statistics, and provided the grade in Economics 43.220 is B- or better.

Academic Standing

Continuation in Honours

In order to continue in an Honours program, at the end of First year, the student must maintain a GPA of 5.0 or better in the Honours subject(s), an overall GPA of 4.0 or better and be recommended by the School. A student beginning the final 10.0 credits towards an Honours degree must present a GPA of 6.0 or better in the Honours subject(s), an overall GPA of 5.0 or better and the recommendation of the School. At the beginning of their last 5.0 credits, students must have:

(a) a GPA of 6.5 or better in the Honours subject or in each Honours subject;

(b) an overall GPA of 5.0 or better;

(c) a grade of C- or better in at least half of the credits to be credited toward their degree;

(d) the recommendation of the School. Otherwise the student may not remain in Honours;

(e) students who have a GPA of 6.3 or 6.4 in their Honours subject may be allowed to continue at the discretion of the School.

Note: The B.Math. Combined Honours program: Computer Science and Mathematics has a higher GPA requirement for continuation than that stated above. Please refer to the combined honours section of this Calendar for further details.

The B.Sc.(Double Honours) program in Mathematics and Physics has a higher GPA requirement for continuation (after First year) than that stated above. Please refer to the combined honours section of this Calendar  for further details.

The combined B.Math./M.Sc. program in Mathematics, or in Statistics has a higher GPA requirement for continuation than that stated above. Please refer to the B.Math./M.Sc. program section  for more details.

The B.Math. Co-op programs in the School of Mathematics and Statistics have a higher GPA requirement for continuation than that stated above. Please refer to the Mathematics and Statistics Co-op program section of this Calendar  for further details.

A student who fails to maintain Honours standing may not remain in Honours, and is recommended to discuss a new program with the Undergraduate Adviser, or with the Associate Director of the School.

Promotion and Failure

Full-time Students

Full-time students in a First-year B.Math. program, in order not to fail their year in May, must, by then, have passed at least 3.0 credits. Students who fail to meet this requirement must apply by June 30 for readmission to a B.Math. program; students who fail a First-year B.Math. program for a second time are not eligible to apply for readmission to the School of Mathematics and Statistics.

In order to be promoted to the credit system from First year, a full-time student must have passed at least 4.0 credits including at least 3.0 credits in Science. The 3.0 credits in Science must include at least 1.0 credit in Mathematics, and at least 1.0 credit from the College of Natural Sciences or from the School of Computer Science.

Of these 4.0 credits, at least 2.0 credits (including at least 1.0 credit in Mathematics) must be completed with grades of C- or better.

Students in an Honours program must have a GPA of 6.0 or better in Mathematics 69.102 and 69.112, and a GPA of 7.0 or better in any credits offered from Mathematics 69.107*, 69.207*, 69.117*, 69.217*, and in addition, an overall GPA of 4.0 or better.

Students in a Major program must have a GPA of 4.0 or better in Mathematics 69.102 and 69.112, and a GPA of 5.0 or better in any credits offered from Mathematics 69.107*, 69.207*, 69.117*, 69.217*.

For a student without advanced standing in any First-year courses, these 4.0 credits must be selected from those approved for a First-year B.Math. program.

For a student (not repeating First year) with advanced standing in some First-year courses, these 4.0 credits must include sufficient courses to complete the First-year B.Math. program; the remainder of the 4.0 credits may include courses beyond the First year provided the student has retained credit for the prerequisite First-year courses. In the Major program one of the grades of C- or better must be in Mathematics.

This must be accomplished in one calendar year (12-month period) with not more than 2.0 credits of Summer courses. The course work of those First-year B.Math. students who almost meet promotion requirements is reviewed by the Dean's Committee on Promotion.

A full-time student who does not meet the requirements of promotion by the end of the August examinations will have failed First year.

Part-time Students

In order to be promoted to the credit system from First year, part-time students must, in the first 6.0 credits of final examination attempts, have passed at least 4.0 credits including at least 3.0 credits in Science. The 3.0 credits in Science must include at least 1.0 credit in Mathematics, and at least 1.0 credit from the College of Natural Sciences or from the School of Computer Science.

Of these 4.0 credits, at least 2.0 credits [including at least 1.0 credit in Mathematics] must be completed with grades of C- or better.

Students in an Honours program must have a GPA of 6.0 or better in Mathematics 69.102 and 69.112, and a GPA of 7.0 or better in any credits offered from Mathematics 69.107*, 69.207*, 69.117*, 69.217*, and in addition, an overall GPA of 4.0 or better.

Students in a Major program must have a GPA of 4.0 or better in Mathematics 69.102 and 69.112, and a GPA of 5.0 or better in any credits offered from Mathematics 69.107*, 69.207*, 69.117*, 69.217*.

Part-time students who fail more than 2.0 credits must apply for readmission to the School of Mathematics and Statistics.

Course Credit System

Students meeting promotion requirements at the end of First year will proceed on the course credit system, and under this system, after First year promotion, there is no further promotion from one year to the next.

(See the section on Limit on Examination Attempts, below.)

Consequences of Failure

Failed students within the limitations specified above may repeat First year, retaining credit toward their degree (but not toward the completion of First year) for all courses graded C- or better.

A student repeating First year may register only in courses approved for a First-year B.Math. program, but may include 2.0 credits beyond the First year provided the student has retained credit for the prerequisite First-year course.

A student who fails First year a second time may not re-enter a B.Math. program.

After promotion to the credit system, the student will accumulate course credits under a pattern approved by the School of Mathematics and Statistics.

Limit on Examination Attempts (after First year Promotion)

Honours degree students have the privilege of repeating or replacing courses subject to the following restriction: After admission to the credit system, the ratio of total number of (full-credit equivalent) examinations to the total number of credits required may not exceed six to five. In particular, a student who requires 15 more credits has the equivalent of at most 18.0 full-credit examinations available to complete the program.

Major degree students have the privilege of repeating or replacing courses, subject to the following restriction: After admission to the credit system, the ratio of total number of (full-credit equivalent) examinations to the total number of credits required may not exceed three to two. In particular, a student who requires ten more credits has the equivalent of at most 15.0 full-credit examinations available to complete his or her program.

The number of examinations available to a student who transfers from another institution or from another program, will be determined on a pro rata basis and will be specified at the time of admission.

When a student is examined in a course that has been previously declared extra to the degree program, this examination does not affect the remaining number of available examinations.

Students who cannot complete their program without exceeding the available number of examinations forfeit their undergraduate status in the program.

Graduation Regulations

In order to graduate, students must fulfill all University graduation regulations and all School regulations and requirements as set out below.

The regulations which follow immediately below, refer to the specific programs indicated. The General Regulations apply to all programs offered by the School of Mathematics and Statistics.

B.Math.(Honours) in Computer Mathematics:

(i) a GPA of 6.5 or better on the minimum of 11.0 required credits in Mathematics; and

(ii) a GPA of 6.5 or better on the minimum of 11.0 credits in Mathematics and 3.0 credits in Computer Science.

B.Math.(Honours) in Computer Mathematics - Information Technology stream:

a GPA of 6.5 or better on the 9.0 required credits in Mathematics; and

(ii) a GPA of 6.5 or better on the 13.5 credits in Mathematics and Computer Science.

B.Math.(Honours) in Computer Statistics:

(i) a GPA of 6.5 or better on the 9.0 required credits in Mathematics; and

(ii) a GPA of 6.5 or better on the 13.5 credits in Mathematics and Computer Science.

B.Math.(Honours) in Statistics:

(i) a GPA of 6.5 or better on the minimum of 11.0 credits in Mathematics and 1.0 credit in Computer Science; and

(ii) a GPA of 6.5 or better on the 5.0 credits in Statistics (Mathematics 70.259*, 70.265*, 70.355*, 70.356*, 70.358*, 70.359*, 70.450*, and the 1.5 credits selected from 70.451* to 70.459*).

For Students in Honours Programs:

The designation of Honours degree will be determined by the student's GPA on all required credits in the Honours subjects, as stated in the program requirements; however, the School may use discretion in counting the number of Honours credits, where students have more than the minimum number of required credits.

For Students in the Combined Honours Programs:

The designation of Honours degree will be determined by the student's GPA on all required credits in the two Honours subjects, as stated in the respective program requirements; however, the department/schools may use discretion in counting the number of Honours credits, where students have more than the minimum number of required credits.

B.Math.(Major) in Computer Mathematics:

(i) a GPA of 4.0 or better on the 6.5 required credits in Mathematics; and

(ii) a GPA of 4.0 or better on the 10.0 credits in Mathematics and Computer Science.

B.Math.(Major) in Statistics:

(i) a GPA of 4.0 or better on the minimum of 6.0 credits in Mathematics; and

a GPA of 4.0 or better on the 3.5 credits in Statistics (Mathematics 69.257*, 69.259*, 69.353*, 69.354*, 69.357*, 69.358* and 69.359*).

General Regulations

1. Every student will be required to complete the last 5.0 credits at Carleton University unless authorized by the School of Mathematics and Statistics to take courses at the University of Ottawa under the Undergraduate Exchange Agreement.

2. A student who takes courses elsewhere with a Letter of Permission from the Science Committee on Admission and Studies may, with the approval of the School of Mathematics and Statistics, use the credit value but not the grades to meet graduation requirements;

3. Students who transfer to the School of Mathematics and Statistics from another institution must include in the courses presented for degree (whether obtained at Carleton or elsewhere) at least:

(a) 2.0 credits of Arts or Social Sciences electives if on transfer they received credit for less than ten credits;

(b) 1.0 credit of Arts or Social Sciences electives if on transfer they received credit for 10.0 or more credits.

Note: See also University graduation regulations

Honours Degree Students

To qualify for graduation with a Bachelor of Mathematics degree with Honours a student must:

1. present credits for at least 20.0 credits of approved full credits (or equivalent) beyond Qualifying-University year, with not more than 2.0 credits below the 100-level and not more than 7.0 below the 200-level;

2. meet the requirements of the Faculty of Science and of the School of Mathematics and Statistics with respect to both course and grade requirements;

3. after entry to the credit system, have completed the program with not more than 6.0 (full credit equivalent) examinations for every 5.0 credits required. (Examinations include course repetitions and replacements.) A part-time student or a full-time student who has interrupted his or her studies must complete the program within seven years after entry to courses beyond First year;

4. include at least 2.0 credits in the Honours subject or subjects in the last 5.0 credits taken;

5. be recommended by the School of Mathematics and Statistics and the Science Faculty Board.

The Honours degree will not be awarded to students taking fewer than 5.0 credits at Carleton.

Designations of Honours Degrees

Three designations of Honours are awarded, determined on the basis of the GPA as follows:

Highest Honours

10.0 - 12.0 in Honours subject, and

8.0 or better overall

High Honours

9.0 or better in Honours subject, and

7.0 or better overall

Honours

6.5 or better in Honours subject, and

5.0 or better overall

The School of Mathematics and Statistics may recommend the higher designation of Honours degree in the case of a student one of whose indices is in the appropriate higher range and the other within 0.2 grade points of the higher range.

To determine the class of degree for students with Combined Honours, the average is computed on the basis of the weighted average of the required number of Honours credits in the two subjects. If agreeable to the committee concerned, the average may be taken in each of the two subjects and the simple average of the two may be used.

The School of Mathematics and Statistics may use discretion for establishing the class of degree in counting the number of Honours credits where students have more than the minimum number of credits.

Combined B.Math./M.Sc. in Mathematics or in Statistics

For graduation requirements, see p.331.

Major Degree Students

To qualify for graduation students must:

1. present credits for 15.0 approved full credits (or equivalent) beyond Qualifying-University year with not more than 2.0 credits below the 100-level and not more than 7.0 below the 200-level;

2. have a grade of C- or better in at least half of the 15.0 credits;

3. have an average of C- or better in the credits in their Major subject or subjects;

4. after entry to the credit system, have completed the program with not more than three (full-course equivalent) examinations for every 2.0 credits required. (Examinations include course repetitions and replacements.) Part-time students or full-time students who have interrupted their studies must complete the program within seven years after entry to courses beyond First year;

5. include at least 2.0 credits in the Major subject or subjects in the last 5.0 credits taken for credit;

6. be recommended by the School of Mathematics and Statistics and the Science Faculty Board.

To meet the requirements for the C- average in the Major stated above, only those credits in the Major necessary to make up the required total for graduation in the School of Mathematics and Statistics need be counted. All obligatory courses must be counted.

Graduating students in a Major program of the School of Mathematics and Statistics will be designated as graduating "with Distinction" if:

1. they have no course failures, course repetitions or course replacements on their Carleton record after promotion to the course-credit system;

2. they have achieved an overall GPA of 8.0 or better calculated on their Carleton record, including all credits extra to the degree;

3. they have successfully completed at Carleton at least 10.0 credits counted toward the degree;

4. after promotion to the course-credit system, they have achieved a GPA of 9.5 or better calculated on all Carleton credits being counted toward the degree.

 

Graduate Programs: M.Sc. and Ph.D.

For requirements for graduate degrees, see the Calendar for the Faculty of Graduate Studies and Research.

Course Numbering

Course numbers prefixed by 70 indicate courses intended primarily for Honours students; all other courses have numbers prefixed by 69. Credit will not be given for two courses having the same number but different prefixes.

Deferred Final Examinations

Examinations deferred from Winter term will normally take place in June.

However, in the following courses in Mathematics and Statistics, where the course is offered in two successive terms, the Deferred Final Examination will be taken in April for Fall term courses, and in December for Summer Session courses: Mathematics 69.007*, 69.017*, 69.107*, 69.109*, 69.117*, 69.119*, 69.207*, 69.208*, 69.217*, 69.257*, 69.259*.

Prerequisites for First-Year Calculus and Algebra Courses

1. Pre-University Calculus:

An OAC in Calculus, or Mathematics 69.007*, or equivalent.

Students lacking an OAC in Calculus (or equivalent) must successfully complete Mathematics 69.007* prior to taking a 100-level Calculus course. For students in any program offered by the School of Mathematics and Statistics, the above requirement of Mathematics 69.007* is in addition to the minimum 15.0 credits in Major programs, or 20.0 credits in Honours programs.

2. Pre-University Algebra:

An OAC in Algebra and Geometry, or Mathematics 69.017*, or equivalent.

Note: An OAC in Finite Mathematics is not an equivalent.

Students lacking an OAC in Algebra and Geometry (or equivalent) must successfully complete Mathematics 69.017* prior to taking a 100-level Algebra course. For students in any program offered by the School of Mathematics and Statistics, the above requirement of Mathematics 69.017* is in addition to the minimum 15.0 credits in Major programs, or 20.0 credits in Honours programs.

First-Year Course Selection

1. Mathematics 69.102, 69.112 (students in the Faculty of Science). This choice is required of students in First year who are in a Mathematics or Statistics program;

2. Fall term: Mathematics 69.104*; Winter term: Mathematics 69.105*, 69.114* (students in the Faculty of Engineering, or in Applied Physics);

3. Fall term: Mathematics 69.107*; Winter term: Mathematics 69.114* (students in the School of Computer Science);

4. Fall term: Mathematics 69.107*; Winter term: Mathematics 69.117* (students in the Faculty of Science);

5. Mathematics 69.102; Fall term: Mathematics 69.117* (students in the Faculty of Science);

6. Fall term: Mathematics 69.107*, 69.117*; Winter term: Mathematics 69.207*, 69.217* (students in the Faculties of Arts and Social Sciences, Public Affairs and Management, or Science);

7. Fall term: Mathematics 69.109*; Winter term: Mathematics 69.119* (students in the School of Business, Department of Economics or in other Arts and Social Sciences/Public Affairs and Management departments).

Note: Credit will only be given for one of: Mathematics 69.102, 69.104*, 69.107*, 69.109*; and one of: Mathematics 69.112, 69.114*, 69.117*, 69.119*.

Courses

Not all of the following courses are offered in a given year. For an up-to-date statement of course offerings for 2001-2002, please consult the Registration Instructions and Class Schedule booklet published in the summer.

Mathematics 69.007*

Introductory Calculus

Limits and continuity. Differentiation. Trigonometric, logarithmic, and exponential functions and their derivatives; curve sketching; applied problems in maxima and minima, and related rates.

Not available for degree credit for students who have successfully completed an OAC in Calculus/or an equivalent High School Calculus course.

Precludes additional credit for Business 42.173.

Prerequisite: Grade 12 Mathematics (Advanced/Academic Level) or Mathematics 69.006* or equivalent. It is strongly recommended that Mathematics 69.017* or the equivalent be taken before 69.007*.

See Deferred Final Examinations Note

Lectures three hours a week and one hour tutorial.

Mathematics 69.017*

Algebra and Geometry

Vectors in the plane and in 3-space. Linear combinations and linear independence. Equations of lines and planes in space. Solution of systems of linear equations. Complex numbers (including de Moivre's Theorem, and n-th roots). Proofs by induction.

Not available for degree credit for students who have successfully completed an OAC in Algebra and Geometry/or an equivalent High School Algebra course.

Prerequisite: Grade 12 Mathematics (Advanced/Academic Level) or Mathematics 69.006* or equivalent.

See Deferred Final Examinations Note.

Lectures three hours a week and one hour tutorial.

 Mathematics 69.102

Calculus

This course is strongly recommended for students intending to specialize in mathematics, statistics, physics, or related areas. Limits, differentiation, the definite integral, elementary functions, techniques of integration, parametric equations and polar coordinates. Improper integrals, L'Hôpital's rules, sequences and series, Taylor's formulae, introduction to differential equations.

Precludes additional credit for Mathematics 69.104*, 69.105*, 69.107*, 69.109*, 69.207*, and for 69.201, 69.202.

Prerequisites: (i) a pre-university calculus course with a grade of 65 percent or better; and (ii) an OAC in Algebra and Geometry, or Mathematics 69.017*, or permission of the School. (See Prerequisites for First-year Calculus and Algebra Courses.)

Lectures three hours a week and one hour tutorial.

Note: Although the main prerequisite for Mathematics 69.102 is a grade of 65 percent or better in a pre-university calculus course, past experience indicates that students with less than 75 percent in their prerequisite calculus have only a small chance of success in Mathematics 69.102.

Mathematics 69.104*

Calculus for Engineering Students

The definite and indefinite integral; numerical approximation. Special functions (trigonometric and inverse trigonometric, logarithm and exponential), their derivatives and integrals. Applications: area, volume, average value. Further techniques of integration: integration by parts, partial fractions, and substitutions. Introduction to differential equations.

Restricted to students in the Faculty of Engineering, or in B.Sc.(Honours) in Applied Physics.

Precludes additional credit for Mathematics 69.102, 69.107*, 69.109*.

Prerequisite: an OAC in Calculus, or Mathematics 69.007* (or equivalent).

Lectures three hours a week and one hour tutorial.

Mathematics 69.105*

Differential Equations and Infinite Series for Engineering Students

Further study of first-order differential equations. Linear differential equations with constant coefficients; undetermined coefficients; annihilator operators. Variation of parameters. Euler-Cauchy differential equation. Indeterminate forms. Sequences and series; convergence tests; estimation of sums. Power series; Taylor series; remainders. Use of power series to solve differential equations.

Restricted to students in the Faculty of Engineering, or in B.Sc.(Honours) in Applied Physics.

Precludes additional credit for: Mathematics 69.102, 69.201, 69.202, 69.207*, 69.244*, 70.244* and 70.260.

Prerequisites: (i) Mathematics 69.104*, or a grade of C- or better in 69.107*; and (ii) an OAC in Algebra and Geometry, or Mathematics 69.017*; or permission of the School.

Lectures three hours a week, tutorial one hour a week.

Mathematics 69.107*

Elementary Calculus I

Definite and indefinite integrals, differentiation and integration of the elementary functions, techniques and applications of integration.

Precludes additional credit for Mathematics 69.102, 69.104*, 69.109*.

Prerequisite: an OAC in Calculus, or Mathematics 69.007* (or equivalent).

See Deferred Final Examinations.

Lectures three hours a week and one hour tutorial.

Notes:

1. Students with less than 60 percent in their pre-university calculus course are advised that past experience indicates their chance of success in Mathematics 69.107* is small.

2. A grade of C- or better in Mathematics 69.107* is a prerequisite for certain 200-level Mathematics courses.

Mathematics 69.109*

Calculus: with Applications to Business and Economics

Definite and indefinite integrals; integration of the elementary functions; some techniques of integration. Functions of several variables; partial differentiation; constrained optimization. Selected applications in business and economics.

Precludes additional credit for Mathematics 69.102, 69.104*, and 69.107*.

Prerequisite: an OAC in Calculus, or Mathematics 69.007* (or equivalent).

See Deferred Final Examinations Note.

Lectures three hours a week and one hour tutorial.

Note: Students with less than 60 percent in their pre-university calculus course are advised that past experience indicates their chance of success in Mathematics 69.109* is small.

Mathematics 69.112

Algebra

Fields, complex numbers, vector algebra and geometry in 2 and 3 dimensions, matrix algebra, linear dependence, bases, linear transformations, bilinear and quadratic forms, inner products, eigenvalues, principal axis theorem. Strongly recommended for students intending to specialize in mathematics, statistics, physics, or related areas.

Precludes additional credit for Mathematics 69.114*, 69.117*, 69.119*, 69.217*.

Prerequisites: (i) a pre-university algebra course with a grade of 65 percent or better, and (ii) an OAC in Calculus, or Mathematics 69.007*, or permission of the School. (See Prerequisites for First-year Calculus and Algebra Courses.)

Lectures three hours a week and one hour tutorial.

Note: Although the main prerequisite for Mathematics 69.112 is a grade of 65 percent or better in a pre-university algebra course, past experience indicates that students with less than 75 percent in their prerequisite mathematics have only a small chance of success in Mathematics 69.112.

Mathematics 69.114*

Linear Algebra for Engineering and Computer Science Students

Systems of linear equations. Matrix algebra. Determinants. Complex numbers. Eigenvalues. Diagonalization and applications.

Restricted to students in the Faculty of Engineering, in the School of Computer Science, or in B.Sc.(Honours) in Applied Physics.

Precludes additional credit for Mathematics 69.112, 69.117*, 69.119*.

Prerequisite: an OAC in Algebra and Geometry, or Mathematics 69.017* (or equivalent).

Lectures three hours a week and one hour tutorial.

Mathematics 69.117*

Linear Algebra I

Systems of linear equations; vector space of n-tuples, subspaces and bases; matrix transformations, kernel, range; matrix algebra and determinants. Inner products and orthogonality. Eigenvalues, diagonalization and applications. Emphasis throughout this course will be on the computational aspects (and not on theoretical aspects).

Precludes additional credit for Mathematics 69.112, 69.114*, 69.119*.

Prerequisite: an OAC in Algebra and Geometry, or Mathematics 69.017* (or equivalent).

See Deferred Final Examinations Note.

Lectures three hours a week and one hour tutorial.

Note: A grade of C- or better in Mathematics 69.117* is a prerequisite for certain 200-level Mathematics courses.

Mathematics 69.119*

Linear Algebra: With Applications to Business and Economics

Algebraic concepts, systems of linear equations, vector algebra; matrix algebra, rank, inversion, determinants; linear programming — geometric approach, simplex method, etc. Applications in the fields of business and economics.

Precludes additional credit for Mathematics 69.112, 69.114*, 69.117*, and for Mathematics 69.132* (Architecture 79.201*).

Prerequisite: An OAC in Algebra and Geometry, or Mathematics 69.017* (or equivalent).

See Deferred Final Examinations Note.

Lectures three hours a week and one hour tutorial.

Mathematics 69.185*

Discrete Structures I

An introduction to discrete mathematics and discrete structures. Topics include: propositional and predicate calculus, Boolean algebra, introduction to complexity of algorithms, mathematical reasoning, counting, recurrences, relations, introduction to graphs. (Also listed as Computer Science 95.185*.)

This course is available to Science students only as a free option.

Prerequisites: Two OACs in Mathematics, and one of Computer Science 95.105* or 95.107* (which may be taken concurrently).

Lectures three hours a week.

Mathematics 69.204*

Multivariable Calculus for Engineering Students

Fourier series; expansions for even and odd functions; half-range expansions. Surfaces in R3. Differential calculus of functions of several variables. Extrema and Lagrange multipliers. Exact differentials. Line integrals. Double integrals; polar coordinates; applications. Triple integrals; cylindrical and spherical coordinates; applications.

Restricted to students in the Faculty of Engineering, or in B.Sc.(Honours) in Applied Physics.

Precludes additional credit for: Mathematics 69.201, 69.202, 69.208*, 69.209* and 70.200.

Prerequisites: (i) Mathematics 69.105* or 69.207*; and (ii) Mathematics 69.114* or 69.117*; or permission of the School.

Lectures three hours a week, tutorial one hour a week.

Mathematics 69.207*

Elementary Calculus II

Further techniques of integration, improper integrals, polar coordinates, parametric equations, indeterminate forms, sequences and series, Taylor's formula and series, first order and linear differential equations.

Precludes additional credit for Mathematics 69.102, 69.105*, and for 69.201, 69.202.

Prerequisites: (i) Mathematics 69.104*, or a grade of C- or better in Mathematics 69.107* or 69.109*; and (ii) an OAC in Algebra and Geometry, or Mathematics 69.017*, or permission of the School.

See Deferred Final Examinations Note.

Lectures three hours a week and one hour tutorial.

Mathematics 69.208*

Intermediate Calculus

Partial differentiation, chain rule, gradient, line and multiple integrals with applications, transformations, implicit and inverse function theorems.

Precludes additional credit for Mathematics 69.204*, 69.209*, 70.200, and for 69.201, 69.202.

Prerequisites: Mathematics 69.102 or 69.207*, and 69.112 or 69.117*.

See Deferred Final Examinations Note.

Lectures three hours a week and one hour tutorial.

Mathematics 69.209*

Intermediate Calculus for Science Students

Differential equations; differential calculus of functions of several variables; multiple integration; introduction to Fourier series.

Precludes additional credit for Mathematics 69.201, 69.202, 69.204*, 69.208* and 70.200.

Prerequisites: (i) Mathematics 69.207*, or 69.102; and (ii) Mathematics 69.117* or 69.114* or 69.112; or their equivalents, or permission of the School.

Lectures three hours a week, tutorial one hour a week.

Mathematics 69.217*

Linear Algebra II

Finite-dimensional vector spaces (over R and C), subspaces, linear independence and bases. Linear transformations and matrices. Inner product spaces (over R and C); Orthonormal bases. Eigenvalues and diagonalization. Bilinear and quadratic forms; principal axis theorem.

Precludes additional credit for Mathematics 69.112.

Prerequisites: (i) Mathematics 69.114*, or a grade of C- or better in Mathematics 69.117* or 69.119*; and (ii) a grade of C- or better in Mathematics 69.107* or equivalent; or permission of the School.

See Deferred Final Examinations Note.

Lectures three hours a week and one hour tutorial.

Mathematics 69.218*

Abstract Algebra I

Sets and relations, number theory, group theory, ring theory, cardinal numbers.

Precludes additional credit for Mathematics 69.311* and 70.210.

Prerequisite: Mathematics 69.112 or 69.217*.

Lectures three hours a week and one hour tutorial.

Mathematics 69.244*

Ordinary Differential Equations I

Ordinary differential equations; applications; special first and second order types. Linear homogeneous and non-homogeneous equations with constant coefficients; variation of parameters; simple harmonic motion. Special linear equations with variable coefficients. Series solutions about ordinary points.

Precludes additional credit for Mathematics 69.105*, 69.201, 69.202, 70.244* and 70.260.

Prerequisites: Mathematics 69.102 and 69.112 (or 69.117* and 69.207*).

Lectures three hours a week and one hour tutorial.

Mathematics 69.257*

Introduction to Statistics

Data analysis; introduction to probability theory; some standard discrete and continuous distributions such as the binomial, Poisson, hypergeometric, normal, t, and chi-square; their application to interval estimation and significance testing; simple linear regression and correlation, contingency tables; testing for goodness-of-fit. Computational aspects of statistics.

Precludes additional credit for Mathematics 69.266*, 69.352*, Economics 43.220 and Geography 45.206*.

Prerequisite: An OAC in Mathematics or equivalent or permission of the School.

See Deferred Final Examinations Note.

Lectures three hours a week and one hour laboratory.

Note: See Note, under Graduation Regulations, regarding Economics 43.220.

Mathematics 69.259*

Computational Statistics

Exploratory data analysis, non-parametric methods, linear regression and correlation, basic experimental designs, related topics. Computer packages are used for statistical analyses.

Precludes additional credit for Mathematics 69.267*, 70.259*, and Economics 43.220.

Prerequisites: (i) Mathematics 69.257* and (ii) an OAC in Algebra and Geometry, or Mathematics 69.017*; or equivalents; or permission of the School.

See Deferred Final Examinations Note.

Lectures three hours a week and one hour laboratory.

Note: See Note, under Graduation Regulations, regarding Economics 43.220.

Mathematics 69.265*

Probability Models

Introductory probability theory. Introduction to stochastic modelling, Markov chains and queueing theory. Random number generation and Monte Carlo simulation. Statistical methods for fitting and evaluating models; estimation and testing. Applications to computer system performance evaluation, analysis of algorithms, reliability, search and decision problems.

Restricted to students in the Bachelor of Computer Science, Computer Mathematics and Computer Statistics programs.

Precludes additional credit for Mathematics 69.352*, 70.260 and 70.265*.

Prerequisites: Mathematics 69.207* (or 69.102) and 69.114* (or 69.117*).

Lectures three hours a week and one hour tutorial.

Mathematics 69.266*

Business Statistics I

Introduction to statistical computing; probability concepts; descriptive statistics; estimation and testing of hypotheses. Emphasis on the development of an ability to interpret results of statistical analyses with applications from business.

Restricted to students in the School of Business.

Precludes additional credit for Mathematics 69.257*, 69.352*, Economics 43.220 and Geography 45.206*.

Prerequisites: either: item (iii); or both of items (i) and (ii):

(i) Mathematics 69.109* with a grade of C- or better; and (ii) an OAC in Algebra and Geometry, or Mathematics 69.017*; (iii) Business 42.173 with a grade of C- or better; or equivalents.

Lectures three hours a week and one hour laboratory.

Mathematics 69.267*

Business Statistics II

Topics include: experimental design, multiple regression and correlation analysis, covariance analysis, and introductory time series. Use of computer packages.

Restricted to students in the School of Business.

Precludes additional credit for Mathematics 69.259*, 70.259* and Economics 43.220.

Prerequisite: Mathematics 69.266*.

Lectures three hours a week and one hour laboratory.

Mathematics 69.280*

Discrete Mathematics and Algorithms

An introduction to discrete mathematics and algorithms in the context of the computational sciences. Basic number theory and counting methods, algorithms for strings, trees and sequences. Applications to DNA and protein sequencing problems. Analysis and complexity of algorithms. (Also listed as Computational Sciences 68.280*.)

Only one of Mathematics 69.185* / Computer Science 95.185* or Mathematics 69.280* / Computational Sciences 68.280* may count for credit in a B.Math. program.

Prerequisites: Computer Science 95.106* and at least one of Mathematics 69.107*, 69.117*, or 69.257*.

Lectures three hours a week.

Mathematics 69.307*

Functions of a Complex Variable

Analytic functions, contour integration, residue calculus, conformal mapping. Intended for non-engineering students.

Precludes additional credit for Mathematics 69.376*, 70.307*, Physics 75.387* and 75.386.

Prerequisite: One of Mathematics 69.201, 69.202, 69.204*, 69.208* or 69.209*, or permission of the School.

Lectures three hours a week and one hour tutorial.

Mathematics 69.309*

Introductory Analysis

The real number system, sequences and series, functions of a single real variable, derivatives, the definite integral, uniform convergence.

Precludes additional credit for Mathematics 70.200.

Prerequisite: One of Mathematics 69.201, 69.202, 69.204*, 69.208*, 69.209*, or permission of the School.

Lectures three hours a week and one hour tutorial.

Mathematics 69.311*

Algebraic Structures with Computer Applications

Introduction to algebraic structures: groups, rings, fields, lattices, and Boolean algebras; with applications of interest to students in Computer Science.

This course may not be used to meet the 300-level course requirements in any Major or Honours program in Mathematics and Statistics.

Precludes additional credit for Mathematics 69.218* and 70.210.

Prerequisite: Mathematics 69.217*, or permission of the School.

Lectures three hours a week and one hour tutorial.

Mathematics 69.317*

Linear Algebra III

Similarity and unitary triangularization of matrices. Direct methods of solving a system of linear equations. Iterative techniques. Bounds for eigenvalues. Power method and deflation techniques of approximation. The emphasis of the course is primarily on computational aspects.

Prerequisites: (i) a grade of C- or better in Mathematics 69.112 or 69.217*; and (ii) credit in Mathematics 69.102 or 69.207*; or permission of the School.

Lectures three hours a week and one hour tutorial.

Mathematics 69.318*

Abstract Algebra II

Groups and rings. Permutations. Finite symmetry groups. Polynomials, unique factorization domains. Quotient rings, ideals. Field extensions, finite fields. Polynomial equations. Geometric constructions - three famous problems: duplication of the cube; trisection of an arbitrary angle; quadrature of the circle.

Precludes additional credit for Mathematics 70.316*, 70.318*, and 70.310.

Prerequisite: Mathematics 69.218*, or permission of the School.

Lectures three hours a week and one hour tutorial.

Mathematics 69.325*

Euclidean Geometry and its Groups

Transformations of the Euclidean plane (isometries, similarities); solutions of geometric problems using these transformations; groups of symmetries of finite plane figures, frieze patterns, and regular polyhedra; inversion and the extension to the inversive plane; problems solved using inversion; orthogonal circles and pencils of coaxial circles.

Prerequisite: Mathematics 69.218*.

Lectures three hours a week and one hour tutorial.

Mathematics 69.326*

Plane Projective Geometry

Axioms of Desarguesian geometry, principle of duality; projectivities, perspectivities, and the fundamental theorem; collineations (homologies and elations); correlations (polarities and conics); algebraic model; introduction to finite projective planes.

Precludes additional credit for Mathematics 70.326*.

Prerequisite: Mathematics 69.218*.

Lectures three hours a week and one hour tutorial.

Mathematics 69.344*

Ordinary Differential Equations II

Series solutions of ordinary differential equations of second order about regular singular points; asymptotic solutions. Systems of ordinary differential equations of first order; matrix methods. Existence and uniqueness theorems. Nonlinear autonomous systems of order 2; qualitative theory. Numerical solutions of ordinary differential equations.

Precludes additional credit for Mathematics 70.308*.

Prerequisites: Mathematics 69.244*, 69.208*; and 69.112 or 69.217*.

Lectures three hours a week and one hour tutorial.

Mathematics 69.352*

Probability and Statistics

Axioms of probability; conditional probability and independence; random variables; distributions: binomial, Poisson, hypergeometric, normal, gamma; central limit theorem; sampling distributions; point estimation: maximum likelihood, and method of moments; confidence intervals; testing of hypotheses: one and two populations; engineering applications: acceptance sampling, control charts, reliability.

Restricted to students in the Faculty of Engineering, or in B.Sc.(Honours) in Applied Physics.

This course may not be used to meet the 300-level course requirements in any Major or Honours program in Mathematics and Statistics.

Precludes additional credit for Mathematics 69.257*, 69.265*, 69.266*, Economics 43.220 and Geography 45.206*.

Prerequisite: Mathematics 69.204*, or 69.201.

Lectures three hours a week and one hour laboratory.

Mathematics 69.353*

Regression Analysis

Review of simple and multiple regression with matrices, Gauss-Markov theorem, polynomial regression, indicator variables, residual analysis, weighted least squares, variable selection techniques, nonlinear regression, correlation analysis and autocorrelation. Computer packages are used for statistical analyses.

Precludes additional credit for Mathematics 70.355*, Economics 43.476*, and for Mathematics 69.351; Psychology 49.300 is precluded for additional credit for students registered in a Mathematics program.

Prerequisites: (i) Mathematics 69.259* or 69.267*, or Economics 43.220, or equivalent; and (ii) Mathematics 69.112 or 69.117* or 69.119* or equivalent; or permission of the School.

Lectures three hours a week and one hour laboratory.

Mathematics 69.354*

Analysis of Variance and Experimental Design

Single and multifactor analysis of variance, orthogonal contrasts and multiple comparisons, analysis of covariance; nested, crossed and repeated measures designs; completely randomized, randomized block, Latin squares, factorial experiments, related topics. Computer packages are used for statistical analyses.

Precludes additional credit for Mathematics 70.355*, and for Mathematics 69.351; Psychology 49.300 is precluded for additional credit for students registered in a Mathematics program.

Prerequisite: Mathematics 69.353* or permission of the School.

Lectures three hours a week and one hour laboratory.

Mathematics 69.357*

Sampling Methodology

The sample survey as a vehicle for information collection in government, business, scientific and social agencies. Topics include: planning a survey, questionnaire design, simple random, stratified, systematic and cluster sampling designs, estimation methods, problem of non-response, related topics.

Prerequisite: One of Mathematics 69.257*, or 69.259*, 69.266*, 69.267*, Economics 43.220 or equivalent; or permission of the School.

Lectures three hours a week and one hour laboratory.

Mathematics 69.358*

Elements of Probability Theory

Discrete and continuous distributions; moment-generating functions, marginal and conditional distributions, transformation theory, limiting distributions.

Precludes additional credit for Mathematics 69.350, 70.350, and 70.358*.

Prerequisites: (i) Mathematics 69.208* [or one of 69.201, 69.202, 69.204*, or 69.209*]; and (ii) one of Mathematics 69.257*, 69.266*, Economics 43.220; or permission of the School.

Lectures three hours a week, tutorial one hour a week.

Mathematics 69.359*

Mathematical Statistics

Point and interval estimation, sufficient statistics, hypothesis testing, chi-square tests with enumeration data.

Precludes additional credit for Mathematics 69.350, 70.350, and 70.359*.

Prerequisite: Mathematics 69.358* or permission of the School.

Lectures three hours a week, tutorial one hour a week.

Mathematics 69.368*

Probability in Communications and Electrical Engineering

Probability models and basic concepts; independence and conditional probabilities; discrete, continuous and multiple random variables; distribution and density functions; expectations and moments; sums of random variables; elementary statistics; introduction to random processes; applications to areas such as communication systems and networks.

Restricted to students in the Faculty of Engineering.

Precludes additional credit for Mathematics 69.358* and 70.358*.

Prerequisite: Mathematics 69.204*, or equivalent.

Lectures three hours a week, tutorial one hour a week.

Mathematics 69.375*

Mathematical Methods I

Laplace transforms, Fourier series and Fourier transforms, solutions of partial differential equations of mathematical physics, boundary value problems, applications.

This course may be taken for credit as a 300-level Honours Mathematics course, by students in any Honours program in the School of Mathematics and Statistics.

Precludes additional credit for Mathematics 69.304*, Physics 75.388*, and 75.386.

Prerequisite: Mathematics 69.201 or 69.202; or (i) Mathematics 69.244* or 69.105*, and (ii) Mathematics 69.204* or 69.208* or 69.209*; or permission of the School.

Lectures three hours a week and one hour tutorial.

Mathematics 69.380*

Modelling and Computational Methods for Experimental Science

Mathematical modelling in the experimental sciences: design, analysis and pitfalls. Computational methods directly applicable to problems in science will be described, including: function evaluation, interpolation, solution of linear equations, root finding, integration, solution of differential equations, Fourier series and Monte Carlo methods. (Also listed as Computational Sciences 68.380*.)

Only one of Mathematics 69.386* / Computer Science 95.386* or Mathematics 69.380* / Computational Sciences 68.380* may count for credit in a B.Math. program.

Prerequisites: Mathematics 69.117*; 69.207* or 69.209*; and Computer Science 95.106*.

Lectures three hours a week.

Mathematics 69.381*

Linear Programming

Formulation of linear programming problems, the simplex method, duality theory, implementations, extensions and applications. Network flow problems and the network simplex method.

Precludes additional credit for Economics 43.404*, Engineering 94.320*.

Prerequisite: Mathematics 69.112 or 69.217*, or permission of the School.

Lectures three hours a week and one hour tutorial.

Mathematics 69.382*

Combinatorial Optimization

Network flow algorithms: max flow, min cost flow. Connections to linear programming. Optimal matching. Heuristic algorithms for tour problems.

Prerequisite: Mathematics 69.112 or 69.217* or permission of the School.

Lectures three hours a week, tutorial one hour a week.

Mathematics 69.384*

Design and Analysis of Algorithms I

An introduction to the design and analysis of algorithms. Topics include: recurrence relations, sorting and searching, divide-and-conquer, dynamic programming, greedy algorithms, amortized analysis. (Also listed as Computer Science 95.384*.)

Prerequisites: Computer Science 95.202*, and either 95.285* or both of Mathematics 69.207* and 69.218* or equivalents.

Lectures three hours a week.

Mathematics 69.386*

Numerical Analysis

Elementary discussion of error, polynomial interpolation, quadrature, linear systems of equations and matrix inversion, non-linear equations, difference equations and ordinary differential equations. (Also listed as Computer Science 95.386*.)

Prerequisites: (i) Mathematics 69.102, 69.105* or 69.207* (or 69.201 or 69.202); and (ii) Mathematics 69.112 or 69.217*; and (iii) knowledge of a computer language.

Lectures three hours a week and one hour tutorial.

Mathematics 69.387*

Mathematical Software

Incorporation of basic numerical methods into efficient, reliable software. The course includes examination of existing software systems, e.g., linear systems, non-linear systems, optimization, or differential equations. (Also listed as Computer Science 95.387*.)

Prerequisite: Mathematics 69.386*.

Lectures three hours a week and one hour tutorial.

Mathematics 69.389*

Introduction to Number Theory and Cryptography

Congruences, distribution of primes, general cryptographic systems, public key cryptographic systems and authentification using number theory, primality testing and factoring in relation to cryptography, continued fractions and diophantine equations.

Prerequisites: Mathematics 69.218* or 69.311* or 70.210; knowledge of a computer language.

Lectures three hours a week and one hour tutorial.

Mathematics 69.397*

Directed Studies

Available only to students whose program requires a 0.5 credit not offered by the School of Mathematics and Statistics.

 Mathematics Courses for Honours Students

Note: Students who have completed Mathematics 69.208* or 69.204*, and/or Mathematics 69.218* or 69.311*, with good grades, and who wish to transfer to an honours program in Mathematics and Statistics should consult the Undergraduate Advisor of the School.

Mathematics 70.200

Calculus and Introductory Analysis

Higher dimensional calculus, chain rule, gradient, line and multiple integrals with applications. Use of implicit and inverse function theorems. Real number axioms, limits, continuous functions, differentiability, infinite series, uniform convergence, the Riemann integral.

Precludes additional credit for Mathematics 69.204*, 69.208*, 69.209*, 69.309*, and for 69.201, 69.202.

Prerequisites: (i) Mathematics 69.102 or 69.207*; and (ii) Mathematics 69.112 or 69.117*; or permission of the School.

Lectures three hours a week and one hour tutorial.

Mathematics 70.210

Algebra

Set theory, algebraic systems, vector spaces, inner product spaces, linear transformations, determinants, quadratic forms, selected applications.

Precludes additional credit for Mathematics 69.218* or 69.311*.

Prerequisite: Mathematics 69.112 or 69.217*.

Lectures three hours a week and one hour tutorial.

Mathematics 70.220*

Co-operative Work Term Report 1

On completion of the work term, the student must submit to the School of Mathematics and Statistics a written report on the work performed. Graded Sat or Uns.

Prerequisites: Registration in the Co-operative Education Option of an Honours program offered by the School of Mathematics and Statistics, and permission of the School.

Mathematics 70.244*

Ordinary Differential Equations

Ordinary differential equations of the first and second order, existence and uniqueness of solutions; numerical solutions, error analysis; linear systems of first order; difference equations; higher order linear equations. Modelling with differential equations. A mathematical computer software package will be used.

Precludes additional credit for Mathematics 69.105*, 69.201, 69.202, 69.244*, 70.260.

Prerequisites: Mathematics 69.102 (or 69.207*) and 69.112 (or 69.217*).

Lectures three hours a week, tutorial one hour a week.

Mathematics 70.259*

Statistics: Theory and Practice

Computational and inferential statistics; basic distributions (normal, t, chi-square, F); maximum likelihood and moment estimators; properties of estimators; confidence intervals (one- and two-sample procedures); testing of simple and composite hypotheses; regression and analysis of variance models; non-parametric procedures; contingency tables. Use of computer packages.

Precludes additional credit for Mathematics 69.259*, 69.267*, Economics 43.220.

Prerequisite: Mathematics 70.265* or 70.260.

Lectures three hours a week and one hour tutorial/laboratory.

Mathematics 70.265*

Introduction to Probability with Applications

Axioms of probability, basic combinatorial analysis, conditional probability and independence, discrete and continuous random variables, joint and conditional distributions, expectation, central limit theorem, sampling distributions, simulation and applications to descriptive statistics. A statistical software package will be used.

Precludes additional credit for Mathematics 69.265* and 70.260.

Prerequisites: Mathematics 69.102 (or 69.207*) and 69.112 (or 69.217*).

Lectures three hours a week, tutorial one hour a week.

Mathematics 70.297*

Directed Studies

Available only to Honours students whose program requires a 0.5 credit not offered by the School of Mathematics and Statistics.

Mathematics 70.301*

Real Analysis

Metric spaces; limits, continuity, open and closed sets, compactness, connectedness and completeness. Uniform convergence of sequences of functions, as convergence in metric spaces of bounded and continuous functions. Weierstrass approximation theorem. Contraction mappings and applications to integral and differential equations.

Prerequisite: Mathematics 70.200 or permission of the School.

Lectures three hours a week and one hour tutorial.

Mathematics 70.302*

Advanced Calculus

Vector fields on surfaces. The functions div, curl and grad. Line and surface integrals. The divergence theorem and Stokes' theorem. Exterior algebra. Stokes' formula. Functions of bounded variation. The Riemann-Stieltjes integral.

Prerequisite: Mathematics 70.200 or permission of the School.

Lectures three hours a week and one hour tutorial.

Mathematics 70.307*

Functions of a Complex Variable

Analytic functions, contour integration, residue calculus, conformal mapping. Precludes additional credit for Mathematics 69.307*, 69.376*, Physics 75.387*, and 75.386.

Prerequisite: Mathematics 70.200 or permission of the School.

Lectures three hours a week and one hour tutorial.

Mathematics 70.308*

Ordinary Differential Equations

Analytic ordinary differential equations: series solutions of ordinary differential equations about ordinary and regular singular points. Asymptotic solutions. Sturm-Liouville theory. Bessel and Legendre functions. Fourier series.

Precludes additional credit for Mathematics 69.344*, Physics 75.388*, and 75.386.

Prerequisites: Mathematics 70.200; and 70.244* or 70.260.

Lectures three hours a week and one hour tutorial.

Mathematics 70.316*

Introduction to Group Theory

Homomorphism theorems; groups acting on sets; permutation groups and groups of matrices; Sylow theory for finite groups; finitely generated abelian groups; generators and relations; applications.

Precludes additional credit for Mathematics 70.310 and 69.318*.

Prerequisite: Mathematics 70.210, or permission of the School.

Lectures three hours a week, tutorial one hour a week.

Mathematics 70.318*

Rings and Fields

Rings; integral domains; Euclidean and principal ideal domains; polynomial rings over a field; modules over principal ideal domains and applications; fields; algebraic extensions of fields; finite fields; applications.

Precludes additional credit for Mathematics 70.310 and 69.318*.

Prerequisite: Mathematics 70.210, or permission of the School.

Lectures three hours a week, tutorial one hour a week.

Mathematics 70.320*

Co-operative Work Term Report 2

On completion of the work term, the student must submit to the School of Mathematics and Statistics a written report on the work performed. Graded Sat or Uns.

Prerequisites: Registration in the Co-operative Education Option of an Honours program offered by the School of Mathematics and Statistics, and permission of the School.

Mathematics 70.321*

Co-operative Work Term Report 3

On completion of the work term, the student must submit to the School of Mathematics and Statistics a written report on the work performed. Graded Sat or Uns.

Prerequisites: Registration in the Co-operative Education Option of an Honours program offered by the School of Mathematics and Statistics, and permission of the School.

Mathematics 70.326*

Foundations of Projective Geometry

Definition of a general projective plane and immediate consequences; finite planes (combinatorial results, sub-planes, incidence matrices) and planar ternary rings; collineations, role of Desargues' configuration, examples of types of planes.

Precludes additional credit for Mathematics 69.326*.

Prerequisite: Mathematics 70.210.

Lectures three hours a week and one hour tutorial.

Mathematics 70.336*

Elements of Set Theory

Axioms of set theory. Development of the systems of natural numbers and the real numbers. Axiom of choice, Zorn's lemma, well-ordering. The Schröder-Bernstein theorem, cardinal numbers, ordinal numbers, transfinite induction, cardinal and ordinal arithmetics.

Prerequisite: Mathematics 70.210 or permission of the School.

Lectures three hours a week and one hour tutorial.

Mathematics 70.346*

Autonomous Dynamical Systems

Basic concepts of dynamical systems. Stability; limit cycles; Lyapunov's direct method. Theory of autonomous dynamical systems. Volterra systems; principle of competitive exclusion in population biology. The threshold theorem of epidemiology. Basic concepts of nonequilibrium statistical mechanics.

Prerequisites: Mathematics 70.200; and 70.244* or 70.260.

Lectures three hours a week and one hour tutorial.

Mathematics 70.355*

Regression and Experimental Design

Linear regression - theory and methods; design of experiments - analysis of the completely randomized, randomized block and Latin square designs; multiple comparisons; factorial experiments; related topics.

Precludes additional credit for Mathematics 69.353*, 69.354*, Economics 43.476*, and for Mathematics 69.351. Psychology 49.300 is precluded for additional credit for students registered in a Mathematics program.

Prerequisites: (i) Mathematics 70.259* or 69.259*; and (ii) 69.112 or 69.217*; or permission of the School.

Lectures three hours a week and one hour laboratory.

Mathematics 70.356*

Stochastic Processes and Queueing Theory

Stochastic modelling, Markov chains, birth and death processes, renewal theory. Queueing theory: analytical and simulation methods. Applications to computer systems, operations research and social sciences.

Prerequisites: Mathematics 70.265* or 70.260; or a GPA of 6.0 or better over the three courses Mathematics 69.207*, 69.217* (or 69.112), and 69.265*; or permission of the School.

Lectures three hours a week and one hour tutorial.

Mathematics 70.358*

Elements of Probability Theory

Random variables and moment-generating functions, concepts of conditioning and correlation; laws of large numbers, central limit theorem; multivariate normal distribution; distributions of functions of random variables, sampling distributions, order statistics.

Precludes additional credit for Mathematics 69.358*, 69.350, 70.350.

Prerequisites: (i) Mathematics 70.265* (or 69.265* or 70.260); and (ii) Mathematics 70.200 (or a grade of C+ or better in 69.208*); or permission of the School.

Lectures three hours a week, tutorial one hour a week.

Mathematics 70.359*

Mathematical Statistics

Empirical distribution functions, Monte Carlo methods, elements of decision theory, point estimation, interval estimation, tests of hypotheses, robustness, nonparametric methods.

Precludes additional credit for Mathematics 69.350, 69.359*, 70.350.

Prerequisite: Mathematics 70.358* or permission of the School.

Lectures three hours a week, tutorial one hour a week.

Mathematics 70.385*

Discrete Structures and Applications

Enumeration: elementary methods, inclusion and exclusion, recurrence relations, generating functions and applications. Graph theory and algorithms: connectivity, planarity, Hamilton and Euler paths.Error-correcting codes. (Also listed as Computer Science 95.385*.)

Prerequisite: One of Mathematics 69.218*, 69.311*, or 70.210.

Lectures three hours a week and one hour tutorial.

A selection of courses in the 400 series will be offered.

Mathematics 70.403*

Functional Analysis

Banach spaces and bounded linear operators, Hahn-Banach extension and separation, dual spaces, bounded inverse theorems, uniform boundedness principle, applications. Compact operators. Differential calculus in Banach spaces, inverse and implicit function theorems and their application to differential equations. Also offered at the graduate level, with additional or different requirements, as Mathematics 70.508, for which additional credit is precluded.

Prerequisite: Mathematics 70.301* or permission of the School.

Lectures three hours a week.

Mathematics 70.407*

Measure and Integration Theory

Lebesgue measure and integration on the real line; sigma algebras and measures; integration theory; Lp spaces; Fubini's theorem; decomposition theorems and Radon-Nikodym derivatives. Also offered at the graduate level, with additional or different requirements, as Mathematics 70.507, for which additional credit is precluded.

Prerequisite: Mathematics 70.301* or 70.302* or permission of the School.

Lectures three hours a week.

Mathematics 70.415*

Rings and Modules

Fundamental concepts in rings and modules, structure theorems, applications.

Prerequisite: Mathematics 70.318* or 70.310 or permission of the School.

Lectures three hours a week.

Mathematics 70.416*

Group Theory

Fundamental principles as applied to abelian, nilpotent, solvable, free and finite groups; representations. Also offered at the graduate level, with additional or different requirements, as Mathematics 70.516, for which additional credit is precluded.

Prerequisite: Mathematics 70.316* or 70.310 or permission of the School.

Lectures three hours a week.

Mathematics 70.417*

Commutative Algebra

Fields, including algebraic and transcendental extensions, Galois theory, valuation theory; Noetherian commutative rings, including Noether decomposition theorem and localization.

Prerequisite: Mathematics 70.318* or 70.310 or permission of the School.

Lectures three hours a week.

Mathematics 70.418*

Homological Algebra and Category Theory

Axioms of set theory; categories, functors, natural transformations; free, projective, injective and flat modules; tensor products and homology functors, derived functors; dimension theory. Also offered at the graduate level, with additional or different requirements, as Mathematics 70.518, for which additional credit is precluded.

Prerequisite: Mathematics 70.318* or 70.310 or permission of the School.

Lectures three hours a week.

Mathematics 70.419*

Fields and Coding Theory

Introduction to field theory, emphasizing the structure of finite fields, primitive elements and irreducible polynomials. The influence of computational problems will be considered. Theory and applications of error-correcting codes: algebraic codes, convolution codes, decoding algorithms, and analysis of code performance.

Prerequisite: Mathematics 70.210, or 69.311* or 69.218* or equivalent; or permission of the School.

Lectures three hours a week.

Mathematics 70.420*

Co-operative Work Term Report 4

On completion of the work term, the student must submit to the School of Mathematics and Statistics a written report on the work performed. Graded Sat or Uns.

Prerequisites: Registration in the Co-operative Education Option of an Honours program offered by the School of Mathematics and Statistics, and permission of the School.

Mathematics 70.421*

Co-operative Work Term Report 5

On completion of the work term, the student must submit to the School of Mathematics and Statistics a written report on the work performed. Graded Sat or Uns.

Prerequisites: Registration in the Co-operative Education Option of an Honours program offered by the School of Mathematics and Statistics, and permission of the School.

Mathematics 70.425*

Introduction to General Topology

Topological spaces, maps, subspaces, product and identification topologies, separation axioms, compactness, connectedness. Also offered at the graduate level, with additional or different requirements, as Mathematics 70.525, for which additional credit is precluded.

Prerequisite: Mathematics 70.301* or permission of the School.

Lectures three hours a week.

Mathematics 70.426*

Introduction to Algebraic Topology

An introduction to homotopy theory. Topics include the fundamental group, covering spaces and the classification of two-dimensional manifolds. Also offered at the graduate level, with additional or different requirements, as Mathematics 70.526, for which additional credit is precluded.

Prerequisites: Mathematics 70.316* (or 70.310) and 70.425*; or permission of the School.

Lectures three hours a week.

Mathematics 70.427*

Foundations of Geometry

A study of at least one modern axiom system of Euclidean and non-Euclidean geometry, embedding of hyperbolic and Euclidean geometries in the projective plane, groups of motions, models of non-Euclidean geometry.

Prerequisite: Mathematics 70.316* (may be taken concurrently) or 70.310, or permission of the School.

Lectures three hours a week.

Mathematics 70.428*

Introduction to Differentiable Manifolds

A study of differentiable manifolds from the point of view of either differential topology or differential geometry. Topics such as smooth mappings, transversality, intersection theory, vector fields on manifolds, Gaussian curvature, Riemannian manifolds, differential forms, tensors and connections are included.

Prerequisite: Mathematics 70.301* or permission of the School.

Lectures three hours a week.

Mathematics 70.435*

Analytic Number Theory

Dirichlet series, characters, Zeta-functions, prime number theorem, Dirichlet's theorem on primes in arithmetic progressions, binary quadratic forms. Also offered at the graduate level, with additional or different requirements, as Mathematics 70.535, for which additional credit is precluded.

Prerequisite: Mathematics 70.307* or permission of the School.

Lectures three hours a week.

Mathematics 70.436*

Algebraic Number Theory

Algebraic number fields, bases, algebraic integers, integral bases, arithmetic in algebraic number fields, ideal theory, class number. Also offered at the graduate level, with additional or different requirements, as Mathematics 70.536, for which additional credit is precluded.

Prerequisite: Mathematics 70.318* (may be taken concurrently) or 70.310, or permission of the School.

Lectures three hours a week.

Mathematics 70.447*

Tensor Analysis and Relativity Theory

Development of tensor analysis, application to Riemannian spaces and relativity theory.

Prerequisites: Mathematics 70.345* and 70.346* or permission of the School.

Lectures three hours a week.

Mathematics 70.450*

Parametric Estimation

Preliminaries on probability theory; exact and asymptotic sampling distributions; unbiasedness, consistency, efficiency, sufficiency and completeness; properties of maximum likelihood estimators; least squares estimation of location and scale parameters based on order statistics and sample quantiles; Best Asymptotically Normal (BAN) estimators. Also offered at the graduate level, with additional or different requirements, as Mathematics 70.560, for which additional credit is precluded.

Prerequisite: Mathematics 70.350 or 70.359* or permission of the School.

Lectures three hours a week.

Mathematics 70.451*

Probability Theory

Introduction to probability, characteristic functions, probability distributions, limit theorems.

Prerequisites: Mathematics 70.356* and 70.358* or permission of the School.

Lectures three hours a week.

Mathematics 70.452*

Survey Sampling

Basic concepts in sampling from finite populations; simple random sampling; stratified sampling; choice of sampling unit; cluster and systematic sampling; introduction to multistage sampling; ratio estimation; sampling with unequal probabilities and with replacement; replicated sampling; related topics.

Prerequisites: (i) Mathematics 70.259* or 69.259*; and (ii) either 70.359* (or 70.350) or a grade of C+ or better in 69.359* (or 69.350); or permission of the School.

Lectures three hours a week.

Mathematics 70.453*

Applied Multivariate Analysis

Selected topics in regression and correlation non-linear models. Multivariate statistical methods, principal components, factor analysis, multivariate analysis of variance, discriminant analysis, canonical correlation, analysis of categorical data. Also offered at the graduate level, with additional or different requirements, as Mathematics 70.559, for which additional credit is precluded.

Prerequisites: Mathematics 70.355*; or 69.359* (or 69.350) and 69.354*; or permission of the School.

Lectures three hours a week.

Mathematics 70.456*

Non-Parametric Methods

Order statistics; rank statistics; permutations; asymptotics; hypothesis of randomness; stochastic ordering; Wilcoxon test; median test; Kolmogorov-Smirnov test; hypothesis of symmetry and random blocks; independence hypothesis; treatment of ties; power and efficiency. Also offered at the graduate level, with additional or different requirements, as Mathematics 70.556, for which additional credit is precluded.

Prerequisite: Mathematics 70.359* (or 70.350) or permission of the School.

Lectures three hours a week.

Mathematics 70.457*

Statistical Inference

Sufficient statistics, simple and composite hypotheses, most powerful and similar region test, distribution-free tests, confidence intervals, goodness-of-fit and likelihood ratio tests, large sample theory, Bayesian and likelihood methods, sequential tests. Also offered at the graduate level, with additional or different requirements, as Mathematics 70.551, for which additional credit is precluded.

Prerequisite: Mathematics 70.450* or permission of the School.

Lectures three hours a week.

Mathematics 70.458*

Stochastic Models

Review of discrete Markov chains and Poisson processes; pure jump Markov processes including the Q-matrix approach; the Kolmogorov equations; classification of states; stationary and limiting distributions; renewal theory. Also offered at the graduate level, with additional or different requirements, as Mathematics 70.571, for which additional credit is precluded.

Prerequisite: Mathematics 70.356* or permission of the School.

Lectures three hours a week.

Mathematics 70.459*

Advanced Mathematical Modelling

Real life situations in the physical, social, and life sciences are often modelled using mathematical tools. This course will examine various models and techniques used in their analysis, e.g., matrix procedures in connection with population models. Students will use a computer package to obtain numerical results. Also offered at the graduate level, with additional or different requirements, as Mathematics 70.561, for which additional credit is precluded.

Prerequisites: Mathematics (i) 70.244* and 70.265* (or 70.260; or 69.244* and 69.265*) and (ii) 70.356*; or permission of the School.

Lectures three hours a week.

Mathematics 70.460*

Case Studies in Operations Research

Applications of the principles of Operations Research to practical problems in business, management, and science. Students present at least one case and analyze cases in the published literature. Cases may also be presented by visiting practitioners.

Note: this course is designed for students in their final year in Honours Operations Research. Students in Honours Mathematics/Statistics programs may only take this course as a free option.

Prerequisites: Mathematics 69.259* (or 70.259*) and 69.381*; or permission of the School.

Seminars three hours a week.

Mathematics 70.470*

Partial Differential Equations

First order linear, quasi-linear, and non-linear equations; second order equations in two and more variables; systems of equations; the wave equation; Laplace and Poisson equations, Dirichlet and Neumann problems; Green's functions. Also offered at the graduate level, with additional or different requirements, as Mathematics 70.546, for which additional credit is precluded.

Prerequisites: Mathematics 70.308* and one of 70.302* or 70.307* or permission of the School.

Lectures three hours a week.

Mathematics 70.471*

Topics in Partial Differential Equations

Theory of distributions, initial-value problems based on 2-dimensions wave equations, Laplace transform, Fourier integral transform, diffusion problems, Helmholtz equation with application to boundary and initial-value problems in cylindrical and spherical coordinates. Also offered at the graduate level, with additional or different requirements, as Mathematics 70.547, for which additional credit is precluded.

Prerequisites: Mathematics 70.308* and one of 70.302* or70.307* or permission of the School.

Lectures three hours a week.

Mathematics 70.472*

Integral Transforms

Laplace, Fourier, Hankel and Mellin transforms, selection of a suitable transform for a given partial differential equation boundary value problem. Operational properties of transforms. Inversion theorems. Approximate evaluation of inversion integrals for small and large values of parameter. Application to the solution of integral equations.

Prerequisite: Mathematics 70.307* or permission of the School.

Lectures three hours a week.

Mathematics 70.473*

Qualitative Theory of Ordinary Differential Equations

Ordinary differential equations: existence-uniqueness theorems, vector formulation for systems; stability theory, Lyapunov theorems, perturbation theorems and structural stability; Poincaré-Bendixon theory.

Prerequisites: Mathematics 70.301*, 70.308*, 70.346*.

Lectures three hours a week.

Mathematics 70.481*

Topics in Combinatorics

An in-depth study of one or more topics from: generating functions, Polya's theory of counting, block designs, coding theory, partially ordered sets and Ramsey theory.

Prerequisites: Mathematics 70.210 and 70.385* or permission of the School.

Lectures three hours a week.

Mathematics 70.482*

Introduction to Mathematical Logic

Symbolic logic, propositional and predicate calculi, set theory and model theory, completeness.

Prerequisite: Mathematics 70.210 or permission of the School.

Lectures three hours a week.

Mathematics 70.483*

Computable Functions

Recursive functions and computability, algorithms, Church's thesis, Turing machines, computational logic, NP-completeness. (Also listed as Computer Science 95.483*.)

Prerequisite: Mathematics 70.210 or 70.385* or permission of the School.

Lectures three hours a week.

Mathematics 70.485*

Theory of Automata

Finite automata and regular expressions, properties of regular sets, context-free grammars, pushdown automata, deterministic context-free languages. Turing machines, the Chomsky hierarchy. Undecidability, intractable problems. Also offered at the graduate level, with additional or different requirements, as Mathematics 70.565, for which additional credit is precluded. (Also listed as Computer Science 95.485*.)

Prerequisite: Mathematics 70.385* or 70.316* or 70.318* (or 70.310) or permission of the School.

Lectures three hours a week.

Mathematics 70.486*

Numerical Linear Algebra

Study of matrix inversion techniques; techniques of finding eigenvalues and eigenvectors, solution of systems of linear equations; direct and indirect methods, their comparison and error analysis; applications in optimization and other areas. (Also listed as Computer Science 95.486*.)

Prerequisites: Mathematics 69.112 or 69.217*; and Mathematics 70.200 or 69.309*, or permission of the School.

Lectures three hours a week.

Mathematics 70.487*

Game Theory

Two-person zero-sum games; infinite games; multistage games; differential games; utility theory; two-person general-sum games; bargaining problem;

n-person games; games with a continuum of players. Also offered at the graduate level, with additional or different requirements, as Mathematics 70.567, for which additional credit is precluded.

Prerequisite: Mathematics 70.301* or permission of the School.

Lectures three hours a week.

Mathematics 70.488*

Graph Theory and Algorithms

Paths, circuits, Eulerian and Hamiltonian graphs, connectivity, colouring problems, matching, Ramsey theory, network flows.

Prerequisites: Mathematics 70.385* or 70.316* or 70.318* (or 70.310) or permission of the School.

Lectures three hours a week.

Mathematics 70.489*

Mathematical Cryptography

Topics covered include: a general survey of public key cryptography; classical applications of finite fields and number theory; relevant background in geometry and algebraic curves; computational issues concerning elliptic curves; elliptic curve cryptosystems; security issues.

Prerequisite: Mathematics 69.389*, or permission of the School.

Lectures three hours a week.

Mathematics 70.495*

Honours Project

Consists of a written report on some approved topic or topics in the field of mathematics, together with a short lecture on the report.

Prerequisite: B.Math.(Honours) students only.

Note: Each student should commence work on the Honours Project under a faculty supervisor before June 1 of the year before he or she intends to graduate (for full-time students, this would be the June 1 between Third and Fourth Year). The first draft of the report must be submitted to the supervisor by November 1, and the final draft to the School by January 15. Students who do not meet this latter deadline will be given the grade F.

 Mathematics 70.496*

Directed Studies

Prerequisite: B.Math.(Honours) students only.

Mathematics 70.497*

Directed Studies

Prerequisite: B.Math.(Honours) students only.

The following courses have not been offered in recent years, but may be offered sometime in the future:

Mathematics 69.376* Mathematical Methods II

Mathematics 70.345* Classical Mechanics

Mathematics 70.390* Mathematical Problem Solving

Mathematics 70.401* Vector Calculus

Mathematics 70.445* Analytical Dynamics

Mathematics 70.446* Hydrodynamics and Elasticity

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2001-2002 Undergraduate Calendar
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