Mathematics and Statistics (MATH)

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Mathematics and Statistics (MATH)

Location

Location

  • Burnside Hall, Room 1005
  • 805 Sherbrooke Street West
  • Montreal, Quebec, H3A 2K6

About Mathematics and Statistics

About Mathematics and Statistics

Mathematics has evolved to a discipline that is mainly characterized by its method of proof, its concern for a progressive broadening of its concepts, and by the search for mathematical entities and operations that represent aspects of reality. It is a subject that is pursued by many for its own sake, and regarded as part of the mainstream of human culture. Mathematics pervades modern society with an impact which, already immense, is rapidly growing.

The two principal divisions of mathematics are pure mathematics and applied mathematics. The pure mathematician is interested in abstract mathematical structures and in mathematics as an intellectual enterprise. The primary concern may not be with its utilitarian aspects or with the current needs of science and technology, although many problems in pure mathematics have developed from the sciences.

The applied mathematician is more interested in how mathematics can be used to study some aspects of the world. Mathematicians are engaged in the creation, study and application of advanced mathematical methods relevant to scientific problems. Statistical science and methodology today is concerned with phenomena in which there is a background of uncertainty arising from inherent variability and the investigator is obliged to arrive at decisions from limited data. A key tool in statistics is probability.

Some of the fields in which pure mathematicians work are algebra, analysis, geometry, topology, number theory and foundations. Applied mathematics, which once referred to the application of mathematics to such disciplines as mechanics and fluid dynamics, has currently assumed a much broader meaning and embraces such diverse fields as communication theory, theory of optimization, theory of games and numerical analysis.

Mathematics offers many vocational possibilities. Such fields as teaching, computing, applied statistics and actuarial science offer opportunities for B.Sc. graduates. Opportunities to do original research in pure and applied mathematics are available in universities and research institutions. Employment is to be found in financially or technologically oriented business firms. The Department of Mathematics and Statistics through its various programs attempts to provide courses to suit the diverse interests within mathematics and statistics.

The Honours Program demands of the student a talent for abstraction in addition to a high level of competence in the use of mathematical tools. This program is intended for students who plan to work in an area where mathematical innovations may be needed. It is almost essential for students contemplating a career in mathematical research.

The Major Program involves the same subjects as the Honours Program but is less demanding in terms of abstraction. It is designed primarily for students who will need mathematical tools in their work but whose creative activity will involve applications of mathematics to other areas. Within the framework of the Mathematics Major, various combinations of courses are suggested to meet the needs of different students. These include course suggestions for secondary school teachers, careers in management, and for careers in industry, government or actuarial sciences.

It is possible for Major students to include a number of Honours courses in their programs. This will be an advantage for those students who plan to use their mathematics in graduate studies.

Students interested in a Mathematics program linked to other disciplines are advised to consider the B.Sc. Liberal Program with a core component in Mathematics or Statistics, or our joint programs with Computer Science, Physiology and Physics.

In planning their programs, students are advised to seriously consider developing some depth in another discipline – preferably one for which mathematics has some relevance and use. Mathematics has been closely linked to areas such as computer science, physics and engineering but has recently come to play an increasingly important role in fields such as biology, linguistics, management and psychology. Students should consider completing the requirements for Minor programs such as those available in Cognitive Science, Computer Science and Statistics.

Students considering programs in Mathematics and Statistics should contact the Department to arrange for academic advising.

The student's attention is called to the fact that a B.Com. degree with a Major in Mathematics is available from the Desautels Faculty of Management. In addition, the Schulich School of Music offers the B.Mus. degree with Honours in Theory with Mathematics Option.

Internship Opportunities

Internship Opportunities

Students who want to get practical experience in industry before graduation are encouraged to participate in one of the following internship programs:

  • The Internship Year in Science (IYS) is an academic program offered for a duration of 8, 12 or 16 months. It is reflected on the transcript and included in the program name (Bachelor of Science - Internship program). Eligible students usually take this program between their U2 and U3 years.
  • The Industrial Practicum (IP) has a duration of 4 months and is usually carried out starting in May. It will appear as a 0-credit, pass/fail course on your transcript.

For more information on these programs, consult Industrial Practicum (IP) and Internship Year in Science (IYS).

Note: Students entering a program listed below that has MATH 222 (Calculus 3) as a required course and who have successfully completed a course equivalent to MATH 222 with a grade of C or better may omit MATH 222 (Calculus 3) from the program, but must replace it with 3 credits of elective courses.

Mathematics and Statistics (MATH) Faculty

Mathematics and Statistics (MATH) Faculty

Chair
Jacques Hurtubise
Emeritus Professors
Michael Barr; A.B., Ph.D.(Penn.) (Peter Redpath Emeritus Professor of Pure Mathematics)
Marta Bunge; M.A., Ph.D.(Penn.)
Jal R. Choksi; B.A.(Cant.), Ph.D.(Manc.)
Ian Connell; B.Sc., M.Sc.(Manit.), Ph.D.(McG.)
Paul Koosis; B.A., Ph.D.(Calif., Berk.)
Joachim Lambek; M.Sc., Ph.D.(McG.), F.R.S.C. (Peter Redpath Emeritus Professor of Pure Mathematics)
Sherwin A. Maslowe; B.Sc.(Wayne State), M.Sc., Ph.D.(Calif.)
Arak M. Mathai; M.Sc.(Kerala), M.A., Ph.D.(Tor.)
Karl Peter Russel; Vor.Dip.(Hamburg), Ph.D.(Calif.)
Georg Schmidt; B.Sc.(Natal), M.Sc.(S.Af.), Ph.D.(Stan.)
V. Seshadri; B.Sc., M.Sc.(Madr.), Ph.D.(Okla.)
George P.H. Styan; M.A., Ph.D.(Col.)
Kwok Kuen Tam; M.A., Ph.D.(Tor.)
John C. Taylor; B.Sc.(Acad.), M.A.(Qu.), Ph.D.(McM.)
Sanjo Zlobec; M.Sc.(Zagreb), Ph.D.(N'western)
Professors
William J. Anderson; B.Eng., Ph.D.(McG.)
William G. Brown; M.A.(Col.), B.A., Ph.D.(Tor.)
Henri Darmon; B.Sc.(McG.), Ph.D.(Harv.), F.R.S.C. (James McGill Professor)
Stephen W. Drury; M.A., Ph.D.(Cant.)
Eyal Z. Goren; B.A., M.S., Ph.D.(Hebrew)
Kohur GowriSankaran; B.A., M.A.(Madr.), Ph.D.(Bom.)
Pengfei Guan; B.Sc.(Zhejiang), M.Sc., Ph.D.(Prin.)
Jacques C. Hurtubise; B.Sc.(Montr.), Ph.D.(Oxf.), F.R.S.C.
Dmitry Jakobson; B.Sc.(MIT), Ph.D.(Prin.) (William Dawson Scholar)
Vojkan Jaksic; B.S.(Belgrade), Ph.D.(Caltech)
Niky Kamran; B.Sc., M.Sc.(Brussels), Ph.D.(Wat.), F.R.S.C. (James McGill Professor)
Olga Kharlampovich; M.A.(Ural State), Ph.D.(Leningrad), Dr.Sc.(Steklov Institute)
Michael Makkai; M.A., Ph.D.(Bud.) (Peter Redpath Professor of Pure Mathematics)
Charles Roth; M.Sc.(McG.), Ph.D.(Hebrew)
F. Bruce Shepherd; B.Sc.(Vic., Tor.), M.Sc., Ph.D.(Wat.) (James McGill Professor)
David A. Stephens; B.Sc., Ph.D.(Nott.)
John A. Toth; B.Sc., M.Sc.(McM.), Ph.D.(MIT) (William Dawson Scholar)
Daniel T. Wise; B.A.(Yeshiva), Ph.D.(Prin.)
David Wolfson; M.Sc.(Natal), Ph.D.(Purd.)
JianJu Xu; B.Sc., M.Sc.(Beijing), M.Sc., Ph.D.(Renss.)
Associate Professors
Masoud Asgharian; B.Sc.(Shahid Beheshti), M.Sc., Ph.D.(McG.)
Peter Bartello; B.Sc.(Tor.), M.Sc., Ph.D.(McG.) (joint appoint. with Atmospheric and Oceanic Sciences)
Antony Humphries; B.A., M.A.(Camb.), Ph.D.(Bath)
Wilbur Jonsson; M.Sc.(Manit.), Dr.Rer.Nat.(Tübingen)
Ivo Klemes; B.Sc.(Tor.), Ph.D.(Calif. Tech.)
James G. Loveys; B.A.(St. Mary's), M.Sc., Ph.D.(S. Fraser)
Neville G.F. Sancho; B.Sc., Ph.D.(Belf.)
Russell Steele; B.S., M.S.(Carn. Mell), Ph.D.(Wash.)
Alain Vandal; B.Sc., M.Sc.(McG.), Ph.D.(Auck.)
Adrian Vetta; B.Sc., M.Sc.(LSE), Ph.D.(MIT) (joint appoint. with Computer Science)
Assistant Professors
Louigi Addario-Berry; B.Sc., M.Sc., Ph.D.(McG.)
Jayce Getz; A.B.(Harv), Ph.D.(Wis.)
Abbas Khalili; B.S., M.S.(Esfahan), Ph.D.(Wat.)
Johanna Neslehova; Vor.Dip.(Prague), Dip.(Hamburg), Ph.D.(Oldenburg)
Gantumur Tsogtgerel; B.Sc.(Mongolia), M.Sc.(Netherlands), Ph.D.(Utrecht)
Associate Members
Xiao-Wen Chang (Computer Science)
Luc P. Devroye (Computer Science)
P.R.L. Dutilleul (Plant Science)
Eliot Fried (Mechanical Engineering)
Leon Glass (Physiology)
James A. Hanley (Epidemiology & Biostatistics)
Lawrence Joseph (Epidemiology & Biostatistics)
Michael Mackey (Physiology)
Lawrence A. Mysak (A.O.S.)
Christopher Conway Paige (Computer Science)
Prakash Panangaden (Computer Science)
Robert W. Platt (Pediatrics)
James O. Ramsay (Psychology)
George Alexander Whitmore (Management)
Christina Wolfson (Epidemiology & Biostatistics)
Adjunct Professors
Vasek Chvatal; M.A.(Charles U., Prague), Ph.D.(Wat.)
Donald A. Dawson; B.Sc., M.Sc.(McG.), Ph.D.(MIT)
Martin J. Gander; M.S.(ETH), M.S., Ph.D.(Stan.)
Andrew Granville; B.A., CASM(Camb.), Ph.D.(Qu.)
Adrian Iovita; B.S.(Buc.), Ph.D.(Boston)
Ming Mei; B.Sc., M.Sc.(Jiangxi Normal University), Ph.D.(Kanazawa)
Alexei Miasnikov; M.Sc.(Novosibirsk), Ph.D., Dr.Sc.(Leningrad)
M. Ram Murty; B.Sc.(Car.), Ph.D.(MIT), F.R.S.C.
Vladimir Remeslennikov; M.Sc.(Perm, Russia), Ph.D.(Novosibirsk)
Robert A. Seely; B.Sc.(McG.), Ph.D.(Cant.)
Thomas Wihler; M.S., Ph.D.(ETH)
Faculty Lecturers
Jose A. Correa; M.Sc.(Wat.), Ph.D.(Car.)
Axel Hundemer; M.Sc., Ph.D.(Munich)
Armel Djivede Kelome; M.Sc.(Benin), M.Sc.(McG.), Ph.D.(Georgia Tech.)
Faculty of Science—2010-2011 (last updated Apr. 22, 2010) (disclaimer)

Bachelor of Science (B.Sc.) - Minor Mathematics (24 credits)

The Minor may be taken in conjunction with any primary program in the Faculty of Science (other than programs in Mathematics). Students should declare their intention to follow the Minor Mathematics at the beginning of the penultimate year and should obtain approval for the selection of courses to fulfil the requirements for the Minor from the Departmental Chief Adviser (or delegate).

It is strongly recommended that students in the Minor Program take MATH 323. The remaining credits may be freely chosen from the required and complementary courses for Majors and Honours students in Mathematics, with the obvious exception of courses that involve duplication of material. Alternatively, up to six credits may be allowed for appropriate courses from other departments.

Generally no more than six credits of overlap are permitted between the Minor and the primary program. However, with an approved choice of substantial courses the overlap restriction may be relaxed to nine credits for students whose primary program requires 60 credits or more and to 12 credits when the primary program requires 72 credits or more.

Required Courses (9 credits)

* MATH 223 may be replaced by MATH 235 and MATH 236. In this case the complementary credit requirement is reduced by three.

MATH 222 (3) Calculus 3
MATH 223* (3) Linear Algebra
MATH 315 (3) Ordinary Differential Equations

Complementary Courses (15 credits)

15 credits selected from the required and complementary courses for Majors and Honours students in Mathematics, with MATH 323 strongly recommended; alternatively, up to 6 credits may be allowed for appropriate courses from other departments.

Faculty of Science—2010-2011 (last updated Apr. 22, 2010) (disclaimer)

Bachelor of Science (B.Sc.) - Minor Statistics (24 credits)

The Minor may be taken in conjunction with any primary program in the Faculty of Science. Students should declare their intention to follow the Minor Statistics at the beginning of the penultimate year and must obtain approval for the selection of courses to fulfil the requirements for the Minor from the Departmental Chief Adviser (or delegate).

All courses counted towards the Minor must be passed with a grade of C or better. Generally no more than six credits of overlap are permitted between the Minor and the primary program. However, with an approved choice of substantial courses the overlap restriction may be relaxed to nine credits for students whose primary program requires 60 credits or more and to 12 credits when the primary program requires 72 credits or more.

Required Courses (15 credits)

* MATH 223 may be replaced by MATH 235 and MATH 236. In this case the complementary credit requirement is reduced by three.

MATH 222 (3) Calculus 3
MATH 223* (3) Linear Algebra
MATH 323 (3) Probability
MATH 324 (3) Statistics
MATH 423 (3) Regression and Analysis of Variance

Complementary Courses (9 credits)

9 credits selected from:

CHEM 593 (3) Statistical Mechanics
GEOG 351 (3) Quantitative Methods
MATH 447 (3) Stochastic Processes
MATH 523 (4) Generalized Linear Models
MATH 525 (4) Sampling Theory and Applications
MATH 556 (4) Mathematical Statistics 1
MATH 557 (4) Mathematical Statistics 2
PHYS 362 (3) Statistical Mechanics
PHYS 559 (3) Advanced Statistical Mechanics
SOCI 504 (3) Quantitative Methods 1
SOCI 505 (3) Quantitative Methods 2

No more than 6 credits may be taken outside the Department of Mathematics and Statistics.

Further credits (if needed) may be freely chosen from the required and complementary courses for Majors and Honours students in Mathematics, with the obvious exception of courses that involve duplication of material.

Faculty of Science—2010-2011 (last updated Apr. 22, 2010) (disclaimer)

Bachelor of Science (B.Sc.) - Liberal Program - Core Science Component Mathematics (45 credits)

Program Prerequisites

Students entering the Core Science Component in Mathematics are normally expected to have completed the courses below or their equivalents. Otherwise, they will be required to make up any deficiencies in these courses over and above the 45 credits required for the program.

MATH 133 (3) Linear Algebra and Geometry
MATH 140 (3) Calculus 1
MATH 141 (4) Calculus 2

Guidelines for Selection of Courses

The following informal guidelines should be discussed with the student's adviser. Where appropriate, Honours courses may be substituted for equivalent Major courses. Students planning to pursue graduate studies are encouraged to make such substitutions.

Students interested in computer science are advised to choose courses from the following: MATH 317, MATH 318, MATH 327, MATH 328, MATH 335, MATH 340, MATH 407, MATH 417 and to complete the Computer Science Minor.

Students interested in probability and statistics are advised to take MATH 204, MATH 324, MATH 407, MATH 423, MATH 447, MATH 523, MATH 525.

Students interested in applied mathematics should take MATH 317, MATH 319, MATH 324, MATH 326, MATH 327, MATH 407, MATH 417.

Students considering a career in secondary school teaching are advised to take MATH 318, MATH 328, MATH 338, MATH 339, MATH 346, MATH 348.

Students interested in careers in business, industry or government are advised to select courses from the following list:

MATH 317, MATH 319, MATH 327, MATH 329, MATH 407, MATH 417, MATH 423, MATH 430, MATH 447, MATH 523, MATH 525.

Required Courses (27 credits)

* Students may select either MATH 249 or MATH 316 but not both.

** Students who have successfully completed a course equivalent to MATH 222 with a grade of C or better may omit MATH 222, but must replace it with three credits of elective courses.

MATH 222** (3) Calculus 3
MATH 235 (3) Algebra 1
MATH 236 (3) Algebra 2
MATH 242 (3) Analysis 1
MATH 243 (3) Analysis 2
MATH 249* (3) Honours Complex Variables
MATH 314 (3) Advanced Calculus
MATH 315 (3) Ordinary Differential Equations
MATH 316* (3) Complex Variables
MATH 323 (3) Probability

Complementary Courses (18 credits)

18 credits selected from the following list, with at least 6 credits selected from:

MATH 317 (3) Numerical Analysis
MATH 324 (3) Statistics
MATH 335 (3) Computational Algebra
MATH 340 (3) Discrete Structures 2

the remainder of the 18 credits to be selected from:

MATH 204 (3) Principles of Statistics 2
MATH 318 (3) Mathematical Logic
MATH 319 (3) Introduction to Partial Differential Equations
MATH 320 (3) Differential Geometry
MATH 326 (3) Nonlinear Dynamics and Chaos
MATH 327 (3) Matrix Numerical Analysis
MATH 328 (3) Computability and Mathematical Linguistics
MATH 329 (3) Theory of Interest
MATH 338 (3) History and Philosophy of Mathematics
MATH 339 (3) Foundations of Mathematics
MATH 346 (3) Number Theory
MATH 348 (3) Topics in Geometry
MATH 352 (1) Problem Seminar
MATH 407 (3) Dynamic Programming
MATH 410 (3) Majors Project
MATH 417 (3) Mathematical Programming
MATH 423 (3) Regression and Analysis of Variance
MATH 430 (3) Mathematical Finance
MATH 447 (3) Stochastic Processes
MATH 523 (4) Generalized Linear Models
MATH 524 (4) Nonparametric Statistics
MATH 525 (4) Sampling Theory and Applications
Faculty of Science—2010-2011 (last updated Apr. 22, 2010) (disclaimer)

Bachelor of Science (B.Sc.) - Liberal Program - Core Science Component Statistics (45 credits)

Program Prerequisites

Students entering the Core Science Component in Statistics are normally expected to have completed the courses below or their equivalents. Otherwise they will be required to make up any deficiencies in these courses over and above the 45 credits required for the program.

MATH 133 (3) Linear Algebra and Geometry
MATH 140 (3) Calculus 1
MATH 141 (4) Calculus 2

Required Courses (27 credits)

* Students who have successfully completed a course equivalent to MATH 222 with a grade of C or better may omit MATH 222, but must replace it with three credits of elective courses.

MATH 222* (3) Calculus 3
MATH 235 (3) Algebra 1
MATH 236 (3) Algebra 2
MATH 242 (3) Analysis 1
MATH 243 (3) Analysis 2
MATH 314 (3) Advanced Calculus
MATH 323 (3) Probability
MATH 324 (3) Statistics
MATH 423 (3) Regression and Analysis of Variance

Complementary Courses (18 credits)

18 credits selected from the following list, with at least 6 credits selected from:

* Students may take either MATH 316 or MATH 249, but not both.

MATH 249* (3) Honours Complex Variables
MATH 315 (3) Ordinary Differential Equations
MATH 316* (3) Complex Variables
MATH 317 (3) Numerical Analysis
MATH 335 (3) Computational Algebra
MATH 340 (3) Discrete Structures 2

at least 7 credits selected from:

MATH 447 (3) Stochastic Processes
MATH 523 (4) Generalized Linear Models
MATH 525 (4) Sampling Theory and Applications

the remainder of the 18 credits to be selected from:

MATH 204 (3) Principles of Statistics 2
MATH 318 (3) Mathematical Logic
MATH 319 (3) Introduction to Partial Differential Equations
MATH 320 (3) Differential Geometry
MATH 326 (3) Nonlinear Dynamics and Chaos
MATH 327 (3) Matrix Numerical Analysis
MATH 328 (3) Computability and Mathematical Linguistics
MATH 329 (3) Theory of Interest
MATH 338 (3) History and Philosophy of Mathematics
MATH 339 (3) Foundations of Mathematics
MATH 346 (3) Number Theory
MATH 348 (3) Topics in Geometry
MATH 352 (1) Problem Seminar
MATH 407 (3) Dynamic Programming
MATH 410 (3) Majors Project
MATH 417 (3) Mathematical Programming
MATH 430 (3) Mathematical Finance
Faculty of Science—2010-2011 (last updated Apr. 22, 2010) (disclaimer)

Bachelor of Science (B.Sc.) - Major Mathematics (54 credits)

Program Prerequisites

Students entering the Major program are normally expected to have completed the courses below or their equivalents. Otherwise, they will be required to make up any deficiencies in these courses over and above the 54 credits of required courses.

MATH 133 (3) Linear Algebra and Geometry
MATH 140 (3) Calculus 1
MATH 141 (4) Calculus 2

Guidelines for Selection of Courses in the Major Program

The following informal guidelines should be discussed with the student's adviser. Where appropriate, Honours courses may be substituted for equivalent Major courses. Students planning to pursue graduate studies are encouraged to make such substitutions.

Students interested in computer science are advised to choose courses from the following: MATH 317, MATH 318, MATH 327, MATH 328, MATH 335, MATH 340, MATH 407, MATH 417 and to complete the Computer Science Minor.

Students interested in probability and statistics are advised to take MATH 204, MATH 324, MATH 407, MATH 423, MATH 447, MATH 523, MATH 525.

Students interested in applied mathematics should take MATH 317, MATH 319, MATH 324, MATH 326, MATH 327, MATH 407, MATH 417.

Students considering a career in secondary school teaching are advised to take MATH 318, MATH 328, MATH 338, MATH 339, MATH 346, MATH 348.

Students interested in careers in business, industry or government are advised to select courses from the following list:

MATH 317, MATH 319, MATH 327, MATH 329, MATH 407, MATH 417, MATH 423, MATH 430, MATH 447, MATH 523, MATH 525.

Required Courses (27 credits)

Note: Students who have done well in MATH 235 and MATH 242 should consider entering the Honours stream by registering in MATH 251 and MATH 255 instead of MATH 236 and MATH 243.

* Students may select either MATH 249 or MATH 316 but not both.

** Students who have successfully completed a course equivalent to MATH 222 with a grade of C or better may omit MATH 222, but must replace it with three credits of elective courses.

MATH 222** (3) Calculus 3
MATH 235 (3) Algebra 1
MATH 236 (3) Algebra 2
MATH 242 (3) Analysis 1
MATH 243 (3) Analysis 2
MATH 249* (3) Honours Complex Variables
MATH 314 (3) Advanced Calculus
MATH 315 (3) Ordinary Differential Equations
MATH 316* (3) Complex Variables
MATH 323 (3) Probability

Complementary Courses (27 credits)

27 credits selected as follows:

21 credits selected from the following list, with at least 6 credits selected from:

MATH 317 (3) Numerical Analysis
MATH 324 (3) Statistics
MATH 335 (3) Computational Algebra
MATH 340 (3) Discrete Structures 2

the remainder of the 21 credits to be selected from:

MATH 204 (3) Principles of Statistics 2
MATH 318 (3) Mathematical Logic
MATH 319 (3) Introduction to Partial Differential Equations
MATH 320 (3) Differential Geometry
MATH 326 (3) Nonlinear Dynamics and Chaos
MATH 327 (3) Matrix Numerical Analysis
MATH 328 (3) Computability and Mathematical Linguistics
MATH 329 (3) Theory of Interest
MATH 338 (3) History and Philosophy of Mathematics
MATH 339 (3) Foundations of Mathematics
MATH 346 (3) Number Theory
MATH 348 (3) Topics in Geometry
MATH 352 (1) Problem Seminar
MATH 407 (3) Dynamic Programming
MATH 410 (3) Majors Project
MATH 417 (3) Mathematical Programming
MATH 423 (3) Regression and Analysis of Variance
MATH 430 (3) Mathematical Finance
MATH 447 (3) Stochastic Processes
MATH 523 (4) Generalized Linear Models
MATH 525 (4) Sampling Theory and Applications

6 additional credits in Mathematics or related disciplines selected in consultation with the adviser.

Faculty of Science—2010-2011 (last updated Apr. 22, 2010) (disclaimer)

Bachelor of Science (B.Sc.) - Major Mathematics and Computer Science (72 credits)

Program Prerequisites

Students entering the Joint Major in Mathematics and Computer Science are normally expected to have completed the courses below or their equivalents. Otherwise, they will be required to make up any deficiencies in these courses over and above the 72 credits of courses in the program specification.

MATH 133 (3) Linear Algebra and Geometry
MATH 140 (3) Calculus 1
MATH 141 (4) Calculus 2

Required Courses (54 credits)

* Students who have sufficient knowledge in a programming language do not need to take COMP 202 but can replace it with an additional Computer Science complementary course.

COMP 202* (3) Introduction to Computing 1
COMP 206 (3) Introduction to Software Systems
COMP 250 (3) Introduction to Computer Science
COMP 251 (3) Data Structures and Algorithms
COMP 273 (3) Introduction to Computer Systems
COMP 302 (3) Programming Languages and Paradigms
COMP 310 (3) Operating Systems
COMP 330 (3) Theoretical Aspects: Computer Science
COMP 360 (3) Algorithm Design Techniques
MATH 222 (3) Calculus 3
MATH 235 (3) Algebra 1
MATH 236 (3) Algebra 2
MATH 242 (3) Analysis 1
MATH 315 (3) Ordinary Differential Equations
MATH 317 (3) Numerical Analysis
MATH 318 (3) Mathematical Logic
MATH 323 (3) Probability
MATH 340 (3) Discrete Structures 2

Complementary Courses (18 credits)

9 credits from the set of courses recommended for a Major or Honours Program in Mathematics.

9 credits selected from Computer Science courses at the 300-level or above (except COMP 364, COMP 396, COMP 400, COMP 431) and ECSE 508.

Faculty of Science—2010-2011 (last updated Apr. 22, 2010) (disclaimer)

Bachelor of Science (B.Sc.) - Major Statistics and Computer Science (72 credits)

This program provides students with a solid training in both computer science and statistics together with the necessary mathematical background. As statistical endeavours involve ever increasing amounts of data, some students may want training in both disciplines.

Program Prerequisites

Students entering the Joint Major in Statistics and Computer Science are normally expected to have completed the courses below or their equivalents. Otherwise they will be required to make up any deficiencies in these courses over and above the 72 credits of required courses.

MATH 133 (3) Linear Algebra and Geometry
MATH 140 (3) Calculus 1
MATH 141 (4) Calculus 2

Required Courses (51 credits)

* Students who have sufficient knowledge in a programming language do not need to take COMP 202 but can replace it with an additional Computer Science complementary course.

** Students take either COMP 350 or MATH 317, but not both.

*** Students take either MATH 223 or MATH 236, but not both.

COMP 202* (3) Introduction to Computing 1
COMP 206 (3) Introduction to Software Systems
COMP 250 (3) Introduction to Computer Science
COMP 251 (3) Data Structures and Algorithms
COMP 273 (3) Introduction to Computer Systems
COMP 302 (3) Programming Languages and Paradigms
COMP 330 (3) Theoretical Aspects: Computer Science
COMP 350** (3) Numerical Computing
COMP 360 (3) Algorithm Design Techniques
MATH 222 (3) Calculus 3
MATH 223*** (3) Linear Algebra
MATH 235 (3) Algebra 1
MATH 236*** (3) Algebra 2
MATH 242 (3) Analysis 1
MATH 314 (3) Advanced Calculus
MATH 317** (3) Numerical Analysis
MATH 323 (3) Probability
MATH 324 (3) Statistics
MATH 423 (3) Regression and Analysis of Variance

Complementary Courses (21 credits)

12 credits in Mathematics selected from:

* Students take either MATH 340 or MATH 350, but not both.

** MATH 578 and COMP 540 cannot both be taken for program credit.

MATH 327 (3) Matrix Numerical Analysis
MATH 340* (3) Discrete Structures 2
MATH 350* (3) Graph Theory and Combinatorics
MATH 352 (1) Problem Seminar
MATH 410 (3) Majors Project
MATH 447 (3) Stochastic Processes
MATH 523 (4) Generalized Linear Models
MATH 524 (4) Nonparametric Statistics
MATH 525 (4) Sampling Theory and Applications
MATH 578** (4) Numerical Analysis 1

9 credits in Computer Science selected as follows:

At least 6 credits selected from:

COMP 423 (3) Data Compression
COMP 424 (3) Artificial Intelligence
COMP 462 (3) Computational Biology Methods
COMP 490 (3) Introduction to Probabilistic Analysis of Algorithms
COMP 526 (3) Probabilistic Reasoning and AI
COMP 540** (3) Matrix Computations
COMP 547 (4) Cryptography and Data Security
COMP 564 (3) Computational Gene Regulation
COMP 566 (3) Discrete Optimization 1
COMP 567 (3) Discrete Optimization 2

The remaining Computer Science credits are selected from COMP courses at the 300-level or above (except COMP 396, COMP 400, and COMP 431) and ECSE 508.

Faculty of Science—2010-2011 (last updated Apr. 22, 2010) (disclaimer)

Bachelor of Science (B.Sc.) - Honours Mathematics (60 credits)

Program Prerequisites

The minimum requirement for entry into the Honours program is that the student has completed with high standing the following courses below or their equivalents. In addition, a student who has not completed the equivalent of MATH 222 must take it in the first term without receiving credits, towards the credits required in the Honours program.

Students who transfer to Honours in Mathematics from other programs will have credits for previous courses assigned, as appropriate, by the Department.

To remain in an Honours program and to be awarded the Honours degree, the student must maintain a 3.00 GPA in the required and complementary Mathematics courses of the program, as well as an overall CGPA of 3.00.

MATH 133 (3) Linear Algebra and Geometry
MATH 140 (3) Calculus 1
MATH 141 (4) Calculus 2

Required Courses (48 credits)

* MATH 314 may be substituted for MATH 248 if MATH 222 had to be taken in the Fall.

MATH 235 (3) Algebra 1
MATH 242 (3) Analysis 1
MATH 248* (3) Honours Advanced Calculus
MATH 251 (3) Honours Algebra 2
MATH 255 (3) Honours Analysis 2
MATH 325 (3) Honours Ordinary Differential Equations
MATH 354 (3) Honours Analysis 3
MATH 355 (3) Honours Analysis 4
MATH 356 (3) Honours Probability
MATH 357 (3) Honours Statistics
MATH 366 (3) Honours Complex Analysis
MATH 370 (3) Honours Algebra 3
MATH 371 (3) Honours Algebra 4
MATH 375 (3) Honours Partial Differential Equations
MATH 380 (3) Honours Differential Geometry
MATH 470 (3) Honours Research Project

Complementary Courses (12 credits)

12 credits selected from:

MATH 350 (3) Graph Theory and Combinatorics
MATH 352 (1) Problem Seminar
MATH 376 (3) Honours Nonlinear Dynamics
MATH 377 (3) Honours Number Theory
MATH 387 (3) Honours Numerical Analysis
MATH 397 (3) Honours Matrix Numerical Analysis
MATH 480 (3) Honours Independent Study
MATH 487 (3) Honours Mathematical Programming
MATH 488 (3) Honours Set Theory

all MATH 500-level courses.

Honours-level courses from related disciplines:

* COMP 250 may be preceded by COMP 202.

COMP 250* (3) Introduction to Computer Science
COMP 252 (3) Algorithms and Data Structures

no more than 6 credits from the following courses for which no Honours equivalent exists:

MATH 204 (3) Principles of Statistics 2
MATH 329 (3) Theory of Interest
MATH 338 (3) History and Philosophy of Mathematics
MATH 339 (3) Foundations of Mathematics
MATH 348 (3) Topics in Geometry
MATH 407 (3) Dynamic Programming
MATH 437 (3) Mathematical Methods in Biology
MATH 447 (3) Stochastic Processes

Students may select other courses with the permission of the Department.

Faculty of Science—2010-2011 (last updated Apr. 22, 2010) (disclaimer)

Bachelor of Science (B.Sc.) - Honours Applied Mathematics (60 credits)

Applied mathematics is a very broad field and students are encouraged to choose a coherent program of complementary courses. Most students specialize in "continuous" or "discrete" applied mathematics, but there are many sensible combinations of courses, and the following informal guidelines should be discussed with the student's advisor. Also, aside from seeking to develop a sound basis in Applied Mathematics, one of the objectives of the program is to kindle the students' interest in possible areas of application. To develop an appreciation of the diversity of Applied Mathematics, students are advised to develop some depth (e.g. by completing a minor) in a field related to Applied Mathematics such as Atmospheric and Oceanic Sciences, Biology, Biochemistry, Chemistry, Computer Science, Earth and Planetary Sciences, Economics, Engineering, Management, Physics, Physiology and Psychology.

Required Courses (42 credits)

* COMP 250 may be preceded by COMP 202.

COMP 250* (3) Introduction to Computer Science
COMP 252 (3) Algorithms and Data Structures
MATH 235 (3) Algebra 1
MATH 242 (3) Analysis 1
MATH 248 (3) Honours Advanced Calculus
MATH 251 (3) Honours Algebra 2
MATH 255 (3) Honours Analysis 2
MATH 325 (3) Honours Ordinary Differential Equations
MATH 350 (3) Graph Theory and Combinatorics
MATH 356 (3) Honours Probability
MATH 357 (3) Honours Statistics
MATH 375 (3) Honours Partial Differential Equations
MATH 376 (3) Honours Nonlinear Dynamics
MATH 470 (3) Honours Research Project

Complementary Courses (18 credits)

Advising Notes:

Students interested in continuous applied mathematics are urged to choose these as part of their Complementary Courses: MATH 354 and MATH 355 and are advised to choose additional courses from MATH 387, MATH 397, MATH 555, MATH 560, MATH 574, MATH 578, MATH 579, MATH 580, MATH 581.

Students interested in discrete applied mathematics are advised to choose from these as part of their Complementary Courses: COMP 362, COMP 490, MATH 370, MATH 371, MATH 407, MATH 447, MATH 487, MATH 550, MATH 552, MATH 560.

3 credits selected from:

MATH 249 (3) Honours Complex Variables
MATH 366 (3) Honours Complex Analysis

at least 3 credits selected from:

MATH 387 (3) Honours Numerical Analysis
MATH 397 (3) Honours Matrix Numerical Analysis

and the remainder of credits selected from:

COMP 362 (3) Honours Algorithm Design
COMP 490 (3) Introduction to Probabilistic Analysis of Algorithms
MATH 352 (1) Problem Seminar
MATH 354 (3) Honours Analysis 3
MATH 355 (3) Honours Analysis 4
MATH 370 (3) Honours Algebra 3
MATH 371 (3) Honours Algebra 4
MATH 377 (3) Honours Number Theory
MATH 380 (3) Honours Differential Geometry
MATH 480 (3) Honours Independent Study
MATH 487 (3) Honours Mathematical Programming
MATH 488 (3) Honours Set Theory
MATH 490 (3) Honours Mathematics of Finance

All MATH 500-level courses.

No more than 6 credits from the following courses for which no Honours equivalent exists:

MATH 204 (3) Principles of Statistics 2
MATH 329 (3) Theory of Interest
MATH 338 (3) History and Philosophy of Mathematics
MATH 339 (3) Foundations of Mathematics
MATH 348 (3) Topics in Geometry
MATH 407 (3) Dynamic Programming
MATH 437 (3) Mathematical Methods in Biology
MATH 447 (3) Stochastic Processes

Other courses with the permission of the department.

Faculty of Science—2010-2011 (last updated Apr. 22, 2010) (disclaimer)

Bachelor of Science (B.Sc.) - Honours Probability and Statistics (64 credits)

Required Courses (49 credits)

* COMP 250 may be preceded by COMP 202.

** Students select either MATH 251 or MATH 247, but not both.

COMP 250* (3) Introduction to Computer Science
MATH 235 (3) Algebra 1
MATH 242 (3) Analysis 1
MATH 247** (3) Honours Applied Linear Algebra
MATH 248 (3) Honours Advanced Calculus
MATH 251** (3) Honours Algebra 2
MATH 255 (3) Honours Analysis 2
MATH 354 (3) Honours Analysis 3
MATH 355 (3) Honours Analysis 4
MATH 356 (3) Honours Probability
MATH 357 (3) Honours Statistics
MATH 470 (3) Honours Research Project
MATH 523 (4) Generalized Linear Models
MATH 533 (4) Honours Regression and Analysis of Variance
MATH 556 (4) Mathematical Statistics 1
MATH 557 (4) Mathematical Statistics 2

Complementary Courses (15 credits)

selected from:

MATH 325 (3) Honours Ordinary Differential Equations
MATH 350 (3) Graph Theory and Combinatorics
MATH 352 (1) Problem Seminar
MATH 366 (3) Honours Complex Analysis
MATH 375 (3) Honours Partial Differential Equations
MATH 380 (3) Honours Differential Geometry
MATH 387 (3) Honours Numerical Analysis
MATH 397 (3) Honours Matrix Numerical Analysis
MATH 480 (3) Honours Independent Study
MATH 490 (3) Honours Mathematics of Finance
MATH 524 (4) Nonparametric Statistics
MATH 525 (4) Sampling Theory and Applications
MATH 550 (4) Combinatorics
MATH 587 (4) Advanced Probability Theory 1
MATH 589 (4) Advanced Probability Theory 2

With at most 3 credits from the following courses for which no Honours equivalent exists:

MATH 204 (3) Principles of Statistics 2
MATH 407 (3) Dynamic Programming
MATH 447 (3) Stochastic Processes
Faculty of Science—2010-2011 (last updated Apr. 22, 2010) (disclaimer)

Bachelor of Science (B.Sc.) - Honours Mathematics and Computer Science (75 credits)

Students may complete this program with a minimum of 72 credits or a maximum of 75 credits depending on whether or not they are exempt from taking COMP 202.

Program Prerequisites

Students must consult an Honours adviser in both departments. Students entering the Joint Honours in Mathematics and Computer Science are normally expected to have completed the courses below or their equivalents. Otherwise, they will be required to make up any deficiencies in these courses over and above the 72 - 75 credits of courses in the program.

MATH 133 (3) Linear Algebra and Geometry
MATH 140 (3) Calculus 1
MATH 141 (4) Calculus 2

Required Courses (45 credits)

* Students who have sufficient knowledge in a programming language are not required to take COMP 202.

COMP 202* (3) Introduction to Computing 1
COMP 206 (3) Introduction to Software Systems
COMP 250 (3) Introduction to Computer Science
COMP 252 (3) Algorithms and Data Structures
COMP 273 (3) Introduction to Computer Systems
COMP 302 (3) Programming Languages and Paradigms
COMP 310 (3) Operating Systems
COMP 330 (3) Theoretical Aspects: Computer Science
COMP 362 (3) Honours Algorithm Design
MATH 235 (3) Algebra 1
MATH 242 (3) Analysis 1
MATH 248 (3) Honours Advanced Calculus
MATH 251 (3) Honours Algebra 2
MATH 255 (3) Honours Analysis 2
MATH 350 (3) Graph Theory and Combinatorics

Complementary Courses (30 credits)

18 credits in Mathematics, at least 12 credits selected from:

* Students with appropriate background in probability may substitute MATH 587 for MATH 356 and must then also register for MATH 355.

MATH 354 (3) Honours Analysis 3
MATH 355 (3) Honours Analysis 4
MATH 356* (3) Honours Probability
MATH 370 (3) Honours Algebra 3
MATH 371 (3) Honours Algebra 4
MATH 387 (3) Honours Numerical Analysis

The remaining credits should be selected from honours courses given by the Department of Mathematics and Statistics.

12 credits in Computer Science, selected from Computer Science courses at the 300-level or above excluding COMP 364, COMP 396 and COMP 431. ECSE 508 may also be taken.

Faculty of Science—2010-2011 (last updated Apr. 22, 2010) (disclaimer)

Bachelor of Science (B.Sc.) - Honours Statistics and Computer Science (79 credits)

This is a challenging program providing students with a solid training in both computer science and statistics suitable for entry into graduate school in either discipline.

Students may complete this program with a minimum of 76 credits or a maximum of 79 credits depending on whether or not they are exempt from taking COMP 202.

Program Prerequisites

Students entering the Joint Honours in Statistics and Computer Science are normally expected to have completed the courses below or their equivalents. Otherwise, they will be required to make up any deficiencies in these courses over and above the 76 - 79 credits of courses in the program.

MATH 133 (3) Linear Algebra and Geometry
MATH 140 (3) Calculus 1
MATH 141 (4) Calculus 2

Required Courses (49 credits)

* Students who have sufficient knowledge in a programming language are not required to take COMP 202.

** Students take either MATH 251 or MATH 247, but not both.

COMP 202* (3) Introduction to Computing 1
COMP 206 (3) Introduction to Software Systems
COMP 250 (3) Introduction to Computer Science
COMP 252 (3) Algorithms and Data Structures
COMP 273 (3) Introduction to Computer Systems
COMP 302 (3) Programming Languages and Paradigms
COMP 330 (3) Theoretical Aspects: Computer Science
COMP 362 (3) Honours Algorithm Design
MATH 235 (3) Algebra 1
MATH 242 (3) Analysis 1
MATH 247** (3) Honours Applied Linear Algebra
MATH 248 (3) Honours Advanced Calculus
MATH 251** (3) Honours Algebra 2
MATH 255 (3) Honours Analysis 2
MATH 356 (3) Honours Probability
MATH 357 (3) Honours Statistics
MATH 533 (4) Honours Regression and Analysis of Variance

Complementary Courses (30 credits)

15 credits in Mathematics selected as follows:

3 credits selected from:

MATH 387 (3) Honours Numerical Analysis
MATH 397 (3) Honours Matrix Numerical Analysis

At least 8 credits selected from:

MATH 523 (4) Generalized Linear Models
MATH 524 (4) Nonparametric Statistics
MATH 525 (4) Sampling Theory and Applications
MATH 556 (4) Mathematical Statistics 1
MATH 557 (4) Mathematical Statistics 2

The remaining Mathematics credits selected from:

** MATH 578 and COMP 540 cannot both be taken for program credit.

MATH 350 (3) Graph Theory and Combinatorics
MATH 352 (1) Problem Seminar
MATH 354 (3) Honours Analysis 3
MATH 355 (3) Honours Analysis 4
MATH 578** (4) Numerical Analysis 1

15 credits in Computer Science selected as follows:

At least 6 credits selected from:

COMP 423 (3) Data Compression
COMP 424 (3) Artificial Intelligence
COMP 462 (3) Computational Biology Methods
COMP 490 (3) Introduction to Probabilistic Analysis of Algorithms
COMP 526 (3) Probabilistic Reasoning and AI
COMP 540** (3) Matrix Computations
COMP 547 (4) Cryptography and Data Security
COMP 552 (4) Combinatorial Optimization
COMP 564 (3) Computational Gene Regulation
COMP 566 (3) Discrete Optimization 1
COMP 567 (3) Discrete Optimization 2

The remaining Computer Science credits are selected from COMP courses at the 300-level or above excluding COMP 396 and COMP 431.

Faculty of Science—2010-2011 (last updated Apr. 22, 2010) (disclaimer)

Mathematics and Statistics (MATH) Related Programs

Mathematics and Statistics (MATH) Related Programs

Joint Major in Biology and Mathematics

Joint Major in Biology and Mathematics

For more information, see Biology (BIOL) > Bachelor of Science (B.Sc.) - Major Biology and Mathematics (76 credits).

Joint Major in Physiology and Mathematics

Joint Major in Physiology and Mathematics

For more information, see Physiology (PHGY) > Bachelor of Science (B.Sc.) - Major Physiology and Mathematics (77 credits).

Joint Honours Program in Mathematics and Physics

Joint Honours Program in Mathematics and Physics

For more information, see Physics (PHYS) > Bachelor of Science (B.Sc.) - Honours Mathematics and Physics (81 credits).

Faculty of Science—2010-2011 (last updated Apr. 22, 2010) (disclaimer)
Faculty of Science—2010-2011 (last updated Apr. 22, 2010) (disclaimer)