Mathematics

Faculty List

Associate Chair:  M. Evans (416-287-7274)

Our Mathematics began in the ancient Mesopotamian civilizations. The Babylonians already knew much of the mathematics taught traditionally in our schools. Their algebra and geometry was phrased in terms of crops and fields and money. Since the Renaissance, much of mathematics has come from problems in physics and astronomy; for example, calculus arose from problems in mechanics. In turn mathematics has provided the theoretical framework and tools in the Physical Sciences. In the 19th century some parts of mathematics appeared to develop away from their origins in the physical world. To the great surprise of many scientists and mathematicians, some of the "pure" mathematics has turned out to be essential in many aspects of 20th century science. Differential geometry provides the language for general relativity and cosmology, and Hilbert space theory and group representations are the tools for quantum mechanics. Similarly, graph theory, combinatorics and number theory play a major role in computer science. 

The Specialist and Major Programs in Mathematics are eligible for inclusion in the Concurrent Teacher Education Program (CTEP). Please refer to the Concurrent Teacher Education section of this Calendar for further information.

Service Learning and Outreach (Previously Known as Science Engagement)
For experiential learning through community outreach and classroom in-reach, please see the Teaching and Learning section of this Calendar.

Mathematics Programs

SPECIALIST PROGRAM IN MATHEMATICS (SCIENCE)

Supervisor of Studies: E. Moore (416-287-7267) Email: emoore@utsc.utoronto.ca

Program Objectives

This program provides the student with a sound foundation in the main areas of mathematics, and some exposure to computer programming and statistics. It comprises four streams: Comprehensive, Statistics, Teaching, and Design-Your-Own, each serving a more specific goal.

The Comprehensive Stream provides a broad and deep knowledge of mathematics at the undergraduate level. It is the recommended program for students who plan to pursue graduate study in mathematics, but it is also suitable for other career paths.

The Statistics Stream provides greater exposure to statistics, and the areas of mathematics most closely associated with it. This stream prepares students for careers in industry, or for graduate study in certain mathematically-oriented subjects, including statistics and financial mathematics.

The Teaching Stream is intended for students with a serious interest in mathematics but whose career objectives lie in mathematics education at the elementary or secondary level.

The Design-Your-Own Stream allows students to tailor their studies in mathematics to specific interests, with guidance from (and approval of) the program supervisor.

Program Requirements

The Program requirements consist of a core 15 courses (7.5 credits), common to all four streams, and additional requirements that depend on the stream, for a total of 26-28 courses (13.0-14.0 credits).

The structure of the programs allows for easy switching between streams until relatively late. Consequently, these programs should not be viewed as rigidly separated channel's feeding students to different career paths, but as a flexible structure that provides guidance to students in their course selection based on their broad (but possible fluid) interests.

Core (7.5 credits)

1. Writing Requirement (0.5 credit)(*)
One of:ANTA01H3, ANTA02H3, (CLAA02H3), (CTLA19H3), CTLA01H3,  ENGA10H3, ENGA11H3, ENGB06H3, ENGB07H3, ENGB08H3, ENGB09H3, ENGB17H3, ENGB19H3, ENGB50H3, ENGB51H3, GGRA02H3, GGRA03H3, GGRB05H3, (GGRB06H3), (HISA01H3), (HLTA01H3), ACMA01H3, (HUMA01H3), (HUMA11H3), (HUMA17H3), (LGGA99H3), LINA01H3, PHLA10H3, WSTA01H3.
(*) It is recommended that this requirement be satisfied by the end of the second year.

2. A-level courses (2.5 credits)
CSCA67H3  Discrete Mathematics for Computer Scientists
MATA23H3  Linear Algebra I
MATA31H3  Calculus I for Mathematical Sciences
MATA37H3  Calculus II for Mathematical Sciences
CSCA08H3  Introduction to Computer Programming

3. B-level courses (3.5 credits)
MATB24H3  Linear Algebra II
MATB41H3  Techniques of the Calculus of Several Variables I
MATB42H3  Techniques of the Calculus of Several Variables II
MATB43H3  Introductions to Analysis
MATB44H3  Differential Equations I
STAB52H3  Introduction to Probablity (**)
STAB57H3  Introduction to Statistics (**)
(**) This course may be taken after second year, except for the Statistics stream.

4. C-level courses (1 credit)
MATC01H3  Groups and Symmetry
MATC34H3  Complex Variables

A. Comprehensive Stream
This stream requires a total of 28 courses (14.0 credits)
In addition to the core requirements 1-4 common to all streams, 13 other distinct courses must be chosen satisfying all of the following requirements:

5. Elementary courses in closely related disciplines (1.5 credits): (***)
CSCA48H3  Introduction to Computer Science
PHYA10H3  Introduction to Physics IA
PHYA21H3  Introduction to Physics IIA
(***) It is recommended that these be taken in first year.

6. Additional courses in analysis and algebra (1.5 credits):
MATC37H3  Introduction to Real Analysis
MATC46H3  Differential Equations II
MATD01H3  Fields and Groups

7. Courses in key areas of mathematics (1.5 credits):
Three of:
      MATC15H3  Introduction to Number Theory
      MATC27H3  Introduction to Topology
      MATD02H3  Classical Plane Geometries and their Transformations
      MATD34H3  Complex Variables II

8. Mathematics of computation (0.5 credit):
One of:
      MATC09H3  Introduction to Mathematical Logic
      MATC32H3  Graph Theory and Algorithms for its Applications
      MATC44H3  Introduction to Combinatorics
      CSCC37H3  Introduction to Numerical Algorithms for Computational Mathematics
      CSCC63H3  Computability and Computational Complexity

9. Electives (1.5 credits):
Three of:
    C- or D-level MAT courses, excluding MATC82H3 and MATC90H3

B. Statistics Stream
This stream requires a total of 26 courses (13.0 credits).
In addition to the core requirements 1-4 common to all streams, 11 other distinct courses must be chosen, satisfying all of the following requirements (in choosing courses to satisfy requirements 7-9, students must select at least one D-level course).

5. Algebra and Analysis (1.5 credits):
MATB61H3  Linear Programming and Optimization
MATC46H3  Differential Equations II
MATD01H3  Fields and Groups

6. Regression Analysis (0.5 credit):
STAC67H3  Regression Analysis

7. Discrete mathematics and geometry (0.5 credit):
One of:
      MATC32H3 Graph Theory and Algorithms for its Applications
      MATC44H3 Introduction to Cominatorics
      MATD02H3 Classical Plane Geometries and their Transformations

8. Upper-level MAT electives (1 credit):
Two of:
      Any C- or D-level MAT courses (*)
(*) For students wishing to pursue graduate studies in Mathematics or Statistics it is recommended that MATC37H3 be chosen as one of these two courses.

9. Upper-level STA electives (2 credits):
Four of:
       (ACTB47H3)  Introductory Life Contingencies
       Any C- or D-level STA course, excluding STAD29H3

C. Teaching Stream
This stream requires a total of 26 courses (13.0 credits).
In addition to the core requirements 1-4 common to all streams, 11 other distinct courses must be chosen, satisfying all of the following requirements:

5. Algebra, analysis, and geometry (2 credits):
MATC15H3  Introduction to Number Theory
MATC82H3  Mathematics for Teachers
MATD01H3  Fields and Groups
MATD02H3  Classical Plane Geometries and their Transformations

6. Discrete mathematics (0.5 credit):
One of:
       MATC32H3  Graph Theory and Algorithms for its Applications
       MATC44H3  Introduction to Combinatorics

7. MAT electives (1.5 credits):
Three of:
        C- or D-level MAT courses

8. MAT/STA/CSC electives (1.5 credits):
Three of:
         C- or D-level MAT, STA, CSC courses, excluding STAD29H3

D. Design-Your-Own-Stream
This stream requires a total of 26 courses (13.0 credits).
In addition to the core requirements 1-4 common to all streams, 11 other distinct courses must be chosen, satisfying the following requirement:

5. Electives (5.5 credits):
11 courses approved by the program supervisor. The core courses together with the approved electives must satisfy the degree requirement so that they include at least 12 courses (6 credits) at the C- or D-level, of which at least two (one credit) are at the D-level.

SPECIALIST (CO-OPERATIVE) PROGRAM IN MATHEMATICS (SCIENCE)

Supervisor of Studies: E. Moore (416-287-7267) Email: emoore@utsc.utoronto.ca
Co-op Contact: askcoop@utsc.utoronto.ca

Program Objectives
This program combines the coursework of the Specialist Program in Mathematics described above with paid work terms in public and private enterprises. It shares the goals and structure of the Specialist Program in Mathematics, including its four streams (Comprehensive, Statistics, Teaching, and Design-Your-Own), but complements study of the subject with considerable work experience.

Admission Requirements
Refer to the Program Admission requirements for the Specialist Program in Mathematics described above and the Co-operative Programs section in this Calendar. Students entering this program must have a CGPA of at least 2.5.

Program Requirements
To remain in the program, a student must maintain a CGPA of 2.5 or higher throughout the program. To complete the program, a student must meet the work term and course requirements described below.

Work Term Requirements
Students must successfully complete three work terms, at most one of which can be during the summer. In addition, prior to their first work term, students must successfully complete the Arts & Science Co-op Work Term Preparation Activities. These include networking sessions, speaker panels and industry tours along with seminars covering resumes, cover letters, job interviews and work term expectations.

Course Requirements
The Co-operative Program can be taken in conjunction with any of the streams in the Specialist Program in Mathematics. The course requirements of the Co-operative Specialist Program in Mathematics are identical to those of the Specialist Program in Mathematics described above.

MAJOR PROGRAM IN MATHEMATICS (SCIENCE)

Supervisor of Studies: S.Chrysostomou (416-287-7264) Email: chrysostomou@utsc.utoronto.ca

Program Objectives
This program provides a solid foundation in basic areas of mathematics, especially those with applications in other disciplines. This program is intended to be combined with other programs, typically a major program in another discipline.

Program Requirements
This stream requires a total of 17 distinct courses or (8.5 credits), chosen so as to satisfy all of the following requirements:

1. Foundational courses (5.5 credits)
CSCA67H3  Discrete Mathematics for Computer Scientists
MATA23H3 Linear Algebra I
One of:
   MATA30H3 Calculus I for Biological and Physical Sciences
   MATA31H3 Calculus I for Mathematical Sciences
One of:
   MATA36H3 Calculus II for Physical Sciences
   MATA37H3 Calculus II for Mathematical Sciences (*)
   CSCA08H3 Introduction to Computer Programming
   MATB24H3 Linear Algebra II
   MATB41H3 Techniques of the Calculus of Several Variables I
   MATB42H3 Techniques of the Calculus of Several Variables II
   MATB44H3 Differential Equations I
   STAB52H3 Introduction to Probability
One of:
   MATC01H3 Groups and Symmetry
   MATC15H3 Introduction to Number Theory

(*) MATA31H3 is required for MATA37H3

2. Further analysis courses (1 credit)
Two of:
   MATB43H3 Introduction to Analysis
   MATC27H3 Introduction to Topology
   MATC34H3 Complex Variables
   MATC35H3 Chaos, Fractals, and Dynamics
   MATC37H3 Introduction to Real Analysis
   MATC46H3 Differential Equations II
   MATD34H3 Complex Variables II

3. Further algebra geometry, and discrete mathematics courses (1 credit)
Two of:
   MATC01H3 Groups and Symmetry
   MATC09H3 Introduction to Mathematical Logic
   MATC15H3 Introduction to Number Theory
   MATC32H3 Graph Theory and Algorithms for its Applications
   MATC44H3 Introduction to Combinatorics
   MATC63H3 Differential Geometry
   MATD01H3 Fields and Groups
   MATD02H3 Classical Plane Geometries and their Transformations

4. Electives (1 credit)
Two of:
   MATB61H3 Linear Programming and Optimization
   STAB57H3 Introduction to Statistics
   any C- or D-level MAT, STA, or CSC course, excluding STAD29H3

Recommended Writing Course: Students are urged to take a course from the following list of courses by the end of their second year.
ANTA01H3, ANTA02H3, (CLAA02H3), (CTLA19H3), CTLA01H3, ENGA10H3, ENGA11H3, ENGB06H3, ENGB07H3, ENGB08H3, ENGB09H3, ENGB17H3, ENGB19H3, ENGB50H3, ENGB51H3, GGRA02H3, GGRA03H3, GGRB05H3, (GGRB06H3), (HISA01H3), (HLTA01H3), ACMA01H3, (HUMA01H3),  (HUMA11H3), (HUMA17H3), (LGGA99H3), LINA01H3, PHLA10H3, PHLA11H3, WSTA01H3.

MAJOR (CO-OPERATIVE) PROGRAM IN MATHEMATICS (SCIENCE)

Supervisor of Studies: S.Chrysostomou (416-287-7264) Email: chrysostomou@utsc.utoronto.ca
Co-op Contact: askcoop@utsc.utoronto.ca

Program Objectives
This program combines the coursework of the Major Program in Mathematics described above with paid work terms in public and private enterprises. It shares the goals and structure of the Major Program in Mathematics, but complements study of the subject with considerable work experience.

Admission Requirements
Refer to the Program Admission requirements for the Major Program in Mathematics described above and the Co-operative Programs section in this Calendar. Students entering this program must have a CGPA of at least 2.5.

Program Requirements
To remain in the program, a student must maintain a CGPA of 2.5 or higher throughout the program. To complete the program, a student must meet the work term and course requirements described below.

Work Term Requirements
Students must successfully complete three work terms, at most one of which can be during the summer. In addition, prior to their first work term, students must successfully complete the Arts & Science Co-op Work Term Preparation Activities. These include networking sessions, speaker panels and industry tours along with seminars covering resumes, cover letters, job interviews and work term expectations.

Course Requirements
The course requirements of the Co-operative Major Program in Mathematics are identical to those of the Major Program in Mathematics described above.

Mathematics Courses

MATA02H3    The Magic of Numbers

A selection from the following topics: the number sense (neuroscience of numbers);  numerical notation in different cultures; what is a number; Zeno’s paradox; divisibility, the fascination of prime numbers; prime numbers and encryption; perspective in art and geometry; Kepler and platonic solids; golden mean, Fibonacci sequence; elementary probability.
Exclusion: (MATA20H3), MATA23H3, MATA30H3, MATA31H3, MATA32H3, MAT102H, MAT123H, MAT125H, MAT133Y, MAT134Y, MAT135Y, MAT137Y, MAT157Y
Breadth Requirement: Quantitative Reasoning

MATA23H3    Linear Algebra I

Systems of linear equations, matrices, Gaussian elimination; basis, dimension; dot products; geometry to Rⁿ; linear transformations; determinants, Cramer's rule; eigenvalues and eigenvectors, diagonalization.
Prerequisite: Grade 12 Calculus and Vectors or [Grade 12 Advanced Functions and Introductory Calculus & Geometry and Discrete Mathematics]
Exclusion: MAT223H
Breadth Requirement: Quantitative Reasoning

MATA30H3    Calculus I for Biological and Physical Sciences

An introduction to the basic techniques of Calculus. Elementary functions: rational, trigonometric, root, exponential and logarithmic functions and their graphs. Basic calculus: limits, continuity, derivatives, derivatives of higher order, analysis of graphs, use of derivatives; integrals and their applications, techniques of integration.
Prerequisite: Grade 12 Calculus and Vectors
Exclusion: (MATA20H3), (MATA27H3), MATA31H3, MATA32H3, MAT123H, MAT124H, MAT125H, MAT126H, MAT133Y, MAT135Y, MAT137Y, MAT157Y, JMB170Y
Breadth Requirement: Quantitative Reasoning

MATA31H3    Calculus I for Mathematical Sciences

Basic techniques of Calculus. Elementary functions including exponential, logarithm and trigonometric functions; limits and continuity; differentiation; indeterminate forms and L'Hopital's rule; optimization and other applications of derivatives; Riemann sums and integration; techniques of integration; improper integrals, applications of integration including areas, volumes, and arc length.
Prerequisite: Grade 12 Calculus and Vectors
Exclusion: (MATA20H3), (MATA27H3), MATA30H3, MATA32H3, MAT123H, MAT124H, MAT125H, MAT126H, MAT133Y, MAT135Y, MAT137Y, MAT157Y, JMB170Y
Breadth Requirement: Quantitative Reasoning

MATA32H3    Calculus for Management I

This is a calculus course with most examples and applications of an economic nature. Topics to be covered: introduction to financial mathematics; continuous functions including exponential and logarithmic functions with applications to finance; differential calculus of one variable; marginal analysis; optimization of single variable functions; techniques of integration.
Prerequisite: Grade 12 Calculus and Vectors
Exclusion: (MATA20H3), (MATA27H3), MATA30H3, MATA31H3, MAT123H, MAT125H, MAT133Y, MAT135Y, MAT136Y, MAT137Y, MAT157Y, JMB170Y
Breadth Requirement: Quantitative Reasoning

MATA33H3    Calculus for Management II

This course will introduce the students to multivariable calculus and linear algebra. Topics will include: linear programming (geometric); matrix algebra; multi-variable functions; contour maps; partial and total differentiation; optimization of multi-variable functions; optimization of constrained multi-variable functions; Lagrange multipliers.
Prerequisite: MATA32H3
Exclusion: (MATA21H3), (MATA27H3), MATA35H3, MATA36H3, MATA37H3, MAT124H, MAT126H, MAT133Y, MAT134Y, MAT135Y, MAT136Y, MAT137Y, MAT157Y, JMB170Y
Breadth Requirement: Quantitative Reasoning

MATA35H3    Calculus II for Biological Sciences

A calculus course emphasizing examples and applications in the biological and environmental sciences. Discrete probability; basic statistics: hypothesis testing, distribution analysis. Basic calculus: extrema, growth rates, diffusion rates; differential equations; population dynamics; vectors and matrices in 2 and 3 dimensions; genetics applications.
Note: This course will not satisfy the Mathematics requirements for any Program in Computer and Mathematical Sciences, nor will it normally serve as a prerequisite for further courses in Mathematics. Students who are not sure which Calculus II course they should choose are encouraged to consult with the supervisor(s) of Programs in their area(s) of interest.
Prerequisite: MATA30H3 or MATA31H3
Exclusion: (MATA21H3), MATA33H3, MATA36H3, MATA37H3, MAT123H, MAT124H, MAT125H, MAT126H, MAT133Y, MAT135Y, MAT137Y, MAT157Y, JMB170Y,(MATA27H3)
Breadth Requirement: Quantitative Reasoning

MATA36H3    Calculus II for Physical Sciences

This course is intended to prepare students for the physical sciences. Topics to be covered include: Newton's method, approximation of functions by Taylor polynomials, numerical methods of integration, complex numbers, sequences, series, Taylor series, differential equations.
Prerequisite: MATA30H3 or MATA31H3
Exclusion: (MATA21H3), MATA33H3, MATA35H3, MATA37H3, MAT123H, MAT124H, MAT125H, MAT126H, MAT133Y, MAT135Y, MAT137Y, MAT157Y, JMB170Y
Breadth Requirement: Quantitative Reasoning

MATA37H3    Calculus II for Mathematical Sciences

A theoretical course in calculus emphasizing proofs and techniques, as well as the intuition behind them.  Axioms and basic properties of real numbers; theorems concerning differentiation and integration; fundamental theorem of calculus; numerical integration; sequences and series; Taylor polynomials and remainder; uniform convergence and power series.
Prerequisite: MATA31H3, CSCA67H3
Exclusion: (MATA21H3), MATA33H3, MATA35H3, MATA36H3, MAT123H, MAT124H, MAT125H, MAT126H, MAT133Y, MAT135Y, MAT137Y, MAT157Y, JMB170Y
Breadth Requirement: Quantitative Reasoning

MATB24H3    Linear Algebra II

Fields, vector spaces over a field, linear transformations; inner product spaces, coordinatization and change of basis; diagonalizability, orthogonal transformations, invariant subspaces, Cayley-Hamilton theorem; hermitian inner product, normal, self-adjoint and unitary operations.  Some applications such as the method of least squares and introduction to coding theory.
Prerequisite: MATA23H3 or MAT223H
Exclusion: MAT224H
Breadth Requirement: Quantitative Reasoning

MATB41H3    Techniques of the Calculus of Several Variables I

Partial derivatives, gradient, tangent plane, Jacobian matrix and chain rule, Taylor series; extremal problems, extremal problems with constraints and Lagrange multipliers, multiple integrals, spherical and cylindrical coordinates, law of transformation of variables.
Prerequisite: [MATA23H3 or MAT223H] & [[MATA36H3 or MATA37H3] or MAT137Y or MAT157Y]]
Exclusion: MAT232H, MAT235Y, MAT237Y, MAT257Y
Breadth Requirement: Quantitative Reasoning

MATB42H3    Techniques of the Calculus of Several Variables II

Fourier series. Vector fields in Rⁿ, Divergence and curl, curves, parametric representation of curves, path and line integrals, surfaces, parametric representations of surfaces, surface integrals. Green's, Gauss', and Stokes' theorems will also be covered. An introduction to differential forms, total derivative.
Prerequisite: MATB41H3
Exclusion: MAT235Y, MAT237Y, MAT257Y, MAT368H
Breadth Requirement: Quantitative Reasoning

MATB43H3    Introduction to Analysis

Generalities of sets and functions, countability.  Topology and analysis on the real line:  sequences, compactness, completeness, continuity, uniform continuity.  Topics from topology and analysis in metric and Euclidean spaces.  Sequences and series of functions, uniform convergence.
Prerequisite: [MATA37H3 or MAT137Y] & MATB24H3
Corequisite: MATB42H3
Exclusion: MAT246Y
Breadth Requirement: Quantitative Reasoning

MATB44H3    Differential Equations I

Ordinary differential equations of the first and second order, existence and uniqueness; solutions by series and integrals; linear systems of first order; non-linear equations; difference equations.
Prerequisite: [MATA36H3 or MATA37H3] & MATA23H3
Corequisite: MATB41H3
Exclusion: MAT244H, MAT267H
Breadth Requirement: Quantitative Reasoning

MATB61H3    Linear Programming and Optimization

Linear programming, simplex algorithm, duality theory, interior point method; quadratic and convex optimization, stochastic programming; applications to portfolio optimization and operations research.
Prerequisite: MATA23H3
Corequisite: MATB42H3
Exclusion: APM236H
Breadth Requirement: Quantitative Reasoning

MATC01H3    Groups and Symmetry

Congruences and fields. Permutations and permutation groups. Linear groups. Abstract groups, homomorphisms, subgroups. Symmetry groups of regular polygons and Platonic solids, wallpaper groups. Group actions, class formula. Cosets, Lagrange's theorem. Normal subgroups, quotient groups. Emphasis on examples and calculations.
Prerequisite: [MATA36H3 or MATA37H3] and [MATB24H3 or MAT224H]
Exclusion: MAT301H, MAT347Y
Breadth Requirement: Quantitative Reasoning

MATC09H3    Introduction to Mathematical Logic

Predicate calculus. Relationship between truth and provability; Gödel's completeness theorem. First order arithmetic as an example of a first-order system. Gödel's incompleteness theorem; outline of its proof. Introduction to recursive functions.
Prerequisite: MATB24H3 & [MATB43H3 or CSCB36H3]
Exclusion: MAT309H, CSC438H
Breadth Requirement: Quantitative Reasoning

MATC15H3    Introduction to Number Theory

Elementary topics in number theory; arithmetic functions; polynomials over the residue classes modulo m, characters on the residue classes modulo m; quadratic reciprocity law, representation of numbers as sums of squares.
Prerequisite: [MATA36H3 or MATA37H3] & MATB24H3
Exclusion: MAT315H
Breadth Requirement: Quantitative Reasoning

MATC16H3    Coding Theory and Cryptography

The main problems of coding theory and cryptography are defined. Classic linear and non-linear codes. Error correcting and decoding properties. Cryptanalysis of classical ciphers from substitution to DES and various public key systems [e.g. RSA] and discrete logarithm based systems. Needed mathematical results from number theory, finite fields, and complexity theory are stated.
Prerequisite: MATB24H3 & STAB52H3
Corequisite: MATC15H3 recommended
Breadth Requirement: Quantitative Reasoning

MATC27H3    Introduction to Topology

Fundamentals of set theory, topological spaces and continuous functions, connectedness, compactness, countability, separatability, metric spaces and normed spaces, function spaces, completeness, homotopy.
Prerequisite: MATB24H3 & MATB43H3
Exclusion: MAT327H
Breadth Requirement: Quantitative Reasoning

MATC32H3    Graph Theory and Algorithms for its Applications

Graphs, subgraphs, isomorphism, trees, connectivity, Euler and Hamiltonian properties, matchings, vertex and edge colourings, planarity, network flows and strongly regular graphs; applications to such problems as timetabling, personnel assignment, tank form scheduling, traveling salesmen, tournament scheduling, experimental design and finite geometries.
Prerequisite: [MATB24H3 or CSCB36H3] & at least one other B-level course in Mathematics or Computer Science
Breadth Requirement: Quantitative Reasoning

MATC34H3    Complex Variables

Theory of functions of one complex variable, analytic and meromorphic functions. Cauchy's theorem, residue calculus, conformal mappings, introduction to analytic continuation and harmonic functions.
Prerequisite: MATB42H3
Exclusion: MAT334H
Breadth Requirement: Quantitative Reasoning

MATC35H3    Chaos, Fractals and Dynamics

Topics covered include: metric spaces, dynamics on the real line, fixed points, periodic points, attractors, repellers, Sharkovski's theorem parametrized families of functions and bifurcations, period doubling, dynamics of the logistic map, symbolic dynamics, chaos, topological equivalence of the logistic map and the shift map, Newton's method; dynamics on the complex line, iterations of rational functions, Julia sets, Mandelbrot set.
Prerequisite: MATB43H3
Exclusion: MAT335H
Breadth Requirement: Quantitative Reasoning

MATC37H3    Introduction to Real Analysis

Topics in measure theory:  the Lebesgue integral, Riemann-Stieltjes integral, Lp spaces, Hilbert and Banach spaces, Fourier series.
Prerequisite: MATB43H3
Exclusion: MAT337H, (MATC38H3)
Recommended Preparation: MATC27H3
Breadth Requirement: Quantitative Reasoning

MATC44H3    Introduction to Combinatorics

Basic counting principles, generating functions, permutations with restrictions. Fundamentals of graph theory with algorithms; applications (including network flows). Combinatorial structures including block designs and finite geometries.
Prerequisite: MATB24H3
Exclusion: MAT344H
Breadth Requirement: Quantitative Reasoning

MATC46H3    Differential Equations II

Sturm-Liouville problems, Green's functions, special functions (Bessel, Legendre), partial differential equations of second order, separation of variables, integral equations, Fourier transform, stationary phase method.
Prerequisite: MATB44H3
Corequisite: MATB42H3
Exclusion: APM346H
Breadth Requirement: Quantitative Reasoning

MATC58H3    An Introduction to Mathematical Biology

Mathematical analysis of problems associated with biology, including models of population growth, cell biology, molecular evolution, infectious diseases, and other biological and medical disciplines. A review of mathematical topics: linear algebra (matrices, eigenvalues and eigenvectors), properties of ordinary differential equations and difference equations.
Prerequisite: MATB44H3
Breadth Requirement: Quantitative Reasoning

MATC63H3    Differential Geometry

Curves and surfaces in Euclidean 3-space. Serret-Frenet frames and the associated equations, the first and second fundamental forms and their integrability conditions, intrinsic geometry and parallelism, the Gauss-Bonnet theorem.
Prerequisite: MATB43H3
Exclusion: MAT363H
Breadth Requirement: Quantitative Reasoning

MATC82H3    Mathematics for Teachers

The course discusses the Mathematics curriculum (K-12) from the following aspects: the strands of the curriculum and their place in the world of Mathematics, the nature of proofs, the applications of Mathematics, and its connection to other subjects.
Prerequisite: [CSCA67H3 or (CSCA65H3)] and MATA23H3 and [MATA37H3 or MATA36H3]
Exclusion: MAT382H
Breadth Requirement: Quantitative Reasoning

MATC90H3    Beginnings of Mathematics

Mathematical problems which have arisen repeatedly in different cultures, e.g. solution of quadratic equations, Pythagorean theorem; transmission of mathematics between civilizations; high points of ancient mathematics, e.g. study of incommensurability in Greece, Pell's equation in India.
Prerequisite: One Grade 12 Mathematics course & 5.0 full university courses
Exclusion: MAT390H
Breadth Requirement: Quantitative Reasoning

MATD01H3    Fields and Groups

Abstract group theory: Sylow theorems, groups of small order, simple groups, classification of finite abelian groups. Fields and Galois theory: polynomials over a field, field extensions, constructibility; Galois groups of polynomials, in particular cubics; insolvability of quintics by radicals.
Prerequisite: MATC01H3
Exclusion: (MAT302H), MAT347Y, (MATC02H3)
Recommended Preparation: MATC34H3
Breadth Requirement: Quantitative Reasoning

MATD02H3    Classical Plane Geometries and their Transformations

An introduction to geometry with a selection of topics from the following: symmetry and symmetry groups, finite geometries and applications, non-Euclidean geometry.
Prerequisite: MATA23H3
Corequisite: MATC01H3
Exclusion: MAT402H, (MAT365H), (MATC25H3)
Breadth Requirement: Quantitative Reasoning

MATD10H3    Topics in Mathematics

A variety of topics from geometry, analysis, combinatorics, number theory and algebra, to be chosen by the instructor.
Prerequisite: MATC01H3 and [MATC35H3 or MATC37H3] and [MATC15H3 or MATD02H3]

MATD11H3    Topics in Mathematics

A variety of topics from geometry, analysis, combinatorics, number theory and algebra, to be chosen by the instructor.
Prerequisite: MATC01H3 and [MATC35H3 or MATC37H3] and [MATC15H3 or MATD02H3]

MATD12H3    Topics in Mathematics

A variety of topics from geometry, analysis, combinatorics, number theory and algebra, to be chosen by the instructor.
Prerequisite: MATC01H3 and [MATC35H3 or MATC37H3] and [MATC15H3 or MATD02H3]

MATD34H3    Complex Variables II

Applications of complex analysis to geometry, physics and number theory. Fractional linear transformations and the Lorentz group. Solution to the Dirichlet problem by conformal mapping and the Poisson kernel. The Riemann mapping theorem. The prime number theorem.
Prerequisite: MATC34H3
Exclusion: MAT354H, (MATC65H3)
Breadth Requirement: Quantitative Reasoning

MATD61H3    Introduction to Industrial Mathematics

Monte Carlo Method (mean time between failures, servicing requests), Data Manipulation (z-transform, filters, Bode Plots), Discrete Fourier Transform (real time processing , FFT, image processing), Regression (best fit to discrete data, Hilbert Space, Gram's theorem), Frequency-Domain Methods, Numerical Models for PDE, Galerkin's methods, Cubic Splines.
The course provides extensions of mathematics useful in industrial problems, interweaving analytic and computing methods during problem solving.
Prerequisite: MATB42H3 & MATB44H3 & STAB52H3
Recommended Preparation: MATB61H3 & MATC46H3
Breadth Requirement: Quantitative Reasoning

MATD92H3    Mathematics Project

A significant project in any area of mathematics. The project may be undertaken individually or in small groups. This course is offered by arrangement with a mathematics faculty member. This course may be taken in any session and the project must be completed by the last day of classes in the session in which it is taken.
Prerequisite: Students must obtain consent from the Supervisor of Studies before registering for this course.
Breadth Requirement: Quantitative Reasoning

MATD93H3    Mathematics Project

A significant project in any area of mathematics. The project may be undertaken individually or in small groups. This course is offered by arrangement with a mathematics faculty member. This course may be taken in any session and the project must be completed by the last day of classes in the session in which it is taken.
Prerequisite: Students must obtain consent from the Supervisor of Studies before registering for this course.
Breadth Requirement: Quantitative Reasoning

MATD94H3    Readings in Mathematics

Independent study under direction of a faculty member.
Prerequisite: MATC01H3 and [MATC35H3 or MATC37H3] and [MATC15H3 or MATD02H3]

MATD95H3    Readings in Mathematics

Independent study under direction of a faculty member.
Prerequisite: MATC01H3 and [MATC35H3 or MATC37H3] and [MATC15H3 or MATD02H3]