University of Toronto at Scarborough 2003/2004 Calendar
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Mathematics

(B.Sc.)
E.W. Ellers, Ph.D. (Hamburg), Professor Emeritus
R.O. Buchweitz, Ph.D. (Hanover), Professor
J. Friedlander, M.A. (Waterloo), Ph.D. (Penn. State), F.R.S.C., Professor
L.C. Jeffrey, A.B. (Princeton), M.A. (Cambridge), Ph.D. (Oxford), Professor
M. Goldstein, Ph.D. (Tashkent), Professor
E. Mendelsohn, B.Sc., M.Sc. (Manitoba), Ph.D. (McGill), Professor
P. Selick, B.Sc., M.Sc., Ph.D. (Princeton), Professor
R.W. Sharpe, M.Sc., Ph.D. (Yale), Professor
C. Albanese, B.Sc., Ph.D. (Zurich), Associate Professor
J. Scherk, D.Phil., (Oxford), Associate Professor
A. Butscher, Ph.D., (Stanford), Assistant Professor
E. Moore, M.A. (Memorial), Ph.D. (Toronto), Senior Lecturer
S.C. Tryphonas, M.Sc. (Toronto), Senior Lecturer
N. Cheredeko, Ph.D. (Moscow State Tech. University), Lecturer
X. Jiang, B.Sc., M.Sc. Ph.D. (Glasgow) Lecturer
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 Programs in Mathematics and in Mathematics and Its Applications, and the Major Program in Mathematical Sciences, are eligible for inclusion in the Co-operative Program in Physical Sciences and the Early Teacher Project in Physical Sciences. Please refer to the Physical Sciences section
(page 185) and to the Co-operative Program (page 71) sections of this Calendar for further information.
Supervisor: E. Moore (416-287-7267)
The Specialist Program in Mathematics is designed to give students a thorough grounding in the main areas of Mathematics, together with an understanding of the close relationship between Mathematics and other Sciences. It provides an excellent education for students who may decide to pursue a career in research, or who wish to go on to careers in non-mathematical fields.
| 1. | (3.0 full credit equivalents - FCEs):
|
| | CSCA48H | Introduction to Computer Science
|
| | MATA23H | Linear Algebra I
|
| | [MATA30H | Calculus I (Grade 12)
|
| or
|
| | MATA31H] | Calculus I (OAC)
|
| | MATA37H | Calculus II for Mathematical Sciences
|
| | PHYA10H | Introduction to Classical Physics
|
| | PHYA21H | Introduction to Modern Physics
|
| 2. | (2.5 FCE):
|
| | [CSCB07H | Software Design
|
| or
|
| | CSCB36H] | Introduction to the Theory of Computation
|
| | MATB24H | Linear Algebra II
|
| | MATB41H | Techniques of the Calculus of Several Variables I
|
| | MATB42H | Techniques of the Calculus of Several Variables II
|
| | MATB43H | Introduction to Analysis
|
| 3. | (1.5 FCE):
|
| | MATB44H | Differential Equations I
|
| | STAB52H | An Introduction to Probability
|
| | STAB57H | An Introduction to Statistics
|
| 4. | (1.5 FCE):
|
| | MATC01H | Groups and Symmetry
|
| | MATC02H | Fields and Groups
|
| | [MATC25H | Classical Plane Geometries and their Transformations
|
| or
|
| | MATC15H] | Introduction to Number Theory
|
| 5. | (1.0 FCE):
|
| | MATC46H | Differential Equations II
|
| | MATC34H | Complex Variables
|
| 6. | (1.0 FCE): Two of:
|
| | MATB61H | Linear Programming and Optimization
|
| | MATC35H | Chaos, Fractals and Dynamics
|
| | MATC38H | Introduction to Real Analysis
|
| | MATC61H | Introduction to Mathematical Finance
|
| | MATC65H | Complex Variables II
|
| 7. | (0.5 FCE): One of:
|
| | CSCC50H | Numerical Algebra and Optimization
|
| | CSCC51H | Numerical Approximation, Integration and Ordinary Differential Equations
|
| | MATC09H | Introduction to Mathematical Logic
|
| | MATC16H | Coding Theory and Cryptography
|
| | MATC44H | Introduction to Combinatorics
|
| | MATC32H | Graph Theory and Algorithms for its Applications
|
| 8. | 1.0 FCE from MAT at B-, C-, or D-level.
|
| 9. | (0.5 FCE):
|
| | CSCD03H | Social Impact of Information Technology
|
|
|
| or
|
| | PSCD02H | Current Questions in Mathematics and Science
|
NOTE:
PSCD01H is a required course for ETP students
Recommended course: PHYB21H
Supervisor: E. Moore (416-287-7267)
The Specialist program in Mathematics and its Applications is recommended to students with strong interests in mathematics and with career goals in areas such as teaching, computer science, the physical sciences and statistics. The program is flexible; there is a core of courses in mathematics and related disciplines, but you can choose among several areas of concentration.
| 1. | (2.0 full credit equivalents):
|
| | [CSCA48H | Introduction to Computer Science
|
| or
|
| | PSCB57H] | Introduction to Scientific Computing (if PSCB57H is selected it should be taken in second year)*
|
| | MATA23H | Linear Algebra I
|
| | [MATA30H | Calculus I (Grade 12)
|
| or
|
| | MATA31H] | Calculus I (OAC)
|
| | [MATA36H | Calculus II for Physical Sciences
|
| or
|
| | MATA37H] | Calculus II for Mathematical Sciences
|
| 2. | (2.5 FCE):
|
| | MATB24H | Linear Algebra II
|
| | MATB41H | Techniques of the Calculus of Several Variables I
|
| | MATB42H | Techniques of the Calculus of Several Variables II
|
| | MATB43H | Introduction to Analysis
|
| | MATB44H | Differential Equations I
|
| 3. | (1.0 FCE):
|
| | STAB52H | An Introduction to Probability**
|
| | STAB57H | An Introduction to Statistics**
|
| 4. | (0.5 FCE):
|
| | MATC01H | Groups and Symmetry
|
| 5. | (0.5 FCE):
|
| | MATC34H | Complex Variables
|
* PSCB57H is required for the Computational Physical Sciences stream
** STAB52H and STAB57H must be taken in second year for the Statistics stream
| 6. | (2.0 FCE):
|
| | MATC02H | Fields and Groups
|
| | MATC15H | Introduction to Number Theory
|
| | MATC25H | Classical Plane Geometries and their Transformations
|
| | [MATC32H | Graph Theory and Algorithms for its Applications
|
| or
|
| | MATC44H] | Introduction to Combinatorics
|
| 7. | (1.5 FCE): Three of:
|
| | MATB61H | Linear Programming and Optimization
|
| | MATC09H | Introduction to Mathematical Logic
|
| | MATC16H | Coding Theory and Cryptography
|
| | MATC35H | Chaos, Fractals and Dynamics
|
| | MATC38H | Introduction to Real Analysis
|
| | MATC46H | Differential Equations II
|
| | MATC63H | Differential Geometry I
|
| | MATC65H | Complex Variables II
|
| 8. | (2.0 FCE): Four C- or D-level CSC, MAT or STA half-credit courses
|
| 9. | (0.5 FCE):
|
| | PSCD02H | Current Questions in Mathematics and Science
|
| or
|
| | CSCD03H | Social Impact of Information Technology
|
NOTE:
Students following this stream are encouraged to apply for acceptance into the Early Teacher Project. ETP students are required to take PSCD01H.
| 6. | (2.5 FCE):
|
| | MATB61H | Linear Programming and Optimization
|
| | MATC02H | Fields and Groups
|
| | MATC25H | Classical Plane Geometries and their Transformations
|
| | MATC46H | Differential Equations II
|
| | MATC61H | Introduction to Mathematical Finance
|
| 7. | (1.0 FCE): Two of:
|
| | MATC35H | Chaos, Fractals and Dynamics
|
| | MATC38H | Introduction to Real Analysis
|
| | MATC65H | Complex Analysis II
|
| 8. | 2.0 FCEs from C-level STA courses and 300- and 400-level STA courses on the St. George campus.
|
| 9. | (0.5 FCE):
|
| | PSCD02H | Current Questions in Mathematics and Science
|
| or
|
| | CSCD03H | Social Impact of Information Technology
|
| 6. | (5.0 FCE):
|
| | ASTA01H | Introduction to Astronomy and Astrophysics I: The Sun and Planets
|
| | ASTA02H | Introduction to Astronomy and Astrophysics II: Beyond the Sun and Planets
|
| | CSCC50H | Numerical Algebra and Optimization
|
| | CSCC51H | Numerical Approximation, Integration and Ordinary Differential Equations
|
| | MATB61H | Linear Programming and Optimization
|
| | MATC35H | Chaos, Fractals and Dynamics
|
| | MATC44H | Introduction to Combinatorics
|
| | MATC46H | Differential Equations II
|
| | PHYA10H | Introduction to Classical Physics
|
| | PHYA21H | Introduction to Modern Physics
|
| 7. | (1.5 FCE): Three of:
|
| | PHYB21H | Electricity and Magnetism
|
| | PHYB24H | Introduction to Quantum Physics
|
| | PHYC20H | Vibrations and Waves
|
| | ASTB21H | Solar System and Stellar Astrophysics
|
| | ASTC22H | Galactic and Extragalactic Astrophysics
|
| 8. | (0.5 FCE): One of:
|
| | CSCD18H | Computer Graphics
|
| | MATC61H | Introduction to Mathematical Finance
|
| | MATC65H | Complex Variables II
|
| | MATD01H | Readings in Mathematics
|
| | [PSCD02H | Current Questions in Mathematics and Science
|
| or
|
| | CSCD03H] | Social Impact of Information Technology
|
See Joint Mathematics stream in Computer Science Specialist Program
| 6. | (6.0 FCE): 12 half-credit courses chosen with the approval of the program supervisor for Mathematics and Its Applications.
|
| 7. | (0.5 FCE):
|
| | PSCD02H | Current Questions in Mathematics and Science
|
| or
|
| | CSCD03H | Social Impact of Information Technology
|
Students must choose one of the following options:
Supervisor: E. Moore (416-287-7267)
| 1. | (5.0 full credit equivalents):
|
| | CSCA48H | Introduction to Computer Science
|
| | [CSCB07H | Software Design
|
| or
|
| | CSCB36H] | Introduction to Theory of Computation
|
| | MATA23H | Linear Algebra I
|
| | [MATA30H | Calculus I (Grade 12)
|
| or
|
| | MATA31H] | Calculus I (OAC)
|
| | [MATA36H | Calculus II for Physical Sciences
|
| or
|
| | MATA37H] | Calculus II for Mathematical Sciences
|
| | MATB24H | Linear Algebra II
|
| | MATC01H | Groups and Symmetry
|
| | MATB41H | Techniques of the Calculus of Several Variables I
|
| | MATB42H | Techniques of the Calculus of Several Variables II
|
| | STAB52H | An Introduction to Probability
|
| 2. | 1.5 FCE from:
MATB43H, MATB44H (C51H), MATC46H (C56H), MATC35H, MATC38H (C57H), MATC34H (C60H), MATC65H
|
| 3. | 0.5 FCE from:
MATB61H, MATC25H (B30H), MATC02H (B32H), MATC09H, MATC15H (B70H), MATC30H, MATC44H (C31H), MATC32H, MATC61H, MATC63H (C54H)
|
| 4. | 1.0 FCE from:
CSC C-level, CSC D-level, CSCD03, MATC16H, MATC44H (C31H), MATC32H, MATD01H, MATD02H, STAB57H, STAC42H, STAC62H, STAC67H, any STA300-level, STA400-level course on St. George Campus
|
Supervisor: M. Evans (416-287-7274)
| 1. | (5.0 full credit equivalents):
|
| | CSCA48H | Introduction to Computer Science
|
| | [CSCB07H | Software Design
|
| or
|
| | CSCB36H] | Introduction to Theory of Computation
|
| | MATA23H | Linear Algebra I
|
| | [MATA30H | Calculus I (Grade 12)
|
| or
|
| | MATA31H] | Calculus I (OAC)
|
| | [MATA36H | Calculus II for Physical Sciences
|
| or
|
| | MATA37H] | Calculus II for Mathematical Sciences
|
| | MATB24H | Linear Algebra II
|
| | MATB41H | Techniques of the Calculus of Several Variables I
|
| | MATB42H | Techniques of the Calculus of Several Variables II
|
| | STAB52H | An Introduction to Probability
|
| | STAB57H | An Introduction to Statistics
|
| 2. | 2.0 FCE from:
STAC42H, STAC52H, STAC57H, STAC62H, STAC67H, any 300- and 400-level STA courses on St. George campus.
|
| 3. | 1.0 FCE from:
any C- or D-level CSC course, CSCD03, MATB43H, MATB44H, any C-level MAT course, STAC42H, STAC52H, STAC57H, STAC62H, STAC67H, any 300- and 400-level STA course on St. George campus.
|
MATA23H3 Linear Algebra I
Systems of linear equations, matrices, Gaussian elimination; vector spaces, basis, dimension; inner product spaces, geometry in R^n; linear transformations; determinants, Cramer's rule; eigenvalues and eigenvectors, diagonalization; orthogonal transformations.
Exclusion: (MATA04), MAT223
Prerequisites: [OAC Calculus & OAC Algebra and Geometry] or [Grade 12 Advanced Functions and Introductory Calculus & Geometry and Discrete Mathematics]
MATA25H3 Calculus B
Second term content of (MATA26Y); the final examination includes topics covered in MATA24H in the 2003 Winter Session. Offered for the last time in the 2003 Summer Session; MATA24H together with MATA25H is equivalent for program and MAT prerequisite purposes to (MATA26Y).
Exclusion: (MATA26Y), (MATA28Y), MATA27H, (MATA29Y), MAT123, MAT124, MAT125, MAT126, MAT133, MAT135, MAT137
Prerequisite: (MATA24H)
MATA27H3 Introduction to Optimization
Areas to be covered include: R^n as a model space in economics, contour maps; exponential functions and logarithms, with applications to finance; review of differential calculus in one variable, marginal analysis; vectors, differential calculus of several variables and optimization, with applications to economics.
Exclusions: (MATA26Y), (MATA28Y), (MATA29Y), (MATA24H), (MATA25H), MAT123, MAT124, MAT125, MAT126, MAT133, MAT135, MAT137, MATA30H, MATA31H, MATA35H, MATA36H, MATA37H
Prerequisite: OAC Calculus or Grade 12 Advanced Functions and Introductory Calculus
NOTE:
This course is intended for students in Management Programs. It does not satisfy the requirements for any Program in the Computer and Mathematical Sciences or Physical and Environmental Sciences or Life Sciences and it may not be used as a prerequisite for any further Mathematics course.
MATA30H3 Calculus I (Grade 12)
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.
Exclusions: MATA31H, MATA27H, (MATA26Y), (MATA28Y), (MATA29Y), (MATA24H), (MATA25H), MAT 123, MAT124, MAT125, MAT126, MAT133, MAT135, MAT137, JMB170
Prerequisites: [Grade 12 Advanced Functions and Introductory Calculus] & [one of Grade 12 Geometry and Discrete Mathematics or Mathematics of Data Management]
MATA31H3 Calculus I (OAC)
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.
Exclusions: MATA30H, MATA27H, (MATA26Y), (MATA28Y), (MATA29Y), (MATA24H), (MATA25H), MAT123, MAT124, MAT125, MAT126, MAT133, MAT135, MAT137, JMB170
Prerequisites: [OAC Calculus] & [one of OAC Algebra and Geometry or OAC Finite Mathematics]
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.
Exclusions: MATA36H, MATA37H, MATA27H, (MATA26Y), (MATA28Y), (MATA29Y), (MATA24H), (MATA25H), MAT123,MAT 124, MAT125, MAT126, MAT133, MAT135, MAT137, JMB170
Prerequisites: MATA30H or MATA31H
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.
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.
Exclusions: MATA35H3, MATA37H3, MATA27H3, (MATA26Y3), (MATA28Y3), (MATA29Y3), (MATA24H3), (MATA25H3), MAT123, MAT124, MAT125, MAT126, MAT133, MAT135, MAT137, JMB170
Prerequisite: MATA30H or MATA31H
MATA37H3 Calculus II for Mathematical Sciences
A calculus course providing a conceptual approach for students needing more than techniques and applications. An introduction to proof and the theoretical side of basic calculus emphasizing intuition. Fundamental Theorem of Calculus, Taylor's Theorem, sequences and series, power series and differential equations.
Exclusions: MATA35H, MATA36H, MATA27H, (MATA26Y), (MATA28Y), (MATA29Y), (MATA24H), (MATA25H), MAT 123, MAT124, MAT125, MAT126, MAT133, MAT135, 137, JMB170
Prerequisite: MATA30H or MATA31H
MATB24H3 Linear Algebra II
Fields, vector spaces over a field, linear transformations; diagonalizability, invariant subspaces, Cayley-Hamilton theorem; hermitian inner product, normal, self-adjoint and unitary operators, method of least squares, introduction to coding theory.
Exclusions: (MATA04Y), MAT224
Prerequisites: MATA23H or MAT223
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.
Exclusions: (MATA28Y), (MATA29Y), (MAT230), (MAT234Y), MAT235, MAT237, (MAT239Y), MAT257
Prerequisites: MATA23H & [MATA36H or MATA37H or (MATA26Y)]
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.
Exclusions: (MAT230), (MAT234Y), MAT235, MAT237, (MAT239Y), MAT257
Prerequisite: MATB41H
MATB43H3 Introduction to Analysis
Calculus revisited rigorously: properties of real numbers, limits, compactness, topology of Euclidean space, continuity, differentiability, fundamental theorem, Riemann integral.
Exclusions: (MATA27Y); MAT246
Prerequisites: [MATA36H or MATA37H or (MATA26Y)] & [MATA23H & MATB24H]
Corequisite: MATB42H
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.
Exclusions: (MATC51), MAT244, MAT267
Prerequisites: [MATA36H or MATA37H or (MATA26Y)] & MATA23H
Corequisites: MATB41H & MATB24H
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.
Exclusion: APM236H, (APM261H)
Prerequisite: MATA23H
Corequisite: MATB42H
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 calulations.
Exclusions: (MATC91H),(MATB31), MAT301, (MAT347)
Prerequisite: MATB24H
MATC02H3 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.
Exclusion: (MATB32H), MAT302 (MAT347)
Prerequisite: MATC01H
MATC09H3 Introduction to Mathematical Logic
Predicate calculus. Relationship between truth and provability; Gdel's completeness theorem. First order arithmetic as an example of a first-order system. Gdel's incompleteness theorem; outline of its proof. Introduction to recursive functions.
Exclusions: MAT309H, CSC438H
Prerequisites: MATB24H & [MATB43H or CSCB38H]
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.
Exclusions: (MATB70), MAT315
Prerequisites: [MATA36H or MATA37H or (MATA26Y)] & [MATB24H or (MATA04Y)]
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.
Prerequisites: MATB24H & STAB52H
Corequisite: MATC15H recommended
MATC25H3 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.
Exclusions: (MATB30), (MAT325), MAT365
Prerequisite: MATA23H
Corequisite: MATC01H
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.
Prerequisites: [MATB24H or CSCB38H] & at least one other B-level course in Mathematics or Computer Science
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.
Exclusions: (MATC60H), MAT334
Prerequisite: MATB42
MATC35H3 Chaos, Fractals and Dynamics
Areas covered include: metric spaces, dynamics on the real line, fixed points, periodic points, attractors, repellors, Sarkovskii's theoren 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.
Exclusion: MAT335
Prerequisite: MATB43H
MATC38H3 Introduction to Real Analysis
Metric spaces, completeness, uniform convergence. Topics in measure theory: the Lebesgue integral, Riemann-Stieltjes integral,
L
p
spaces, Fourier series.
Exclusion: MAT337, (MAT338)
Prerequisites: MATB42H & MATB43H
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.
Exclusions: (MATC31), MAT344
Prerequisite: MATB24H
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.
Exclusions: (MATC56), AMP346H
Prerequisites: MATB44H & MATB24H
Corequisite: MATB42
MATC61H3 Introduction to Mathematical Finance
Brownian motions, Fokker-Planck equation, stopping times, reflection principle, Girsanov theorem; Stochastic calculus, Ito's lemma, martingales; stochastic optimization, Black-Scholes equation. The course provides an introduction to methods of interest in financial mathematics.
Prerequisites: MATB42H, [(STAB47H) or STAB52H]
Corequisites: MATB61H & MATC46H
Recommended: STAC62H
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.
Exclusions: MATC54, MAT363
Prerequisite: MATB43
MATC65H3 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.
Exclusion: MAT354
Prerequisite: MATC34H
MATD01H3 Readings in Mathematics
Independent study under the direction of a faculty member.
Prerequisite: A GPA of 2.5 or more and consent of the instructor.
MATD02H3 Readings in Mathematics II
Independent study under the direction of a faculty member.
Prerequisite: A GPA of 2.5 or more and consent of the instructor.
University of Toronto at Scarborough 2003/2004 Calendar
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