**1000-level** | 2000-level | 3000-level | 4000-level

MATH 1005H - *Applied calculus*

An introduction to the methods and applications of calculus. Derivatives, exponential and logarithmic functions, optimization problems, related rates, integration, partial derivatives, differential equations. Selected applications from the natural and social sciences.

**Prerequisite:** A Grade 12U mathematics course or its equivalent. Not available to students enrolled in or with credit for MATH 1100Y (110) or 1101Y. Not for credit towards a major or minor in Mathematics. Excludes MATH 105H.

**Offered** in Peterborough in Fall 2012 (Reem Yassawi) and again in Winter 2013 (Nick Faulkner).

MATH 1050Y - *A non-calculus-based introduction to probability and statistical methods*

Data summary, elementary probability, estimation, hypothesis testing, analysis of variance, regression, nonparametric methods. Applications in a variety of areas are discussed.

**Prerequisite:** This course uses high school mathematics as a foundation and involves the use of computers. *Not for credit towards a major or minor in Mathematics, nor available to students enrolled in, or with credit for MATH 1100Y (110) or 1101Y or 2560H (256H).* Excludes MATH 150.

**Offered** in 2012-2013 in Oshawa (Instructor to be announced) and in Peterborough (Section A, Jaclyn Semple; Section B, Kaukab Kamran).

MATH 1100Y - *Calculus I: Calculus of one variable*

An examination of the concepts and techniques of calculus, with applications to other areas of mathematics and the physical and social sciences, including an introduction to the use of "Maple" software.

**Prerequisite:** Grade 12 Advanced Functions or equivalent with at least 60%; a pass mark on math skills assessment administered by department of Mathematics; or permission of instructor. Grade 12U Calculus and Vectors is strongly recommended. Excludes MATH 110, 1101Y.

**Offered** in Peterborough in 2012-2013 (Marcus Pivato).

MATH 1100Y and 1101Y are essentially the same course and are completely equivalent as prerequisites for other courses. 1101Y is intended for students whose pre-calculus skills, especially in algebra, are not as strong. It has an extra lecture hour each week to allow some time to firm up these skills and allow a more leisurely development of the core concepts and techniques of single-variable calculus.

For the Fall/Winter session, students normally enroll in MATH 1101Y and are placed in MATH 1100Y if they pass an online math skills assessment. (Students are normally notified by e-mail when the test becomes available.) It is possible to transfer between the two courses, with permission of the instructor, during the first few weeks of the school year. In the Summer session, normally only MATH 1100Y is offered and the math skills assessment is waived.

MATH 1101Y - *Calculus I: Functions and calculus of one variable*

An examination of the concepts and techniques of calculus, with applications to other areas of mathematics and the physical and social sciences, including an introduction to the use of "Maple" software. Includes same content as MATH 1100Y with an additional lecture hour per week devoted to development of pre-calculus skills.

**Prerequisite:** Grade 12 Advanced Functions or equivalent with at least 60%; completion of math skills assessment administered by department of Mathematics; or permission of instructor. Excludes MATH 110, 1100Y.

**Offered** in Peterborough in 2012-2013 (Stefan Bilaniuk).

MATH 1350H - *Linear algebra I: Matrix algebra*

Vectors, systems of linear equations, matrices, determinants, linear transformations, eigenvalues and eigenvectors.

**Prerequisite:** A Grade 12U mathematics course with at least 60% or permission of instructor. Recommended: Grade 12U Calculus and Vectors. Excludes MATH 135H.

**Offered** in Peterborough in Fall 2012 (David Poole).

MATH 1550H - *Introduction to probability*

Probability, random variables, probability distributions. Note that MATH 1550H does not count as the Introductory Statistics course required for admission into some professional schools.

**Prerequisite:** MATH 1005H (105H), or MATH 1100Y (110) or 1101Y, or permission of instructor. MATH 1100Y (110) or 1101Y may be taken as a co-requisite. Excludes MATH 155H.

**Offered** in Peterborough in Winter 2013 (Sohee Kang).

1000-level | **2000-level** | 3000-level | 4000-level

MATH 2080Y - *Mathematics for teacher education*

A course in mathematics and mathematical thinking for prospective elementary school teachers. Number systems and counting, graphs and networks, symmetry and patterns, mathematics in nature and art, probability and statistics, measurement and growth.

**Prerequisite:** Normally open only to students who are in the Concurrent Education program or who are pursuing the Emphasis in Teacher Education. Permission of department required. Excludes MATH 280 and any Mathematics course, or its equivalent, which counts toward a major or minor in Mathematics. *This course does not satisfy the mathematics requirement for a Bachelor of Science degree.*

**Offered** in 2012-2013 in Oshawa (Gary Zuliani) and in Peterborough (Nicholas Faulkner).

MATH 2110H - *Calculus II: Calculus of several variables*

Multivariable functions, curves and surfaces in two and three dimensions. Partial differentiation and applications. Multiple integrals.

**Prerequisite:** 60% or higher in MATH 1100Y (110) or 1101Y and MATH 1350H (135H) (1350H may be taken as a co-requisite); or permission of instructor. Excludes MATH 200, 201H.

**Offered** in Peterborough in Fall 2012 (Kenzu Abdella).

MATH 2120H - *Calculus III: Vector calculus*

Parametric curves and surfaces, vector functions and fields. Line integrals, Green's Theorem. Surface integrals, curl and divergence, Stokes' and Divergence Theorems.

**Prerequisite:** 60% or higher in MATH 2110H (201H) or permission of instructor. Excludes MATH 200, 202H.

**Offered** in Peterborough in Winter 2013 (Kenzu Abdella).

MATH-PHYS 2150H - *Ordinary differential equations*

First order equations; qualitative and numerical methods. Second order linear equations. Linear systems. Applications to physical and biological models. Laplace transforms.

**Prerequisite:** 60% or higher in MATH 1100Y (110) or 1101Y; or permission of instructor. Recommended: MATH 1350H (135H). Excludes MATH - PHYS 205H.

**Offered** in Peterborough in Fall 2012 (Wenying Feng).

MATH-COIS 2180H - *Introduction to numerical and computational methods*

Error analysis, nonlinear equations, linear systems, interpolation methods, numerical differentiation and integration and initial value problems.

**Prerequisite:** 60% or higher in MATH 1005H (105H) or 1100Y (110) or 1101Y; or permission of instructor. Excludes MATH 207H, MATH-COSC 203H.

**Offered** in Peterborough in Fall 2012 (Kenzu Abdella).

MATH 2200H - *Mathematical reasoning*

This course introduces concepts/methods that are essential for all advanced courses in pure mathematics. It is intended for Mathematics majors early in their program. Logic, abstraction, proof techniques. Basic combinatorics. Sets, functions, (in/sur/bi)jections. Cantor’s transfinite arithmetic. Number theory: divisibility, prime factorization, modular arithmetic. Optional: basic group theory and topology.

**Prerequisite:** 60% in MATH 1100Y (110) or 1101Y and MATH 1350H (135H) (each may be taken as co-requisites); or permission of instructor. Excludes MATH 220H.

**Offered** in Peterborough in Fall 2012 (David Poole).

MATH 2260H - *Geometry I: Euclidean geometry*

Elements of Euclidean geometry stressing links to modern mathematical methods. Geometric transformations and symmetry. Recommended for Education students.

**Prerequisite:** 60% or higher in MATH 1005H (105H) or 1100Y (110) or 1101Y or 1350H (135H); or permission of instructor. Excludes MATH 226H.

**Offered** in Peterborough in Winter 2013 (Stefan Bilaniuk).

MATH 2350H - *Linear algebra II: Vector spaces*

Vector spaces, basis and dimension, inner product spaces, orthogonality, linear transformations, diagonalization, quadratic forms, least squares, the singular value decomposition.

**Prerequisite:** 60% or higher in MATH 1350H (135H); or permission of instructor. Excludes MATH 235H.

**Offered** in Peterborough in Winter 2013 (David Poole).

MATH 2560H - *Introduction to statistical inference*

Introduction to mathematical statistics: Methods of point estimation, confidence intervals, hypoth- eses testing, comparative inferences, nonparametric methods. Assumes a background in probability and calculus.

**Prerequisite:** 60% or higher in MATH 1550H (155H) or permission of instructor. Excludes MATH 355, 256H.

**Offered** in Peterborough in Fall 2012 (Sohee Kang).

MATH-COIS 2600H - *Discrete structures*

Mathematics related to Computer Science including sets and relations, counting techniques and recursive relations, trees and networks. Applications to analysis of algorithms, data structure and optimization problems.

**Prerequisite:** 60% or higher in either MATH 1100Y (110) or 1101Y and 1350H (135H); or 60% or higher in COIS 1020H (COSC 102H), MATH 1005H (105H) and 1350H (135H); or permission of instructor. Excludes MATH-COSC 260.

**Offered** in Peterborough in Fall 2012 (Marco Pollanen).

1000-level | 2000-level | **3000-level** | 4000-level

MATH-PHYS 3130H - *Classical mechanics*

Taught by the Department of Physics & Astronomy. **Offered** in Peterborough in Fall 2012 (Peter Dawson).

MATH-PHYS 3140H - Advanced classical mechanics

Taught by the Department of Physics & Astronomy. **Offered** in Peterborough in Winter 2013 (Peter Dawson).

MATH-PHYS 3150H - *Partial differential equations*

First order PDEs: method of characteristics, applications to ODEs. Second order PDEs: classification, boundary conditions. Finite difference method. Frequency methods. Linear elliptic operators, eigen- values and eigenfunctions for boundary value problems. Symmetric operators. Minimum principle for eigenvalues. Completeness of eigenfunctions. Fourier method (eigenfunction expansion). Regularity, stability, and semi-group properties for evolution equations.

**Prerequisite:** 60% or higher in MATH 2150H (205H) or 2110H (201H), or permission of instructor. MATH 2110H (201H) may be taken as a co-requisite. Strongly recommended: MATH 1350H (135H). Excludes MATH-PHYS 305H.

**Offered** in Peterborough in Fall 2012 (Marcus Pivato).

MATH-PHYS 3160H - *Methods of applied mathematics*

Differential equations in applied mathematics, including Bessel, Legendre, hypergeometric, Laguerre, Hermite, Chebyshev, etc. Series and numerical solutions. Properties of the special functions arising from these equations.

**Prerequisite:** 60% or higher in MATH-PHYS 2150H (205H); or permission of instructor. Recommended: MATH 2200H (220H). Excludes MATH 303H, 308H.

**Offered** in Peterborough in Winter 2013 (Kenzu Abdella).

MATH 3200H - *Number theory*

Divisibility (GCDs, LCMs, Euclidean algorithm, Bezout’s identity). Linear Diophantine Equations. Prime numbers (Factorization; Fermat/Mersenne numbers; pseudoprimes; Carmichael numbers). Modular Arithmetic (Chinese Remainder Theorem; Fermat/Euler theorem). Group of units mod m. Primitive roots. Quadratic Residues (Legendre symbols; Quadratic Reciprocity).

**Prerequisite:** 60% or higher in MATH 1350H (135H) and 2200H (220H); or permission of instructor. Excludes MATH 320H, 322.

**Not offered** in 2012-2013.

MATH-COIS 3210H - *Mathematical cryptography*

Public vs. private key cryptosystems: cyphertexts, plaintexts, and Kerkhoff’s principle. Shannon’s theory of perfect secrecy. Modular arithmetic: Chinese reminder theorem, Fermat/Euler theorems. RSA cryptosystem: definition and vulnerabilities. El-Gamal cryptosystem. Rabin cryptosystem. Quadratic residue theory. Probabilistic primality tests and factoring algorithms. Optional: discrete logarithm algorithms and elliptic curve cryptosystems.

**Prerequisite:** 60% or higher in MATH 2200H (220H); or permission of instructor. Recommended: MATH-COIS 2600H or MATH-COSC 260; or both MATH 1550H (155H) and COIS 2120H (202H). Excludes MATH-COSC 321H.

**Offered** in Peterborough in Winter 2013 (Marco Pollanen).

MATH 3260H - *Geometry II: Projective and non-euclidean geometry*

Elements of projective and non-Euclidean geometry, including an introduction to axiomatic systems.

**Prerequisite:** 60% or higher in MATH 1350H (135H); or permission of instructor. Excludes MATH 326H.

**Not offered** in 2012-2013.

MATH 3310H - *Algebra III: Introduction to abstract algebra*

An introduction to the fundamental algebraic structures: groups, rings, fields. Subgroups and subrings, homomorphisms and isomorphisms, quotient structures, finite fields. Selected applications.

**Prerequisite:** 60% or higher in MATH 2200H and 2350H, or permission of the instructor. Excludes MATH 330, 332H, 3320H, 3360H.

**Offered** in Peterborough in Winter 2013 (David Poole).

MATH-COIS 3350H - *Linear programming*

Introduction to the concepts, techniques and applications of linear programming and discrete optimization, Topics include the simplex method, duality, game theory and integer programming.

**Prerequisite:** 60% or higher in MATH 1350H (135H); or permission of instructor. Excludes MATH-COSC 335H.

**Offered** in Peterborough in Fall 2012 (Marco Pollanen).

MATH 3510H - *Mathematical finance*

Elements of stochastic calculus. Discrete time market models and continuous time market models. Self-financing strategies and arbitrage. Replication of claims. Completeness of market models. Pricing of derivatives: binomial model, Black-Scholes model. Historical and implied volatility. Prerequi- site: 60% or higher in MATH 1550H (155H) and 2150H (205H); or permission of instructor. Excludes MATH 351H.

**Offered** in Peterborough in Fall 2012 (Marco Pollanen).

MATH 3560H - *Linear statistical models*

Linear regression and correlation, multiple regression, analysis of variance and experimental designs. Assumes background in probability and uses introductory linear algebra.

**Prerequisite:** 60% or higher in MATH 2560H (256H) with at least 60%, or permission of instructor. Strongly recommended: MATH 1350H (135H). Excludes MATH 355, 356H.

**Offered** in Peterborough in Fall 2012 (Sohee Kang).

MATH 3570H - *Introduction to stochastic processes*

This course covers a variety of important models used in modeling of random events that evolve in time. These include Markov chains (both discrete and continuous), Poisson processes and queues. The rich diversity of applications of the subject is illustrated through varied examples.

**Prerequisite:** 60% or higher in MATH 1350H (135H) and 1550H (155H) or permission of instructor. Excludes MATH 357H.

**Not offered** in 2012-2013.

MATH 3610H - *Discrete optimization*

Introduction to the concepts, techniques and applications of discrete optimization. Topics include transportation problems, assignment problems, matchings in graphs, network flow theory and combinatorial optimization.

**Prerequisite:** 60% or higher in MATH 1350H (135H) and 60% or higher in MATH 2200H (220H) or MATH-COIS 2600H or MATH-COSC 260; or permission of instructor. Excludes MATH 361H.

**Offered** in Peterborough in Fall 2012 (Marco Pollanen).

MATH 3700H - *Metric geometry and topology*

Metric spaces. Limits and continuity. Completeness: the Baire Category Theorem; normed linear spaces and Banach spaces; the Contraction Mapping Theorem and applications. Compact, separ- able, and (first/second) -countable spaces: the Heine-Borel and Lindelof theorems. Topological spaces. Hausdorff axiom and (non) metrizability. Product spaces and quotient spaces. Compactness and Tychonoff’s theorem. (Path)-connectedness.

**Prerequisite:** 60% or higher in MATH 2200H (220H); or permission of instructor. Excludes MATH 310H.

**Not offered** in 2012-2013.

MATH 3770H - *Aanalysis II: Complex analysis*

Complex numbers, limits and series. Complex functions, Holomorphic functions. Complex contour integrals; Cauchy integral theorems. Taylor series. Laurent series. Calculus of residues. The Funda- mental Theorem of Algebra. Frequency analysis: Fourier transform, Laplace transform, Fourier series, Z-transform.

**Prerequisite:** 60% or higher in MATH 2120H (202H) or 200; or permission of instructor. Excludes MATH 306H, 307H.

**Offered** in Peterborough in Fall 2012 (Reem Yassawi).

MATH 3790H - *Analysis I: Introduction to analysis*

The real number system. Limits. Continuity. Differentiability. Mean-value theorem. Convergence of sequences and series. Uniform convergence.

**Prerequisite:** 60% or higher in MATH 1100Y (110) or 1101Y. 60% or higher in MATH 2200H (220H) (may be taken as co-requisite); or permission of instructor. Excludes MATH 206H, 309H.

**Offered** in Peterborough in Winter 2013 (Reem Yassawi).

MATH 3810H - *Ancient and classical mathematics*

This course traces the historical development of mathematics from prehistory to medieval times, and the interactions between the development of mathematics and other major trends in human culture and civilization. We will study the mathematics of ancient Egypt and Mesopotamia, and classical Greece and Rome.

**Prerequisite:** 60% or higher in MATH 1100Y (110) or 1101Y; or permission of instructor. Recommended: MATH 2200H (220H) or 2350H (235H). Excludes MATH 380, 381H.

Normally offered in alternate years with MATH 3820H. **Not offered** in 2012-2013.

MATH 3820H - *Mathematics from medieval to modern times*

Traces the development of mathematical ideas, abstraction and proofs. The genesis of modern arithmetic in medieval India, the birth of algebra in the Islamic world, and their influence on medieval European mathematics. Renaissance mathematics (polynomial equations, analytic geometry). The Enlightenment (calculus, number theory). The apotheosis of rigour since the 19th century.

**Prerequisite:** 60% or higher in MATH 1100Y (110) or 1101Y; or permission of instructor. Recommended: MATH 2200H (220H) or 2350H (235H). Excludes MATH 380, 382H.

Normally offered in alternate years with MATH 3820H. **Offered** in Peterborough in Fall 2012 (Stefan Bilaniuk).

MATH 3900Y, 3901H, 3902H, 3903H, 3904H - *Reading course*

Details may be obtained by consulting the department.

**Prerequisite:** 85% minimum in any prerequisite for the course; or permission of department chair.

1000-level | 2000-level | 3000-level | **4000-level**

MATH 4120H - *Mathematical modeling I*

This course provides an introduction to the mathematical modeling process and applies this process to simple mathematical modeling problems arising from a variety of application areas in science and engineering. Mathematical modeling techniques, such as differential equations, discrete systems and numerical methods along with computer aids will be utilized.

**Prerequisite:** 60% or higher in MATH-PHYS 2150H (205H); or permission of instructor. Excludes MATH 411, 412H.

**Offered** in Peterborough in Winter 2013 (Kenzu Abdella).

MATH 4130H - *Mathematical modeling II*

This course further develops the mathematical modeling techniques introduced in MATH 4120H (412H). Topics include dimensional analysis and partial differential equation models such as diffusion processes, wave motions and fluid flows.

**Prerequisite:** 60% or higher in MATH 4120H (412H) and one of MATH-PHYS 3180H or 3150H (305H); or permission of instructor. Excludes MATH 411, 413H.

**Not offered** in 2012-2013.

MATH 4160H - *Advanced methods of applied mathematics*

This course deals with a variety of applied mathematics techniques, focusing on dimensional analysis and scaling, perturbation techniques for algebraic and differential equations, and asymptotic expan- sions of integrals. Topics include Laplace’s method, Watson’s Lemma, methods of stationary phase, method of steepest descent, regular and perturbation, boundary layer theory, and matched asymp- totic expansions.

**Prerequisite:** 60% or higher in MATH 2150H (205H) and 3160H; or permission of instructor. Recommended: MATH 2200H (220H). Excludes MATH 405H.

**Not offered** in 2012-2013.

MATH 4180H - *advanced numerical methods*

This course deals with a variety of numerical methods for solving ordinary and partial differential equations arising from scientific and engineering applications. The topics covered include finite difference, adaptive techniques, multi-step methods, Runge-Kutta methods, direct and iterative methods for systems, stability and convergence.

**Prerequisite:** 60% or higher in MATH 2180H (203H) and 2150H (205H); or permission of instructor. Excludes MATH 403H.

**Not offered** in 2012-2013.

MATH-COIS 4215H - *Mathematical logic*

An introduction to the syntax and semantics of propositional and first-order logics through the Soundness, Completeness and Compactness Theorems.

**Prerequisite:** 60% or higher in MATH-COIS 2600H or MATH-COSC 260; or permission of instructor. Excludes MATH-COSC 415H.

**Offered** in Peterborough in Fall 2012 (Stefan Bilaniuk).

MATH-COIS 4216H - *Computability*

An introduction to computability via Turing machines and recursive functions, followed either by applications to the Incompleteness Theorem or by an introduction to complexity theory.

**Prerequisite:** 60% or higher in COIS 3050H (COSC 305H) or MATH-COIS 4215H (MATH-COSC 415H); or permission of instructor. Excludes MATH-COSC 416H.

**Not offered** in 2012-2013.

MATH 4260H - *Topics in geometry*

Excludes MATH 426H.

**Not offered** in 2012-2013.

MATH 4310H - Algebra IV: Galois theory

Extension fields and Galois groups; the fundamental theorem of Galois Theory; the insolubility of the quintic.

**Prerequisite:** 60% or higher in MATH 3310H or permission of instructor. Excludes MATH 431H.

**Not offered** in 2012-2013.

MATH 4320H - *Algebra V: Topics in algebra*

**Prerequisite:** 60% or higher in MATH 3310H or permission of instructor. Excludes MATH 432H.

**Not offered** in 2012-2013.

MATH 4400H - *Mathematics through problem-solving*

A seminar-based course in problem solving. Topics include invariants, number properties, polynom- ials, functional equations, inequalities, combinatorial games.

**Prerequisite:** 70% in MATH 1100Y (110) or 1101Y and 1350H, and permission of instructor. Excludes MATH 4951H. Recommended: MATH 2200H.

**Not offered** in 2012-2013.

MATH 4450H - *Voting, bargaining and social choice*

Voting systems: Condorcet cycles, Borda count and other positional systems, voting paradoxes, Arrow’s impossibility theorem. Social choice functions: (relative) utilitarian, egalitarian; properties and axiomatic characterizations. Bargaining theory: Nash solution, Kalai-Smorodinsky, utilitarian, and egalitarian solutions. Strategic voting: Gibbard-Satterthwaite theorem; implementation theory.

**Prerequisite:** MATH 1350H (135H), 2110H (201H), and 2200H (220H); or ECON 3000H and 3250H. ECON 3160H and 4000H also recommended. Excludes MATH 4952H.

**Offered** in Peterborough in Winter 2013 (Marcus Pivato).

MATH 4510H - *Mathematical risk management*

Basic mathematical theory and computational techniques for how financial institutions can quantify and manage risks in portfolios of assets. Topics include: mean-variance portfolio analysis, the capital asset pricing model and Value at Risk (VaR).

**Prerequisite:** 60% or higher in MATH 1550H (155H) and 2150H (205H); or permission of instructor. Excludes MATH 451H.

**Offered** in Peterborough in Winter 2013 (Marco Pollanen).

MATH 4560H - *Topics in statistics*

**Prerequisite:** 60% or higher in MATH 2560H (256H); or permission of instructor. Strongly recommended: MATH 3560H (356H). Excludes MATH 456H.

**Offered** in Peterborough in Fall 2012 (Sohee Kang).

MATH 4561H - *Sampling*

The goal of this course is to study the statistical aspects of taking and analyzing a sample. Topics covered include simple random, systematic, stratified, cluster, two-stage and probability proportional to size designs. Applications in a variety of areas are discussed.

**Prerequisite:** 60% or higher in
MATH 2560H (256H); or permission of instructor. Recommended: MATH 3560H (356H). Excludes MATH 456H.

MATH 4562H - *Design of experiments*

The goal of this course is to introduce students to the principles and methods of designed experi- ments. Designs commonly used in research will be studied, with focus both on analysis and construction of designs. Students will apply the concepts studied in applications.

**Prerequisite:** 60% or higher in MATH 2560H (256H); or permission of instructor. Recommended: MATH 3560H (356H).

**Not offered** in 2012-2013.

MATH 4563H - *Foundations of research design and data analysis*

Students enrolled in this course will follow the course syllabus for BIOL-ERSC 4030H (403H) (please consult course description for the latter). Students registered in MATH 4563H will complete assignments for BIOL - ERSC 4030H (403H), with theoretical assignments replacing some of the labs required there.

**Prerequisite:** 60% or higher in MATH 2560H (256H) and 3560H (356H); or permission of instructor.

**Not offered** in 2012-2013.

MATH 4570H - *Topics in probability: a second course in stochastic processes*

Stochastic calculus and stochastic differential equations.

**Prerequisite:** 60% or higher in MATH 3570H
(357H); or permission of instructor. Excludes MATH 457H.

**Not offered** in 2012-2013.

MATH 4610H - *Introduction to graph theory*

An introduction to graph theory with emphasis on both theory and applications and algorithms related to computer science, operation research and management science.

**Prerequisite:** 60% or higher in MATH-COIS 2600H (or MATH-COSC 260) and in MATH 2200H (220H); or permission of instructor. Excludes MATH 461H.

**Not offered** in 2012-2013.

MATH 4620H - *Introduction to combinatorics*

An introduction to combinatorics. The topics include counting techniques, generating functions and block design.

**Prerequisite:** 60% or higher in MATH 2200H (220H); or permission of instructor. Excludes MATH 460, 462H.

**Not offered** in 2012-2013.

MATH 4700H - *Topics in topology*

**Prerequisite:** 60% or higher in MATH 3700H (310H); or permission of instructor. Excludes MATH
410H.

**Not offered** in 2012-2013.

MATH 4710H - *Chaos, symbolic dynamics, fractals*

An introduction to discrete dynamical systems. Periodicity, attraction. Parametrized families of func- tions, bifurcation, chaos. Symbolic dynamics, conjugacy, Cantor Sets. Deterministic fractals, fractal dimension, Lyapunov exponents, entropy.

**Prerequisite:** 60% or higher in MATH 3700H (310H); or permission of instructor. Excludes MATH 470, 471H.

**Offered** in Peterborough in Winter 2013 (Reem Yassawi).

MATH 4720H - *Fractals and complex dynamics*

Discrete two-dimensional linear systems, the stable and unstable manifolds. Symbolic dynamics; the horseshoe map; hyperbolicity; the Poincare-Bendixson theorem; complex dynamics; Julia sets, Mandelbrot sets.

**Prerequisite:** 60% or higher in MATH 4710H (471H); or permission of instructor. Excludes MATH 470, 472H.

MATH 4770H - *Analysis IV: Topics in complex analysis*

Mobius transformations and the Riemann Sphere, automorphisms of the disc, the Poincare metric. Infinite products. Analytic continuation and applications. Harmonic functions and applications. The Riemann mapping theorem and Picard’s theorem.

**Prerequisite:** 60% or higher in MATH 3770H (307H); or permission of instructor. Excludes MATH 407H.

**Not offered** in 2012-2013.

MATH 4790H - *Analysis III: Measure and integration*

Riemann and Lebesgue measure, integration.

**Prerequisite:** 60% or higher in MATH 3700H (310H); or permission of instructor. Excludes MATH 406H, 409H.

**Not offered** in 2012-2013.

MATH 4810H - *Perspectives in mathematics I*

This course is team taught by three instructors. Each instructor will teach a four-week module on a special topic.

**Prerequisite:** 60% or higher in 1.0 3000-level MATH credit; or permission of instructor. Excludes MATH 491H, 481H.

**Not offered** in 2012-2013.

MATH 4820H - *Perspectives in mathematics II*

This course is team taught by three instructors. Each instructor will teach a four-week module on a special topic.

**Prerequisite:** 60% or higher in 1.0 3000-level MATH credit; or permission of instructor. Excludes MATH 492H, 482H.

**Offered** in Peterborough in Winter 2013 (Stefan Bilaniuk, Wenying Feng, and Reem Yassawi).

MATH 4850Y, 4851H, 4852H - *Community-based research project*

Students are placed in research projects with community organizations in the Peterborough area. Each placement is supervised jointly by a faculty member and a representative of a community organization. For details see Community-Based Education Program in the Academic Calendar.

**Prerequisite:** MATH 2560H and either MATH 3560H or 4561H or 4562H and a cumulative average of at least 75%. Students may take either MATH 4850Y or, one or both of 4851H and 4852H for credit.

MATH 4900Y, 4903H, 4904H - *Reading course*

Details may be obtained by consulting the department.

**Prerequisite:** 85% minimum in any prerequisite for the course, or permission of department chair.

Maintained by Stefan Bilaniuk. Last updated 2012.10.25.