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Telephone: (705) 748-1011 ext. 7531
Fax: (705) 748-1155
E-mail: math@trentu.ca
Web: http://euclid.trentu.ca/math
Associate Professor and Chair of the Department
R. Yassawi, B.Sc. (London School of Economics), M.A., Ph.D. (McGill)
Professors
K. Abdella, B.Sc. (Trent), M.Sc. (Alberta) , Ph.D. (Western Ontario) (on leave 2008–2009);
D. G. Poole, B.Sc. (Acadia) , M.Sc., Ph.D. (McMaster); B. Zhou, B.Sc. (Shanghai), Ph.D. (South Carolina)
Associate Professors
S. Bilaniuk, B.Sc. (Toronto) , A.M., Ph.D. (Dartmouth); N. Dokuchaev, M.Sc., Ph.D. (St. Petersburg); W. Feng, M.Sc. (Shaanxi) , Ph.D. (Glasgow); M. Pivato, B.Sc. (Alberta), Ph.D. (Toronto)
Assistant Professors
M. Boue, B.Sc. (ITAM), M.Sc., Ph.D. (Brown); M. Pollanen, B.Sc. (Carleton), M.Sc., Ph.D (Toronto)
Professors Emeriti
I. C. Chakravartty, M.Sc. (Gauhati) , Ph.D. (Saskatchewan); G. F. Hamilton, B.A.Sc., M.A., Ph.D. (Toronto) , P. Eng.; T. N. Murphy, B.Sc. (Liverpool); E. A. Maxwell, M.Sc., Ph.D. (Toronto)
The curriculum in Mathematics has been designed to accommodate a wide variety of interests in both pure and applied mathematics. All students in the Mathematics major program must take core courses in calculus and algebra. Most of the remaining courses have been divided into three categories corresponding to the major areas of Mathematics. The intent is to provide students with both breadth and depth in Mathematics while allowing them to pursue those areas that interest them.
Revision and Expansion of Program
The Mathematics curriculum has been revised in 2008. Please take note of the following changes:
New Courses
MATH 4561H, 4562H, 4563H
Full course to half course
MATH – COSC 260 into MATH – COIS 2600H
New Specializations and Programs
Please note that a new Specialization in Statistics is offered in 2008. Also, new programs in Mathematical Computer Science and Mathematical Physics are being introduced in 2008. Please consult appropriate sections in this calendar.
Course Renumberings
The Department has moved to a four digit course numbering system for 2008-2009. Please consult course descriptions for new numberings. The old three digit course number appears as an exclusion. Wherever a course is required as a Pre- or co-requisite, the old three digit number appears in parenthesis after the new four digit course number.
Frequency of Course Offerings
Some courses are offered only in alternate years, and some courses are offered in only the Fall or the Winter term. Please refer to the department website at http://euclid.trentu.ca/ mathematics for general information, and for scheduled course offerings in any year. Courses will be offered only if there is adequate staffing and demand . It is important that you plan your courses at least one year in advance to ensure that you will be able to satisfy all of the prerequisites for future courses.
Notes
- C- (60%) or higher in a Mathematics course at the 100-level is a prerequisite for all upper-level Mathematics courses. For specific prerequisites, see individual course descriptions.
- Students who have fulfilled the requirements for a single-major Honours degree in another subject may apply to the Office of the Registrar for a minor in Mathematics, if they have at least 5 credits in Mathematics, excluding MATH 1005H (105H), 1050 (150) , and 2080 (280) , 2084H (284H) , 2085H (285H) .
- Please refer to the department website at http://euclid.trentu.ca/math for updated course information. MATH 2080 (280), 2084H (284H) , 2085H (285H) do not satisfy the mathematics requirement for a Bachelor of Science degree.
Bachelor of Science program in Mathematics
– See Degree Requirements for requirements which apply to all undergraduate degree programs.
– The same course may not simultaneously satisfy the requirements of both programs in a joint-major degree.
– C- (60%) or higher is required in a course if it is to serve as a prerequisite for another course in the program.
– The following core courses are required of all students in the Mathematics majors program: MATH 1100 (110), 1350H (135H), 2110H (201H), 2120H (202H) and 2350H (235H) .
– Most other courses in Mathematics are divided into four categories. Some courses appear in more than one category, but no course may fulfill more than one category requirement. For specific stream requirements for the major, see the table below. The courses listed below will be offered only if there is adequate staffing and student demand .
Category A
Analysis and Topology |
Category B
Algebra, Geometry, and Discrete Mathematics |
Category C
Modeling and Statistics |
Category D
Miscellaneous |
3720H (302H)
3160H (303H)
3150H (305H)
3770H (307H)
3790H (309H)
3700H (310H)
4160H (405H)
4770H (407H)
4790H (409H)
4700H (410H)
4330H (433H)
470
4710H (471H)
4720H (472H) |
2260H (226H)
260
2600H
3720H (302H)
3200H (320H)
3210H (321H)
322
3260H (326H)
330
3320H (332H)
3350H (335H)
3360H (336H)
341
3610H (361H)
4215H (415H)
4216H (416H)
4260H (426H)
4310H (431H)
4320H (432H)
4330H (433H)
4350H (435H)
4370H (437H)
460
4610H (461H)
4620H (462H) |
2180H (203H)
2150H (205H)
207H
2560H (256H)
3160H (303H)
3150H (305H)
308H
311
312
3130H (313H)
3140H (314H)
3510H (351H)
355
3560H (356H)
3570H (357H)
3610H (361H)
4180H (403H)
4160H (405H)
411
4120H (412H)
4130H (413H)
4510H (451H)
4560H (456H)
4561H
4562H
4563H
4570H (457H) |
2110H (201H)
2120H (202H)
2200H (220H)
2350H (235H)
380
3810H (381H)
3820H (382H)
3900 (390)
3901H (391H)
3902H (392H)
3903H (393H)
3904H (394H)
4810H
4820H (482H)
491H
492H
4903H (493H)
4904H (494H)
4950 (495) |
- An information meeting concerning upper level courses in Mathematics will be arranged in the Winter session.
The single-major Honours program. At least 11 credit in Mathematics, including:
– 3.0 credits consisting of MATH 1100 (110), 1350H (135H) , 2110H (201H), 2120H (202H) and 2350H (235H)
– 2.0 credits from one of categories A, B and C
– 2.0 credits from another one of categories A, B and C
– 0.5 credit from the remaining category of categories A, B, and C.
– 3.5 credits in addition to the above
– at least 6 of the credits beyond the 2000-level, including at least 2 at the 4000-level
The joint-major Honours program. At least 7.5 credits in Mathematics, including:
– 3.0 credits consisting of MATH 1100 (110), 1350H (135H), 2110H (201H), 2120H (202H) and 2350H (235H)
– 1.0 credit from one of categories A, B and C
– 1.0 credit from another one of categories A, B and C
– 0.5 credit from the remaining category of categories A, B, and C.
– 2.0 credits in addition to the above
– at least 3 of the credits beyond the 2000-level, including at least 1 at the 4000-level
The single-major General program. At least 6 credits in Mathematics, including:
– 3.0 credits consisting of MATH 1100 (110) , 1350H (135H) , 2110H (201H) , 2120H (202H) and 2350H (235H)
– 0.5 credit from one of categories A, B and C
– 0.5 credit from another one of categories A, B and C
– 2.0 credits in addition to the above
– at least 1 of the credits beyond the 2000-level
The joint-major General program. At least 5 credits in Mathematics, including:
– 3.0 credits consisting of MATH 1100 (110) , 1350H (135H) , 2110H (201H) , 2120H (202H) and 2350H (235H)
– 2.0 additional credits from categories A, B or C
– at least 1 of the credits beyond the 2000-level
SPECIALIZATION IN MATHEMATICAL FINANCE
The specialization in Mathematical Finance is available to students in the single-major Honours program in Mathematics. The transcripts of students graduating with an Honours degree in Mathematics, who have successfully completed the requirements of the Specialization, will contain the notation “with a Specialization in Mathematical Finance”.
The single-major Honours program with a Specialization in Mathematical Finance. At least 11 credits in Mathematics. The program must include:
– 10 credits in MATH consisting of MATH 1100 (110), 1350H (135H), 1550H (155H), 2110H (201H), 2120H (202H), 2180H (203H or 207H), 2150H (205H) , 2350H (235H), 2560H (256H), 3160H (303H or 308H), 3150H (305H), 3350H (335H), 3510H (351H), 3560H (356H), 3570H (357H), 3610H (361H), 4180H (403H), 4510H (451H) and 4570H (457H)
– 0.5 credit in MATH in addition to the above, at the 4000-level
– 0.5 credit in MATH in addition to the above, at the 3000- or 4000-level
– ECON 101H, 102H, and 302H
The following courses are recommended: COIS 1020H, MATH 4790H (409H) , 4120H (412H) , 4560H (456H)
SPECIALIZATION IN STATISTICS
The Specialization in Statistics (Honours) is available to students in the single or joint major Honours program in Mathematics. The transcripts of students graduating with a single or joint Honours degree in Mathematics who have successfully completed the requirements of the Specialization will contain the notation “with a Specialization in Statistics.”
Note:
• The following courses are strongly recommended for students planning to pursue graduate studies in statistics: MATH 2200H (220H), 3770H (307H), 3790H (309H) and 4790H (409H) and one credit in any writing-intensive course offered at Trent (for example, ENGL1000, PHIL101).
Courses Required for the Specialization:
– 2.5 MATH credits consisting of MATH 1550H (155H), 2150H (205H), 2180H (203H), 2560H (256H) and 3560H (356H)
– 0.5 MATH credits from MATH 4561H or 4562H
– 2.0 credits in addition to the above from 3570H (357H), 4560H (456H), 4561H, 4562H, 4563H, 4570H (457H), 4850 or COIS 4400H
– 1.0 COIS credit consisting of COIS 1010H and 1020H
– a minor from another department at Trent, following the academic calendar, or 3 credits beyond the 2000-level from one program other than Mathematics.
Please consult the academic timetable, available through myTrent, for information on courses that will be offered in 2008-2009 including when they will be scheduled.
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. Not available to students enrolled in or with credit for MATH 1100 (110). Not for credit towards a major or minor in Mathematics. Prerequisite: A Grade 12U mathematics course, or its equivalent. Excludes Math 105H.
MATH 1050 – A non-calculus-based introduction to probability and statistical methods
Data summary, elementary probability, estimation, hypothesis testing, comparative methods, analysis of variance, regression, nonparametric methods, introduction to elementary applications of statistical computing. 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 1100 (110) or 2560H (256H) . Excludes Math 150.
MATH 1100 – 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. Prerequisite: Grade 12 Advanced Functions or equivalent with at least 60% or permission of instructor. Strongly Recommended: Grade 12U Calculus and Vectors. Excludes MATH 110.
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. Excludes MATH 135H.
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. Pre- or co-requisite or permission of instructor: MATH 1005H (105H) or 1100 (110). Excludes MATH 155H.
MATH 2080 – 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. This course cannot be used toward the mathematics requirement for a B.Sc. Normally open only to students who are in the Concurrent Education program or who are pursuing the Emphasis in Teacher Education. Permission of the department required. Excludes MATH 280 and any Mathematics course, or its equivalent, which counts toward a major or minor in Mathematics.
MATH 2084H – Recreational mathematics
A look at parts of mathematics that are done for fun. Topics may include magic squares, logic puzzles, toys and tricks with mathematical content, polygonal dissections and tiling problems. We will also look at the mathematical theories behind these puzzles and surprising phenomena. Prerequisite: Grade 12 Mathematics credit or equivalent and two full credits in any subject(s) at the 100 level with at least 60% or permission of instructor. Not for credit towards a major or minor in mathematics. Excludes MATH 284H.
MATH 2085H – The mathematics of art, architecture and music
This interdisciplinary course explores how mathematics can be used to understand art, and how artists are inspired by mathematics. Topics include: Symmetry (tilings, crystallography) . Self-similarity and fractals. The Golden ratio and Fibonacci sequence. Musical harmony. Modular arithmetic. Self-reference and recursion. Architecture. Labyrinths. Art and literature inspired by mathematics. Prerequisite: Grade 12 Mathematics credit or equivalent and two full credits in any subject(s) at the 100 level with at least 60% or permission of the instructor. It is suggested that students take MATH 2260H (226H) or CUST 211, 216 or 245 or CUST – ENGL 229 before or along with this course. Not for credit towards a major or minor in mathematics. Excludes MATH 285H.
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: MATH 1100 (110) with at least 60%. Pre- or co-requisite: Math 1350H (135H) with at least 60% or permission of instructor. Excludes MATH 200 and 201H.
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: MATH 2110H (201H) with at least 60% or permission of instructor. Excludes MATH 200 and 202H.
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: MATH 1100 (110) with at least 60% or permission of instructor. Recommended: MATH 1350H (135H). Excludes MATH – PHYS 205H.
MATH – COIS 2180H – Introduction to numerical and computational methods
Error analysis, non-linear equations, linear systems, interpolation methods, numerical differentiation and integration and initial value problems. Prerequisite: MATH 1005H (105H) or 1100 (110) with at least 60% or permission of instructor. Excludes MATH 207H and MATH – COSC 203H.
MATH 2200H – Mathematical Reasoning
This course and 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. Pre- or co-requisite: MATH 1100 (or 110) and MATH 1350H (or 135H) with at least 60% or permission of instructor. Excludes MATH 220H.
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: either MATH 1005H (105H) or 1100 (110) or 1350H (135H) with at least 60% or permission of instructor. Excludes MATH 226H.
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: MATH 1350H (135H) with at least 60% or permission of instructor. Excludes MATH 235H.
MATH 2560H – Introduction to statistical inference
Introduction to mathematical statistics: Methods of point estimation, confidence intervals, hypotheses testing, comparative inferences, nonparametric methods. Assumes a background in probability and calculus. Prerequisite: MATH 1550H (155H) with at least 60% or permission of instructor. Excludes MATH 355 and 256H.
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: either MATH 1100 (110) and 1350H (135H); or COIS 1020H (COSC 102H), MATH 1005H (105H) and 1350H (135H) with at least 60% or permission of instructor. Excludes MATH – COSC 260.
MATH – PHYS 3130H – Classical mechanics (see Physics & Astronomy)
Excludes MATH – PHYS 313H.
MATH – PHYS 3140H – Advanced classical mechanics (see Physics & Astronomy)
Excludes MATH – PHYS 314H.
MATH – PHYS 3150H – Partial differential equations
An introduction to methods for the solution of partial differential equations. Fourier analysis. Prerequisite: MATH 2150H (205H) . Co-requisite: MATH 2110H (201H) with at least 60% or permission of instructor. Strongly recommended: MATH 1350H (135H) . Recommended: MATH 2200H (220H). Excludes MATH – PHYS 305H.
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: MATH – PHYS 2150H (205H) with at least 60% or permission of instructor. Recommended: MATH 2200H (220H). Excludes MATH 308H and 303H.
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: MATH 1350H (135H) and 2200H (220H) with at least 60% or permission of instructor. Excludes MATH 322 and 320H
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: MATH 2200H (220H) with at least 60% 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.
MATH 3260H – Geometry II: Projective and non-Euclidean geometry
Elements of projective and non-Euclidean geometry, including an introduction to axiomatic systems. Prerequisite: MATH 1350H (135H) with at least 60% or permission of instructor. Excludes MATH 326H.
MATH 3320H – Groups and symmetry
Geometric symmetry groups. Transformation groups (permutations, matrices) . Abstract groups. Cyclic and abelian groups. Generators. (Normal) subgroups, cosets, Lagrange’s theorem. Homomorphisms and quotient groups. The four Isomorphism Theorems. Direct products; structure theory. Group actions. Basic ring theory (if preceding MATH 4310H [431H]) or free groups and group presentations (if preceding MATH 4330H [433H]). Prerequisite: MATH 2350H (235H) and 2200H (220H) with at least 60% or permission of instructor. Excludes MATH 330 and 332H.
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: MATH 1350H (135H) with at least 60% or permission of instructor. Excludes MATH – COSC 335H.
MATH 3360H – Rings and fields
Rings and subrings (e.g. integers, polynomials, functions, matrices) . Homomorphisms, quotient rings, and ideals. The four Isomorphism Theorems. Divisibility, zero divisors, integral domains. Principal ideal domains, Euclidean domains and unique factorization domains. Fields and field extensions. Basic group theory (if preceding MATH 4350H (435H), or commutative ideal theory (if preceding MATH 4370H (437H) . Prerequisite: MATH 2350H (235H) and 2200H (220H) with at least 60% or permission of instructor. Excludes MATH 330 and 336H.
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. Prerequisite: MATH 1550H (155H) and 2150H (205H) with at least 60% or permission of instructor. Excludes MATH 351H.
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: Mathematics 2560H (256H) with at least 60% or permission of instructor. Strongly recommended: Mathematics 1350H (135H). Excludes MATH 355 and 356H.
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: MATH 1350H (135H) and 1550H (155H) with at least 60% or permission of instructor. Excludes MATH 357H.
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: MATH 1350H (135H) together with one of Math 2200H (220H) or MATH – COIS 2600H or MATH – COSC 260 with at least 60% or permission of instructor. Excludes MATH 361H.
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, separable, 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: MATH 2120H (202H) and 2200H (220H) , and one of MATH 3720H (302H) 3770H (307H) or 3790H (309H) with at least 60% or permission of instructor. Excludes MATH 310H.
MATH 3720H – Differential geometry
Tensor calculus: (co) vector fields and frame fields; multilinear forms and differential forms. Surfaces and coordinate patches. Differential forms: integration, Stokes theorem and topological consequences. Connection forms. Gaussian curvature; Theorema Egregium. Optional: Frenet’s theory of curves. Mean curvature and minimal surfaces. (pseudo) Riemannian geometry and Einstein manifolds. Simplectic geometry and Hamiltonian manifolds. Prerequisite: MATH 2120H (202H) , 2200H (220H) and 2350H (235H) with at least 60% or permission of instructor. Excludes MATH 302H.
MATH 3770H – Complex analysis
Functions of a complex variable, analytic functions, complex integrals, Cauchy integral theorems, Taylor series, Laurent series, residue calculus. Prerequisite: MATH 2120H (202H) or 200 with at least 60% or permission of instructor. Excludes MATH 306H and 307H.
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: MATH 1100 (110), with at least 60%. Pre- or co-requisite: Math 2200H (220H) with at least 60% or permission of instructor. Excludes MATH 206H and 309H.
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: MATH 1100 (110) with at least 60% or permission of instructor. Recommended: MATH 2200H (220H) or 2350H (235H). Excludes MATH 380 and 381H.
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: MATH 1100 (110) with at least 60% or permission of instructor. Recommended: MATH 2200H (220H) or 2350H (235H). Excludes MATH 380 and 382H.
MATH 3900 – Reading-seminar course
Details may be obtained by consulting the department.
MATH 3901H, 3902H, 3903H, 3904H – Reading-seminar courses
Details may be obtained by consulting the department.
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: MATH – PHYS 2150H (205H) with at least 60% or permission of instructor. Excludes MATH 411 and 412H.
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: MATH 4120H (412H) and one of MATH – PHYS 3180H or 3150H (305H) with at least 60% or permission of instructor. Excludes MATH 411 and 413H.
MATH 4160H – Advanced methods of applied mathematics
This course deals with a variety of applied mathematics techniques, focussing on dimensional analysis and scaling, perturbation techniques for algebraic and differential equations, and asymptotic expansions 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 asymptotic expansions. Prerequisite: MATH 2150H (205H) and 3160H with at least 60% or permission of instructor. Recommended: Math 2200H (220H). Excludes MATH 405H.
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: MATH 2180H (203H) and 2150H (205H) with at least 60% or permission of instructor. Excludes MATH 403H.
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: MATH – COIS 2600H or MATH – COSC 260 with at least 60% or permission of instructor. Excludes MATH – COSC 415H.
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: COIS 3050H (COSC 305H) or MATH – COIS 4215H (MATH – COSC 415H) with at least 60% or permission of instructor. Excludes MATH – COSC 416H.
MATH 4260H – Topics in geometry
Excludes MATH 426H.
MATH 4263H – Projective geometry
Projective lines and projective planes, and their combinatorial properties. Collineations, transitivity, Desargue’s Theorem. Coordinates and ternary rings. Constructing projective planes using affine planes, skew fields and free completions. Prerequisite: 2260H (226H) or 3260H (326H) with at least 60% or permission of instructor.
MATH 4310H – Algebra IV: Galois theory
Extension fields and Galois groups. The Fundamental Theorem of Galois Theory. The insolubility of the quintic. Prerequisite: MATH 3320H (332H) with at least 60% or permission of instructor. Excludes MATH 431H.
MATH 4320H – Algebra V: Topics in algebra
Prerequisite: 3320H (332H) or 330 or 3360H (336H) with at least 60% or permission of instructor. Excludes MATH 432H.
MATH 4330H – Homological algebra and algebraic topology
Homotopy of paths and functions. Fundamental group: covering spaces, Seifert-van Kampen theorem. Higher homotopy groups. Categories and functors. Homological algebra: chain complexes and their homology groups, long exact sequences. Simplicial (co) homology groups: simplicial complexes, Mayer-Vietoris sequences, Euler-Poincare characteristic, Poincare duality. Optional: applications to fixed point theorems. Prerequisite: MATH 3320H (332H) and 2110H (201H) with at least 60% or permission of instructor. Recommended: MATH 2120H (202H) or 3770H (307H) . Excludes MATH 433H.
MATH 4350H – Modules, multilinear algebra, and linear groups
Modules, submodules, and module homomorphisms. The structure theory of finitely generated modules over principal ideal domains. The rational canonical form and Jordan canonical form for linear operators. Spectral theory. Linear groups. Dual spaces. Bilinear forms, Multilinear functions and tensor algebra. Group representation theory; Schur’s lemma. Projective and injective modules. Prerequisite: MATH 3360H (336H) with at least 60% or permission of instructor. Recommended: MATH 3320H (332H) . Excludes MATH 435H.
MATH 4370H – Commutative algebra and algebraic geometry
Affine and projective algebraic varieties over the complex numbers and other algebraically complete fields. Hilbert basis theorem, Zariski topology, and Nullstellensatz. Coordinate rings, (iso) morphisms, (bi) rational maps. Tangent spaces and dimension. Applications to elliptic curves and cubic surfaces. Prerequisite: MATH 3360H (336H) and 2110H (201H) with at least 60% or permission of instructor. Excludes MATH 437H.
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: MATH 1550H (155H) and 2150H (205H) with at least 60% or permission of instructor. Excludes MATH 451H.
MATH 4560H – Topics in statistics
Prerequisite: MATH 2560H (256H) with at least 60% or permission of instructor. Strongly recommended: Math 3560H (356H). Excludes MATH 456H.
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: MATH 2560H (256H), with at least 60% 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 experiments. 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: MATH 2560H (256H), with at least 60% or permission of instructor. Recommended: MATH 3560H (356H) .
MATH 4563H – Foundations of research design and data analysis
Students enrolled in this course will follow the course syllabus for BIOL – ERSC 403H (please consult course description for the latter) . Students registered in MATH 4563H will complete assignments for BIOL – ERSC 403H, with theoretical assignments replacing some of the labs required there. Prerequisite: MATH 2560H (256H) and 3560H (356H) with at least 60% or permission of instructor.
MATH 4570H – Topics in probability: A second course in stochastic processes. Stochastic calculus and stochastic differential equations. Prerequisite: MATH 3570H (357H) with at least 60% or permission of instructor. Excludes MATH 457H.
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: either MATH – COIS 2600H or MATH – COSC 260 and Math 2200H (220H) with at least 60% or permission of instructor. Excludes MATH 461H.
MATH 4620H – Introduction to combinatorics
An introduction to combinatorics. The topics include counting techniques, generating functions and block design. Prerequisite: MATH 2200H (220H) with at least 60% or permission of instructor. Excludes MATH 460 and 462H.
MATH 4700H – Topology III: Topics in topology
Prerequisite: 3700H (310H) with at least 60% or permission of instructor. Excludes MATH 410H.
MATH 4710H – Chaos, symbolic dynamics, fractals
An introduction to discrete dynamical systems. Periodicity, attraction. Parametrized families of functions, bifurcation, chaos. Symbolic dynamics, conjugacy, Cantor Sets. Deterministic fractals, fractal dimension, Lyapunov exponents, entropy. Prerequisite: MATH 3700H (310H) with at least 60% or permission of instructor. Excludes MATH 470 and 471H.
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: MATH 4710H (471H) with at least 60% or permission of instructor. Excludes MATH 470 and 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: MATH 3770H (307H) with at least 60% or permission of instructor. Excludes MATH 407H.
MATH 4790H – Analysis III: Measure and integration
Riemann and Lebesgue measure, integration. Prerequisite: MATH 3700H (310H) with at least 60% or permission of instructor. Excludes MATH 406H and 409H.
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: One 300-level MATH credit with at least 60% or permission of instructor. Excludes MATH 491H and 481H.
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: One 300-level MATH credit with at least 60% or permission of instructor . Excludes MATH 492H and 482H.
MATH 4850 – 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’ (p. 226). Prerequisite: MATH 2560H and either MATH 3560H or 4561H or 4562H and a cumulative average of at least 75%.
MATH 4900 – Reading-seminar course
Details may be obtained by consulting the department.
MATH 4903H, 4904H (494H) – Reading-seminar courses
Details may be obtained by consulting the department.
MATH 4950 – Special topics
Details may be obtained by consulting the department.
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