Academic Calendar - 2018

Western University Academic Calendar. - 2018

Courses


Course Numbering

0001-0999* Pre-University level introductory courses
1000-1999 Year 1 courses
2000-4999 Senior-level undergraduate courses
5000-5999 Professional Degree courses in Dentistry, Education, Law, Medicine and Theology (MTS, MDiv)
6000-6999 Courses offered by Continuing Studies
9000-9999 Graduate Studies courses

* These courses are equivalent to pre-university introductory courses and may be counted for credit in the student's record, unless these courses were taken in a preliminary year. They may not be counted toward essay or breadth requirements, or used to meet modular admission requirements unless it is explicitly stated in the Senate-approved outline of the module.


Suffixes

no suffix 1.0 course not designated as an essay course
A 0.5 course offered in first term
B 0.5 course offered in second term
A/B 0.5 course offered in first and/or second term
E 1.0 essay course
F 0.5 essay course offered in first term
G 0.5 essay course offered in second term
F/G 0.5 essay course offered in first and/or second term
H 1.0 accelerated course (8 weeks)
J 1.0 accelerated course (6 weeks)
K 0.75 course
L 0.5 graduate course offered in summer term (May - August)
Q/R/S/T 0.25 course offered within a regular session
U 0.25 course offered in other than a regular session
W/X 1.0 accelerated course (full course offered in one term)
Y 0.5 course offered in other than a regular session
Z 0.5 essay course offered in other than a regular session

Glossary


Prerequisite

A course that must be successfully completed prior to registration for credit in the desired course.


Corequisite

A course that must be taken concurrently with (or prior to registration in) the desired course.


Antirequisite

Courses that overlap sufficiently in course content that both cannot be taken for credit.


Essay Courses

Many courses at Western have a significant writing component. To recognize student achievement, a number of such courses have been designated as essay courses and will be identified on the student's record (E essay full course; F/G/Z essay half-course).


Principal Courses

A first year course that is listed by a department offering a module as a requirement for admission to the module. For admission to an Honors Specialization module or Double Major modules in an Honors Bachelor degree, at least 3.0 courses will be considered principal courses.



Campus





Course Level






Course Type




Mathematics


Set theory, algebra, functions and relations, trigonometry, logarithms and exponents.

Antirequisite(s): Ontario Secondary School MCV4U, any university level calculus course.

Prerequisite(s): One or more of Ontario Secondary School MCF3M, MCR3U, or equivalent.

Extra Information: 3 hours.

Course Weight: 0.50
More details

This course is also offered at:

King's

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Set theory, algebra, functions and relations, trigonometry, logarithms and exponents.

Antirequisite(s): Ontario Secondary School MCV4U, any university level calculus course.

Prerequisite(s): One or more of Ontario Secondary School MCF3M, MCR3U, or equivalent.

Extra Information: 3 hours.

Course Weight: 0.50
More details

This course is also offered at:

Brescia

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Introduction to differential calculus including limits, continuity, definition of derivative, rules for differentiation, implicit differentiation, velocity, acceleration, related rates, maxima and minima, exponential functions, logarithmic functions, differentiation of exponential and logarithmic functions, curve sketching.


Prerequisite(s): One or more of Ontario Secondary School MCF3M, MCR3U, or equivalent.

Extra Information: 4 lecture hours.

Course Weight: 0.50
More details

This course is also offered at:

Huron King's Brescia

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Introduction to differential calculus including limits, continuity, definition of derivative, rules for differentiation, implicit differentiation, velocity, acceleration, related rates, maxima and minima, exponential functions, logarithmic functions, differentiation of exponential and logarithmic functions, curve sketching.


Prerequisite(s): One or more of Ontario Secondary School MCF3M, MCR3U, or equivalent.

Extra Information: 4 lecture hours.

Course Weight: 0.50
More details

This course is also offered at:

Western Main Campus Huron King's

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Introduction to differential calculus including limits, continuity, definition of derivative, rules for differentiation, implicit differentiation, velocity, acceleration, related rates, maxima and minima, exponential functions, logarithmic functions, differentiation of exponential and logarithmic functions, curve sketching.


Prerequisite(s): One or more of Ontario Secondary School MCF3M, MCR3U, or equivalent.

Extra Information: 4 lecture hours.

Course Weight: 0.50
More details

This course is also offered at:

Western Main Campus King's Brescia

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Introduction to differential calculus including limits, continuity, definition of derivative, rules for differentiation, implicit differentiation, velocity, acceleration, related rates, maxima and minima, exponential functions, logarithmic functions, differentiation of exponential and logarithmic functions, curve sketching.


Prerequisite(s): One or more of Ontario Secondary School MCF3M, MCR3U, or equivalent.

Extra Information: 4 lecture hours.

Course Weight: 0.50
More details

This course is also offered at:

Western Main Campus Huron Brescia

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Primarily for students interested in pursuing a degree in one of the mathematical sciences. Logic, set theory, relations, functions and operations, careful study of the integers, discussion of the real and complex numbers, polynomials, and infinite sets.

Antirequisite(s): Mathematics 2155F/G, or the former Mathematics 2155A/B.

Prerequisite(s): One or more of Ontario Secondary School MCV4U, Mathematics 1600A/B.

Extra Information: 4 lecture hours.

Course Weight: 0.50
More details
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Elementary techniques of integration; applications of Calculus such as area, volume, and differential equations; functions of several variables, Lagrange multipliers. This course is intended primarily for students in the Social Sciences, but may meet minimum requirements for some Science modules. It may not be used as a prerequisite for any Calculus course numbered 1300 or above.

Antirequisite(s) at Main campus: Applied Mathematics 1201A/B, Applied Mathematics 1413, Calculus 1301A/B, Calculus 1501A/B, Mathematics 1230A/B. If Calculus 1000A/B or Calculus 1500A/B was completed after September 1, 2016 it is an antirequisite, but not if it was completed before that time. Antirequisite(s) at Brescia, Huron, King's campus: Applied Mathematics 1201A/B, Applied Mathematics 1413, Calculus 1301A/B, Calculus 1501A/B, Mathematics 1230A/B, Calculus 1000A/B or Calculus 1500A/B taken after September 1, 2016.

Prerequisite(s): Ontario Secondary School MCV4U or Mathematics 0110A/B.

Extra Information: 3 lecture hours.

Course Weight: 0.50
More details

This course is also offered at:

Huron King's Brescia

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Elementary techniques of integration; applications of Calculus such as area, volume, and differential equations; functions of several variables, Lagrange multipliers. This course is intended primarily for students in the Social Sciences, but may meet minimum requirements for some Science modules. It may not be used as a prerequisite for any Calculus course numbered 1300 or above.

Antirequisite(s) at Main campus: Applied Mathematics 1201A/B, Applied Mathematics 1413, Calculus 1301A/B, Calculus 1501A/B, Mathematics 1230A/B. If Calculus 1000A/B or Calculus 1500A/B was completed after September 1, 2016 it is an antirequisite, but not if it was completed before that time. Antirequisite(s) at Brescia, Huron, King's campus: Applied Mathematics 1201A/B, Applied Mathematics 1413, Calculus 1301A/B, Calculus 1501A/B, Mathematics 1230A/B, Calculus 1000A/B or Calculus 1500A/B taken after September 1, 2016.

Prerequisite(s): Ontario Secondary School MCV4U or Mathematics 0110A/B.

Extra Information: 3 lecture hours.

Course Weight: 0.50
More details

This course is also offered at:

Western Main Campus Huron King's

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Elementary techniques of integration; applications of Calculus such as area, volume, and differential equations; functions of several variables, Lagrange multipliers. This course is intended primarily for students in the Social Sciences, but may meet minimum requirements for some Science modules. It may not be used as a prerequisite for any Calculus course numbered 1300 or above.

Antirequisite(s) at Main campus: Applied Mathematics 1201A/B, Applied Mathematics 1413, Calculus 1301A/B, Calculus 1501A/B, Mathematics 1230A/B. If Calculus 1000A/B or Calculus 1500A/B was completed after September 1, 2016 it is an antirequisite, but not if it was completed before that time. Antirequisite(s) at Brescia, Huron, King's campus: Applied Mathematics 1201A/B, Applied Mathematics 1413, Calculus 1301A/B, Calculus 1501A/B, Mathematics 1230A/B, Calculus 1000A/B or Calculus 1500A/B taken after September 1, 2016.

Prerequisite(s): Ontario Secondary School MCV4U or Mathematics 0110A/B.

Extra Information: 3 lecture hours.

Course Weight: 0.50
More details

This course is also offered at:

Western Main Campus King's Brescia

Return to top
Elementary techniques of integration; applications of Calculus such as area, volume, and differential equations; functions of several variables, Lagrange multipliers. This course is intended primarily for students in the Social Sciences, but may meet minimum requirements for some Science modules. It may not be used as a prerequisite for any Calculus course numbered 1300 or above.

Antirequisite(s) at Main campus: Applied Mathematics 1201A/B, Applied Mathematics 1413, Calculus 1301A/B, Calculus 1501A/B, Mathematics 1230A/B. If Calculus 1000A/B or Calculus 1500A/B was completed after September 1, 2016 it is an antirequisite, but not if it was completed before that time. Antirequisite(s) at Brescia, Huron, King's campus: Applied Mathematics 1201A/B, Applied Mathematics 1413, Calculus 1301A/B, Calculus 1501A/B, Mathematics 1230A/B, Calculus 1000A/B or Calculus 1500A/B taken after September 1, 2016.

Prerequisite(s): Ontario Secondary School MCV4U or Mathematics 0110A/B.

Extra Information: 3 lecture hours.

Course Weight: 0.50
More details

This course is also offered at:

Western Main Campus Huron Brescia

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Permutations and combinations; probability theory. This course is intended primarily for students in the Social Sciences, but may meet minimum requirements for some Science modules.


Prerequisite(s): One or more of Ontario Secondary School MCV4U, MHF4U, MDM4U, Mathematics 0110A/B, Mathematics 1225A/B, Mathematics 1229A/B.

Extra Information: 3 lecture hours.

Course Weight: 0.50
More details

This course is also offered at:

Huron King's Brescia

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Permutations and combinations; probability theory. This course is intended primarily for students in the Social Sciences, but may meet minimum requirements for some Science modules.


Prerequisite(s): One or more of Ontario Secondary School MCV4U, MHF4U, MDM4U, Mathematics 0110A/B, Mathematics 1225A/B, Mathematics 1229A/B.

Extra Information: 3 lecture hours.

Course Weight: 0.50
More details

This course is also offered at:

Western Main Campus Huron King's

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Permutations and combinations; probability theory. This course is intended primarily for students in the Social Sciences, but may meet minimum requirements for some Science modules.


Prerequisite(s): One or more of Ontario Secondary School MCV4U, MHF4U, MDM4U, Mathematics 0110A/B, Mathematics 1225A/B, Mathematics 1229A/B.

Extra Information: 3 lecture hours.

Course Weight: 0.50
More details

This course is also offered at:

Western Main Campus King's Brescia

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Permutations and combinations; probability theory. This course is intended primarily for students in the Social Sciences, but may meet minimum requirements for some Science modules.


Prerequisite(s): One or more of Ontario Secondary School MCV4U, MHF4U, MDM4U, Mathematics 0110A/B, Mathematics 1225A/B, Mathematics 1229A/B.

Extra Information: 3 lecture hours.

Course Weight: 0.50
More details

This course is also offered at:

Western Main Campus Huron Brescia

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Matrix algebra including vectors and matrices, linear equations, determinants. This course is intended primarily for students in the Social Sciences, but may meet minimum requirements for some Science modules.


Prerequisite(s): One or more of Ontario Secondary School MCF3M, MCR3U, or equivalent.

Extra Information: 3 lecture hours.

Course Weight: 0.50
More details

This course is also offered at:

Huron King's Brescia

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Matrix algebra including vectors and matrices, linear equations, determinants. This course is intended primarily for students in the Social Sciences, but may meet minimum requirements for some Science modules.


Prerequisite(s): One or more of Ontario Secondary School MCF3M, MCR3U, or equivalent.

Extra Information: 3 lecture hours.

Course Weight: 0.50
More details

This course is also offered at:

Western Main Campus Huron King's

Return to top
Matrix algebra including vectors and matrices, linear equations, determinants. This course is intended primarily for students in the Social Sciences, but may meet minimum requirements for some Science modules.


Prerequisite(s): One or more of Ontario Secondary School MCF3M, MCR3U, or equivalent.

Extra Information: 3 lecture hours.

Course Weight: 0.50
More details

This course is also offered at:

Western Main Campus King's Brescia

Return to top
Matrix algebra including vectors and matrices, linear equations, determinants. This course is intended primarily for students in the Social Sciences, but may meet minimum requirements for some Science modules.


Prerequisite(s): One or more of Ontario Secondary School MCF3M, MCR3U, or equivalent.

Extra Information: 3 lecture hours.

Course Weight: 0.50
More details

This course is also offered at:

Western Main Campus Huron Brescia

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Review of differential calculus with transcendental functions; methods of integration; constrained and unconstrained multivariable optimization, with applications; mathematical modelling with differential equations, including applications in management, finance, economics, and social science.


Prerequisite(s): One or more of Ontario Secondary School MCV4U, Mathematics 0110A/B.

Extra Information: 4 lecture hours.

Course Weight: 0.50
More details

This course is also offered at:

Huron King's

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Review of differential calculus with transcendental functions; methods of integration; constrained and unconstrained multivariable optimization, with applications; mathematical modelling with differential equations, including applications in management, finance, economics, and social science.


Prerequisite(s): One or more of Ontario Secondary School MCV4U, Mathematics 0110A/B.

Extra Information: 4 lecture hours.

Course Weight: 0.50
More details

This course is also offered at:

King's Brescia

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Review of differential calculus with transcendental functions; methods of integration; constrained and unconstrained multivariable optimization, with applications; mathematical modelling with differential equations, including applications in management, finance, economics, and social science.


Prerequisite(s): One or more of Ontario Secondary School MCV4U, Mathematics 0110A/B.

Extra Information: 4 lecture hours.

Course Weight: 0.50
More details

This course is also offered at:

Huron Brescia

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Properties and applications of vectors; matrix algebra; solving systems of linear equations; determinants; vector spaces; orthogonality; eigenvalues and eigenvectors.


Prerequisite(s): One or more of Ontario Secondary School MCV4U, Mathematics 1229A/B, Calculus 1000A/B or Calculus 1500A/B, the former Calculus 1100A/B. Calculus 1000A/B or Calculus 1500A/B may be taken as a pre-or corequisite.

Extra Information: 3 lecture hours, 1 laboratory hour.

Course Weight: 0.50
More details

This course is also offered at:

Huron King's Brescia

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Properties and applications of vectors; matrix algebra; solving systems of linear equations; determinants; vector spaces; orthogonality; eigenvalues and eigenvectors.


Prerequisite(s): One or more of Ontario Secondary School MCV4U, Mathematics 1229A/B, Calculus 1000A/B or Calculus 1500A/B, the former Calculus 1100A/B. Calculus 1000A/B or Calculus 1500A/B may be taken as a pre-or corequisite.

Extra Information: 3 lecture hours, 1 laboratory hour.

Course Weight: 0.50
More details

This course is also offered at:

Western Main Campus Huron King's

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Properties and applications of vectors; matrix algebra; solving systems of linear equations; determinants; vector spaces; orthogonality; eigenvalues and eigenvectors.


Prerequisite(s): One or more of Ontario Secondary School MCV4U, Mathematics 1229A/B, Calculus 1000A/B or Calculus 1500A/B, the former Calculus 1100A/B. Calculus 1000A/B or Calculus 1500A/B may be taken as a pre-or corequisite.

Extra Information: 3 lecture hours, 1 laboratory hour.

Course Weight: 0.50
More details

This course is also offered at:

Western Main Campus King's Brescia

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Properties and applications of vectors; matrix algebra; solving systems of linear equations; determinants; vector spaces; orthogonality; eigenvalues and eigenvectors.


Prerequisite(s): One or more of Ontario Secondary School MCV4U, Mathematics 1229A/B, Calculus 1000A/B or Calculus 1500A/B, the former Calculus 1100A/B. Calculus 1000A/B or Calculus 1500A/B may be taken as a pre-or corequisite.

Extra Information: 3 lecture hours, 1 laboratory hour.

Course Weight: 0.50
More details

This course is also offered at:

Western Main Campus Huron Brescia

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A rigorous development of lines and planes in Rn; linear transformations and abstract vector spaces. Determinants and an introduction to diagonalization and its applications including the characteristic polynomials, eigenvalues and eigenvectors.

Antirequisite(s): Mathematics 2211A/B.

Prerequisite(s): Mathematics 1600A/B.

Extra Information: 3 lecture hours.

Course Weight: 0.50
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A rigorous introduction to analysis on the real line. Sets and functions, logic and mathematical proof, the natural and real numbers, completeness and its consequences, limits of sequences, limits of real functions, continuity and uniform continuity.

Prerequisite(s): Calculus 1501A/B or Applied Mathematics 1413, with a minimum mark of 60%, or Calculus 1301A/B with a minimum mark of 85%.

Extra Information: 3 lecture hours, 1 tutorial hour.

Course Weight: 0.50
More details
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Primarily for Mathematics students, but will interest other students with ability in and curiosity about mathematics in the modern world as well as in the past. Stresses development of students' abilities to solve problems and construct proofs. Topics will be selected from: counting, recurrence, induction; number theory; graph theory; parity, symmetry; geometry.

Prerequisite(s): Calculus 1501A/B or Applied Mathematics 1413, with a minimum mark of 60%, or Calculus 1301A/B with a minimum mark of 85%.

Extra Information: 3 lecture hours.

Course Weight: 0.50
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Logic, sets and functions, algorithms, mathematical reasoning, counting, relations, graphs, trees, Boolean Algebra, computation, modeling.

Antirequisite(s): Mathematics 2155F/G, the former Mathematics 2155A/B, the former Software Engineering 2251A/B.


Extra Information: 3 lecture hours. Note: this course is offered only to software engineering students enrolled in the Faculty of Engineering.

Course Weight: 0.50
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This course provides an introduction to logical reasoning and proofs. Topics include sets, counting (permutations and combinations), mathematical induction, relations and functions, partial order relations, equivalence relations, binary operations, elementary group theory and applications to error-correcting codes.

Antirequisite(s): Mathematics 2151A/B or the former Software Engineering 2251A/B, the former Mathematics 2155A/B.

Prerequisite(s): 1.0 course from: Mathematics 1120A/B, Mathematics 1600A/B, Applied Mathematics 1413, Calculus 1000A/B, Calculus 1500A/B, Calculus 1301A/B, Calculus 1501A/B, or the former Calculus 1100A/B, in each case with a minimum mark of 60%; or permission of the department.

Extra Information: 3 lecture hours.

Course Weight: 0.50
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This course continues the development of logical reasoning and proofs begun in Mathematics 2155F/G. Topics include elementary number theory (gcd, lcm, Euclidean algorithm, congruences, Chinese remainder theorem) and graph theory (connectedness, complete, regular and bipartite graphs; trees and spanning trees, Eulerian and Hamiltonian graphs, planar graphs; vertex, face and edge colouring; chromatic polynomials).

Prerequisite(s): Mathematics 2155F/G or the former Mathematics 2155A/B.

Extra Information: 3 lecture hours.

Course Weight: 0.50
More details
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Linear transformations, matrix representation, rank, change of basis, eigenvalues and eigenvectors, inner product spaces, quadratic forms and conic sections. Emphasis on problem-solving rather than theoretical development. Cannot be taken for credit by students in honors Mathematics programs.


Prerequisite(s): Mathematics 1600A/B.

Extra Information: 3 lecture hours.

Course Weight: 0.50
More details

This course is also offered at:

King's

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Linear transformations, matrix representation, rank, change of basis, eigenvalues and eigenvectors, inner product spaces, quadratic forms and conic sections. Emphasis on problem-solving rather than theoretical development. Cannot be taken for credit by students in honors Mathematics programs.


Prerequisite(s): Mathematics 1600A/B or the former Linear Algebra 1600A/B

Extra Information: 3 lecture hours.

Course Weight: 0.50
More details

This course is also offered at:

Western Main Campus

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A survey of some important basic concepts of mathematics in a historical setting, and in relation to the broader history of ideas. Topics may include: the evolution of the number concept, the development of geometry, Zeno's paradoxes.

Antirequisite(s): Philosophy 2251F/G.

Prerequisite(s): 1.0 course of university level Mathematics.

Extra Information: 3 lecture hours.

Course Weight: 0.50
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Properties of integers, rational, real and complex numbers: commutativity, associativity, distributivity. Polynomials, prime and irreducible elements. Rings, ideals, integral and Euclidean domains, fields, and unique factorization. First isomorphism theorem, quotient rings and finite fields. Introduction to groups.


Extra Information: 3 lecture hours.

Course Weight: 0.50
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An introduction to the theory of groups: cyclic, dihedral, symmetric, alternating; subgroups, quotient groups, homomorphisms, cosets, Lagrange's theorem, isomorphism theorems; group actions, class equation, p-groups, Sylow theorems; direct and semidirect products, wreath products, finite abelian groups; Jordan-Hölder theorem, commutator subgroup, solvable and nilpotent groups; free groups, generators and relations.


Extra Information: 3 lecture hours.

Course Weight: 0.50
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A continuation of the material of Mathematics 2120A/B including properties of complex numbers and the principal axis theorem; singular value decomposition; linear groups; similarity; Jordan canonical form; Cayley-Hamilton theorem; bilinear forms; Sylvester's theorem.

Antirequisite(s): The former Mathematics 2121A/B.

Prerequisite(s): Mathematics 2120A/B.

Extra Information: 3 lecture hours.

Course Weight: 0.50
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Differentiation, the Mean Value Theorem, and integration. Metric spaces, including topology, convergence, compactness, completeness, and connectedness. Uniform convergence of functions. Selected additional topics.

Prerequisite(s): Mathematics 2122A/B or the former Mathematics 2123A/B, each with a minimum mark of 60%.

Extra Information: 3 lecture hours, 1 tutorial hour.

Course Weight: 0.50
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Rigorous introduction to ordinary differential equations. Existence, uniqueness, and continuation of solutions. Linear systems with constant coefficients. Flows and dynamical systems. Series solutions.


Extra Information: 3 lecture hours.

Course Weight: 0.50
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The Cauchy-Riemann equations, elementary functions, branches of the logarithm and argument, Cauchy's integral theorem and formula, winding number, Liouville's theorem and the fundamental theorem of algebra, the identity theorem, the maximum modulus theorem, Taylor and Laurent expansions, isolated singularities, the residue theorem and applications, the argument principle and applications.

Antirequisite(s): Applied Mathematics 3811A/B.

Prerequisite(s): Mathematics 2122A/B.

Extra Information: 3 lecture hours.

Course Weight: 0.50
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Divisibility, primes, congruences, theorems of Fermat and Wilson, Chinese remainder theorem, quadratic reciprocity, some functions of number theory, diophantine equations, simple continued fractions.

Prerequisite(s): 1.0 course in Mathematics, Applied Mathematics, or Calculus at the 2100 level or higher.

Extra Information: 3 lecture hours.

Course Weight: 0.50
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Arithmetic functions, perfect numbers, the Möbius inversion formula, introduction to Dirichlet series and the Riemann zeta function, some methods of combinatorial number theory, primitive roots and their relationship with quadratic reciprocity, the Gaussian integers, sums of squares and Minkowski's theorem, square and triangular numbers, Pell's equation, introduction to elliptic curves.


Extra Information: 3 lecture hours.

Course Weight: 0.50
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Enumeration, recursion and generating functions, linear programming, Latin squares, block designs, binary codes, groups of symmetries, orbits, and counting.

Prerequisite(s): 0.5 course from: Mathematics 2120A/B, Mathematics 2155F/G, Mathematics 2211A/B, Applied Mathematics 2811B, or permission of the Department.

Extra Information: 3 lecture hours.

Course Weight: 0.50
More details
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Network problems: shortest path, spanning trees, flow problems, matching, routing. Complexity. Integer programming.

Prerequisite(s): One of: Mathematics 2156A/B, Mathematics 3152A/B, or permission of the Department.

Extra Information: 3 lecture hours.

Course Weight: 0.50
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Geometry of algebraic curves over the rational, real and complex fields. Classification of affine conics, singularities, intersection numbers, tangents, projective algebraic curves, multiplicity of points, flexes. Some discussion of cubic curves.

Prerequisite(s): Mathematics 1600A/B, Mathematics 2120A/B, Mathematics 2122A/B, Mathematics 2124A/B, Mathematics 2155F/G, Mathematics 3121A/B, the former Mathematics 2121A/B, or the former Mathematics 2155A/B; an additional 0.5 course in Mathematics, Applied Mathematics, Calculus at the 2100 level or above.

Extra Information: 3 lecture hours.

Course Weight: 0.50
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A first course in the mathematical theory of games. Topics begin with the modelling of games: extensive and strategic forms; perfect information; chance. Sprague-Grundy theory of impartial combinatorial games. Modelling preferences with utility functions. Nash equilibria, analysis of two-player games.


Extra Information: 3 lecture hours.

Course Weight: 0.50
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Modern cryptological algorithms will be discussed with an emphasis placed on their mathematical foundation. Main topics will include: basic number theory, complexity of algorithms, symmetric-key cryptosystems, public-key cryptosystems, RSA encryption, primality and factoring, discrete logarithms, elliptic curves and information theory.


Extra Information: 3 lecture hours.

Course Weight: 0.50
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Extra Information: 3 lecture hours.

Prerequisite(s): Permission of the Department.

Course Weight: 0.50
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Extra Information: 3 lecture hours.

Prerequisite(s): Permission of the Department.

Course Weight: 0.50
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Automorphisms of fields, separable and normal extensions, splitting fields, fundamental theorem of Galois theory, primitive elements, Lagrange's theorem. Finite fields and their Galois groups, cyclotomic extensions and polynomials, applications of Galois theory to geometric constructions and solution of algebraic equations.


Extra Information: 3 lecture hours.

Course Weight: 0.50
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Topological spaces, neighbourhoods, bases, subspaces, product and quotient spaces, connectedness, compactness, separation axioms.

Antirequisite(s): The former Mathematics 3132B.

Prerequisite(s): Mathematics 3122A/B.

Extra Information: 3 lecture hours.

Course Weight: 0.50
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Lebesgue measure, measurable sets and functions, Littlewood principles; the Lebesgue integral, basic convergence theorems, approximation theorems; measure spaces, signed measures, Radon-Nikodym Theorem.

Prerequisite(s): Mathematics 3122A/B.

Extra Information: 3 lecture hours.

Course Weight: 0.50
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Rings: fractions and localization, Chinese Remainder Theorem, factorization in commutative rings, Euclidean algorithm, PIDs, algebraic integers, polynomials and formal power series, factorization in polynomial rings; Modules: generation, direct products and sums, freeness, presentations, tensor algebras, exact sequences, projectivity, injectivity, Hom and duality, Zorn's Lemma, chain conditions, modules over PIDs.

Prerequisite(s): Mathematics 3020A/B.

Extra Information: 3 lecture hours. Note: It is recommended that Mathematics 3121A/B (or the former Math 2121A/B) be taken before or concurrently with Mathematics 4123A/B.

Course Weight: 0.50
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Algebraic numbers, cyclotomic fields, low dimensional Galois cohomology, Brauer groups, quadratic forms, local and global class fields, class field theory, Galois group representations, modular forms and elliptic curves, zeta function and L-series.

Prerequisite(s): Mathematics 4120A/B; Mathematics 3151A/B strongly recommended but not required.

Extra Information: 3 lecture hours.

Course Weight: 0.50
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Homotopy, fundamental group, Van Kampen's theorem, covering spaces, simplicial and singular homology, homotopy invariance, long exact sequence of a pair, excision, Mayer-Vietoris sequence, degree, Euler characteristic, cell complexes, projective spaces. Applications include the fundamental theorem of algebra, the Brouwer fixed point theorem, division algebras, and invariance of domain.

Prerequisite(s): Mathematics 3120A/B and either Mathematics 4121A/B or the former Mathematics 3132B.

Extra Information: 3 lecture hours.

Course Weight: 0.50
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Affine and projective varieties, coordinate rings and function fields, birational correspondences, sheaves, dimension theory, regularity.

Prerequisite(s): Mathematics 4123A/B.

Extra Information: 3 lecture hours.

Course Weight: 0.50
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Hilbert spaces: L^2 spaces, orthogonal complements, dual spaces, Riesz representation theorem, the Fredholm alternative, spectral resolution of compact normal operators. Banach spaces: Hahn-Banach theorem, bounded linear operators, adjoints, closed graph and Banach Steinhaus theorems.

Prerequisite(s): Mathematics 2120A/B, Mathematics 3122A/B. Pre-or Corequisite(s): Mathematics 3124A/B.

Extra Information: 3 lecture hours.

Course Weight: 0.50
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Manifolds (definition, examples, constructions), orientation, functions, partitions of unity, tangent bundle, cotangent bundle, vector fields, integral curves, differential forms, integration, manifolds with boundary, Stokes' theorem, submersions, immersions, embeddings, submanifolds, Sard's theorem, Whitney embedding theorem.

Prerequisite(s): Calculus 2503A/B and Mathematics 3122A/B.

Extra Information: 3 lecture hours.

Course Weight: 0.50
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Linear-fractional transformations, Schwarz's lemma, Reflection Principle, the Argument principle, the Riemann mapping theorem, Runge's theorem, the Mittag-Lefler and Weierstrass theorems.

Prerequisite(s): Mathematics 3124A/B.

Extra Information: 3 lecture hours.

Course Weight: 0.50
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Entire and meromorphic functions, infinite products, canonical products, the Weierstrass factorization and Mittag-Leffler theorems, the Hadamard factorization theorem; simply periodic and doubly periodic functions, elliptic functions; the Picard theorems (with Schottky's, Montel's, and Landau's theorems); the prime number theorem (with the Gamma and Riemann Zeta functions).

Prerequisite(s): Mathematics 4156A/B or Mathematics 3124A/B with the permission of the Department.

Extra Information: 3 lecture hours.

Course Weight: 0.50
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Set theory: axioms, ordinal numbers, transfinite induction, cardinality, the axiom of choice. Foundations of mathematics: construction of the real numbers from the natural numbers by one of the standard methods. First-order logic: propositional calculus, quantifiers, truth and satisfaction, models of first-order theories, consistency, completeness and compactness.

Prerequisite(s): Permission of the Department.

Extra Information: 3 lecture hours.

Course Weight: 0.50
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Extra Information: 3 lecture hours

Course Weight: 0.50
More details
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Extra Information: 3 lecture hours.

Prerequisite(s): Permission of the Department.

Course Weight: 0.50
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