Calculus 050a/b, 051a/b, 081a/b, 250a/b, 251a/b, 280a/b, and 281a/b are offered jointly by the Departments of Applied Mathematics and Mathematics.
Calculus 091a/b is offered by the Department of Applied Mathematics.
Differential Equations 215a is offered jointly by the Departments of Applied Mathematics and Mathematics.
Linear Algebra 040a/b is offered jointly by the Departments of Applied Mathematics and Mathematics.
Please refer to the CALCULUS (S), DIFFERENTIAL EQUATIONS (S), and LINEAR ALGEBRA (S) subjects for those first and second year course offerings.
Note: Combinations of the courses Mathematics 012a/b, 017a/b, 028a/b, 030, 031, Calculus 081a/b, Calculus 091a/b will not satisfy the Mathematics prerequisites of certain programs/modules offered by the Faculty of Science. |
| Mathematics 012a/b, Introductory Calculus | |
| | Description: 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. | | Antirequisite(s): Grade 12U Advanced Functions and Introductory Calculus (MCB4U), the former OAC Calculus, Applied Mathematics 026, Mathematics 030, Calculus 050a/b. | | Prerequisite(s): Grade 11 Functions (MCF3M), or Functions and Relations (MCR3U) or the former Ontario Grade 12 Advanced Level Mathematics or equivalent. | | 4 lecture hours, 0.5 course. | | back to top |
| Mathematics 017a/b, Algebra and Geometry | |
| | Description: Transformations and matrices, conic sections, vectors, linear combinations, equations of lines and planes, complex numbers, mathematical induction. | | Antirequisite(s): Grade 12U Geometry and Discrete Mathematics (MGA4U), the former OAC Algebra and Geometry; Linear Algebra 040a/b, Mathematics 030, 031, Applied Mathematics 025a/b; all courses in Mathematics numbered 100 or above. | | Prerequisite(s): Grade 11 Functions (MCF3M), or Functions and Relations (MCR3U), or the former Ontario Grade 12 Advanced Level Mathematics, or equivalent. | | 3 lecture hours, 1 tutorial hour, 0.5 course. | | back to top |
| Mathematics 028a/b, Finite Mathematics | |
| | Description: Permutations and combinations; probability theory. | | Antirequisite(s): Mathematics 031, 208a/b, 222a, Statistical Sciences 135, 241a/b, the former Statistical Sciences 232a. | | Prerequisite(s): Grade 12U Geometry and Discrete Mathematics (MGA4U), or Grade 12U Advanced Functions and Introductory Calculus (MCB4U), or Grade 12U Mathematics of Data Management (MDM4U) or any former OAC Mathematics courses, or Mathematics 012a/b or Mathematics 017a/b. | | 3 lecture hours, 0.5 course. | | back to top |
| Mathematics 030, Calculus and Linear Algebra | |
| | Description: Calculus including elementary techniques of integration; applications such as area, volume, probability; functions of several variables, Lagrange multipliers. Linear algebra including vectors and matrices, linear equations, determinants. | | Antirequisite(s): Calculus 050a/b, 051a/b, 081a/b, Linear Algebra 040a/b, Applied Mathematics 025a/b, 026, 213b, Mathematics 031, 200a/b, 283b, the former Mathematics 202a, 203b. | | Prerequisite(s): OAC Calculus or Grade 12U Advanced Functions and Introductory Calculus (MCB4U), or Mathematics 012a/b. | | 3 lecture hours, 1.0 course. | | back to top |
| Mathematics 031, Finite Mathematics | |
| | Description: Set theory and logic, permutations and combinations, probability, discrete and continuous random variables, vectors and matrices, linear equations, determinants. | | Antirequisite(s): Applied Mathematics 025a/b, 213b, Linear Algebra 040a/b; Mathematics 028a/b, 030, 208a/b, 222a, 283b; the former Mathematics 202a, 203b; Statistical Sciences 241a/b. | | Prerequisite(s): Any Grade 12U Mathemaics, or any the former OAC Mathematics, or Mathematics 012a/b, or Mathematics 017a/b. | | 3 lecture hours, 1.0 course. | | back to top |
| Mathematics 060a/b, Fundamental Concepts in Mathematics | |
| | Description: 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 222a. | | Prerequisite(s): Grade 12 Geometry and Discrete Mathematics (MGA4U) or the former OAC Algebra and Geometry or Mathematics 017a/b. | | 4 lecture hours, 0.5 course. | | back to top |
| Mathematics 200a/b, Intermediate Linear Algebra I | |
| | Description: 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 283b and the former Mathematics 203b. | | Prerequisite(s): Linear Algebra 040a/b with a minimum mark of 60% or Mathematics 060a/b with a minimum mark of 70% or permission of the Mathematics Department. | | 3 lecture hours, 0.5 course. | | back to top |
| Mathematics 201a/b, Intermediate Linear Algebra II | |
| | Description: A continuation of the material of Mathematics 200a/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. | | Prerequisite(s): Mathematics 200a/b | | 3 lecture hours, 0.5 course. | | back to top |
| Mathematics 207a/b, Real Analysis I | |
| | Description: A rigorous introduction to analysis on the real line, primarily for honors students. Sets, functions, natural numbers. Axioms for the real numbers. Completeness and its consequences. Sequences and limits. Continuous and differentiable functions. The Mean Value Theorem. | | Prerequisite(s): Calculus 051a/b or Applied Mathematics 026, with a minimum mark of 60%, or Calculus 081a/b with a minimum mark of 85%. | | 4 lecture hours, 0.5 course. | | back to top |
| Mathematics 208a/b, Introduction to Mathematical Problems | |
| | Description: 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 051a/b or Applied Mathematics 026, with a minimum mark of 60%, or Calculus 081a/b with a minimum mark of 85% or permission of the instructor. | | 3 lecture hours, 0.5 course. | | back to top |
| Mathematics 217a/b, Real Analysis II | |
| | Description: A continuation of the rigorous introduction to analysis on the real line, begun in Mathematics 207a/b, primarily for honors students. Uniform continuity. The Riemann integral. Series of numbers, convergence theory. Power series and Taylor series. Sequences and series of functions. Uniform convergence. | | Antirequisite(s): Mathematics 306a/b. | | Prerequisite(s): Mathematics 207a/b with a minimum mark of 60%, or permission of the Department. | | 3 lecture hours, 0.5 course. | | back to top |
| Mathematics 221F/G, Conceptual Development of Mathematics | |
| | Description: 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 221F/G, the former Philosophy 121 | | Prerequisite(s): 1.0 course of university level Mathematics | | 3 lecture hours, 0.5 course. | | back to top |
| Mathematics 222a, Discrete Structures I | |
| | Description: 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, groups and applications to error-correcting codes. | | Antirequisite(s): Software Engineering 251a/b | | Prerequisite(s): 1.0 course from: Mathematics 030, 060a/b, Applied Mathematics 026, Calculus 050a/b, Calculus 051a/b or 081a/b, Linear Algebra 040a/b, (in each case with a minimum mark of 60%) | | 4 lecture hours, 0.5 course. | | back to top |
| Mathematics 223b, Discrete Structures II | |
| | Description: This course continues the development of logical reasoning and proofs begun in Mathematics 222a. 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 222a. | | 4 lecture hours, 0.5 course. | | back to top |
| Mathematics 227b, Complex Variables | |
| | Description: Complex numbers, Cauchy-Riemann equations, elementary functions, integrals, Cauchy's theorem and integral formula and applications, Taylor and Laurent expansions, isolated singularities, residue theorem and applications. Cannot be taken for credit by students in honors Mathematics programs. | | Antirequisite(s): Mathematics 307b, Applied Mathematics 301a, or the former Mathematics 306a/b. | | Prerequisite(s): Calculus 250a/b or Calculus 280a/b. | | 3 lecture hours, 0.5 course. | | back to top |
| | Description: An introduction to abstract algebra, with principal emphasis on the structure of groups, rings, integral domains and fields. Cannot be taken for credit by students in honors Mathematics programs. | | Antirequisite(s): Mathematics 302a, the former Mathematics 303b. | | Prerequisite(s): 0.5 course from: Linear Algebra 040a/b, Mathematics 200a/b, or the former Mathematics 202a. | | 3 lecture hours, 1.0 course. | | back to top |
| Mathematics 231, Synthetic Geometry | |
| | Description: Groups of transformations of the Euclidean plane, inversion, the projective plane. | | Antirequisite(s): The former Mathematics 319a/b, Mathematics 419a/b. | | Prerequisite(s): 1.0 course from: Calculus 050a/b, 051a/b or 081a/b, Applied Mathematics 026, Mathematics 028a/b, 030, 031, 060a/b; Linear Algebra 040a/b. | | 3 lecture hours, 1.0 course. | | back to top |
| Mathematics 236, Elementary Operations Research with Applications | |
| | Description: Linear programming, basic probability and statistical distributions, networks, decision analysis, utility, game theory, inventory analysis, queuing theory, simulation, Markovian decision model, forecasting. Cannot be taken for credit by students in honors Mathematics programs. | | Antirequisite(s): Applied Mathematics 325a/b, Statistical Sciences 437a/b, the former Actuarial Science 325a, 326b, the former Statistical Sciences 236. | | Prerequisite(s): 1.0 course from: Calculus 050a/b, 051a/b or 081a/b, Applied Mathematics 026, Mathematics 028a/b, 030, 031, 060a/b, Linear Algebra 040a/b. If Mathematics 028a/b or 031 is not taken, one of the following is also required, either as a prerequisite or a fall term co-requisite: Economics 122a/b, 222a/b, Statistical Sciences 135, 241a/b. | | 3 lecture hours, 1.0 course. | | back to top |
| Mathematics 240, Elementary Theory of Numbers | |
| | Description: Euclidean algorithm, congruences, indices, continued fractions, Gaussian integers, partitions and Diophantine equations. | | Antirequisite(s): Mathematics 310a, the former Mathematics 311b. | | Prerequisite(s): 1.0 course from: Calculus 050a/b, 051a/b or 081a/b, Applied Mathematics 026, Mathematics 028a/b, 030, 031, 060a/b, Linear Algebra 040a/b. | | 3 lecture hours, 1.0 course. | | back to top |
| Mathematics 283b, Linear Algebra | |
| | Description: 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. | | Antirequisite(s): Applied Mathematics 213b, Mathematics 200a/b, the former Mathematics 203b. | | Prerequisite(s): Linear Algebra 040a/b or Mathematics 060a/b with a minimum mark of 70%, or the former Applied Mathematics 202a or 212a. | | 3 lecture hours, 0.5 course. | | back to top |
| Mathematics 302a, Group Theory | |
| | Description: An introduction to the theory of groups: cyclic, dihedral, symmetric, alternating, matrix, and quaternion groups; subgroups, quotient groups and homomorhpisms, cosets and Lagrange's theorem, isomorphism theorems, solvable groups; group actions and representations, the class equation, Sylow theorems; direct products, the fundamental theorem of finitely-generated abelian groups. | | Prerequisite(s): A minimum mark of 60% in one of the following: Mathematics 200a/b, Applied Mathematics 213b or the former Mathematics 203b. | | 3 lecture hours, 0.5 course. | | back to top |
| Mathematics 304a/b, Metric Space Topology | |
| | Description: An introduction to the theory of metric spaces with emphasis on the point-set topology of Euclidean n-space, including convergence, compactness, completeness, continuity, uniform continuity, homeomorphism, equivalence of metrics, connectedness, path-connectedness, fixed-point theorem for contractions, separability, complete normality, product spaces, category. | | Prerequisite(s): Either Mathematics 207a/b or Mathematics 217a/b, each with a minimum mark of 60%. | | 3 lecture hours, 0.5 course. | | back to top |
| Mathematics 305a/b, Differential Equations | |
| | Description: Rigorous introduction to ordinary differential equations. Existence, uniqueness, and continuation of solutions. Linear systems with constant coefficients. Flows and dynamical systems. Series solutions. | | Prerequisite(s): 2.0 crouses: Calculus 251a/b or the former Mathematics 205b; Mathematics 217a/b or the former Mathematics 306a/b; Mathematics 304a/b; Mathematics 200a/b; or Applied Mathematics 213b or the former Mathematics 203b. | | 3 lecture hours, 0.5 course. | | back to top |
| Mathematics 307a/b, Complex Analysis I | |
| | Description: 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 301a. | | Prerequisite(s): Mathematics 217a/b or the former Mathematics 306a/b. | | 3 lecture hours, 0.5 course. | | back to top |
| Mathematics 308a/b, Rings and Modules | |
| | Description: Commutative rings, ring homorphisms and quotient rings, ideals, rings of fractions, the Chinese remainder theorem; Euclidean domains, principal ideal domains, unique factorization domains; polynomial rings over fields; modules, direct sums of modules, free modules; modules over a principal ideal domain, the rational canonical form, the Jordan canonical form. | | Antirequisite(s): The former Mathematics 303b. | | Prerequisite(s): Mathematics 302a. | | 3 lecture hours, 0.5 course. | | back to top |
| Mathematics 310a, Elementary Number Theory I | |
| | Description: Divisibility, primes, congruences, theorems of Fermat and Wilson, Chinese remainder theorem, quadratic reciprocity, some functions of number theory, diophantine equations, simple continued fractions. | | Antirequisite(s): Mathematics 240. | | Prerequisite(s): 1.0 course in Mathematics, Applied Mathematics, Calculus, or Differential Equations at the 200 level or higher. | | 3 lecture hours, 0.5 course. | | back to top |
| Mathematics 313a/b, Elementary Number Theory II | |
| | Description: 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. | | Antirequisite(s): Mathematics 240 | | Prerequisite(s): Mathematics 310a or Mathematics 223b | | 3 lecture hours, 0.5 course. | | back to top |
| Mathematics 329a/b, Introduction to Algebraic Curves | |
| | Description: 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. | | Antirequisite(s): Mathematics 231 and the former Mathematics 319a/b. | | Prerequisite(s): Linear Algebra 040a/b or Mathematics 200a/b; Mathematics 201a/b, 207a/b, 208a/b, or 222a; an additional 0.5 course in Mathematics, Applied Mathematics, Calculus, or Differential Equations at the 200 level or above. | | 3 lecture hours, 0.5 course. | | back to top |
| Mathematics 343a/b, Combinatorial Mathematics | |
| | Description: 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 200a/b, 223b, 283b, Applied Mathematics 213b or the former Mathematics 203b, or permission of the Department. | | 3 lecture hours, 0.5 course. | | back to top |
| Mathematics 344a/b, Discrete Optimization | |
| | Description: Network problems: shortest path, spanning trees, flow problems, matching, routing. Complexity. Integer programming. | | Prerequisite(s): One of: Mathematics 223b, 343a/b, the former Statistical Sciences 236, the former Actuarial Science 325a/b, or permission of the Department. | | 3 lecture hours, 0.5 course. | | back to top |
| Mathematics 398a/b, Special Topics in Mathematics | |
| | Description: | | Prerequisite(s): Permission of the Department. | | 3 lecture hours, 0.5 course. | | back to top |
| Mathematics 399a/b, Special Topics in Mathematics | |
| | Description: | | Prerequisite(s): Permission of the Department. | | 3 lecture hours, 0.5 course. | | back to top |
| Mathematics 402a/b, Linear Algebra III | |
| | Description: Advanced topics in linear algebra: linear functionals and dual spaces; determinants; eigenvalues and eigenvectors, diagonalizable and triangulable operators, similarity, rational and Jordan canonical forms, invariant factors; bilinear, quadratic and Hermitian forms, congruence; positive forms and operators; inner product spaces, orthogonal and unitary operators, self-adjoint and normal operators, the spectral theorem. | | Prerequisite(s): The former Mathematics 303b. | | 3 lecture hours, 0.5 course. | | back to top |
| Mathematics 403a/b, Field Theory | |
| | Description: 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. | | Prerequisite(s): Mathematics 308a/b or the former Mathematics 303b. | | 3 lecture hours, 0.5 course. | | back to top |
| Mathematics 404a, General Topology | |
| | Description: Topological spaces, operations on subsets (e.g. closure), neighbourhoods, bases, subspaces, quotient spaces, product spaces, connectedness, compactness, countability and separation axioms, function spaces. | | Prerequisite(s): Mathematics 304a/b. | | 3 lecture hours, 0.5 course. | | back to top |
| Mathematics 406a/b, Lebesgue Integration and Fourier Series | |
| | Description: Lebesgue measure, measurable sets and functions, approximation theorems, the Lebesgue integral, comparison with the Riemann integral, the basic convergence theorems and continuity properties, the space L2, the Riesz-Fischer theorem and completeness of the trigonometric system, pointwise convergence of Fourier series, Fejér's theorem. | | Prerequisite(s): Mathematics 304a/b. | | 3 lecture hours, 0.5 course. | | back to top |
| Mathematics 411a/b, Algebraic Number Theory | |
| | Description: 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. | | Antirequisite(s): The former Mathematics 311b. | | Prerequisite(s): Mathematics 403a/b; Mathematics 313a/b strongly recommended but not required. | | 3 lecture hours, 0.5 course. | | back to top |
| Mathematics 414b, Algebraic Topology | |
| | Description: Homotopy, fundamental group, Van Kampen's theorem, fundamental theorem of algebra, Jordan curve theorem, singular homology, homotopy invariance, long exact sequence of a pair, excision, Mayer-Vietoris sequence, Brouwer fixed point theorem, Jordan-Brouwer separation theorem, invariance of domain, Euler characteristic, cell complexes, projective spaces, Poincaré theorem. | | Prerequisite(s): Mathematics 302a, Mathematics 404a. | | 3 lecture hours, 0.5 course. | | back to top |
| Mathematics 415a/b, Ordinary Differential Equations | |
| | Description: Laplace transforms and their application to solving differential equations. Sturm-Liouville systems; eigenvalue problems, expansions, Fourier series, autonomous systems; linear and non-linear problems, types of critical points, stability. | | Prerequisite(s): Mathematics 305a/b or Differential Equations 215a. | | 3 lecture hours, 0.5 course. | | back to top |
| Mathematics 416a, Complex Variables II | |
| | Description: Moebius transformations; local behavior of analytic functions, open and inverse mapping theorems; Schwarz's lemma; harmonic functions, solution of the Dirichlet problem on the disk, the Jensen and Poisson- Jensen formulas, the Schwarz reflection principle; analytic continuation; normal families, the Riemann mapping theorem, the homotopic version of Cauchy's theorem; conformal mapping. | | Prerequisite(s): Mathematics 307a/b. | | 3 lecture hours, 0.5 course. | | back to top |
| Mathematics 417b, Complex Variables III | |
| | Description: 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 416a or Mathematics 307a/b with the permission of the Department. | | 3 lecture hours, 0.5 course. | | back to top |
| Mathematics 418a/b, Introduction to Functional Analysis | |
| | Description: Banach and Hilbert spaces, dual spaces, annihilators, Hahn-Banach theorem, Riesz representation theorems, bounded linear operators, adjoints, closed graph and Banach-Steinhaus theorems, compact operators, the Fredholm alternative, the operational calculus, spectral resolution of compact normal operators, applications to integral equations. | | Prerequisite(s): Mathematics 200a/b or the former Mathematics 203b, Mathematics 304a/b, Mathematics 307a/b. | | 3 lecture hours, 0.5 course. | | back to top |
| Mathematics 419a/b, Algebraic Geometry | |
| | Description: Affine and projective varieties, coordinate rings and function fields, birational correspondences, sheaves, dimension theory, regularity. | | Prerequisite(s): Mathematics 403a/b; Mathematics 329a/b is recommended but not required. | | 3 lecture hours, 0.5 course. | | back to top |
| Mathematics 420a/b, Foundations of Mathematics | |
| | Description: 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): The permission of the Department. | | 3 lecture hours, 0.5 course. | | back to top |
| Mathematics 424a/b, Multivariable Calculus | |
| | Description: Review of differentiability in Euclidean space, inverse and implicit function theorems, integration in Euclidean space, Fubini's theorem, partitions of unity, change of variable, multilinear functions, tensor and wedge product, vector fields, differential forms, Poincaré's lemma, Stokes' theorem, manifolds, fields and forms on manifolds, Stokes' theorem on manifolds. | | Prerequisite(s): Calculus 251a/b or the former Mathematics 205b, and Mathematics 304a/b. | | 3 lecture hours, 0.5 course. | | back to top |
| Mathematics 425a/b, Linear Ordinary Differential Equations | |
| | Description: First order vector systems and nth order single equations; adjoint systems and boundary value problems; Green's functions and self adjoint eigenvalue problems; expansion theory and spectral decomposition. | | Prerequisite(s): Mathematics 305a/b or Differential Equations 215a. | | 3 lecture hours, 0.5 course. | | back to top |
| Mathematics 498a/b, Special Topics in Mathematics | |
| | Description: | | Prerequisite(s): Permission of the Department. | | 3 lecture hours, 0.5 course. | | back to top |
| Mathematics 499a/b, Special Topics in Mathematics | |
| | Description: | | Prerequisite(s): Permission of the Department. | | 3 lecture hours, 0.5 course. | | back to top |
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