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Mathematics, Faculty of Science

MATH: Mathematics

The first digit in the number of a course is intended to convey the level of mathematical maturity at which the course is conducted rather than the year in which it must be taken. Students who expect to follow an Honours Science program or one with high mathematical content are urged to apply for admission to MATH 120 and 121. The following courses are for students in the Faculty of Applied Science: MATH 152, MATH 253, MATH 255, MATH 256, MATH 257, MATH 263, MATH 265, MATH 267. Secondary-school calculus is a prerequisite for MATH 100, 102, and 104. Students with this qualification should see "UBC-SFU-UVIC-UNBC Calculus Examination Certificate" in the Admissions section. MATH 180 and 184 are designed for students without high-school calculus. Continuing Studies offers MATH 001, 002, 003, and 004, refresher courses in pre-calculus material. For further information see the department's website at www.math.ubc.ca.


MATH 001 (0) Algebra
Numbers and their properties; exponents, radicals, absolute value, inqualities, functions and their graphs; factoring; solving polynomial, rational, and exponetial equations; and the sine and cosine law. Non-credit Math course offered by Continuing Studies in consultation with the Mathematics Department and taught by Continuing Studies instructors.
Prerequisite: Mathematics 11 is recommended.
MATH 002 (0) Pre-Calculus
Composite, inverse, polynomial, rational, trigonometric, exponential, and logarithmic functions; sequences and series; and analytical geometry. Non-credit Math course offered by Continuing Studies in consultation with the Mathematics Department and taught by Continuing Studies instructors.
Prerequisite: MATH 001 or a score of 73% or higher in Principlies of Mathematics 11 or Pre-calculus 11.
MATH 003 (0) Differential Calculus I
Review of piecewise and composite functions; evaluating limits analytically, graphically & numerically; and using a variety of techniques to determine the derivatives of elementary functions. Non-credit Math course offered by Continuing Studies in consultation with the Mathematics Department and taught by Continuing Studies instructors.
Prerequisite: MATH 002 or Principles of Mathematics 12 or Pre-calculus 12.
MATH 004 (0) Differential Calculus II
Applications of the derivative, including graphing, optimization problems and related rates; Newton's method; recognizing antidifferentiation as the reverse of the differentiation process. Non-credit Math course offered by Continuing Studies in consultation with the Mathematics Department and taught by Continuing Studies instructors.
Prerequisite: MATH 003.
MATH 100 (3) Differential Calculus with Applications to Physical Sciences and Engineering
Derivatives of elementary functions. Applications and modeling: graphing, optimization. Consult the Faculty of Science Credit Exclusion List: www.students.ubc.ca/calendar/index.cfm?tree=12,215,410,414. [3-0-0]
Prerequisite: High-school calculus and one of (a) a score of 80% or higher in BC Principles of Mathematics 12 or Pre-calculus 12, (b) a score of 73% or higher in the BC provincial examination for Principles of Mathematics 12 or Pre-calculus 12, or (c) a satisfactory score in the UBC Mathematics Basic Skills Test.
MATH 101 (3) Integral Calculus with Applications to Physical Sciences and Engineering
The definite integral, integration techniques, applications, modeling, infinite series. Please consult the Faculty of Science Credit Exclusion List: www.students.ubc.ca/calendar/index.cfm?tree=12,215,410,414. [3-0-0]
Prerequisite: One of MATH 100, MATH 102, MATH 104, MATH 110, MATH 111, MATH 120, MATH 180, MATH 184.
MATH 102 (3) Differential Calculus with Applications to Life Sciences
Functions, derivatives, optimization, growth and decay, discrete probability. Please consult the Faculty of Science Credit Exclusion List: www.students.ubc.ca/calendar/index.cfm?tree=12,215,410,414. [3-0-0]
Prerequisite: High-school calculus and one of (a) a grade of 80% or higher in BC Principles of Mathematics 12 or Pre-calculus 12 (b) a score of 73% or higher in the BC provincial examination for Principles of Mathematics 12 or Pre-calculus 12, or (c) a satisfactory score in the UBC Mathematics Basic Skills Test.
MATH 103 (3) Integral Calculus with Applications to Life Sciences
Antiderivatives and definite integrals, infinite series, applications to probability and dynamical systems. Please consult the Faculty of Science Credit Exclusion List: www.students.ubc.ca/calendar/index.cfm?tree=12,215,410,414. [3-0-0]
Prerequisite: One of MATH 100, MATH 102, MATH 104, MATH 110, MATH 111, MATH 120, MATH 180, MATH 184.
MATH 104 (3) Differential Calculus with Applications to Commerce and Social Sciences
Derivatives and rates of change, exponential and trigonometric functions, Newton's method, Taylor polynomials, maxima and minima, and graphing. Please consult the Faculty of Science Credit Exclusion List: www.calendar.ubc.ca/vancouver/index.cfm?tree=12,215,410,414. [3-0-0]
Prerequisite: High-school calculus and one of (a) a grade of 80% or higher in BC Principles of Mathematics 12 or Pre-calculus 12, (b) a score of 73% or higher in the BC provincial examination for Principles of Mathematics 12 or Pre-calculus 12, or (c) a satisfactory score in the UBC Mathematics Basic Skills Test.
MATH 105 (3) Integral Calculus with Applications to Commerce and Social Sciences
Antiderivatives, the definite integral, techniques of integration, infinite series, partial derivatives, maxima and minima with constraints, discrete and continuous random variables. Please consult the Faculty of Science Credit Exclusion List: www.students.ubc.ca/calendar/index.cfm?tree=12,215,410,414. [3-0-0]
Prerequisite: One of MATH 100, MATH 102, MATH 104, MATH 110, MATH 111, MATH 120, MATH 180, MATH 184.
MATH 110 (6) Differential Calculus
Topics as for MATH 100, but including relevant topics from algebra, geometry, functions, trigonometry, logarithms, and exponentials. [3-0-1.5]
Prerequisite: Pre-requisite: BC Principles of Mathematics 12 or Pre-calculus 12 (or equivalent), plus permission of the Mathematics Department; permission will normally be based on a low grade in BC Principles of Mathematics 12 or Pre-calculus 12 (or equivalent) and a low score in the optional UBC Mathematics Basic Skills Test if taken. See http://www.math.ubc.ca/Ugrad/m110.shtml for details.
MATH 120 (4) Honours Differential Calculus
Limits, derivatives, Mean Value Theorem and applications, elementary functions, optimization, Taylor series, approximation. Please consult the Faculty of Science Credit Exclusion List: www.students.ubc.ca/calendar/index.cfm?tree=12,215,410,414. [4-0-0]
Prerequisite: MATH 12. High-school calculus and one of (a) a score of 95% or higher in BC Principles of Mathematics 12 or Pre-calculus 12; or (b) a score of 95% or higher in the BC provincial examination for Principles of Mathematics 12 or Pre-calculus 12; or (c) BC Principles of Mathematics 12 or Pre-calculus 12 with a letter of invitation from the Mathematics Department based on performance in the Euclid Contest; or (d) permission from Mathematics Department Head.
MATH 121 (4) Honours Integral Calculus
Definite integrals and the Fundamental Theorem of Calculus, techniques and applications of integration, infinite series. Please consult the Faculty of Science Credit Exclusion List: www.students.ubc.ca/calendar/index.cfm?tree=12,215,410,414. [4-0-0]
Prerequisite: Either (a) a score of 68% or higher in MATH 120 or (b) a score of 80% or higher in one of MATH 100, MATH 102, MATH 104, MATH 180, MATH 184 or (c) a score of 5 in AP Calculus AB.
MATH 152 (3) Linear Systems
2D and 3D geometry, vectors and matrices, eigenvalues and vibration, physical applications. Laboratories demonstrate computer solutions of large systems. Please consult the Faculty of Science Credit Exclusion List: www.students.ubc.ca/calendar/index.cfm?tree=12,215,410,414. [3-1*-0]
Corequisite: MATH 101.
MATH 180 (4) Differential Calculus with Physical Applications
Topics as for Math 100; intended for students with no previous knowledge of Calculus. Please consult the Faculty of Science Credit Exclusion List: www.students.ubc.ca/calendar/index.cfm?tree=12,215,410,414. Not for credit for students with AP Calculus AB, AP Calculus BC, or a passing score on the UBC-SFU-UVIC-UNBC Calculus Challenge Examination. [3-0-1.5]
Prerequisite: One of BC Principles of Mathematics 12 or Pre-calculus 12 and one of (a) a grade of 80% or higher in BC Principles of Mathematics 12 or Pre-calculus 12, (b) a score of 73% or higher in the BC provincial examination for Principles of Mathematics 12 or Pre-calculus 12, or (c) a satisfactory score in the UBC Mathematics Basic Skills Test.
MATH 184 (4) Differential Calculus for Social Science and Commerce
Topics as for Math 104; intended for students with no previous knowledge of Calculus. Please consult the Faculty of Science Credit Exclusion List: www.students.ubc.ca/calendar/index.cfm?tree=12,215,410,414. Not for credit for students with AP Calculus AB, AP Calculus BC, or a passing score on the UBC-SFU-UVIC-UNBC Calculus Challenge Examination. [3-0-1.5]
Prerequisite: One of BC Principles of Mathematics 12 or Pre-calculus 12 and one of (a) a grade of 80% or higher in BC Principles of Mathematics 12 or Pre-calculus 12, (b) a score of 73% or higher in the BC provincial examination for Principles of Mathematics 12 or Pre-calculus 12, or (c) a satisfactory score in the UBC Mathematics Basic Skills Test.
MATH 190 (4) Calculus Survey
Functions, derivatives, integrals, curve sketching growth functions, volume calculations. Only for credit in the Faculty of Forestry. Students with credit for MATH 100, 102, 104, 120, 180, or 184 cannot in the same term or later terms obtain credit for MATH 190. [3-0-2]
Prerequisite: Principles of Mathematics 12 or Pre-calculus 12 and registration in the B.S.F. or B.Sc.N. programs.
MATH 200 (3) Calculus III
Analytic geometry in 2 and 3 dimensions, partial and directional derivatives, chain rule, maxima and minima, second derivative test, Lagrange multipliers, multiple integrals with applications. Please consult the Faculty of Science Credit Exclusion List: www.students.ubc.ca/calendar/index.cfm?tree=12,215,410,414. [3-0-0]
Prerequisite: One of MATH 101, MATH 103, MATH 105, MATH 121, SCIE 001.
MATH 210 (3) Introduction to Mathematical Computing
Introduction to numerical computation, computer algebra, mathematical graphics. Primarily for second year students taking a degree in mathematics. One hour laboratory each week. [3-1-0]
Prerequisite: One of MATH 101, MATH 103, MATH 105, MATH 121, SCIE 001.
Corequisite: One of MATH 215, MATH 255, MATH 256, MATH 265 and one of MATH 152, MATH 221, MATH 223.
MATH 215 (3) Elementary Differential Equations I
First-order equations; linear equations; linear systems; Laplace transforms; numerical methods; trajectory analysis of plane nonlinear systems. Applications of these topics will be emphasized. Please consult the Faculty of Science Credit Exclusion List: www.students.ubc.ca/calendar/index.cfm?tree=12,215,410,414. [3-0-0]
Prerequisite: One of MATH 101, MATH 103, MATH 105, MATH 121, SCIE 001 and one of MATH 152, MATH 221, MATH 223.
Corequisite: One of MATH 200, MATH 217, MATH 226, MATH 253, MATH 263.
MATH 217 (4) Multivariable and Vector Calculus
Partial differentiation, extreme values, multiple integration, vector fields, line and surface integrals, the divergence theorem, Green's and Stokes' theorems. Intended for students in Honours Physics and Engineering Physics. Please consult the Faculty of Science Credit Exclusion List: www.students.ubc.ca/calendar/index.cfm?tree=12,215,410,414. [4-0-0]
Prerequisite: A score of 68% or higher in one of PHYS 101, PHYS 107, PHYS 153, SCIE 001 and a score of 68% or higher in one of PHYS 102, PHYS 108, PHYS 153, SCIE 001 and a score of 68% or higher in one of MATH 101, MATH 103, MATH 105, MATH 121, SCIE 001.
Corequisite: One of MATH 152, MATH 221, MATH 223.
MATH 220 (3) Mathematical Proof
Sets and functions; induction; cardinality; properties of the real numbers; sequences, series, and limits. Logic, structure, style, and clarity of proofs emphasized throughout. [3-0-0]
Prerequisite: Either (a) a score of 64% or higher in one of MATH 101, MATH 103, MATH 105, SCIE 001 or (b) one of MATH 121, MATH 200, MATH 217, MATH 226, MATH 253, MATH 263.
MATH 221 (3) Matrix Algebra
Systems of linear equations, operations on matrices, determinants, eigenvalues and eigenvectors, diagonalization of symmetric matrices. Please consult the Faculty of Science Credit Exclusion List: www.students.ubc.ca/calendar/index.cfm?tree=12,215,410,414. [3-0-0]
Prerequisite: Either (a) a score of 64% or higher in one of MATH 100, MATH 102, MATH 104, MATH 110, MATH 120, MATH 180, MATH 184 or (b) one of MATH 101, MATH 103, MATH 105, MATH 121, SCIE 001 or (c) advanced credit for MATH 100.
MATH 223 (3) Linear Algebra
Matrices, eigenvectors, diagonalization, orthogonality, linear systems, applications. Intended for Honours students. Please consult the Faculty of Science Credit Exclusion List: www.students.ubc.ca/calendar/index.cfm?tree=12,215,410,414. [3-0-0]
Prerequisite: Either (a) MATH 121 or (b) a score of 68% or higher in one of MATH 101, MATH 103, MATH 105, SCIE 001.
MATH 226 (3) Advanced Calculus I
Functions of several variables: limits, continuity, differentiability; implicit functions; Taylor's theorem; extrema; Lagrange multipliers; multiple integration, Fubini's theorem; improper integrals. Please consult the Faculty of Science Credit Exclusion List: www.students.ubc.ca/calendar/index.cfm?tree=12,215,410,414. [3-0-0]
Prerequisite: Either (a) a score of 68% or higher in MATH 121 or (b) a score of 80% or higher in one of MATH 101, MATH 103, MATH 105, SCIE 001.
Corequisite: One of MATH 152, MATH 221, MATH 223.
MATH 227 (3) Advanced Calculus II
Parametrization of curves and surfaces; line and surface integrals; theorems of Green, Gauss, Stokes; applications to physics and/or introduction to differential forms. Please consult the Faculty of Science Credit Exclusion List: www.students.ubc.ca/calendar/index.cfm?tree=12,215,410,414. [3-0-0]
Prerequisite: A score of 68% or higher in MATH 226.
MATH 230 (3) Introduction to Finite Mathematics
Difference equations, number theory, counting. Intended primarily for students not in the Faculty of Science who wish to have some exposure to mathematical thinking. Students who obtain credit for MATH 100, MATH 102, MATH 104, MATH 110, MATH 111, MATH 120, MATH 180, MATH 184, or SCIE 001 cannot in the same year or in later years obtain credit for MATH 230. Please consult the Faculty of Science Credit Exclusion List: www.students.ubc.ca/calendar/index.cfm?tree=12,215,410,414. [3-0-0]
Prerequisite: Principles of Mathematics 11.
MATH 253 (3) Multivariable Calculus
Partial and directional derivatives; maxima and minima; Lagrange multipliers and second derivative test; multiple integrals and applications. Please consult the Faculty of Science Credit Exclusion List: www.students.ubc.ca/calendar/index.cfm?tree=12,215,410,414. [3-0-0]
Prerequisite: One of MATH 101, MATH 103, MATH 105, MATH 121, SCIE 001.
MATH 255 (3) Ordinary Differential Equations
Review of linear systems; nonlinear equations and applications; phase plane analysis; Laplace transforms; numerical methods. Please consult the Faculty of Science Credit Exclusion List: www.students.ubc.ca/calendar/index.cfm?tree=12,215,410,414. [3-0-0]
Prerequisite: One of MATH 101, MATH 103, MATH 105, MATH 121, SCIE 001 and one of MATH 152, MATH 221, MATH 223.
Corequisite: One of MATH 200, MATH 217, MATH 226, MATH 253, MATH 263.
MATH 256 (3) Differential equations
Linear ordinary differential equations, Laplace transforms, Fourier series and separation of variables for linear partial differential equations. Tutorial session focuses on examples from chemical and biological engineering. Consult the Faculty of Science Credit Exclusion List: www.students.ubc.ca/calendar/index.cfmtree=12,215,410,414. [3-0-1]
Prerequisite: One of MATH 101, MATH 103, MATH 105, MATH 121, SCIE 001 and one of MATH 152, MATH 221, MATH 223.
Corequisite: One of MATH 200, MATH 217, MATH 226, MATH 253, MATH 263.
MATH 257 (3) Partial Differential Equations
Introduction to partial differential equations; Fourier series; the heat, wave and potential equations; boundary-value problems; numerical methods. Please consult the Faculty of Science Credit Exclusion List: www.students.ubc.ca/calendar/index.cfm?tree=12,215,410,414. [3-0-0]
Prerequisite: One of MATH 215, MATH 255, MATH 265.
MATH 263 (4) Multivariable and Vector Calculus
Partial and directional derivatives, multiple integrals, divergence, gradient, curl, vector fields, potentials, line and surface integrals, theorems of Gauss, Green and Stokes. For students in Electrical and Computer Engineering. Please consult the Faculty of Science Credit Exclusion List: www.students.ubc.ca/calendar/index.cfm?tree=12,215,410,414. [4-0-0]
Prerequisite: One of SCIE 001, PHYS 101, PHYS 107, PHYS 153 and one of SCIE 001, PHYS 102, PHYS 108, PHYS 153 and one of SCIE 001, MATH 101, MATH 103, MATH 105, MATH 121.
Corequisite: One of MATH 152, MATH 221, MATH 223.
MATH 264 (1) Vector Calculus for Electrical Engineering
Divergence, gradient, curl, theorems of Gauss and Stokes. Applications to Electrostatics and Magnetostatics. MATH 264 content is strongly coupled to EECE 261 with topics and student evaluations weighted accordingly. This course is not eligible for Credit/D/Fail grading.
Prerequisite: One of MATH 200, MATH 217, MATH 226, MATH 253, MATH 263.
Corequisite: EECE 261.
MATH 265 (2) Linear Differential Equations
Linear ordinary differential equations. Complex numbers, Laplace transforms, frequency reponse, resonance, step response, systems. Please consult the Faculty of Science Credit Exclusion List: www.students.ubc.ca/calendar/index.cfm?tree=12,215,410,414. [2-0-1*]
Prerequisite: One of MATH 101, MATH 103, MATH 105, MATH 121, SCIE 001 and one of MATH 152, MATH 221, MATH 223.
Corequisite: One of MATH 200, MATH 217, MATH 226, MATH 253, MATH 263.
MATH 267 (3) Mathematical Methods for Electrical and Computer Engineering
Fourier series and transforms, wave equation, d'Alembert's solution, modes. Discrete Fourier tranform. Recurrence relations, z-transform, generating functions, applications. [3-0-1*]
Prerequisite: One of MATH 215, MATH 255, MATH 256, MATH 265 and one of MATH 152, MATH 221, MATH 223.
MATH 300 (3) Introduction to Complex Variables
Functions of a complex variable, Cauchy-Riemann equations, elementary functions, Cauchy's theorem and contour integration, Laurent series, poles and residues. Please consult the Faculty of Science Credit Exclusion List: www.students.ubc.ca/calendar/index.cfm?tree=12,215,410,414. [3-0-0]
Prerequisite: One of MATH 200, MATH 217, MATH 226, MATH 253, MATH 263.
Corequisite: One of MATH 217, MATH 227, MATH 263, MATH 317.
MATH 301 (3) Applied Analysis
Integrals involving multi-valued functions, conformal mapping and applications, analytic continuation, Laplace and Fourier transforms. [3-0-0]
Prerequisite: One of MATH 300, MATH 305 and one of MATH 215, MATH 255, MATH 256, MATH 265.
Corequisite: One of MATH 256, MATH 257, MATH 316.
MATH 302 (3) Introduction to Probability
Basic notions of probability, random variables, expectation and conditional expectation, limit theorems. Please consult the Faculty of Science Credit Exclusion List: www.students.ubc.ca/calendar/index.cfm?tree=12,215,410,414. [3-0-0]
Prerequisite: One of MATH 200, MATH 217, MATH 226, MATH 253, MATH 263.
Equivalency: STAT 302.
MATH 303 (3) Introduction to Stochastic Processes
Discrete-time Markov chains, Poisson processes, continuous time Markov chains, renewal theory. Please consult the Faculty of Science Credit Exclusion List: www.students.ubc.ca/calendar/index.cfm?tree=12,215,410,414. [3-0-0]
Prerequisite: One of MATH 302, STAT 302.
MATH 305 (3) Applied Complex Analysis
Functions of a complex variable, Cauchy-Riemann equations, contour integration, Laurent series, residues, integrals of multi-valued functions, Fourier transforms. See Credit Exclusion List [link to http://www.students.ubc.ca/calendar/index.cfm?tree=12,215,410,414]. [3-0-0]
Prerequisite: One of MATH 200, MATH 217, MATH 226, MATH 253, MATH 263 and one of MATH 215, MATH 255, MATH 256, MATH 265.
Corequisite: One of MATH 256, MATH 257, MATH 316.
MATH 307 (3) Applied Linear Algebra
Applications of linear algebra to problems in science and engineering; use of computer algebra systems for solving problems in linear algebra. [3-0-0]
Prerequisite: One of MATH 152, MATH 221, MATH 223 and one of MATH 200, MATH 217, MATH 226, MATH 253, MATH 263.
MATH 308 (3) Euclidean Geometry
Classical plane geometry, solid geometry, spherical trigonometry, polyhedra, linear and affine transformations. Linear algebra proofs are used. It is suggested that MATH 307 be taken concurrently. [3-0-0]
Prerequisite: One of MATH 152, MATH 221, MATH 223 and one of MATH 220, MATH 226, CPSC 121.
MATH 309 (3) Topics in Geometry
Topics chosen by the instructor. These may include conic sections, projective configuration, convexity, non-Euclidean geometries, fractal geometry, combinatorial problems of points in the plane. [3-0-0]
Prerequisite: One of MATH 152, MATH 221, MATH 223 and one of MATH 220, MATH 226, CPSC 121.
MATH 310 (3) Abstract Linear Algebra
Linear spaces, duality, linear mappings, matrices, determinant and trace, spectral theory, Euclidean structure. Consult the Faculty of Science Credit Exclusion List: www.students.ubc.ca/calendar/index.cfmtree=12,215,410,414. [3-0-0]
Prerequisite: One of MATH 152, MATH 221 and one of MATH 220, MATH 226, CPSC 121.
MATH 312 (3) Introduction to Number Theory
Euclidean algorithm, congruences, Fermat's theorem, applications. Some diophantine equations. Distribution of the prime numbers. Please consult the Faculty of Science Credit Exclusion List: www.students.ubc.ca/calendar/index.cfm?tree=12,215,410,414.
Prerequisite: One of MATH 220, MATH 226, CPSC 121 and 9 additional credits of mathematics courses.
MATH 313 (3) Topics in Number Theory
Topics chosen by the instructor. These might include: division algorithms, group theory, continued fractions, primality testing, factoring. Please consult the Faculty of Science Credit Exclusion List: www.students.ubc.ca/calendar/index.cfm?tree=12,215,410,414. [3-0-0]
Prerequisite: MATH 312.
MATH 316 (3) Elementary Differential Equations II
Power series methods (ordinary and regular singular points, Bessel's equation); boundary value problems and separation of variables (Fourier series and other orthogonal series), applications to the vibrating string, heat flow, potentials. Please consult the Faculty of Science Credit Exclusion List: www.students.ubc.ca/calendar/index.cfm?tree=12,215,410,414. [3-0-0]
Prerequisite: One of MATH 215, MATH 255, MATH 265.
MATH 317 (3) Calculus IV
Parametrizations, inverse and implicit functions, integrals with respect to length and area; grad, div, and curl, theorems of Green, Gauss, and Stokes. Please consult the Faculty of Science Credit Exclusion List: www.students.ubc.ca/calendar/index.cfm?tree=12,215,410,414. [3-0-0]
Prerequisite: One of MATH 200, MATH 226, MATH 253. MATH 221 is recommended.
MATH 318 (3) Probability with Physical Applications
Random variables, discrete and continuous distributions. Random walk, Markov chains, Monte Carlo methods. Characteristic functions, limit laws. Please consult the Faculty of Science Credit Exclusion List: www.students.ubc.ca/calendar/index.cfm?tree=12,215,410,414. [3-0-0]
Prerequisite: One of MATH 152, MATH 221, MATH 223 and one of MATH 215, MATH 255, MATH 256, MATH 265.
Corequisite: One of MATH 256, MATH 257, MATH 267, MATH 316.
MATH 320 (3) Real Variables I
The real number system; real Euclidean n-space; open, closed, compact, and connected sets; Bolzano-Weierstrass theorem; sequences and series. Continuity and uniform continuity. Differentiability and mean-value theorems. [3-0-0]
Prerequisite: Either (a) a score of 68% or higher in MATH 226 or (b) one of MATH 200, MATH 217, MATH 226, MATH 253, MATH 263 and a score of 80% or higher in MATH 220.
MATH 321 (3) Real Variables II
The Riemann or Riemann-Stieltjes integrals. Sequences and series of functions, uniform convergence. Approximation of continuous functions by polynomials. Fourier series. Functions from Rm to Rn, inverse and implicit function theorems. [3-0-0]
Prerequisite: MATH 320.
MATH 322 (3) Introduction to Group Theory
Groups, cosets, homomorphisms, group actions, p-groups, Sylow theorems, composition series, finitely generated Abelian groups. [3-0-0]
Prerequisite: Either (a) a score of 68% or higher in one of MATH 223, MATH 310 or (b) one of MATH 152, MATH 221, MATH 223 and a score of 80% or higher in MATH 220.
MATH 323 (3) Introduction to Rings and Modules
Rings, ideals, unique factorization, Euclidean rings, fields, polynomial rings, modules; structure theory of modules over a principal ideal domain. [3-0-0]
Prerequisite: MATH 322.
MATH 331 (3) Problem Solving
Intended for honours students. A seminar on the techniques and art of solving problems based primarily on the mathematics curriculum of the first two years. [3-0-0]
Prerequisite: Either (a) MATH 223 or (b) a score of 68% or higher in one of MATH 152, MATH 221; and either (a) MATH 226 or (b) a score of 68% or higher in one of MATH 200, MATH 217, MATH 253, MATH 263.
MATH 335 (4) Introduction to Mathematics
Intensive course with required tutorial. Combinatorics, probability, geometry and elementary number theory. Not for credit in the Faculty of Science. Students who obtain credit at UBC for any other mathematics course cannot in the same or later years obtain credit for MATH 335. Please consult the Faculty of Science Credit Exclusion List: www.students.ubc.ca/calendar/index.cfm?tree=12,215,410,414. [3-0-2]
MATH 336 (3) Mathematics by Inquiry
A problem-based exploration of topics selected from the BC secondary school curriculum. Formal language and notation minimized. Intended for those with minimal background in Mathematics. Not for credit in the Faculty of Science. [3-0-0]
Prerequisite: Two years teaching experience, normally a teaching certificate, and permission of the department head.
MATH 337 (3) Mathematics for Teaching
An overview of mathematical topics of the grade 8 to 10 BC school curriculum. Not for credit in the Faculty of Science. [3-0-0]
Prerequisite: MATH 336.
MATH 340 (3) Introduction to Linear Programming
Linear programming problems, dual problems, the simplex algorithm, solution of primal and dual problems, sensitivity analysis. Additional topics chosen from: Karmarkar's algorithm, non-linear programming, game theory, applications. [3-0-0]
Prerequisite: One of MATH 152, MATH 221, MATH 223.
MATH 342 (3) Algebra and Coding Theory
Error-correcting codes via abstract and linear algebra. Emphasis on proofs and computation. Finite fields, Hamming distance and error-correction, upper and lower bounds on the size of a code, linear codes, groups and cosets, encoding and decoding schemes. [3-0-0]
Prerequisite: One of MATH 152, MATH 221, MATH 223 and one of MATH 220, MATH 226, CPSC 121.
MATH 345 (3) Applied Nonlinear Dynamics and Chaos
Phase plane methods, bifurcation and stability theory, limit-cycle behavior and chaos for nonlinear differential equations with applications to the sciences. Assignments involve the use of computers. [3-1-0]
Prerequisite: A score of 68% or higher in one of MATH 215, MATH 255, MATH 256, MATH 265.
MATH 358 (3) Engineering Analysis
Fourier series; auto- and cross-correlation; power spectra; discrete Fourier transform; boundary-value problems; numerical methods; partial differential equations; heat, wave, Laplace, Poisson, and wave equations. Applications to mechanical engineering and practical computing applications emphasized. Credit will be granted for only one of MECH 358 or MATH 358. [3-2*-0]
Prerequisite: All of MECH 224, MECH 225.
Equivalency: MECH 358.
MATH 360 (3) Mathematical Modeling in Science
Principles of model selection and basic modeling techniques in biology, earth science, chemistry and physics. Optimization, dynamical systems and stochastic processes. Preference will be given to Combined Major in Science students, or to students in Year 3 or higher. This course is not eligible for Credit/D/Fail grading. [3-0-0]
Prerequisite: One of MATH 101, MATH 103, MATH 105, MATH 121, SCIE 001.
MATH 361 (3) Introduction to Mathematical Biology
Mathematical modeling of basic biological processes in ecology, physiology, neuroscience and genetics. Dynamic behavior of difference equations, differential equations, and partial differential equations, explained with reference to concrete biological examples. [3-0-0]
Prerequisite: One of BIOL 301, MATH 215, MATH 255, MATH 256, MATH 265.
MATH 398 (3) Co-operative Work Placement I
Approved and supervised technical work experience involving mathematics in industry for a minimum of 3.5 months. Technical report required. Restricted to students admitted to the Mathematics Co-operative Education Program. This course is not eligible for Credit/D/Fail grading.
MATH 399 (3) Co-operative Work Placement II
Approved and supervised technical work experience involving mathematics in industry for a minimum of 3.5 months. Technical report required. Restricted to students admitted to the Mathematics Co-operative Education Program. This course is not eligible for Credit/D/Fail grading.
Prerequisite: MATH 398.
MATH 400 (3) Applied Partial Differential Equations
Separation of variables, first order equations, Sturm-Liouville theory, integral transform methods. [3-0-0]
Prerequisite: One of MATH 300, MATH 305 and one of MATH 256, MATH 257, MATH 316.
MATH 401 (3) Green's Functions and Variational Methods
Green's functions for partial differential equations. Calculus of variations. Eigenfunction expansions. Rayleigh-Ritz and finite element methods. See Faculty of Science credit exclusion list: http://www.calendar.ubc.ca/vancouver/index.cfm?tree=12,215,410,414. [3-0-0]
Prerequisite: Either (a) a score of 80% or higher in one of MATH 256, MATH 257, MATH 316 or (b) MATH 400.
MATH 402 (3) Calculus of Variations
Classical variational problems; necessary conditions of Euler, Weierstrass, Legendre, and Jacobi; Erdmann corner conditions, transversality, convex Lagrangians, fields of extremals, sufficient conditions for optimality, numerical methods; applications to classical mechanics, engineering and economics. [3-0-0]
Prerequisite: A score of 68% or higher in one of MATH 301, MATH 320.
MATH 403 (3) Stabilization and Optimal Control of Dynamical Systems
Dynamical systems; stability by Liapunov's direct method; controllability and eigenvalue assignment for autonomous linear systems; linear-quadratic regulator, time optimal control, Pontryagin maximum principle, dynamic programming; applications in engineering, economics and resource management. [3-0-0]
Prerequisite: A score of 68% or higher in one of MATH 301, MATH 320. MATH 402 is recommended.
MATH 405 (3) Numerical Methods for Differential Equations
Interpolation, numerical integration, numerical solution of ordinary and partial differential equations. Practical computational methods emphasized and basic theory developed through simple models. See Faculty of Science credit exclusion list: http://www.calendar.ubc.ca/vancouver/index.cfm?tree=12,215,410,414. [3-0-0]
Prerequisite: One of MATH 256, MATH 257, MATH 316.
MATH 406 (3) Variational and Approximate Methods in Applied Mathematics
Variational and Green's function methods for ordinary and partial differential equations, introduction to finite difference, finite element and boundary element methods. See Faculty of Science Credit exclusion list: http://www.calendar.ubc.ca/vancouver/index.cfm?tree=12,215,410,414 [3-0-0]
Prerequisite: One of MATH 307, CPSC 302 and either (a) a score of 80% or higher in one of MATH 256, MATH 257, MATH 316 or (b) MATH 400.
MATH 407 (3) Applied Matrix Analysis
Numerical analysis of matrices, including solution of linear systems and eigenvalue/eigenvector calculations. Please consult the Faculty of Science Credit Exclusion List: www.students.ubc.ca/calendar/index.cfm?tree=12,215,410,414. [3-0-0]
Prerequisite: MATH 307.
MATH 412 (3) Advanced Linear Algebra
Topics include decompositions of linear operators, multi linear algebra, bilinear forms, metric spaces. [3-0-0]
Prerequisite: A score of 68% or higher in all of MATH 320, MATH 322.
MATH 414 (3) Mathematical Demonstrations
Students will prepare material illustrating ideas and applications of mathematics and present it to audiences outside the University. Intended for third or fourth year Mathematics students and Math/Science Education students. [2-0-0; 1-0-0] or [3-0-0]
Prerequisite: 24 credits in MATH.
MATH 415 (3) Introduction to Mathematical Logic
Predicate calculus, models, theories. Introduction to recursive functions. The Goedel incompleteness theorem. [3-0-0]
Prerequisite: 24 credits of MATH courses.
MATH 416 (3) Ordinary Differential Equations
Existence and uniqueness, first order systems, stability, attractors, oscillation and comparison theorems, Sturm-Liouville theory, solution of partial differential equations by separation of variables. [3-0-0]
Prerequisite: A score of 68% or higher in all of MATH 215, MATH 321.
MATH 417 (3) Partial Differential Equations
Poisson, heat, and wave equations; uniqueness theorems, maximum principle, Green's function, existence for the Dirichlet problem. Cauchy problem for the heat and wave equations, variational principles and generalized solutions, Fourier/Galerkin approximations, Sobolev spaces, spectral theorem, initial boundary value problems. [3-0-0]
Prerequisite: Either (a) MATH 416 or (b) a score of 68% or higher in MATH 321 and consent of the instructor.
MATH 418 (3) Probability
Probability spaces, random variables, distributions, expectation, conditional probabilities, convergence of random variables, generating and characteristic functions, weak and strong laws of large numbers, central limit theorem. [3-0-0]
Prerequisite: A score of 68% or higher in MATH 321.
MATH 419 (3) Stochastic Processes
Random walks, Markov chains, branching processes, Poisson processes, continuous time Markov chains, martingales, Brownian motion. [3-0-0]
Prerequisite: MATH 418.
MATH 420 (3) Real Analysis I
Sigma-algebras, Lebesgue measure, Borel measures, measurable functions, integration, convergence theorems, Lp spaces, Holder and Minkowski inequalities, Lebesgue and/or Radon-Nikodym differentiation. [3-0-0]
Prerequisite: A score of 68% or higher in MATH 321.
MATH 421 (3) Real Analysis II
Banach spaces, linear operators, bounded and compact operators, strong, weak, and weak* topology. Hahn-Banach, open mapping, and closed graph theorems. Hilbert spaces, symmetric and self-adjoint operators, spectral theory for bounded operators. [3-0-0]
Prerequisite: MATH 420.
MATH 422 (3) Fields and Galois Theory
Field extensions, the Galois correspondence, finite fields, insolvability in radicals, ruler and compass constructions, additional topics chosen by instructor. [3-0-0]
Prerequisite: MATH 323.
MATH 423 (3) Topics in Algebra
Commutative algebra, algebraic geometry, algebraic number theory, Lie theory, homological algebra and category theory, or some other advanced topic in algebra. [3-0-0]
Prerequisite: A score of 68% or higher in one of MATH 412, MATH 422.
MATH 424 (3) Classical Differential Geometry
The differential geometry of curves and surfaces in three-dimensional Euclidean space. Mean curvature and Gaussian curvature. Geodesics. Gauss's Theorema Egregium. [3-0-0]
Prerequisite: Either (a) a score of 68% or higher in MATH 223 or (b) a score of 80% or higher in one of MATH 152, MATH 221; and either (a) a score of 68% or higher in MATH 227 or (b) a score of 80% or higher in one of MATH 217, MATH 263, MATH 317.
MATH 425 (3) Introduction to Modern Differential Geometry
Riemannian manifolds, tensors and differential forms, curvature and geodesics. [3-0-0]
Prerequisite: MATH 424.
MATH 426 (3) Introduction to Topology
General topology, combinatorial topology, fundamental group and covering spaces, topics chosen by the instructor. [3-0-0]
Prerequisite: A score of 68% or higher in all of MATH 321, MATH 322.
MATH 427 (3) Topics in Topology
Homology theory, homotopy theory, manifolds, and other topics chosen by the instructor. [3-0-0]
Prerequisite: MATH 426.
MATH 428 (3) Mathematical Classical Mechanics I
Newton's equation, conservation laws, the Euler-Lagrange equation; Hamilton's principle of least action, Hamilton's equations, Lagrangian mechanics on manifolds. [3-0-0]
Prerequisite: MATH 215 and one of PHYS 206, PHYS 306.
Corequisite: MATH 320.
MATH 429 (3) Mathematical Classical Mechanics II
Differential forms, symplectic manifolds, canonical transformations, Hamilton-Jacobi equation, integrable systems, Liouville-Arnold theorem, perturbations of integrable systems. [3-0-0]
Prerequisite: MATH 428.
Corequisite: MATH 321.
MATH 430 (2-6) c Special Topics in Analysis
The student should consult the Mathematics Department for the particular topics offered in a given year. [3-0-0]
MATH 431 (2-6) c Special Topics in Geometry
The student should consult the Mathematics Department for the particular topics offered in a given year. [3-0-0]
MATH 432 (2-6) c Special Topics in Algebra
The student should consult the Mathematics Department for the particular topics offered in a given year. [3-0-0]
MATH 437 (3) Number Theory
Divisibility, congruences, Diophantine equations, arithmetic functions, quadratic reciprocity, advanced topics. Please consult the Faculty of Science Credit Exclusion List: www.students.ubc.ca/calendar/index.cfm?tree=12,215,410,414. [3-0-0]
Corequisite: One of MATH 320, MATH 322.
MATH 440 (3) Complex Analysis
The residue theorem, the argument principle, conformal mapping, the maximum modulus principle, harmonic functions, representation of functions by integrals, series, and products. Other topics at the discretion of the instructor. [3-0-0]
Prerequisite: MATH 300 and a score of 68% or higher in MATH 320.
MATH 441 (3) Mathematical Modeling: Discrete Optimization Problems
Formulation of real-world optimization problems using techniques such as linear programming, network flows, integer programming, dynamic programming. Solution by appropriate software. [3-0-0]
Prerequisite: MATH 340.
MATH 442 (3) Optimization in Graphs and Networks
Basic graph theory, emphasizing trees, tree growing algorithms, and proof techniques. Problems chosen from: shortest paths, maximum flows, minimum cost flows, matchings, graph colouring. Linear programming duality will be an important tool. [3-0-0]
Prerequisite: MATH 340.
MATH 443 (3) Graph Theory
Introductory course in mostly non-algorithmic topics including: planarity and Kuratowski's theorem, graph colouring, graph minors, random graphs, cycles in graphs, Ramsey theory, extremal graph theory. Proofs emphasized. Intended for Honours students. [3-0-0]
Prerequisite: A score of 68% or higher in one of MATH 220, MATH 226, CPSC 121. And at least 6 credits of Mathematics courses numbered 300 or above.
MATH 444 (3) Mathematical Research and Writing
Current research topics in pure and applied mathematics are explored at the undergraduate level. Technical communication and research skills are developed. [3-0-0]
Prerequisite: One of MATH 220, MATH 226 and 6 credits of MATH courses numbered 300 or higher.
MATH 445 (3) Mathematical Modeling: Applications in the Natural and Social Sciences
Formulation, analysis, simulation, and interpretation for practical problems. An integration of dynamical, continuous optimization, and probabilistic techniques in modeling. [3-0]
Prerequisite: One of MATH 215, MATH 255, MATH 256, MATH 265 and one of MATH 200, MATH 217, MATH 253, MATH 263 and one of STAT 241, STAT 251, MATH 302, MATH 318, STAT 302. MATH 302, MATH 318 or STAT 302 may be taken as a co-requisite.
MATH 446 (3) Topics in the History of Mathematics I
Historical development of concepts and techniques in areas chosen from Geometry, Number Theory, Algebra, Calculus, Probability, Analysis. The focus is on historically significant writings of important contributors and on famous problems of Mathematics. [3-0-0]
Prerequisite: 27 credits in Mathematics.
MATH 447 (3) Topics in the History of Mathematics II
A continuation of MATH 446. [3-0-0]
Prerequisite: MATH 446.
MATH 448 (3) Directed Studies in Mathematics
Introduction to the methods of mathematical research through an exploration of a mathematical topic under the supervision of a faculty member. Written report required. [3-0-0]
Prerequisite: Third- or fourth-year standing and permission of the Department Head.
MATH 449 (2-6) c Honours Reading
Independent reading by Honours students in Mathematics under the direction of a faculty member. Written report required.
Prerequisite: Permission of the Department Head
MATH 450 (3) Asymptotic and Perturbation Methods
Asymptotic expansions. Asymptotic evaluation of integrals; WKBJ methods. Regular and singular expansions. Boundary layer theory; matched asymptotic expansions. Multiple scale techniques. [3-0-0]
Prerequisite: All of MATH 301, MATH 400.
MATH 462 (3) Projects in Mathematical Biology
Development and analysis of mathematical models for complex systems in ecology, evolution, cell biology, neurophysiology, and other biological and medical disciplines. [3-0-0]
Prerequisite: One of MATH 361, MATH 345.
MATH 498 (3) Co-operative Work Placement III
Approved and supervised technical work experience involving mathematics in industry for a minimum of 3 1/2 months. Technical report required. Restricted to students admitted to the Mathematics Co-operative Education Program. This course is not eligible for Credit/D/Fail grading.
Prerequisite: MATH 399.
MATH 499 (3) Co-operative Work Placement IV
Approved and supervised technical work experience involving mathematics in industry for a minimum of 3 1/2 months. Technical report required. Restricted to students admitted to the Mathematics Co-operative Education Program. This course is not eligible for Credit/D/Fail grading.
Prerequisite: MATH 498.
MATH 500 (3) Mathematical Logic
This course is not eligible for Credit/D/Fail grading.
MATH 501 (3) Algebra I
This course is not eligible for Credit/D/Fail grading.
MATH 502 (3) Algebra II
This course is not eligible for Credit/D/Fail grading.
MATH 503 (3) Discrete Mathematics
This course is not eligible for Credit/D/Fail grading.
MATH 507 (3) Measure Theory and Integration
This course is not eligible for Credit/D/Fail grading.
MATH 508 (3) Complex Analysis
This course is not eligible for Credit/D/Fail grading.
MATH 510 (3) Functional Analysis
This course is not eligible for Credit/D/Fail grading.
MATH 511 (3) Operator Theory and Applications
This course is not eligible for Credit/D/Fail grading.
MATH 512 (3) Quantum Theory
This course is not eligible for Credit/D/Fail grading.
MATH 513 (3) Mathematical Classical Mechanics
This course is not eligible for Credit/D/Fail grading.
MATH 514 (3) Ordinary Differential Equations
This course is not eligible for Credit/D/Fail grading.
MATH 515 (3) Partial Differential Equations of Fluid Mechanics
This course is not eligible for Credit/D/Fail grading.
MATH 516 (3) Partial Differential Equations I
This course is not eligible for Credit/D/Fail grading.
MATH 517 (3) Partial Differential Equations II
This course is not eligible for Credit/D/Fail grading.
MATH 518 (3) Nonlinear Differential Equations
This course is not eligible for Credit/D/Fail grading.
MATH 519 (3) Fluid Mechanics I
This course is not eligible for Credit/D/Fail grading.
MATH 520 (3) Fluid Mechanics II
This course is not eligible for Credit/D/Fail grading.
MATH 521 (3) Numerical Analysis of Partial Differential Equations
This course is not eligible for Credit/D/Fail grading.
MATH 522 (3) Numerical Analysis
This course is not eligible for Credit/D/Fail grading.
MATH 523 (3) Combinatorial Optimization
This course is not eligible for Credit/D/Fail grading.
MATH 525 (3) Differential Geometry I
This course is not eligible for Credit/D/Fail grading.
MATH 526 (3) Differential Geometry II
This course is not eligible for Credit/D/Fail grading.
MATH 527 (3) Algebraic Topology I
This course is not eligible for Credit/D/Fail grading.
MATH 528 (3) Algebraic Topology II
This course is not eligible for Credit/D/Fail grading.
MATH 529 (3) Differential Topology
This course is not eligible for Credit/D/Fail grading.
MATH 530 (3) Geometric Topology
This course is not eligible for Credit/D/Fail grading.
MATH 532 (3) Algebraic Geometry I
This course is not eligible for Credit/D/Fail grading.
MATH 533 (3) Algebraic Geometry II
This course is not eligible for Credit/D/Fail grading.
MATH 534 (3) Lie Theory I
This course is not eligible for Credit/D/Fail grading.
MATH 535 (3) Lie Theory II
This course is not eligible for Credit/D/Fail grading.
MATH 537 (3) Elementary Number Theory
This course is not eligible for Credit/D/Fail grading.
MATH 538 (3) Algebraic Number Theory
This course is not eligible for Credit/D/Fail grading.
MATH 539 (3) Analytic Number Theory
This course is not eligible for Credit/D/Fail grading.
MATH 541 (3) Harmonic Analysis I
This course is not eligible for Credit/D/Fail grading.
MATH 542 (3) Harmonic Analysis II
This course is not eligible for Credit/D/Fail grading.
MATH 543 (3) Discrete Harmonic Analysis
This course is not eligible for Credit/D/Fail grading.
MATH 544 (3) Probability I
This course is not eligible for Credit/D/Fail grading.
MATH 545 (3) Probability II
This course is not eligible for Credit/D/Fail grading.
MATH 546 (3) Continuous Time Stochastic Processes
This course is not eligible for Credit/D/Fail grading. Prerequisite: All of MATH 544, MATH 545.
MATH 547 (3) Optimal Control Theory
Optimal control of systems governed by ordinary differential equations. The control problem will be carefully stated, and existence results and necessary conditions will be established. Hamilton-Jacobi-Bellman theory will be introduced. This course is not eligible for Credit/D/Fail grading.
MATH 548 (3) Discrete Random Processes
This course is not eligible for Credit/D/Fail grading. Prerequisite: All of MATH 544, MATH 545.
MATH 549 (6/12) c Thesis for Master's Degree
This course is not eligible for Credit/D/Fail grading.
MATH 550 (3) Methods of Asymptotic Analysis
This course is not eligible for Credit/D/Fail grading. Prerequisite: Applied complex analysis (MATH 301 or equivalent) and ordinary and partial differential equations (MATH 400 or equivalent).
MATH 551 (3) Perturbation Methods for Differential Equations
This course is not eligible for Credit/D/Fail grading. Prerequisite: MATH 550. Ordinary and partial differential equations (MATH 400 or equivalent).
MATH 552 (3) Introduction to Dynamical Systems
Ideas, methods and applications of bifurcation theory and dynamical systems: differential and difference equations, local bifurcations, perturbation methods, chaos. This course is not eligible for Credit/D/Fail grading.
Prerequisite: One of MATH 215, MATH 255, MATH 256 and one of MATH 256, MATH 257, MATH 316.
MATH 553 (3) Advanced Dynamical Systems
Topics from: hyperbolic invariant sets and symbolic dynamics, global bifurcations, local bifurcations for partial differential equations, multiple bifurcations, bifurcations and symmetry, applications. This course is not eligible for Credit/D/Fail grading.
Prerequisite: MATH 552.
MATH 554 (3) Symmetries and Differential Equations
Dimensional analysis, modelling, and invariance. Lie groups of transformations, infinitesimal transformations. Applications to ordinary and partial differential equations. No knowledge of group theory will be assumed. This course is not eligible for Credit/D/Fail grading.
Prerequisite: Elementary courses in differential equations and linear algebra.
MATH 555 (3) Compressed Sensing
This course is not eligible for Credit/D/Fail grading.
MATH 556 (3) Industrial Mathematical Modelling
This course is not eligible for Credit/D/Fail grading.
MATH 557 (3) Linear and Nonlinear Waves
Classical and recent results in linear and nonlinear waves. Geometrical acoustics and kinematic waves; large amplitude waves in weakly stratified media; small amplitude waves in strongly stratified media. Dispersive waves; group velocity; applications. This course is not eligible for Credit/D/Fail grading.
Prerequisite: MATH 400 and some knowledge of either fluid mechanics or elasticity.
MATH 559 (3) Complex Fluids
This course is not eligible for Credit/D/Fail grading.
MATH 560 (3) Mathematical Biology
Mathematical methods in modeling biological processes, at levels from cell biochemistry to community ecology. This course is not eligible for Credit/D/Fail grading.
MATH 561 (3) Mathematics of Infectious Diseases and Immunology
Mathematical models for disease spread in populations. Within-host infectious disease dynamics. Models of the immune system and immune cells. This course is not eligible for Credit/D/Fail grading.
MATH 562 (3) Mathematical Electrophysiology
Formulation and analysis of models of excitable media. FitzHugh-Nagumo model, ionic models of membrane excitability (e.g., Hodgkin-Huxley), calcium excitability, bursting phenomena. This course is not eligible for Credit/D/Fail grading.
MATH 563 (3) Modeling of Cell-Scale Biology
Concepts and techniques for modeling cellular and subcellular dynamics in biological systems. Topics may include complex biochemical systems, biopolymers in cell motility and division, continuum mechanics, and membrane dynamics. This course is not eligible for Credit/D/Fail grading.
MATH 564 (3) Evolutionary Dynamics
Mathematical models of evolution and evolutionary game theory. Stochastic dynamics in finite populations, dynamics in spatially structured populations, and adaptive dynamics. Applications include the origin of species and the problem of cooperation. This course is not eligible for Credit/D/Fail grading.
MATH 566 (3) Theory of Optimal Transportation
This course is not eligible for Credit/D/Fail grading.
MATH 567 (3) Nonlinear Wave Equations
This course is not eligible for Credit/D/Fail grading.
MATH 589 (3) M.Sc. Major Essay
This course is not eligible for Credit/D/Fail grading.
MATH 590 (2-6) c Graduate Seminar
Presentation and discussion of recent results in the mathematical literature. This course is not eligible for Credit/D/Fail grading.
MATH 591 (2) Graduate Seminar in Applied Mathematics
This course is not eligible for Credit/D/Fail grading.
MATH 592 (2-15) d Topics in Automorphic Forms
This course is not eligible for Credit/D/Fail grading.
MATH 597 (3) Co-operative Work Placement I
This course is not eligible for Credit/D/Fail grading. Prerequisite: Registration in Mathematics M.Sc. program, Mathematical Finance Option, and approval of the mathematical finance program director.
MATH 598 (3) Co-operative Work Placement II
This course is not eligible for Credit/D/Fail grading. Prerequisite: MATH 597 and approval of the mathematical finance program director.
MATH 599 (1) Mathematics Teaching Techniques
This course is not eligible for Credit/D/Fail grading. [3-0-0]
MATH 600 (2-15) c Topics in Algebra
This course is not eligible for Credit/D/Fail grading.
MATH 601 (2-15) c Topics in Analysis
This course is not eligible for Credit/D/Fail grading.
MATH 602 (2-15) c Topics in Geometry
This course is not eligible for Credit/D/Fail grading.
MATH 603 (2-15) c Topics in Topology
This course is not eligible for Credit/D/Fail grading.
MATH 604 (2-15) c Topics in Optimization
This course is not eligible for Credit/D/Fail grading.
MATH 605 (2-15) c Topics in Applied Mathematics
This course is not eligible for Credit/D/Fail grading.
MATH 606 (2-15) c Topics in Differential Equations
This course is not eligible for Credit/D/Fail grading.
MATH 607 (2-15) c Topics in Numerical Analysis
This course is not eligible for Credit/D/Fail grading.
MATH 608 (2-15) c Topics in Probability
This course is not eligible for Credit/D/Fail grading.
MATH 609 (2-15) c Topics in Mathematical Physics
This course is not eligible for Credit/D/Fail grading.
MATH 610 (2-15) c Topics in Pure Mathematics
This course is not eligible for Credit/D/Fail grading.
MATH 612 (2-15) c Topics in Mathematical Biology
This course is not eligible for Credit/D/Fail grading.
MATH 613 (2-15) d Topics in Number Theory
This course is not eligible for Credit/D/Fail grading.
MATH 614 (2-15) d Topics in Mathematical Finance
This course is not eligible for Credit/D/Fail grading.
MATH 615 (2-15) d Topics in Algebraic Geometry
This course is not eligible for Credit/D/Fail grading.
MATH 616 (2-15) d Topics in Discrete Mathematics
This course is not eligible for Credit/D/Fail grading.
MATH 620 (2-15) c Directed Studies in Mathematics
Advanced study under the direction of a faculty member may be arranged in special situations. This course is not eligible for Credit/D/Fail grading.
MATH 649 (0) Doctoral Dissertation

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