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_V 120 and 121. The following courses are for students in the Faculty of Applied Science: MATH_V 152, MATH_V 253, MATH_V 255, MATH_V 256, MATH_V 257, MATH_V 265, MATH_V 267. Secondary-school calculus is a prerequisite for MATH_V 100, 102, and 104. Students with this qualification should see "UBC-SFU-UVIC-UNBC Calculus Examination Certificate" in the Admissions section (https://vancouver.calendar.ubc.ca/admissions/advanced-credit-or-placeme…). MATH_V 180 and 184 are designed for students without high-school calculus. Continuing Studies offers MATH_V 001, 002, 003, and 004, refresher courses in pre-calculus material. Students with credit for MATH_V 110, 180, or 184 will be deemed to have satisfied MATH_V 100, 102, and 104 requirements. For further information see the department's website at www.math.ubc.ca.
Derivatives of elementary functions. Applications and modelling: graphing, optimization. Consult the Faculty of Science Credit Exclusion List: https://vancouver.calendar.ubc.ca/faculties-colleges-and-schools/facult… [3-0-0] Prerequisite: A score of 80% or higher in BC Pre-calculus 12. High school calculus is strongly recommended.
The definite integral, integration techniques, applications, modelling, infinite series. Equivalency: MATH_V 103, 105. [3-0-0] Prerequisite: One of MATH_V 100, MATH_V 102, MATH_V 104, MATH_V 110, MATH_V 120, MATH_V 180, MATH_V 184.
Functions, derivatives, optimization, growth and decay, discrete probability. Equivalency: MATH_V 100, 104. [3-0-0] Prerequisite: High-school calculus and a score of 80% or higher in BC Principles of Mathematics 12 or Pre-calculus 12.
Antiderivatives and definite integrals, infinite series, applications to probability and dynamical systems. Equivalency: MATH_V 101, 105. [3-0-0] Prerequisite: One of MATH_V 100, MATH_V 102, MATH_V 104, MATH_V 110, MATH_V 120, MATH_V 180, MATH_V 184.
Derivatives and rates of change, exponential and trigonometric functions, Newton's method, Taylor polynomials, maxima and minima, and graphing. Equivalency: MATH_V 100, 102. [3-0-0] Prerequisite: High-school calculus and a score of 80% or higher in BC Principles of Mathematics 12 or Pre-calculus 12.
Antiderivatives, the definite integral, techniques of integration, infinite series, partial derivatives, maxima and minima with constraints, discrete and continuous random variables. Equivalency: MATH_V 101, 103. [3-0-0] Prerequisite: One of MATH 100, MATH 102, MATH 104, MATH 110, MATH 120, MATH 180, MATH 184.
Topics as for MATH 100, but including relevant topics from algebra, geometry, functions, trigonometry, logarithms, and exponentials. [3-0-1.5; 3-0-1.5] Prerequisite: A grade of 65% or higher in BC Principles of Mathematics 12 or Pre-calculus 12.
Limits, derivatives, Mean Value Theorem and applications, elementary functions, optimization, Taylor series, approximation. Please consult the Faculty of Science Credit Exclusion List: https://vancouver.calendar.ubc.ca/faculties-colleges-and-schools/facult… [4-0-0] Prerequisite: 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) permission from the Mathematics Department Head.
Definite integrals and the Fundamental Theorem of Calculus, techniques and applications of integration, infinite series. Please consult the Faculty of Science Credit Exclusion List: https://vancouver.calendar.ubc.ca/faculties-colleges-and-schools/facult… [4-0-0] Prerequisite: Either(a) MATH 120 or (b) one of MATH 100, MATH 102, MATH 104, MATH 180, MATH 184. Prerequisite grade requirement: 80% in MATH184,MATH180,MATH104,MATH102,MATH100. 68% in MATH120. or (c) a score of 5 in AP Calculus AB.
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: https://vancouver.calendar.ubc.ca/faculties-colleges-and-schools/facult… [3-1*-0] Corequisite: [MATH101]
Topics as for Math 100; intended for students with no previous knowledge of Calculus. Please consult the Faculty of Science Credit Exclusion List: https://vancouver.calendar.ubc.ca/faculties-colleges-and-schools/facult…. 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: A grade of 80% or higher in BC Principles of Mathematics 12 or Pre-calculus 12.
Topics as for Math 104; intended for students with no previous knowledge of Calculus. Please consult the Faculty of Science Credit Exclusion List: https://vancouver.calendar.ubc.ca/faculties-colleges-and-schools/facult…. 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: A grade of 80% or higher in BC Principles of Mathematics 12 or Pre-calculus 12.
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.
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: https://vancouver.calendar.ubc.ca/faculties-colleges-and-schools/facult…. [3-0-0] Prerequisite: One of MATH 101, MATH 103, MATH 105, MATH 121, SCIE 001.
Introduction to mathematical software and numerical methods. Numbers, arrays, functions, vectorization and iteration. Sequences and series, root finding, numerical integration, numerical methods for differential equations, systems of linear equations, mathematical graphics. [3-0-0] Prerequisite: One of MATH 101, MATH 103, MATH 105, MATH 121, SCIE 001. Corequisite: One of MATH 215, MATH 255, MATH 256, MATH 258 and one of MATH 152, MATH 221, MATH 223.
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: https://vancouver.calendar.ubc.ca/faculties-colleges-and-schools/facult…. [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 254.
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: https://vancouver.calendar.ubc.ca/faculties-colleges-and-schools/facult… [4-0-0] Prerequisite: A score of 68% or higher in one of PHYS 102, PHYS 108, PHYS 118, PHYS 153, PHYS 158, 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.
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 254.
Systems of linear equations, operations on matrices, determinants, eigenvalues and eigenvectors, diagonalization of symmetric matrices. This course is intended for first and second year students. Please consult the Faculty of Science Credit Exclusion List: https://vancouver.calendar.ubc.ca/faculties-colleges-and-schools/facult… [3-0-0] Prerequisite: Either (a) one of MATH 100, MATH 102, MATH 104, MATH 110, MATH 120, MATH 180, MATH 184, SCIE 001 or (b) advanced credit for MATH 100.
Matrices, eigenvectors, diagonalization, orthogonality, linear systems, applications. This course is intended for first and second-year students. Students who obtain credit for MATH 223 cannot in the same or later terms obtain credit for MATH 152 or MATH 221. [3-0-0] Prerequisite: Either (a) one of MATH 120, MATH 121, SCIE 001 or (b) a score of 80% or higher in one of MATH 100, MATH 102, MATH 104, MATH 110, MATH 180, MATH 184 or (c) a score of 68% or higher in one of MATH 101, MATH 103, MATH 105, MATH 152, MATH 221.
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: https://vancouver.calendar.ubc.ca/faculties-colleges-and-schools/facult… [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.
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: https://vancouver.calendar.ubc.ca/faculties-colleges-and-schools/facult… [3-0-0] Prerequisite: MATH 226. Prerequisite grade requirement: 68% in MATH226.
A variety of topics in mathematics, showcasing its beauty and utility. Intended for a general audience of students whose degrees have no mathematics requirements, but who may be curious about practical and recreational mathematics. Not for credit in the Faculty of Science. Students who obtain UBC credit for any other mathematics course cannot in the same or later years obtain credit for MATH 230. [3-0-0]
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: https://vancouver.calendar.ubc.ca/faculties-colleges-and-schools/facult… [3-0-0] Prerequisite: One of MATH 101, MATH 103, MATH 105, MATH 121, SCIE 001.
Partial differentiation, extreme values, multiple integration, vector fields, line and surface integrals, the divergence and Stokes' theorems; applications to fluid mechanics: buoyancy, hydrostatic force, pipe flow, drag; applications to thermodynamics: work, entropy, heat transfer; numerical methods. Emphasis on mechanical engineering applications. [3-0-1*] Prerequisite: MATH 101 and one of MATH 152, MATH 221, MATH 223. Corequisite: All of MECH 222, MECH 225.
Review of linear systems; nonlinear equations and applications; phase plane analysis; Laplace transforms; numerical methods. Please consult the Faculty of Science Credit Exclusion List: https://vancouver.calendar.ubc.ca/faculties-colleges-and-schools/facult… [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 254.
Linear ordinary differential equations, Laplace transforms, Fourier series and separation of variables for linear partial differential equations. Consult the Faculty of Science Credit Exclusion List: https://vancouver.calendar.ubc.ca/faculties-colleges-and-schools/facult…. [3-0-0] Prerequisite: One of MATH_V 101, MATH_V 103, MATH_V 105, MATH_V 121, SCIE_V 001 and one of MATH_V 152, MATH_V 221, MATH_V 223. Corequisite: One of MATH_V 200, MATH_V 217, MATH_V 226, MATH_V 253.
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: https://vancouver.calendar.ubc.ca/faculties-colleges-and-schools/facult… [3-0-0] Prerequisite: One of MATH 215, MATH 255, MATH 256, MATH 258.
First-order equations; linear equations; linear systems; Laplace transforms; trajectory analysis of plane nonlinear systems; translational and rotational vibrations; applications to RLC circuit analysis; numerical and graphical methods. Emphasis on mechanical engineering applications. [3-0-1*] Prerequisite: MATH 101 and one of MATH 152, MATH 221, MATH 223. Corequisite: All of MECH 221, MECH 224.
Divergence, gradient, curl, theorems of Gauss and Stokes. Applications to Electrostatics and Magnetostatics. MATH 264 content is strongly coupled to BMEG 220 and ELEC 211 with topics and student evaluations weighted accordingly. Prerequisite: One of MATH 200, MATH 217, MATH 226, MATH 253, MATH 254. Corequisite: One of BMEG 220, ELEC 211. This course is not eligible for Credit/D/Fail grading.
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: https://vancouver.calendar.ubc.ca/faculties-colleges-and-schools/facult… [3-0-0] Corequisite: One of MATH 217, MATH 227, MATH 254, MATH 317.
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. Corequisite: One of MATH 256, MATH 257, MATH 316, MATH 358, MECH 358, PHYS 312.
Basic notions of probability, random variables, expectation and conditional expectation, limit theorems. Please consult the Faculty of Science Credit Exclusion List: https://vancouver.calendar.ubc.ca/faculties-colleges-and-schools/facult… [3-0-0] Prerequisite: One of MATH 200, MATH 217, MATH 226, MATH 253, MATH 254. Equivalency: STAT302
Discrete-time Markov chains, Poisson processes, continuous time Markov chains, renewal theory. Please consult the Faculty of Science Credit Exclusion List: https://vancouver.calendar.ubc.ca/faculties-colleges-and-schools/facult… [3-0-0] Prerequisite: One of MATH 302, STAT 302.
Functions of a complex variable, Cauchy-Riemann equations, contour integration, Laurent series, residues, integrals of multi-valued functions, Fourier transforms. Please consult the Faculty of Science Credit Exclusion List: https://vancouver.calendar.ubc.ca/faculties-colleges-and-schools/facult… [3-0-0] Prerequisite: One of MATH 200, MATH 217, MATH 226, MATH 253, MATH 254. Corequisite: One of MATH 256, MATH 257, MATH 316, MATH 358, MECH 358, PHYS 312.
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 254.
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: Either (a) one of MATH 152, MATH 221 and one of MATH 220, MATH 226, CPSC 121; or (b) MATH 223.
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: Either (a) one of MATH 152, MATH 221 and one of MATH 220, MATH 226, CPSC 121; or (b) MATH 223.
Linear spaces, duality, linear mappings, matrices, determinant and trace, spectral theory, Euclidean structure. Consult the Faculty of Science Credit Exclusion List: https://vancouver.calendar.ubc.ca/faculties-colleges-and-schools/facult… [3-0-0] Prerequisite: One of MATH 152, MATH 221 and one of MATH 220, MATH 226, CPSC 121.
Euclidean algorithm, congruences, Fermat's theorem, applications. Some diophantine equations. Distribution of the prime numbers. Please consult the Faculty of Science Credit Exclusion List: https://vancouver.calendar.ubc.ca/faculties-colleges-and-schools/facult… Prerequisite: One of MATH 220, MATH 223, MATH 226, CPSC 121. and 9 additional credits of mathematics courses.
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: https://vancouver.calendar.ubc.ca/faculties-colleges-and-schools/facult…. [3-0-0] Prerequisite: [MATH312]
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: https://vancouver.calendar.ubc.ca/faculties-colleges-and-schools/facult… [3-0-0] Prerequisite: One of MATH 215, MATH 255, MATH 256, MATH 258.
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: https://vancouver.calendar.ubc.ca/faculties-colleges-and-schools/facult… [3-0-0] Prerequisite: One of MATH 200, MATH 226, MATH 253. One of MATH 152, MATH 221, MATH 223 is recommended.
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: https://vancouver.calendar.ubc.ca/faculties-colleges-and-schools/facult… [3-0-0] Prerequisite: One of MATH 152, MATH 221, MATH 223. Corequisite: One of MATH 256, MATH 257, MATH 316, MATH 358, MECH 358, PHYS 312.
Ideas and methods of real analysis and their application. Countability and topology of the reals; convergence, continuity and differentiability of functions; metric spaces. Please consult the Faculty of Science credit exclusion list: https://vancouver.calendar.ubc.ca/faculties-colleges-and-schools/facult… [3-0-0] Prerequisite: Either (a) a score of 68% or higher in MATH 220 or (b) a score of 55% or higher in one of MATH 223, MATH 226.
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 254 and a score of 80% or higher in MATH 220.
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.
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.
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.
Ideas and methods of group theory and their applications. Groups, subgroups, and cosets; homomorphisms, isomorphisms, and associated theorems. Consult the Faculty of Science Credit Exclusion List: https://vancouver.calendar.ubc.ca/faculties-colleges-and-schools/facult… [3-0-0] Prerequisite: Either (a) one of MATH_V 152, MATH_V 221, and one of MATH_V 220, MATH_V 226, CPSC_V 121, or (b) MATH_V 223
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: https://vancouver.calendar.ubc.ca/faculties-colleges-and-schools/facult… [3-0-2]
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.
Introduction to ideas and methods of discrete mathematics and their application. [3-0-0] Prerequisite: One of MATH 220, MATH 223, MATH 226, CPSC 121.
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: Either (a) one of MATH 152, MATH 221 and one of MATH 220, MATH 226, CPSC 121; or (b) MATH 223.
Introduction to mathematical game theory and its applications. [3-0-0] Prerequisite: Either (a) one of MATH 152, MATH 221 and one of MATH 220, MATH 226, CPSC 121; or (b) MATH 223.
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 258.
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: MECH358
Construction and evaluation of deterministic, stochastic, and data-driven models. Software-assisted simulations and numerical solutions involving ordinary differential equations, stochastic processes, and basic machine learning algorithms. Examples from science, engineering, and economics. [3-0-0] Prerequisite: One of MATH 200, MATH 217, MATH 226, MATH 253, MATH 254 and one of MATH 210, CPSC 203, CPSC 210 and one of MATH 215, MATH 255, MATH 256, MATH 258.
Mathematical modelling 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 258.
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.
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. Prerequisite: [MATH398] This course is not eligible for Credit/D/Fail grading.
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 358, MECH 358, PHYS 312.
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: https://vancouver.calendar.ubc.ca/faculties-colleges-and-schools/facult… [3-0-0] Prerequisite: Either (a) a score of 80% or higher in one of MATH 256, MATH 257, MATH 316, MATH 358, MECH 358, PHYS 312 or (b) MATH 400.
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. Recommended pre-requisites: a score of 68% or higher in one of MATH 301, MATH 320, or, a score of 80% or higher in MATH 319. [3-0-0]
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. Recommended pre-requisites: MATH 402, and one of (a) a score of 68% or higher in one of MATH 301, MATH 320, or (b) a score of 80% or higher in MATH 319. [3-0-0]
Harmonic analysis on Euclidean spaces, with applications to number theory, partial differential equations and geometric measure theory. [3-0-0] Prerequisite: MATH 300 and a score of 68% or higher in MATH 321. Corequisite: MATH 420.
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: https://vancouver.calendar.ubc.ca/faculties-colleges-and-schools/facult… [3-0-0] Prerequisite: One of MATH 256, MATH 257, MATH 316, MATH 358, MECH 358, PHYS 312.
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: https://vancouver.calendar.ubc.ca/faculties-colleges-and-schools/facult… [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, MATH 358, MECH 358, PHYS 312 or (b) MATH 400.
Topics include decompositions of linear operators, multilinear algebra, bilinear forms, metric spaces. [3-0-0] Prerequisite: A score of 68% or higher in MATH 322 and either (a) a score of 68% or higher in MATH 320 or (b) a score of 80% or higher in MATH 319.
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.
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: MATH 321. Prerequisite grade requirement: 68% in MATH321.
Random walks, Markov chains, branching processes, Poisson processes, continuous time Markov chains, martingales, Brownian motion. [3-0-0] Prerequisite: [MATH418]
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: MATH 321. Prerequisite grade requirement: 68% in MATH321.
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: [MATH420]
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.
Commutative algebra; homological algebra or representation theory of finite groups. [3-0-0] Prerequisite: MATH 323 and a score of 68% or higher in one of MATH 412, MATH 422.
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 254, MATH 264, MATH 317.
Smooth manifolds, smooth maps, immersions and submersions, vector fields, vector bundles, tangent and cotangent bundles, tensors and differential forms, orientation of manifolds, integration of forms, and selected topics. [3-0-0] Prerequisite: One of MATH 221, MATH 223 and one of MATH 217, MATH 227, MATH 254, MATH 264, MATH 317 and one of MATH 319, MATH 320.
General topology, combinatorial topology, fundamental group and covering spaces, topics chosen by the instructor. [3-0-0] Prerequisite: All of MATH 321, MATH 322. Prerequisite grade requirement: 68% in MATH322,MATH321.
Homology theory, homotopy theory, manifolds, and other topics chosen by the instructor. [3-0-0] Prerequisite: [MATH426]
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: One of MATH 215, MATH 255, MATH 256, MATH 258 and one of PHYS 216, PHYS 306, ENPH 270. Corequisite: MATH 320 (waived for students with a score of 80% or higher in MATH 319).
The student should consult the Mathematics Department for the particular topics offered in a given year. [3-0-0]
The student should consult the Mathematics Department for the particular topics offered in a given year. [3-0-0]
Divisibility, congruences, Diophantine equations, arithmetic functions, quadratic reciprocity, advanced topics. Please consult the Faculty of Science Credit Exclusion List: https://vancouver.calendar.ubc.ca/faculties-colleges-and-schools/facult…. [3-0-0] Corequisite: One of MATH 320 (waived for students with a score of 80% or higher in MATH 319), MATH 322.
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 either (a) a score of 68% or higher in MATH 320 or (b) a score of 80% or higher in MATH 319 and permission of the Department Head in Mathematics.
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: [MATH340]
Graph theory, emphasizing trees, tree growing algorithms, and proof techniques. Other topics chosen from shortest paths, maximum flows, minimum cost flows, matchings, and graph colouring. [3-0-0] Prerequisite: 3rd year standing and one of MATH 220, MATH 223, MATH 226 or CPSC 221.
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 223, MATH 226, CPSC 121. And 6 credits of MATH numbered 300 or above.
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_V 220, MATH_V 223, MATH_V 226, and 6 credits of MATH_V courses numbered 300 or higher.
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: 21 credits of MATH.
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.
Independent reading by Honours students in Mathematics under the direction of a faculty member. Written report required. Prerequisite: Permission of the Department Head
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: MATH 400.
Computational methods for mathematical modelling. Numerical methods for partial differential equations, stochastic processes, and data-driven models. Includes student-directed projects on current research and applications. [3-0-0] Prerequisite: Either (a) MATH 360 or (b) one of MATH 210, CPSC 203, CPSC 210 and one of MATH 345, MATH 361.
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.
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. Prerequisite: [MATH399] This course is not eligible for Credit/D/Fail grading.
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. Prerequisite: [MATH498] This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
Prerequisite: All of MATH 544, MATH 545. This course is not eligible for Credit/D/Fail grading.
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.
Prerequisite: All of MATH 544, MATH 545. This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
Prerequisite: [MATH550] Ordinary and partial differential equations (MATH 400 or equivalent). This course is not eligible for Credit/D/Fail grading.
Ideas, methods and applications of bifurcation theory and dynamical systems: differential and difference equations, local bifurcations, perturbation methods, chaos. Recommended pre-requisites: one of MATH 215, MATH 255, MATH 256 and one of MATH 256, MATH 257, MATH 316. This course is not eligible for Credit/D/Fail grading.
Topics from: hyperbolic invariant sets and symbolic dynamics, global bifurcations, local bifurcations for partial differential equations, multiple bifurcations, bifurcations and symmetry, applications. Prerequisite: [MATH552] This course is not eligible for Credit/D/Fail grading.
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. Recommended pre-requisite: elementary courses in differential equations and linear algebra. This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
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. Recommended pre-requisites: MATH 400 and some knowledge of either fluid mechanics or elasticity. This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
Mathematical methods in modelling biological processes, at levels from cell biochemistry to community ecology. This course is not eligible for Credit/D/Fail grading.
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.
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.
Concepts and techniques for modelling 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.
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.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
Presentation and discussion of recent results in the mathematical literature. This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
[3-0-0] This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
This course is not eligible for Credit/D/Fail grading.
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.
This course is not eligible for Credit/D/Fail grading.