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A place to share course materials including videos, photos, tutorials, syllabi and other tools to assist with teaching and learning across all areas of undergraduate mathematics. Please review the license information provided for each item as usage rights vary.Collections in this community
UBC-MATH 152: Linear Systems
2D and 3D geometry, vectors and matrices, eigenvalues and vibration, physical applications. Laboratories demonstrate computer solutions of large systems.
UBC-MATH 256: 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. Equivalency: MECH 221.
UBC-MATH 307: Applied Linear Algebra
Applications of linear algebra to problems in science and engineering; use of computer algebra systems for solving problems in linear algebra.
UBC-MATH 317: Calculus IV
Parametrizations, inverse and implicit functions, integrals with respect to length and area; grad, div, and curl, theorems of Green, Gauss, and Stokes.
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UBC-MATH 001: 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.
UBC-MATH 002: Pre-Calculus
Composite, inverse, polynomial, rational, trigonometric, exponential, and logarithmic functions; sequences and series; and analytical geometry.
UBC-MATH 100: Differential Calculus with Applications to Physical Sciences and Engineering
Derivatives of elementary functions. Applications and modeling: graphing, optimization.
UBC-MATH 101: Integral Calculus with Applications to Physical Sciences and Engineering
The definite integral, integration techniques, applications, modeling, infinite series.
UBC-MATH 102: Differential Calculus with Applications to Life Sciences
Functions, derivatives, optimization, growth and decay, discrete probability.
UBC-MATH 103: Integral Calculus with Applications to Life Sciences
Antiderivatives and definite integrals, infinite series, applications to probability and dynamical systems.
UBC-MATH 104/184: Differential Calculus for Social Science and Commerce
Derivatives and rates of change, exponential and trigonometric functions, Newton's method, Taylor polynomials, maxima and minima, and graphing.
UBC-MATH 105: 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.
UBC-MATH 110: Differential Calculus
Topics as for MATH 100, but including relevant topics from algebra, geometry, functions, trigonometry, logarithms, and exponentials.
UBC-MATH 120: Honours Differential Calculus
Limits, derivatives, Mean Value Theorem and applications, elementary functions, optimization, Taylor series, approximation.
UBC-MATH 121: Honours Integral Calculus
Definite integrals and the Fundamental Theorem of Calculus, techniques and applications of integration, infinite series.
UBC-MATH 180: Differential Calculus with Physical Applications
Topics as for Math 100; intended for students with no previous knowledge of Calculus.
UBC-MATH 190: Calculus Survey
Functions, derivatives, integrals, curve sketching growth functions, volume calculations.
UBC-MATH 200: 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.
UBC-MATH 210: 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.
UBC-MATH 215: 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.
UBC-MATH 217: Multivariable and Vector Calculus
Partial differentiation, extreme values, multiple integration, vector fields, line and surface integrals, the divergence theorem, Green's and Stokes' theorems.
UBC-MATH 220: 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.
UBC-MATH 221: Matrix Algebra
Systems of linear equations, operations on matrices, determinants, eigenvalues and eigenvectors, diagonalization of symmetric matrices.
UBC-MATH 223: Linear Algebra
Matrices, eigenvectors, diagonalization, orthogonality, linear systems, applications.
UBC-MATH 226: 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.
UBC-MATH 227: 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.
UBC-MATH 230/335: Finite Mathematics (Math for future element. school teachers)
Difference equations, number theory, counting.
UBC-MATH 253: Multivariable Calculus
Partial and directional derivatives; maxima and minima; Lagrange multipliers and second derivative test; multiple integrals and applications. Equivalency MECH 222.
UBC-MATH 255: Ordinary Differential Equations
Review of linear systems; nonlinear equations and applications; phase plane analysis; Laplace transforms; numerical methods.
UBC-MATH 257: Partial Differential Equations
Introduction to partial differential equations; Fourier series; the heat, wave and potential equations; boundary-value problems; numerical methods.
UBC-MATH 264: Vector Calculus for Electrical Engineering
Divergence, gradient, curl, theorems of Gauss and Stokes. Applications to Electrostatics and Magnetostatics.
UBC-MATH 265: Linear Differential Equations
Linear ordinary differential equations. Complex numbers, Laplace transforms, frequency reponse, resonance, step response, systems.
UBC-MATH 267: 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.
UBC-MATH 300: 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.
UBC-MATH 301: Applied Analysis
Integrals involving multi-valued functions, conformal mapping and applications, analytic continuation, Laplace and Fourier transforms.
UBC-MATH 302: Introduction to Probability
Basic notions of probability, random variables, expectation and conditional expectation, limit theorems. Equivalency: UBC STAT 302
UBC-MATH 303: Introduction to Stochastic Processes
Discrete-time Markov chains, Poisson processes, continuous time Markov chains, renewal theory.
UBC-MATH 305: Applied Complex Analysis
Functions of a complex variable, Cauchy-Riemann equations, contour integration, Laurent series, residues, integrals of multi-valued functions, Fourier transforms.
UBC-MATH 308: Euclidean Geometry
Classical plane geometry, solid geometry, spherical trigonometry, polyhedra, linear and affine transformations. Linear algebra proofs are used.
UBC-MATH 309: 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.
UBC-MATH 310: Abstract Linear Algebra
Linear spaces, duality, linear mappings, matrices, determinant and trace, spectral theory, Euclidean structure.
UBC-MATH 312: Introduction to Number Theory
Euclidean algorithm, congruences, Fermat's theorem, applications. Some diophantine equations. Distribution of the prime numbers.
UBC-MATH 313: Topics in Number Theory
Topics chosen by the instructor. These might include: division algorithms, group theory, continued fractions, primality testing, factoring.
UBC-MATH 316: 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.
UBC-MATH 318: Probability with Physical Applications
Random variables, discrete and continuous distributions. Random walk, Markov chains, Monte Carlo methods. Characteristic functions, limit laws.
UBC-MATH 320: 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.
UBC-MATH 321: 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.
UBC-MATH 322: Introduction to Group Theory
Groups, cosets, homomorphisms, group actions, p-groups, Sylow theorems, composition series, finitely generated Abelian groups.
UBC-MATH 323: Introduction to Rings and Modules
Rings, ideals, unique factorization, Euclidean rings, fields, polynomial rings, modules; structure theory of modules over a principal ideal domain.
UBC-MATH 335: Introduction to Mathematics
Intensive course with required tutorial. Combinatorics, probability, geometry and elementary number theory.
UBC-MATH 340: 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.
UBC-MATH 341: Introduction to Discrete Mathematics
Introduction to ideas and methods of discrete mathematics and their application.
UBC-MATH 342: 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.
UBC-MATH 344: Mathematical Game Theory
Introduction to mathematical game theory and its applications.
UBC-MATH 345: 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.
UBC-MATH 358: 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.
UBC-MATH 360: 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.
UBC-MATH 361: 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.
UBC-MATH 400: Applied Partial Differential Equations
Separation of variables, first order equations, Sturm-Liouville theory, integral transform methods.
UBC-MATH 401: Green's Functions and Variational Methods
Green's functions for partial differential equations. Calculus of variations. Eigenfunction expansions. Rayleigh-Ritz and finite element methods.
UBC-MATH 402: 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.
UBC-MATH 403: 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.
UBC-MATH 405: 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.
UBC-MATH 406: 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.
UBC-MATH 412: Advanced Linear Algebra
Topics include decompositions of linear operators, multi linear algebra, bilinear forms, metric spaces.
UBC-MATH 414: Mathematical Demonstrations
Students will prepare material illustrating ideas and applications of mathematics and present it to audiences outside the University.
UBC-MATH 418: 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.
UBC-MATH 419: Stochastic Processes
Random walks, Markov chains, branching processes, Poisson processes, continuous time Markov chains, martingales, Brownian motion.
UBC-MATH 420: 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.
UBC-MATH 421: 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.
UBC-MATH 422: Fields and Galois Theory
Field extensions, the Galois correspondence, finite fields, insolvability in radicals, ruler and compass constructions, additional topics chosen by instructor.
UBC-MATH 423: Topics in Algebra
Commutative algebra, algebraic geometry, algebraic number theory, Lie theory, homological algebra and category theory, or some other advanced topic in algebra.
UBC-MATH 424: 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.
UBC-MATH 425: Introduction to Modern Differential Geometry
Riemannian manifolds, tensors and differential forms, curvature and geodesics.
UBC-MATH 426: Introduction to Topology
General topology, combinatorial topology, fundamental group and covering spaces, topics chosen by the instructor.
UBC-MATH 427: Topics in Topology
Homology theory, homotopy theory, manifolds, and other topics chosen by the instructor.
UBC-MATH 428: 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.
UBC-MATH 430: Special Topics in Analysis
The student should consult the Mathematics Department for the particular topics offered in a given year.
UBC-MATH 432: Special Topics in Algebra
The student should consult the Mathematics Department for the particular topics offered in a given year.
UBC-MATH 437: Number Theory
Divisibility, congruencies, Diophantine equations, arithmetic functions, quadratic reciprocity, advanced topics.
UBC-MATH 440: 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.
UBC-MATH 441: 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.
UBC-MATH 442: 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.
UBC-MATH 443: 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.
UBC-MATH 444: 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.
UBC-MATH 446: 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.
UBC-MATH 450: 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.
UBC-MATH 462: 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.