## Courses

See also Adult Basic Education (ABE) Upgrading Courses.

## University/Career/Technology Courses

The following courses are offered through the Faculty of Science and Technology.

*Course offerings vary from year to year. Check Generate a Timetable for available course offerings.*

#### MATH 100 (3) Calculus for Engineering and Physical Sciences I

Functions and graphs; limits; derivatives; techniques of differentiation, applications; L'Hospital's rule; antiderivatives; definite integral; trigonometric, logarithmic and exponential functions; and Newton's method. Credit will only be granted for one of MATH 121 or MATH 191 or MATH 100. (4:0:0)

*Prerequisite: Minimum "B" in Principles of Mathematics 12 or Pre-calculus 12; or minimum "B-" in both Principles of Mathematics 12 and Calculus 12; or minimum "B-" in both Pre-calculus 12 and Calculus 12.*

#### MATH 101 (3) Calculus for Engineering and Physical Sciences II

Area, volumes, arc length, surface area, techniques of integration, polar coordinates and area, Simpson's and trapezoidal methods, Taylor's formula, improper integrals, series and tests for convergence, power series and Taylor series, and complex numbers. Credit will only be granted for one of MATH 122 or MATH 192 or MATH 101. (4:0:0)

*Prerequisite: Min. "C" in MATH 100.*

#### MATH 110 (1) Additional Calculus Topics

Topics covered in MATH 100 and MATH 101 that are not covered in MATH 121 and MATH 122 (polar coordinates and area, Taylor's formula, series and tests for convergence, power series and Taylor series, and complex numbers). (2:0:0)

*Prerequisite: Min. "B-" in one of MATH 100, MATH 121, or MATH 191.*

#### MATH 111 (3) Introductory Finite Mathematics I

An introduction to basic non-calculus mathematics useful to students in Applied Mathematics, Computing Science, Business and the Social and Biological Sciences. Topics include linear equations, matrices with applications, compound interest and annuities, sets and counting techniques, linear programming and probability. (4:0:0)

*Prerequisite: Min. "C" in one of Pre-calculus 11, Foundations of Mathematics 11, Principles of Mathematics 11, or Applications of Mathematics 11; or a pass in one of Pre-calculus 12, Foundations of Mathematics 12, Principles of Mathematics 12, or Applications of Mathematics 12; or equivalent.*

#### MATH 121 (3) Calculus I

An introduction to differential calculus of one variable intended primarily for science students. The course focuses on problem solving with applications, placing emphasis on underlying concepts. Topics include limits and continuity, the mean value theorem, inverse functions, differentiation, elementary transcendental functions, optimization and curve sketching. Credit will only be granted for one of MATH 100 or MATH 191. or MATH 121. (4:0:0)

*Prerequisite: Min. "B" in either Pre-calculus 12, Principles of Mathematics 12, MATH 152, or equivalent. Students with only a "C+" or "B-" in any of the abovementioned mathematics courses can meet the prerequisite by obtaining a min. "B" in MATH 151.*

#### MATH 122 (3) Calculus II

A continuation of MATH 121 (Calculus 1). This course focuses on integration, infinite sequences and series. Topics include antiderivatives, definite integrals, The Fundamental Theorem of Calculus, applications of integration, introduction to differential equations, infinite sequences and series, Taylor series with applications. Credit will only be granted for one of MATH 101 or MATH 192 or MATH 122. (4:0:0)

*Prerequisite: Min. "C" in MATH 121 or min. "C-" in MATH 100.*

#### MATH 123 (3) Logic and Foundations

Topics include: set theory, functions, relations, partial orderings, equivalence relations and partitions, connectives and truth tables, quantifiers, number of ways of arranging n items, number of ways of selecting r items out of n, methods of proof including mathematical induction, trees, graphs, asymptotic notation, exact and asymptotic solutions of recurrence relations, properties of integers. (4:0:0)

*Prerequisite: Min. "C" in MATH 100 or MATH 121.*

#### MATH 131 (3) Mathematics for Elementary Education I

An introductory mathematics course designed for those who wish to teach elementary school in British Columbia. The overall theme of the course is the development of numbers from the earliest beginnings through to the real numbers. Topics include numeration, set theory, the integers, elementary number theory, the rationals and the real numbers. (4:0:0)

*Prerequisite: Min. "C" in Pre-calculus 11 or Foundations of Mathematics 11; or a pass in Pre-Calculus 12 or Foundations of Mathematics 12; or equivalent.*

#### MATH 132 (3) Mathematics for Elementary Education II

A continuation of MATH 131. May not be taken for credit towards the VIU B.Sc. degree. (4:0:0)

*Prerequisite: MATH 131.*

#### MATH 135 (3) From Puzzles to the Poetry of Patterns

An exploration of the most fascinating ideas, results and achievements in mathematics. No math background is required (mathphobics especially welcome, come and be cured!) Puzzles (problems), practical or philosophical, answered by patterns (mathematics). Gain an appreciation for mathematics as a cornerstone of civilization, while developing problem-solving and critical-thinking skills. (4:0:0)

*Prerequisite: None.*

#### MATH 141 (3) Matrix Algebra for Engineers

An examination of vectors, matrices and their operations, linear systems, determinants, linear dependence and independence, eigenvalues and eigenvectors, and applications. (4:0:0)

*Prerequisite: Min. "C" in MATH 100 or MATH 121. May not be taken for credit by students who have received credit for MATH 241 or equivalent.*

#### MATH 151 (3) Introductory College Algebra I

An introduction to relations, functions and their inverses, linear and quadratic functions, systems and matrices. For students who plan to take further courses in mathematics for which a good Mathematics 12 background is a prerequisite. May not be taken for credit towards the VIU B.Sc. degree. (4:0:0)

*Prerequisite: Min. "C+" in one of Principles of Mathematics 11, Pre-calculus 11, Applications of Mathematics 12, or Foundations of Mathematics 12; or a pass in Pre-calculus 12 or Principles of Mathematics 12; or equivalent. May not be taken for credit by students who have received credit for any of the following (or equivalent): MATH 100, MATH 121, or MATH 191.*

#### MATH 152 (3) Introductory College Algebra II

A continuation of MATH 151 including logarithmic and exponential functions, trigonometric functions, polar coordinates, complex numbers, analytic geometry, sequences, series, and elementary combinatorics. May not be taken for credit towards the VIU B.Sc. degree. (4:0:0)

*Prerequisite: Min. "C" in MATH 151; or min. "C+" in one of Pre-calculus 12, Principles of Mathematics 12, or equivalent. May not be taken for credit by students who have received credit for any of the following (or equivalent): MATH 100, MATH 121, or MATH 191.*

#### MATH 161 (3) Introduction to Statistics for Social Sciences

An introduction to statistics for non-science students. Topics include descriptive statistics, basic probability techniques, random variables and commonly occurring probability distributions, applications including confidence intervals and hypothesis testing, chi-square tests, and simple linear regression and correlation. May not be taken for credit towards the VIU B.Sc. Degree. Credit will only be granted for one of MATH 181; MATH 211; MATH 254 or MATH 161. (4:0:0)

*Prerequisite: One of Pre-calculus 11, Foundations of Mathematics 11, Principles of Mathematics 11, or Applications of Mathematics 11.*

#### MATH 181 (3) Introduction to Statistics

An introduction to statistics for the technology programs. Topics include descriptive statistics, probability, probability distributions, confidence intervals, hypothesis testing, linear regression, correlation and chi-square tests. Credit will only be granted for one of MATH 161; MATH 211; MATH 254 or MATH 181. (4:0:1)

*Prerequisite: Min. "C" in one of Pre-calculus 11, Foundations of Mathematics 11, Principles of Mathematics 11, or Applications of Mathematics 11.*

#### MATH 191 (3) Calculus with Economic and Business Applications I

A first calculus course intended for those studying business, economics, or other related programs. The course includes a brief review of algebra. Topics include limits; derivatives; logarithmic, exponential and trigonometric functions; applications to business such as marginal economics, propensity to consume, elasticity of demand, optimization and approximation methods. Credit will only be granted for one of MATH 100 or MATH 121. or MATH 191. (4:0:0)

*Prerequisite: Min. "B" in one of Pre-calculus 12, Principles of Mathematics 12, MATH 151, or equivalent.*

#### MATH 200 (3) Calculus of Several Variables

Vector functions, solid analytic geometry, partial differentiation, directional derivatives and the gradient vector, Lagrange multipliers, multiple integration, cylindrical and spherical coordinates, surface area, line integrals, Green's theorem, surface integrals, and divergence theorem. (4:0:0)

*Prerequisite: Min. "C" in MATH 101 or min. "C+" in each of MATH 122 and MATH 110.*

#### MATH 203 (3) Biometrics

A statistical course designed for biology majors. Topics include descriptive statistics, confidence intervals, hypothesis testing, multiple regression, sampling techniques, analysis of variance and non-parametric techniques with a statistical computer software involvement and numerous simulation studies. (3:0:2)

*Prerequisite: One of Pre-calculus 12, Foundations of Mathematics 12, Principles of Mathematics 12, Applications of Mathematics 12, MATH 151, or MATH 181.*

#### MATH 211 (3) Fundamentals of Statistics I

A non-calculus introduction to probability and statistics. Topics include descriptive statistics, elementary concepts in probability, random variables and probability distributions, distribution of the sample mean and the central limit theorem, confidence intervals, hypothesis testing, chi-square tests and simple linear regression. Credit will only be granted for one of MATH 161; MATH 181; MATH 254 or MATH 211. (4:0:1)

*Prerequisite: One of Pre-calculus 12, Foundations of Mathematics 12, Principles of Mathematics 12, Applications of Mathematics 12, or MATH 151.*

#### MATH 212 (3) Statistics II

A non-calculus continuation of MATH 211. Topics include advanced probability theory, mathematical expectations, nonparametric statistics, multiple regression, and analysis of variance. Credit will not be granted for both MATH 203 and 212. (4:0:1)

*Prerequisite: Min "C" in Math 211 or min. "B" in Math 181.*

#### MATH 223 (3) Discrete and Combinatorial Mathematics

A second course in discrete mathematics. Topics include counting, combinatorial arguments, the pigeonhole principle, the principle of inclusion and exclusion, partial orders and equivalence relations, recurrence relations, generating functions, graph theory. (4:0:0)

*Prerequisite: Min. "C" in MATH 123.*

#### MATH 241 (3) Linear Algebra

A study of vectors and matrices, systems of linear equations, determinants, linear transformations from Rn to Rm, change of bases, diagonalization, eigenvalues, eigenvectors, and applications. (4:0:0)

*Prerequisite: Min. "C" in either MATH 101 or MATH 122.*

#### MATH 251 (3) Differential Equations

Topics include first order differential equations, second order linear differential equations, series solution, Laplace transforms, systems of first order linear differential equations, numerical methods, non-linear differential equations, and applications. (4:0:0)

*Prerequisite: Min. "C+" in MATH 101 or MATH 122 and min. "C+" in MATH 141 or MATH 241.*

#### MATH 254 (3) Statistics I

A calculus-based introduction to statistics. Topics include an introduction to probability including conditional probability and independence, discrete and continuous random variables and their probability distributions, joint distributions, expectation, sampling distributions and the central limit theorem, point estimation, confidence intervals and hypothesis testing (both single and two sample), correlation and linear regression, and chi-square procedures. Credit will only be granted for one of MATH 161; MATH 181; MATH 211 or MATH 254. (4:0:1)

*Prerequisite: Min. "C" in MATH 101 or MATH 122.*

#### MATH 255 (3) Statistics II

This course is a continuation of MATH 254. Topics to be covered include correlation and regression, analysis of variance, analysis of categorical data and distribution-free procedures. The mathematical foundations of statistical inference will be introduced and illustrated with examples from a variety of disciplines. (4:0:1)

*Prerequisite: One of MATH 254, min. "B-" in MATH 203, min. "B-" in MATH 211, or min. "A-" in MATH 181.*

#### MATH 300 (3) Geometry

Plane and solid Euclidean geometry, non-Euclidean geometries, fractal geometry. (3:0:0)

*Prerequisite: Min. "C" in one of MATH 200, MATH 223, or MATH 241.*

#### MATH 310 (3) Introduction to Graph Theory

An introduction to the theory of Graphs. Topics include graphs and subgraphs, trees, connectivity, Euler tours and Hamilton cycles, matchings, graph colouring, and planar graphs. (3:0:0)

*Prerequisite: Min. "C" in MATH 223 or min. "C" in each of MATH 123 and MATH 241.*

#### MATH 317 (3) Vector Calculus

A second course in multivariable calculus covering arc length, curvature, motion in space, vector fields, line integrals, curl, divergence, parametric surfaces, surface integrals, Green's Theorem, the Divergence Theorem and Stokes Theorem. Not offered every year. (3:0:0)

*Prerequisite: Min. "C+" in MATH 200.*

#### MATH 320 (3) Applied Probability

An introduction to probability models and their applications, including: basic limit theorems and inequalities, conditioning, Markov chains, the Poisson process, renewal processes, introduction to queuing theory, and introduction to statistical simulation. Not offered every year. (3:0:0)

*Prerequisite: Min. "B-" in MATH 241 and MATH 254; and min. "B" in one of MATH 101, MATH 122, or MATH 110.*

#### MATH 321 (3) Statistics II: An Introduction to Mathematical Statistics

An introduction to the mathematical theory of statistics. Topics include sampling distributions, UMVU estimators, sufficiency and completeness, pivots and interval estimation, hypothesis tests and composite hypotheses, uniformly most powerful tests, generalized likehood ratio tests, and chi-square techniques and introduction to Baysian statistics. (3:0:0)

*Prerequisite: Min. "C+" in MATH 254.*

#### MATH 325 (3) Regression Analysis

Linear regression analysis with applications, multiple linear regression, polynomial regression, model adequacy checking, variable transformations, variable selection, indicator variables, diagnostics for leverage and influential observations, checking for multicollinearity, model selection, stepwise regression, prediction and inference. The data analysis is implemented using statistical software. (3:0:0)

*Prerequisite: At least one of MATH 254, MATH 255, min. "A" in MATH 181 together with a min. "C" in one of MATH 122 or MATH 101, min. "B" in MATH 203 together with a min. "C" in one of MATH 122 or MATH 101, or min. "B" in MATH 211 together with a min. "C" in one of MATH 122 or MATH 101.*

#### MATH 326 (3) Design of Experiments

An introduction to the principles of experimental design and the techniques of analysis of variance. Topics covered include randomization, blocking, covariates, 2^k and fractional factorial designs, repeated measures designs, multiple comparisons and orthogonal contrasts. Emphasis is placed on the assumptions, implications, and rationale of particular designs. Not offered every year. (3:0:0)

*Prerequisite: At least one of MATH 254, MATH 255, min. "A" in MATH 181 together with a min. "C" in one of MATH 122 or MATH 101, min. "B" in MATH 203 together with a min. "C" in one of MATH 122 or MATH 101, or min. "B" in MATH 211 together with a min. "C" in one of MATH 122 or MATH 101.*

#### MATH 330 (3) Introduction to Abstract Algebra

Development of the number systems of elementary algebra; groups, rings, integral domains and fields; polynomials. Not open to students with credit in MATH 230. (3:0:0)

*Prerequisite: Min. "C" in MATH 241 and min. "C" in one of MATH 200 or MATH 223.*

#### MATH 331 (3) Cryptography

The mathematics of data integrity. The course examines historically important encryption systems such as substitution, Vigenere, Playfair, and Hill ciphers and the Enigma machine. The mathematics of permutations, factoring, and primality testing are developed in conjunction with the modern cryptographic systems RSA, DES, and their offshoots. (3:0:0)

*Prerequisite: Min. "C" in MATH 241 or min. "C" in each of MATH 141 and MATH 223.*

#### MATH 335 (3) Numerical Analysis I

Major computational methods for interpolation, least squares, approximation, numerical quadrature, numerical solution of nonlinear equations, systems of linear equations, and initial value problems for ordinary differential equations. Emphasis on the methods and their computational properties rather on their analytic aspects. Offered alternate years. (2:0:1)

*Prerequisite: Min. "B-" in each of MATH 200 and MATH 241.*

#### MATH 340 (3) Applications of Mathematics

A survey of some of the important applications of calculus and matrix algebra. Topics include least squares analysis, linear programming, Fourier series, stochastic processes, population dynamics. Phenomena modelled may vary from year to year. (3:0:0)

*Prerequisite: Min. "C" in each of MATH 200 and MATH 241.*

#### MATH 341 (3) Linear Algebra II

A second course in linear algebra with applications. Orthogonal and unitary matrices and transformations. Orthogonal projections, Gram-Schmidt procedure, best approximations, least-squares. Inner products, angles and orthogonality, orthogonal diagonalization, singular value decomposition, applications. Not offered every year. (3:0:0)

*Prerequisite: Min. "C" in each of MATH 241 and MATH 335.*

#### MATH 345 (3) Mathematical Modeling

An introduction to the application of mathematics as a tool for studying complex systems in science and engineering. Topics include model fitting, experimental modeling, modeling with ordinary and partial differential equations, and optimization. (3:0:0)

*Prerequisite: Min. "B" in each of MATH 100 ( or MATH 121) and MATH 101 (or MATH 122) and min. "C" in MATH 141.*

#### MATH 346 (3) Mathematical Biology

An introduction to classical mathematical models from population biology and ecology. Topics chosen from harvesting models, competition models, epidemic models for HIV, SARS, West Nile, and Bird Flu, models of population outbreaks, models of marine protected areas, metapopulation and patch models, chemostat models, and nonlinear host-parasitoid models. Credit will only be granted for one of MATH 345 or MATH 346. (3:0:0)

*Prerequisite: Min. "B" in each of MATH 121 (or MATH 100) and MATH 122 (or MATH 101).*

#### MATH 350 (3) History of Mathematics

The development of mathematics from its first primitive forms through to the present. Emphasis is placed on the evolution of the mathematics taught in high school. (3:0:0)

*Prerequisite: Six credits of 200-level Math with a min. "C" in each course.*

#### MATH 360 (3) Problem Solving

A study of the techniques and strategies for solving mathematical problems. Develops problem-solving abilities from the formulation of a problem in mathematical terms to its solution. A survey of the types of problem solving expected of high school students. Problems range in difficulty from those in high school to more difficult problems requiring two years of university math as well as considerable patience, industry and creativity. (3:0:0)

*Prerequisite: Min. "C" in MATH 241 and a min. "C" in either MATH 200 or MATH 223.*

#### MATH 362 (3) Elementary Number Theory

Divisibility, primes, congruences, arithmetic functions, primitive roots, quadratic residues, basic representation and decimals, and a selection from the following topics: Pythagorean triples, representation as sums of squares, infinite descent, rational and irrational numbers, and distribution of primes. (3:0:0)

*Prerequisite: MATH 123 and 6 credits of 200-level math courses (excluding MATH 203, 211 and 254) with a min. "C" in each course.*

#### MATH 370 (3) Topics in Mathematics

Topics in mathematics that are not covered in the calendar list of courses. Selection of topic would vary from year to year from topics such as complex variables, analysis, linear programming, mathematical biology, group theory, etc.. NOTE: May be taken for credit more than once if the topics are different. (3:0:0)

*Prerequisite: Six credits of 200-level Mathematics courses (excluding Math 203). Additional prerequisites, depending on the topic to be studied, may be in effect.*

#### MATH 370A (3) Topics in Mathematics: Advanced Abstract Algebra

Topics in mathematics that are not covered in the calendar list of courses. Selection of topic would vary from year to year from topics such as complex variables, analysis, linear programming, mathematical biology, group theory, etc. NOTE: May be taken for credit more than once if the topics are different. (3:0:0)

*Prerequisite: Six credits of 200-level Mathematics courses (excluding MATH 203). Additional prerequisites, depending on the topic to be studied, may be in effect.*

#### MATH 370B (3) Topics in Mathematics: Topology

Topics in mathematics that are not covered in the calendar list of courses. Selection of topic would vary from year to year from topics such as complex variables, analysis, linear programming, mathematical biology, group theory, etc. NOTE: May be taken for credit more than once if the topics are different. (3:0:0)

*Prerequisite: Six credits of 200-level Mathematics courses (excluding MATH 203). Additional prerequisites, depending on the topic to be studied, may be in effect.*

#### MATH 371 (3) Introductory Real Analysis

An introduction to mathematical analysis and the theory underlying calculus. Topics include: set theory and proofs, real numbers, sequences and series, continuous functions, derivatives, the Riemann integral, and sequences of functions. (3:0:0)

*Prerequisite: Min. "B-" in each of MATH 123 and MATH 200.*

#### MATH 372 (3) Introductory Complex Variables

An introduction to Complex variables, beginning with the algebra and geometry of the complex number system. Topics include: complex functions, analytic functions, Cauchy's theorem and its consequences, Taylor and Laurent series, residue calculus, evaluations of real integrals and summation of series. (3:0:0)

*Prerequisite: Min. "B-" in each of MATH 123 and MATH 200.*

#### MATH 421 (3) Introduction to Mathematical Statistics

The course places emphasis on the mathematics of statistics. Topics to be covered include: probability models, random variables and their distributions, mathematical expectation, moment generating functions, sums of random variables, sampling distributions, the theory of point and interval estimation, and hypothesis testing. Not offered every year. (3:0:0)

*Prerequisite: At least one of MATH 325, MATH 326, a min. "C" in MATH 255 together with a min. "C+" in MATH 200, or a min. "B-" in MATH 254 together with a min. "C+" in MATH 200.*

#### MATH 430 (3) Abstract Algebra II

Advanced topics in group and field theory: Fundamental Theorem of Finite Abelian Groups, Sylow Theorems, vector spaces over general fields, splitting fields, field extensions, classification of finite fields, introduction to Galois Theory and the connection of fields with angle trisection and other historical geometric problems. Not offered every year. (3:0:0)

*Prerequisite: Min. "C" in MATH 330.*

#### MATH 441 (3) Abstract Linear Algebra

A rigorous and extended treatment of the topics in MATH 241. Topics will include Vector Spaces and Linear Maps, Matrices and Determinants, Cayley-Hamilton Theorem, Spectral Theorems, Jordan Form and Inner Product Spaces. Not offered every year. (3:0:0)

*Prerequisite: Min. "C" in each of MATH 123 and MATH 241.*

#### MATH 443 (3) Introduction to Linear Programming

An introduction to the mathematics of linear constrained optimization. Topics include the simplex method, revised simplex method, duality, and sensitivity analysis. Additional topics will be chosen from: integer programming, game theory, network flows and nonlinear programming. Not offered every year. (3:0:0)

*Prerequisite: Min. "C" in each of MATH 123 and MATH 241.*

#### MATH 450 (3) Topology

An introduction to general topology. Fundamental concepts covered will include metric spaces, topological spaces, continuity, compactness, connectedness, Hausdorff spaces, homeomorphisms, Cantor sets and an introduction to manifolds. Not offered every year. (3:0:0)

*Prerequisite: Min. "C+" in one of MATH 330, MATH 371 or MATH 372.*

#### MATH 451 (3) Introduction to Partial Differential Equations

Introduction to partial differential equations with an emphasis on the wave, diffusion and Laplace equations. Methods include fundamental solutions and transform methods for problems on the line, and separation of variables using orthogonal series for problems in regions with boundary. Convergence of Fourier series is covered. Not offered every year. (3:0:0)

*Prerequisite: Min. "B-" in each of MATH 200, MATH 251 and MATH 371.*

#### MATH 465 (3) Error Correcting Codes

An introduction to the mathematics protecting information from errors during transmission or storage. Topics include introduction to error-correcting codes, introduction to finite fields, linear codes, dual codes, hamming codes, BCH codes. Optional topics include perfect codes, codes and Latin squares, cyclic codes and weight enumerators. Not offered every year. (3:0:0)

*Prerequisite: Min. "C" in each of MATH 123 and MATH 241.*

#### MATH 470 (3) Advanced Topics in Mathematics

Advanced topics in mathematics that are not covered in the calendar list of courses. Selection of topic varies; may be taken for credit more than once if the topics are different. Not offered every year. (3:0:0)

*Prerequisite: Topic dependent.*

#### MATH 471 (3) Real Analysis II

A continuation of MATH 371: Metric spaces, topology, completeness, compactness, fixed point theorems, introduction to Lebesgue measure and integration. Not offered every year. (3:0:0)

*Prerequisite: Min. "B-" in MATH 371.*

#### MATH 472 (3) Complex Variables II

A continuation of MATH 372. Topics include the residue theorem, the argument principle, conformal mapping, the maximum modulus principle, harmonic functions, representation of functions by integrals, series, and products. Not offered every year. (3:0:0)

*Prerequisite: Min. "B-" in MATH 372.*