Academic Calendar Fall 2017

Mathematics

Notes on prerequisites

Unless stated otherwise, the minimum grade acceptable in all course prerequisites is a C-. In exceptional cases, course prerequisites may be waived by an instructor. Students will need the instructor’s written permission for the waiver of a prerequisite.

If more than three calendar years have elapsed since credit was obtained for any course prerequisite, the student should contact the course instructor for further instructions before the course begins. A preliminary assessment test may have to be passed to satisfy the prerequisite.

Students applying for Math courses below the 100 level must write a UUP assessment.

Math and Stats Centre

UFV is committed to helping students succeed in their study of mathematics and statistics. The Math and Stats Centres in Abbotsford and Chilliwack are open frequently throughout the week, Monday to Friday. Students are encouraged to come to the centres for help with math or stats questions. Software including versions of MAPLE and MINITAB is available on centre computers for student use. Students may also sign out math books to supplement their course work.

New label for statistics courses

All statistics courses are now labeled STAT rather than MATH. If you are looking for STAT 104 (formerly MATH 104) or STAT 106 (formerly MATH 106) for example, please see the STAT course descriptions.


English language proficiency requirements

Students registering in post-secondary level courses (numbered 100 to 499) will be required to meet the English language entrance proficiency requirements. Students in ESL or the University Foundations programs can register in those courses identified in the University Foundations program with lower levels of language proficiency.

Please note that not all courses are offered every semester.

MATH 052

1.5 credits

Fundamental Math I

Prerequisite(s): UUP Department permission (assessment may be required)

This is the first of four basic mathematics courses. At this beginning level, students will be introduced to number sense, four operations on whole numbers, and some geometric shapes and measurement units. Estimation and problem-solving will also be part of this course. Student learning issues such as “math anxiety” will be addressed through individual attention and a variety of instructional approaches.

MATH 053

1.5 credits

Fundamental Math II

Prerequisite(s): Completion of Math 052 or UUP Department permission (assessment may be required).

This is the second of four basic mathematics courses. At this level, students will be introduced to operations on decimals and fractions. Estimation, measurements, and problem-solving will also be part of this course. Student learning issues such as “math anxiety” will be addressed through individual attention and a variety of instructional approaches.

MATH 062

1.5 credits

Fundamental Math III

Prerequisite(s): One of the following: MATH 051, MATH 053, or Upgrading and University Preparation department permission (assessment may be required).

The third of four basic mathematics courses introduces ratios, proportions, percentages, metric conversions, graphs, tables, and topic-related problem solving. Developing learning strategies is also an important component of this course.

MATH 063

1.5 credits

Fundamental Math IV

Prerequisite(s): MATH 062 or Upgrading and University Preparation department permission (assessment may be required).

The last of four basic mathematics courses introduces basic algebraic concepts, units of measurement, concepts of geometry, and statistical graphs, and encourages using critical thinking and setting further numeracy goals.

MATH 075

1.5 credits

Intermediate Math I

Prerequisite(s): One of the following: MATH 061, MATH 063, or UUP department permission (assessment may be required).

Students will review fractions, decimals, ratio, proportion, and the metric system. Course topics include integers, primes, factors, and multiples; perimeter, area and volume; signed (rational) numbers; and an introduction to formulas, equations, expressions, and polynomials.

MATH 076

1.5 credits

Intermediate Math II

Prerequisite(s): MATH 075 or UUP Department permission (assessment may be required)

Students will review primes, factors, multiples, integers, formulas, expressions, equations, and polynomials. Course topics include percent applications, geometry, graphing, introduction to algebra and trigonometry, powers, roots, and scientific notations.

MATH 084

3 credits

Introductory Algebra and Trigonometry

Prerequisite(s): One of the following: MATH 072 or MATH 076; Foundations of Mathematics and Pre-calculus 10 with at least a C; Principles of Mathematics 11, Applications of Mathematics 11, Foundations of Mathematics 11, or Pre-calculus 11 with at least a C-; or UUP department permission (assessment may be required).

This course reviews operations with real numbers and the solution of linear equations. It introduces linear inequalities; the solution of quadratic, rational, and radical equations; operations with polynomial, rational, and radical expressions; and the graphing of equations, particularly linear equations. It also reviews basic geometry concepts and right angle trigonometry. Right angle trigonometry is used to solve practical problems.
MATH 084 is intended for students who need to gain or refresh knowledge and skills to ensure success at Intermediate Algebra and Trigonometry (MATH 085).
This course may be used as a math credit for the UUP Advanced Level certificate or the Provincial Adult Dogwood. It can also be used as preparation for some vocational, career, and technical programs. For academic programs, students must complete MATH 085.

MATH 085

3 credits

Intermediate Algebra and Trigonometry

Prerequisite(s): One of the following: MATH 084, (Foundations of Mathematics and Pre-calculus 10 with at least a B), (one of Principles of Mathematics 11, Applications of Mathematics 11, Foundations of Mathematics 11, or Pre-calculus 11 with at least a C), (one of Foundations of Mathematics 12 or Pre-Calculus 12 with at least a C-), or UUP department permission (assessment may be required).

Review of basic algebraic and trigonometric concepts. Study of linear, absolute value, polynomial, rational, radical, and quadratic expressions, equations, and functions. Use of function notation and graphs. Use of the laws of sines and cosines to solve practical problems.

MATH 092

3 credits

Algebra and Functions

Prerequisite(s): One of the following: MATH 085, (Principles of Mathematics 11 or Pre-calculus 11 with a C+ or higher), Principles of Mathematics 12, Pre-calculus 12, or Upgrading and University Preparation assessment.

Provides students with the algebraic background of pre-calculus 12. Content includes absolute value, polynomial, rational, radical, exponential and logarithmic expressions, equations, and functions, including graph transformations. A focus is placed on properties of functions and their applications in word problems.

MATH 093

3 credits

Trigonometry and Conics

Prerequisite(s): One of the following: MATH 092, MATH 094, MATH 096, MATH 140, Principles of Mathematics 12, Pre-calculus 12, or Upgrading and University Preparation assessment.

Supplements MATH 092 to provide students with pre-calculus 12 requirements. Content includes trigonometric and inverse trigonometric expressions, equations, and functions, as well as conics, and systems of nonlinear equations.

MATH 094

4 credits

Introduction to College Math I

Prerequisite(s): Principles of Math 12 or Pre-calculus 12; or at least a C in one of the following: Principles of Math 11, Pre-calculus 11, MATH 085, Applications of Math 12; or at least a B in Foundations of Math 12.

Manipulation of algebraic expressions; zeroes of quadratic and polynomial functions; equations involving rational exponents, radicals, rational functions, and absolute values. Functions, with emphasis on notation, graphing, transformations, inverses, and compositions. Nonlinear systems and complex numbers. Applications include optimization, motion, and area problems.

Note: This course, followed by MATH 095, is recommended for students intending to major in a science, engineering, or technology program who do not have the required Grade 12 math prerequisites. MATH 094 and MATH 095 are together equivalent to provincial Mathematics 12 and they provide the foundation for calculus courses.

MATH 095

4 credits

Introduction to College Math II

Prerequisite(s): MATH 094 with at least a C

MATH 094 and MATH 095 are together equivalent to provincial Math 12. Logarithmic and exponential functions, trigonometric functions, and geometric and arithmetic sequences and series and as time permits binomial theorem, matrices, and vectors.

MATH 096

3 credits

Algebra and Trigonometry

Prerequisite(s): One of the following: (C+ or better in MATH 085), (B- or better in one of Principles of Math 11 or Pre-calculus 11), (C or better in one of Principles of Math 12, Pre-calculus 12, or MATH 094), or Upgrading and University Preparation assessment.

Students examine an extensive variety of functions and operations on functions with emphasis on notation and graphs; solve a variety of equations and practical problems; solve combinational problems; and evaluate sums of finite or infinite series using summation notation.

Note: Students with credit for MATH 094 and MATH 095 cannot take this course for further credit.

MATH 105

4 credits

Math for the Elementary School Teacher

Prerequisite(s): One of the following: (C or better in one of Principles of Math 11 or MATH 085) or (C or better in both Foundations of Mathematics 11 and Precalculus 11) or (B or better in one of Foundations of Mathematics 11 or Precalculus 11) or (C+ or better in Applications of Math 11) or (one of Foundations of Mathematics 12 or Precalculus 12 or MATH 096; or both MATH 094 and MATH 095.)

It has been recognized by various study groups that if teachers are not at ease with mathematics, their resulting fears and prejudices are communicated to the students. This course is designed to provide a direct experience of mathematics and to allow the students to explore their reasoning strategies and gain greater confidence in their mathematical abilities. Understanding of the pertinent subject material is essential to effective teaching. It must be stressed that MATH 105 is a mathematics course aimed at developing mathematical ability and is not a course in the methods of teaching. Topics include strategies in problem solving, sets and their applications, numeration systems, properties of real numbers and their subsets, number theory, and plane geometry.

MATH 110

4 credits

Pre-Calculus Math

Prerequisite(s): One of the following: (C or better in one of Principles of Math 12 or Precalculus 12) or (C- or better in both MATH 094 and MATH 095) or (C- in MATH 096) or (C+ or better in Applications of Math 12) or (at least 55% on the MDPT).

This course is required for students who intend to study calculus and who have not obtained a mark of at least a B in Principles of Math 12 or equivalent.
MATH 110 is intended to give students an opportunity to develop the mathematics they have seen in high school and progress into a successful completion of first-year calculus. In particular, it is meant to help students strengthen their basic algebraic skills, to re-examine functions including rational, exponential, logarithmic, trigonometric, and inverse functions, and to provide a general introduction to the instantaneous rate of change as studies in calculus. Practical applications are emphasized. As the use of technology can greatly facilitate the study of mathematics, students will require a graphing calculator.

Note: Students with credit for MATH 140 cannot take this course for further credit.

MATH 111

4 credits

Calculus I

Prerequisite(s): One of the following: (B or better in one of Principles of Math 12, Precalculus 12, or MATH 096) or (B or better in MATH 095) or (C+ or better in MATH 110) or (at least 70% on the MDPT).

The study of calculus represents a major step in your education. Mathematics, previous to this subject, dealt with the description of static phenomena. During the latter part of the 17th century, a mathematical description was developed to describe and predict changing phenomena. This mathematics of change is now called calculus.
Topics include limits, derivatives, applications of derivatives such as analysis of function behaviour, optimization and related rates, antidifferentiation, polar coordinates, and parametric functions.

Note: Students with credit for MATH 141 (formerly MATH 115) cannot take this course for further credit.
Note: MATH 094 is a prerequisite for MATH 095.

MATH 112

4 credits

Calculus II

Prerequisite(s): MATH 111 with a C or better

Calculus I is concerned with finding the characteristics of change of a given quantity. In Calculus II, we examine the change in the reverse: if we know the way a quantity changes, can we determine what the quantity is? Topics include techniques of integration; application of the definite integral to various problems such as areas, volumes, average value of a function, and others from the natural and social sciences; approximate integration methods; improper integrals and their applications; an introduction to differential equations; polynomial approximations to functions; and sequences and series.

Note: Students with credit for MATH 118 cannot take this course for further credit.

MATH 118

4 credits

Calculus II for Life Sciences

Prerequisite(s): MATH 111 with a C or better

Pre- or corequisite(s): BIO 112

In this course we study the problem of how to determine a quantity given only knowledge of its rate of change. After learning the solution to such a problem, we will apply the tools of calculus to modeling systems in biology. Topics include the definite integral; interpretation and application of the definite integral; improper integrals and their applications; an introduction to differential equations; an introduction to numerical techniques of integration; analysis of models describing population dynamics, epidemics, genetics, chemical reactions, and excitable tissue.
Note: Students may receive credit for only one of MATH 112, MATH 118, and MATH 116.

MATH 123

3 credits

Everyday Math and Stats

Prerequisite(s): One of the following: (C or better in one of Principles of Mathematics 11, Applications of Mathematics 11, MATH 085, Foundations of Mathematics 11, or Pre-Calculus 11) or (B or better in Apprenticeship and Workplace Mathematics 12) or (one of Foundations of Mathematics 12, Pre-Calculus 12, Principles of Mathematics 12, or Applications of Mathematics 12) or (any MATH or STAT course numbered 094 or higher) or (45 university-level credits with department permission).

Designed for Arts and General Studies students, and anyone interested in the beauty and practical applications of mathematics and statistics in daily life. Critical thinking, problem solving, models of growth, everyday geometry, rates and percentages, normal distribution, linear regression, personal finance.

Note: Students with credit for MATH 105 cannot take this course for further credit.

MATH 124

4 credits

Finite Math with Applications in the Information Sciences

Prerequisite(s): One of the following: (C or better in one of Precalculus 11, Foundations of Mathematics 11, Principles of Mathematics 11, or MATH 085) or (one of Principles of Mathematics 12, Foundations of Mathematics 12, Precalculus 12, or MATH 094).

This class is intended to reinforce skills in algebra, graphing, and problem solving, and to provide an introduction to finite mathematical structures, algorithms, and techniques important in discrete math, statistics, and computer science. Whenever possible, concepts are motivated by information sciences applications.

MATH 125

4 credits

Introduction to Discrete Mathematics

Prerequisite(s): One of the following: (C+ or better in Principles of Math 12) or (C or better in one of MATH 124, MATH 096, Foundations of Mathematics 12, or Precalculus 12) or (C or better in both MATH 094 and MATH 095) or (B or better in Applications of Math 12) or (MATH 110).

Discrete mathematics is a new and important part of mathematics, and is concerned primarily with the analysis and computational representation of ‘finite structures’. Its applications are widespread in modern technology and include scheduling, network construction, data communications, and computer engineering. This course serves as an introduction to some of the basic techniques of the discipline, including methods of counting, modular arithmetic, and formal logic. The focus of the course will be on formulating problems into mathematical models and on methods applicable to the analysis of these models.

MATH 140

3 credits

Algebra and Functions for Business

Prerequisite(s): One of the following: C+ or better in one of Foundations of Mathematics 11 or Pre-calculus 11; or C or better in one of Principles of Math 11 or MATH 085; or one of Foundations of Mathematics 12, Pre-calculus 12, or Principles of Math 12; or a score of 17/25 or better on Part A of the MSAT.

This course is intended to give students an opportunity to develop the mathematical skills and techniques necessary for the study of differential and integral calculus with business applications. Students will strengthen their basic algebraic skills, solve small linear systems of equations by various methods, examine linear, quadratic, cubic, rational, exponential, logarithmic, and logistic models and their graphs, and study various measures of change of functions. Practical applications in business, economics, and the social sciences are emphasized. Many applications involve modeling data with piecewise continuous models.

Note: Students with credit for MATH 110 cannot take this course for further credit.

MATH 141

3 credits

Calculus for Business

Prerequisite(s): One of the following: (C+ or better in one of Foundations of Mathematics 12, Precalculus 12, Principles of Math 12, MATH 096, or MATH 110) or (C+ or better in both MATH 094 and 095) or (C or better in MATH 140) or (a score of 17/25 or better on Part B of the MSAT together with a score of 34/50 or better on Parts A and B combined).

Functions used in business, economics, and social science are analyzed, using techniques of single-variable differential and integral calculus, and the applications of these results are interpreted. Single-variable differential calculus topics include optimization, curvature analysis, related rates, marginal analysis, and linear approximation. Single-variable integral calculus topics include approximating total change and average value by antidifferentiation and the Fundamental Theorem of Calculus. Many single-variable applications make use of piecewise continuous models that are built from real data.

Note: Students with credit for MATH 111 or MATH 115 cannot take this course for further credit.

MATH 152

4 credits

Linear Algebra for Engineering

Pre- or corequisite(s): MATH 112

This course covers the solutions to linear systems of equations, vector spaces, applications to 2D and 3D geometry, linear dependence and independence, matrix algebra, determinants, orthogonal transformations and bases, application to Fourier series, eigenvalues, diagonalization, symmetric matrices, the algebra of complex numbers, the differential equations of vibrational models and linear systems of equations. This course is designed for students seeking a career in engineering. Students intending on a BSc or BA degree are recommended to take MATH 221 instead of ENGR/MATH 152.
Note: UFV math degrees require MATH 221, not MATH 152. Credit cannot be obtained for both MATH 152 and ENGR 152. This course is also listed as ENGR 152.

MATH 205

4 credits

Math for the Elementary School Teacher II

Prerequisite(s): MATH 105 with a C or better

This course will continue the aims of MATH 105 by providing a direct experience of mathematics and by encouraging students to explore reasoning strategies in solving problems appropriate to the elementary school curriculum. This course is designed to develop confidence in verbalizing mathematics to one’s peers. Topics include strategies in problem solving, descriptive statistics, an introduction to probability, coordinate geometry, elementary logic, modular arithmetic, and an introduction to graph theory.

MATH 211

3 credits

Calculus III

Prerequisite(s): C or better in one of the following: MATH 112, MATH 116, or MATH 118

This course extends the concepts of first-year calculus from the one-variable setting to a multi-variable setting. Topics include 3-dimensional analytic geometry, euclidean spaces, partial derivatives and gradient, optimization, multiple integrals, and applications.

MATH 221

3 credits

Linear Algebra

Prerequisite(s): MATH 112 with C or better, or MATH 118 with a C or better

Ideas and techniques from linear algebra lie at the core of much of mathematics and its applications in other sciences and technology. Topics include systems of linear equations, matrix algebra and determinants, vector spaces, linear transformations, diagonalization, and inner product spaces.

MATH 225

3 credits

Topics in Discrete Mathematics

Prerequisite(s): C+ or better in either MATH 112 or MATH 118

This course introduces the student to some of the most useful types of combinatorial structures: graphs, trees, generating functions, and recurrence relations, all of which play an important role in the mathematics of computers and computation.

MATH 255

3 credits

Ordinary Differential Equations

Prerequisite(s): MATH 112 or at least a B in Math 118

Pre- or corequisite(s): MATH 211 and one of the following: MATH 152, MATH 221, or PHYS 221.

This course provides theory and techniques needed to solve ordinary differential equations, with an emphasis on applications. Topics include first- and second-order linear differential equations, nonlinear equations, series solutions, Laplace transform methods, and linear systems of differential equations.

Note: This course is offered as MATH 255 and ENGR 255. Students may take only one of these for credit.

MATH 265

3 credits

Transition to Advanced Mathematics

Prerequisite(s): C+ or better in either MATH 112 or MATH 118

Students will learn to understand the language of mathematics through careful statement of definitions and construction of proofs. Important topics will be strategies for writing proofs of theorems, and how to effectively communicate mathematics to others. Upon completion of this course students will be prepared to take upper-level mathematics courses. Mathematical contexts: elementary theories of sets, integers, and the real numbers.

Note: Students with credit for MATH 214 may not take this course for further credit.

MATH 270

4 credits

Introduction to Probability and Statistics

Prerequisite(s): One of the following: MATH 112, MATH 118, or a B or better in MATH 141.

An introduction to the theory and practice of statistics for engineering and science students who have experience with calculus. Topics include descriptive statistics, probability, random variables, bionomial, hypergeometric, Poisson, uniform, normal and exponential distributions, sampling distributions, confidence intervals and hypothesis tests for means and proportions, Pearson's Chi-squared test, correlation, and linear regression.

Note: This course is offered as STAT 270 and MATH 270. Students may only take one of these for credit.

Note: Students with credit for STAT 104 or STAT 106 may subsequently take STAT 270/MATH 270, but students with credit for STAT 270/MATH 270 may not subsequently take STAT 104 or STAT 106.

MATH 312

3 credits

Vector Calculus

Prerequisite(s): MATH 211

This course extends the ideas and techniques of calculus to higher dimensions. Topics include the calculus of space curves (parametrization, tangent/normal/binormal, Frenet formulae, curvature), general orthogonal curvilinear coordinates, the calculus of vector fields (line integrals, surface integrals) and the core results of vector calculus (Stokes' Theorem, Divergence Theorem, and Green's Theorem).

MATH 316

3 credits

Numerical Analysis

Prerequisite(s): MATH 112 and one of the following: MATH 221 or MATH 152.

Pre- or corequisite(s): COMP 150 or COMP 152.

This course covers the construction and application of numerical computing solutions to mathematical problems that include applications of linear algebra, differentiation and integration, non-linear equations, the approximation of functions, and ordinary differential equations.

MATH 322

3 credits

Complex Variables

Prerequisite(s): MATH 211, and either MATH 112 with at least a C or MATH 118 with at least a B.

This course provides an introduction to complex analysis and its applications. Topics include the algebra of complex numbers, geometry of the complex plane, analytic functions, contour integration, complex power series, residue theory, and an introduction to conformal mapping.

MATH 339

3 credits

Introduction to Applied Algebraic Systems

Prerequisite(s): MATH 265 with a C or better and MATH 221

This course is an introduction to some of the fundamental structures of modern algebra; groups, rings and fields, with special attention to applications. The emphasis will be on polynomial rings, finite fields, and various concrete groups such as symmetry groups and permutation groups. Applications covered including error-correcting codes, enumeration techniques, and geometric construction arguments.

MATH 340

3 credits

Introduction to Analysis

Prerequisite(s): MATH 265

Provides an introduction to some of the fundamental ideas of mathematical analysis, the subject which forms the rigorous foundation for calculus. Limits and convergence of sequences and functions, continuity, differentiability, Cauchy sequences, the Extreme and Mean Value theorems, uniform continuity, convergence and uniform convergence of infinite series, Taylor series, the Riemann integral, and improper integrals.

Note: Students with credit for MATH 214 or MATH 320 cannot take this course for further credit.

MATH 343

3 credits

Applied Discrete Mathematics

Prerequisite(s): One of MATH 225, MATH 221, or COMP 251

Just as there is a continuum between applied math and theoretical physics, there is a continuum between applied discrete math and theoretical computing. This course is an introduction to algorithms, but with a discrete math – rather than a computing – emphasis. In particular, this course will cover some standard algorithms in combinatorics, running time analysis, correctness of algorithms, and techniques for selecting an appropriate algorithm to solve a problem.

MATH 345

3 credits

Modern Geometries

Prerequisite(s): MATH 265, MATH 211, and MATH 221, all with a C or better

Euclidean and non-Euclidean geometries, such as projective geometry, spherical geometry, and hyperbolic geometry, including transformations, symmetries, and applications.

MATH 355

3 credits

Number Theory and Applications

Prerequisite(s): MATH 265 with a grade of C or better.

An introduction to the fundamental properties of the integers and their consequences, with applications in computation, crytopgraphy, and communications. Topics include primes and gcds, congruence, (modular arithmetic), and applications (hashing functions, check digits), factorization methods, and cryptology.

MATH 368

3 credits

Operations Research

Prerequisite(s): MATH 221, or both MATH 152 and MATH 211.

Operations research is a scientific approach to decision making that seeks to best design and operate a system, usually under conditions requiring the allocation of scarce resources. This course provides an introduction to various concepts and their applications, with attention to model building and computation. An in class presentation is also a component of this course.

Topics include linear programming, sensitivity analysis and duality, integer programming, dynamic programming, game theory, and queuing theory

Note: Students with credit for MATH 308 or MATH 360 may not take MATH 368 for further credit.

MATH 370

3 credits

Probability and Stochastic Processes

Prerequisite(s): MATH 211

This course covers the theory of probability and stochastic processes for science and mathematics students who have experience with third semester calculus. Topics include probability space, conditional probability and independence, continuous and discrete random variables, jointly distributed random variables, expectation, conditional expectation and properties, limit theorems, Markov chains and Poisson processes, and simulation.

Note: This course is offered as STAT 370 and MATH 370. Students may only take one of these for credit.

MATH 381

3 credits

Mathematical Physics

Prerequisite(s): MATH 211 and (one of the following: PHYS 221 or MATH 255) and (one of the following: PHYS 112 or any other MATH course 200-level or above).

Partial and ordinary differential equations. Fourier series/transforms. Legendre polynomials. Laplace transforms. Applications to heat flow and waves. Laplace's equation in 1D, 2D, 3D using Cartesian, polar, and spherical co-ordinates. Special functions including Dirac Delta, Heaviside Theta, Si, Ci, Ei, Erf, Gamma.

Note: This course is offered as PHYS 381, MATH 381, and ENGR 257. Students may take only one of these for credit.

MATH 410

3 credits

History of Mathematics

Prerequisite(s): 21 credits in mathematics courses numbered above 110

This course surveys the development of mathematical thought from antiquity to the present day. Emphasis is placed on topics likely to be familiar to undergraduates, which include numeration, arithmetic, geometry, number theory, calculus, probability, statistics, set theory, abstract algebra, and analysis. While most of the course is concerned with so-called “Western” mathematics, consideration is paid to the development of mathematical concepts in other societies, such as the Chinese and the Mayan. The cultural and historical context in which mathematicians worked will be examined, along with the ways in which ideas about the nature and role of mathematics have changed over the centuries. Recommended for students considering a career in teaching as well as those wishing to know how their math courses fit into general and intellectual history.

MATH 415

3 credits

Ordinary Differential Equations II

Prerequisite(s): MATH 211, MATH 255, one of (MATH 214 or MATH 265), and one of (MATH 152 or MATH 221).

Qualitative properties of differential equations and systems of differential equations. Existence and uniqueness theorems for nonlinear systems, iterative techniques to approximate solutions, oscillation and comparison theorems for second-order linear equations, matrix techniques for linear systems, diffeomorphisms for nonlinear systems, and Lyapunov functions.

MATH 438

3 credits

Advanced Linear Algebra

Prerequisite(s): MATH 221, MATH 265, and at least two MATH courses 300 level or higher.

Vector spaces; linear functionals; linear operators and their representation; polynomial techniques; orthogonal projection; the adjoint; unitary and orthogonal operators; canonical forms; the singular value decomposition.

MATH 439

3 credits

Modern Algebra

Prerequisite(s): MATH 339 or MATH 355

This course is a detailed study of some of the fundamental structures of modern algebra: groups, rings, and fields, which are core to much of mathematics and have applications in physics and other sciences. The emphasis will be on the logical development of the subject and the study of fundamental examples. Precise thinking, writing, and the ability to abstract are essential.

MATH 440

3 credits

Fourier Analysis

Prerequisite(s): MATH 211, MATH 265, and one of MATH 152 or MATH 221

Fourier analysis involves the breakdown of functions into sine and cosine components. This can be done on the circle, real line, or on groups. These expansions have many applications in mathematics to areas such as signal processing and rapid numerical computations. Topics will include Fourier series and their properties, Fourier transforms, types of convergence, distributions, filtering, noise reduction, reconstruction of musical tones, and Fast Fourier transform. This will be a seminar-based course. Students will develop their presentation skills, will engage in in-depth class discussion of the course materials, and will write an independently-researched paper.

MATH 444

3 credits

Metric Spaces

Prerequisite(s): MATH 221 and either MATH 320 or MATH 340

Metric spaces are sets with a generalized notion of distance. This is a wide-reaching concept and it allows us to define properties such as continuity and convergence in many more settings than the real line. Topics will include examples of metric spaces, topological concepts such as open and closed sets, convergence, completeness, and continuity. Further topics will be drawn from contraction mappings, normed spaces, topological spaces, and fractals.

MATH 445

3 credits

Introduction to Graph Theory

Prerequisite(s): MATH 211, MATH 221 and at least two upper-level Math courses

This course is an introduction to graph theory and its applications.

MATH 450

3 credits

Statistical Distribution Theory

Prerequisite(s): MATH 370/STAT 370.

A course in mathematical statistics. Distributions of functions of random variables; transformations; beta, t, F, multivariate normal distributions; order statistics; convergence in distribution and probability; Law of Large Numbers; Central Limit Theorem; method of maximum likelihood; inference

Note: This course is offered as STAT 450 and MATH 450. Students may only take one of these for credit.

MATH 480

3 credits

Selected Topics in Mathematics

Prerequisite(s): Four upper-level Mathematics courses. Certain programs of study may require more particular prerequisites. The written permission of the instructor is required.

This course is designed for students who wish to examine in greater depth a particular topic in mathematics. It will be offered either as an individual reading course or as a seminar, depending on student and faculty interest.
Note: This course can be taken for further credit on different topics.

MATH 481

1 credit

Seminar in Mathematics

Prerequisite(s): Permission of instructor and at least 6 credits in MATH 211 or higher. Certain topics of study may require additional prerequisites.

This seminar course will examine in greater depth a particular topic of current research interest in mathematics. Topic varies depending on student and faculty interests.

MATH 499

1 credit

Honours Module

Prerequisite(s): Admission to the Mathematics Honours (Bachelor of Science) program.

Corequisite(s): The underlying course which this is supplementing (one of MATH 370, 438, 439, 440, or 444).

This course serves students in the Mathematics Honours program. It may be offered as a supplement to an upper level MATH course. Topics and course description will vary.
Note: This course will be offered under different letter designations as the accompanying course varies, and may be repeated for credit provided the letter designation differs.

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