MATH 052
1.5 credits
Fundamental Math I
Prerequisite(s): UUP department permission (assessment is required).
The first of four fundamental-level mathematics courses. Covers place value, estimation, operations on whole numbers, area and perimeter, and initial measurement.
MATH 053
1.5 credits
Fundamental Math II
Prerequisite(s): UUP department permission (assessment is required).
The second of four fundamental-level mathematics courses. Introduces operations on fractions and decimals, and covers estimation, measurement, and problem solving.
MATH 062
1.5 credits
Fundamental Math III
Prerequisite(s): One of the following: MATH 051, MATH 053, or UUP department permission (assessment is required).
The third of four fundamental-level 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 UUP department permission (assessment is required).
The last of four fundamental-level 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 is 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 is 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 a C or better), (Principles of Mathematics 11, Applications of Mathematics 11, Foundations of Mathematics 11, or Pre-calculus 11 with a C- or better), or UUP department permission (assessment is required).
Provides skills in algebraic manipulations to satisfy MATH 085 prerequisites.
Note: This course can be used as a mathematics credit for the UUP Advanced Level certificate, the Provincial Adult Dogwood, or as preparation for some vocational, career, and technical programs.
MATH 085
3 credits
Intermediate Algebra and Trigonometry
Prerequisite(s): One of the following: MATH 084, (Foundations of Mathematics and Pre-calculus 10 with a B or better), (one of Principles of Mathematics 11, Applications of Mathematics 11, Foundations of Mathematics 11, or Pre-calculus 11 with a C or better), (one of Foundations of Mathematics 12 or Pre-Calculus 12 with a C- or better), or UUP department permission (assessment is 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 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 Mathematics 11 or Pre-calculus 11), (C or better in one of Principles of Mathematics 12, Pre-calculus 12, MATH 092, 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, or MATH 092 and MATH 093 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 Mathematics 11, Pre-calculus 11, Foundations of Mathematics 12, or MATH 085) or (C+ or better in Applications of Mathematics 12) or (B or better in one of Foundations of Mathematics 11, Calculus 12, Geometry 12, or Statistics 12) or (Pre-calculus 12) or (any UFV MATH course numbered 092 or higher) or (a score of 17/25 or better on Part A of the MSAT).
Designed for students interested in teaching at the elementary level. Students will work towards developing a profound understanding of fundamental mathematics through physical, pictorial, and symbolic representations. Students will be provided with direct experiences of elementary mathematics through examples of young learners’ mathematical methods. Topics include problem solving strategies, sets, numeration systems, conceptualizations and arithmetic of rational numbers, number theory, ratios, and Euclidean geometry.
Note: MATH 105 is a mathematics course aimed at developing mathematical ability and is not a course in the methods of teaching.
MATH 110
4 credits
Pre-Calculus Math
Prerequisite(s): One of the following: (C or better in one of Principles of Mathematics 12 or Pre-calculus 12) or (B or better in Calculus 12) or (both MATH 092 and MATH 093) or (both MATH 094 and MATH 095) or (MATH 096) or (C+ or better in Applications of Mathematics 12) or (at least 55% on the MDPT).
Designed to prepare students for first-year calculus courses. Topics include basic algebraic skills, operations, and properties and graphs of functions including polynomial, rational, exponential, logarithmic, trigonometric, and inverse functions.
MATH 111
4 credits
Calculus I
Prerequisite(s): One of the following: (A or better in Calculus 12) or (B or better in one of Principles of Mathematics 12, Precalculus 12, MATH 095, or MATH 096) or (B or better in both MATH 092 and MATH 093) or (C+ or better in MATH 110) or (at least 70% on the MDPT).
Note: MATH 094 is a prerequisite for MATH 095.
Covers differential calculus of a function of one variable. Topics include: limits, continuity, differentiation of algebraic, trigonometric, inverse trigonometric, exponential and logarithmic functions, curve sketching, optimization, related rate problems, an introduction to antidifferentiation, polar coordinates and parametric equations.
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.
Students will study the problem of determining a quantity given only knowledge of its rate of change. Designed for students with interest
in life sciences, the topics will be motivated by authentic biological, chemical, ecological, epidemiological, and medical applications.
Note: Students with credit for MATH 112 cannot take this course for further credit.
MATH 123
3 credits
Everyday Math and Stats
Prerequisite(s): One of the following: (C or better in one of Applications of Mathematics 11, Foundations of Mathematics 11, Principles of Mathematics 11, Pre-calculus 11, Apprenticeship Mathematics 12, Calculus 12, Geometry 12, Statistics 12, or MATH 085) or (B or better in one of History of Mathematics 11, Workplace Mathematics 11, or Apprenticeship and Workplace Mathematics 12) or (one of Applications of Mathematics 12, Foundations of Mathematics 12, Principles of Mathematics 12, or Pre-calculus 12) or (any MATH or STAT course numbered 092 or higher) or (a score of 17/25 or higher on Part A of the MSAT) or (45 university-level credits).
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, and personal finance are covered.
MATH 124
4 credits
Finite Math with Applications in the Information Sciences
Prerequisite(s): One of the following: (C+ or better in both Statistics 12 and Computer Science 12) or (C or better in one of Foundations of Mathematics 11, Principles of Mathematics 11, Pre-calculus 11, or MATH 085) or (one of Foundations of Mathematics 12, Principles of Mathematics 12, Pre-calculus 12, MATH 092, MATH 094, or MATH 096) or (a score of 17/25 or better on Part A of the MSAT).
Reinforces skills in algebra, graphing, and problem solving, and provides 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 both Pre-calculus 11 and Geometry 12) or (C+ or better in both Pre-calculus 11 and Statistics 12) or (C+ or better in Principles of Mathematics 12) or (C or better in one of Foundations of Mathematics 12, Pre-calculus 12, MATH 092, MATH 096, or MATH 124) or (C or better in both MATH 094 and MATH 095) or (B or better in Applications of Mathematics 12) or (MATH 110) or (a score of 17/25 or better on Part B of the MSAT together with a score of 34/50 on Parts A and B combined).
Serves as an introduction to some basic techniques in discrete mathematics, including methods of counting, recursion, 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 Pre-calculus 11 or Calculus 12) or (C or better in one of Principles of Mathematics 11, Pre-calculus 12, or MATH 085) or (one of Principles of Mathematics 12, MATH 092, or MATH 096) or (a score of 17/25 or better on Part A of the MSAT).
Develops mathematical skills and techniques necessary for the study of calculus with business applications. Topics include small linear systems of equations, linear, polynomial, rational, exponential, and logarithmic functions and their properties. Applications in business, economics, and the social sciences are emphasized.
MATH 141
3 credits
Calculus for Business
Prerequisite(s): One of the following: MATH 140 or MATH 110 or (B or better in Calculus 12) or (C+ or better in one of Principles of Mathematics 12, Pre-calculus 12, MATH 096, or MATH 092) or (C+ or better in both MATH 094 and 095) 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. Topics include optimization, curvature analysis, related rates, marginal analysis, linear approximation, and approximation of total change and average value by antidifferentiation and the Fundamental Theorem of Calculus.
MATH 152
4 credits
Linear Algebra for Engineering
Pre- or corequisite(s): MATH 112
Intended for engineering students, this course covers basic problems and concepts in Euclidean space, such as matrix algebra, solutions to linear systems of equations, determinants, and eigenvalue problems. Emphasis throughout the course is placed on applications in science and engineering.
Note: This course is offered as MATH 152 and ENGR 152. Students may take only one of these for credit.
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 MATH 112 or MATH 118.
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): C or better in one of MATH 112 or MATH 118.
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.
Introduces students 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.
Introduction to elementary logic, structures and discourse of mathematics, and the communication of mathematical ideas. Topics include logic, proof techniques, set theory, number theory, real and complex numbers, proof structure, strategy, effective mathematical communication and the LaTeX typesetting language.
Note: Students with credit for MATH 214 cannot 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 and their probability distributions, sampling distributions, confidence intervals and hypothesis tests for means and proportions, Pearson’s Chi-squared tests, 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: As a general rule, students with Mathematics 11 are prepared to take STAT 104, those with Mathematics 12 are prepared to take STAT 106, and those with a full year of calculus are prepared to take STAT/MATH 270. Before registering, students should check the requirements of their program. The Mathematics major program requires STAT/MATH 270, while the Mathematics minor program requires STAT 106 or STAT/MATH 270.
MATH 312
3 credits
Vector Calculus
Prerequisite(s): MATH 211.
This course concludes the traditional calculus sequence. Fundamental forms of derivative and integral are extended into two- and three-dimensional settings. Focus of the course is geometry of space curves and core results of calculus on vector fields
Note: Students with credit for MATH 212 cannot take this course for further credit.
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 one of MATH 112 with a C or better or MATH 118 with B or better.
Introduces 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 further topics such as conformal mappings, fractals, and stereographic projections, as time permits.
MATH 339
3 credits
Introduction to Field Theory and Applications
Prerequisite(s): MATH 221 and MATH 265.
An introduction to fields and rings, two of the fundamental structures of modern algebra, with special attention to applications. Applications covered include public key cryptography, error-correcting codes, 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.
Algorithms are studied with an emphasis on discrete math, rather than programming. 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 211, MATH 221, and MATH 265.
Students will study problems and constructions in Euclidean and non-Euclidean geometries, such as projective geometry, spherical geometry, and hyperbolic geometry. Topics include the parallel postulate and its consequences, transformations, symmetries and applications.
MATH 355
3 credits
Number Theory and Applications
Prerequisite(s): MATH 265.
An introduction to the fundamental properties of the integers and their consequences, with applications in computation, cryptography, 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.
Theory of probability and stochastic processes for science and mathematics students. Topics include probability space, conditional probability and independence, continuous and discrete random variables, jointly distributed random variables, expectation
conditional expectation and properties, simulating data from distributions, limit theorems, Markov chains and Poisson processes, and Markov Chains Monte Carlo (MCMC).
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.
Surveys the development of mathematical thought from antiquity to the present day. Students will examine historically significant writings, important contributions and famous problems stemming from a variety of cultures. Mathematical material will be considered within the cultural and historical context.
Note: 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 416
3 credits
Partial Differential Equations
Prerequisite(s): MATH 211, one of (MATH 152 or MATH 221), MATH 255, and MATH 265.
First order equations, characteristics, and shocks; classification of second order equations; well-posed problems; eigenfunction expansions; maximum principles and qualitative methods. Examples drawn from gas dynamics, heat flow, wave phenomena, and financial mathematics.
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
Group Theory
Prerequisite(s): MATH 339 or MATH 355.
Groups are a fundamental structure of modern algebra with many applications in the sciences. Introduces the basic examples, constructions, and theorems of elementary group theory and explores applications within mathematics and beyond.
MATH 440
3 credits
Fourier Analysis
Prerequisite(s): MATH 211, MATH 265, and one of MATH 152/ENGR 152 or MATH 221.
The decomposition into trigonometric components of functions defined on the real line, on the circle, and on groups. Convergence criteria. Topics will be chosen from signal processing, filtering, Fast Fourier Transform, distributions, and reconstruction of musical signals.
MATH 444
3 credits
Metric Spaces
Prerequisite(s): MATH 221 and MATH 340.
Metrics are generalized notions of distance, allowing concepts such as continuity and convergence to be studied in more general settings than Euclidean space. Topics include topological concepts such as open and closed sets, convergence,completeness, continuity, connectedness and compactness.
MATH 445
3 credits
Introduction to Graph Theory
Prerequisite(s): One of (MATH 221, MATH 265, or MATH 225) and (at least two MATH courses 300-level and above).
Graphs are used to model a wide variety of practical problems, such as scheduling and network architecture, facilitating the visualization of small instances of problems with diagrams. Topics covered include connectivity, trees, planarity, colouring, matchings, independent sets, and Eulerian and Hamiltonian graphs.
MATH 450
3 credits
Statistical Theory
Prerequisite(s): MATH 370/STAT 370 or (MATH 270/STAT 270 and MATH 211).
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 and instructor's permission. Certain programs of study may require more particular prerequisites.
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 will be offered under different letter designations (e.g. C-Z) representing different topics. This course may be repeated for credit provided the letter designation differs.
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.
