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 waiver of a prerequisite.
If, for any student, more than three calendar years have elapsed since credit was obtained for any course prerequisite, the student concerned 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 wishing to enroll in Math 085, 094, 095 must write a Math Placement test. All other students applying for Math courses below the 100 level must write a CCP assessment.
The department will consider exceptional students for advanced standing into certain mathematics courses. See Advanced Standing.
Math Centre
UCFV is committed to helping students succeed in their study of mathematics. The Math Centres in Abbotsford and Chilliwack are open at various times throughout the week, Monday to Friday. Students are encouraged to come to the centres for help with math questions. Videos are available for courses below the 100-level; cassette tapes are available for introductory statistics; and computer 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.

MATH 0521.5 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 place value and the addition, subtraction, multiplication, and division of whole numbers. 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 0531.5 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 addition, subtraction, multiplication, and division of decimals and fractions. 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 0621.5 credits
Fundamental Math III
Prerequisite(s): Completion of MATH 051 or 053; or UUP Department permission
(assessment may be required).
This is the third of four basic mathematics courses. At this level, students will be introduced to ratios, proportion, and percent. Students will solve problems that determine a missing term. Student learning strategies include building confidence, working independently, and locating and correcting errors.

MATH 0631.5 credits
Fundamental Math IV
Prerequisite(s): MATH 062
This is the last of four basic mathematics courses. At this level, students will be introduced to units of measurement and concepts of geometry. They will also learn to obtain information from statistical graphs. They will be encouraged to use critical thinking skills throughout the course and to set further numeracy goals for themselves at the end of the course.

MATH 0714 credits
Intermediate Business Mathematics
Prerequisite(s): MATH 061 or individual assessment by UUP department
This course consists of a brief review of basic mathematics followed by the metric system, ratio and proportion, percent, statistics, positive and negative numbers, expressions and equations, percentage applications, calculating interest, perimeter, area, Pythagorean rule, and complex word problems.

MATH 0751.5 credits
Intermediate Math I
Prerequisite(s): MATH 061 or 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, percentage, and an introduction to formulas, equations, expressions, and polynomials.

MATH 0761.5 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 geometry, statistics, graphing, introduction to algebra and trigonometry, powers, roots, and scientific notations.

MATH 0843 credits
Introductory Algebra and Trigonometry
Prerequisite(s): MATH 072, MATH 076, 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 0853 credits
Intermediate Algebra and Trigonometry
Prerequisite(s): MATH 084 or UUP department permission (assessment may be required).
This course reviews basic algebraic concepts and skills, including linear functions. Absolute value, polynomial, rational, radical, and quadratic expressions, equations, and functions are studied in detail. Students will use function notation and graph relations and functions. The course reviews right-angle trigonometry and introduces the laws of sines and cosines to solve non-right triangles, with an emphasis on solving practical problems.
MATH 085 is intended to provide the background necessary for success at college level mathematics (MATH 094/095). As a prerequisite for entry into many college and university programs, MATH 085 serves as an equivalent to Principles or Applications of Math 11.

MATH 0944 credits
Introduction to College Math I
Prerequisite(s): Principles of Math 12 or at least a C in one of the following: Principles of Math 11, MATH 085, Applications of Math 12.
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.
Topics include manipulation of algebraic expressions; zeroes of quadratic and polynomial functions; equations involving rational exponents, radicals, rational functions and absolute values. Functions are studied, with emphasis on notation, graphing, transformations, inverses and compositions. Practical applications include optimization, motion, and area problems. Nonlinear systems and complex numbers are included.

MATH 0954 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. In MATH 095 the students examine logarithmic and exponential functions, trigonometric functions, and geometric and arithmetic sequences and series. Additional topics covered as time allows include the binomial theorem, matrices, and vectors.

MATH 1044 credits
Introductory Statistics
Prerequisite(s): One of the following: C or better in one of Principles of Math 11, Applications of Math 11, MATH 085, Foundations of Mathematics 11, or Precalculus 11; or B or better in Apprenticeship and Workplace Mathematics 12; or one of Foundations of Mathematics 12, Precalculus 12, Principles of Math 12, or Applications of Math 12; or 45 university-level credits with department permission.
This course is an introduction to descriptive statistics, sampling, probability, estimation, hypothesis testing, correlation, and regression. It provides an intuitive approach to why and when the procedures may be used, without involving mathematical proofs. This course is recommended for anyone who wishes to develop the ability to intelligently evaluate published statistical data, and for students of arts, criminal justice, education, and social science in particular.
As a general rule, students with Math 11 are expected to take MATH 104, those with Math 12 are expected to take MATH 106, and those with a full year of calculus are expected to take MATH 270. Students should check program requirements.
Students with credit for MATH 106 or MATH 270 are not allowed to take MATH 104. Students with MATH 104 may subsequently take MATH 270 in order to satisfy the requirements for a math degree.

MATH 1054 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 C+ or better in Applications of Math 11; or one of Foundations of Math 12 or Precalculus 12.
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 1064 credits
Statistics I
Prerequisite(s): One of the following: C or better in one of Principles of Math 12, Applications of Math 12, Foundations of Mathematics 12, Precalculus 11, MATH 110, MATH 124, or MATH 140; or C or better in both MATH 094 and MATH 095; or Precalculus 12.
This course is an introduction to descriptive statistics, sampling, probability, estimation, hypothesis testing, correlation, regression, and analysis of variances. This course is similar to MATH 104, but includes multiple regression, one-way ANOVA, and a more detailed discussion of probability results. Facility with Grade 12 level algebra is expected, but no calculus is required. As a general rule, students with Math 11 are expected to take MATH 104, those with Math 12 are expected to take MATH 106, and those with a full year of calculus are expected to take MATH 270.
Before registering, students should check the requirements of their program. UFV mathematics degrees require MATH 270. While MATH 106 is not equivalent to MATH 270, students with credit for MATH 270 are not allowed to take MATH 106. Those with credit for MATH 106 may subsequently take MATH 270 in order to satisfy the requirements for a math degree.

MATH 1083 credits
Statistics for Nursing Research
Prerequisite(s): Entry into the Nursing degree program, or permission of the Nursing Department
The emphasis of this course is on the understanding of nursing research papers. Topics include: types of data and corresponding graphical and summary description; methods of sampling from finite populations; two-way tables and independence; sensitivity and specificity; prevalence and incidence; the normal distribution; regression and correlation; measure of association; sampling proportions and rates; Pearson's chi-square; hypotheses and confidence intervals; multiple regression, validity and reliability; and experimental versus observational data. Students will use computer software, such as Minitab, or a spreadsheet.
Note: It is not intended to fulfil a statistics requirement for any program other than Nursing.

MATH 1104 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+ 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 studied in calculus. Practical applications are emphasized. As the use of technology can greatly facilitate the study of mathematics, students will require a graphing calculator.
Students may receive credit for only one of MATH 094/095 or MATH 110.

MATH 1114 credits
Calculus I
Prerequisite(s): One of the following: B or better in one of Principles of Math 12 or Precalulus 12; or B average in MATH 094 and 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.
Students may receive credit for only one of MATH 111 or MATH 115.

MATH 1124 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, fluid pressure and population growth; improper integrals and their applications; an introduction to differential equations; polynomial approximations to functions; and sequences and series.
Students may receive credit for only one of MATH 112 and MATH 116.

MATH 1244 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 Math 11, or MATH 085; or one of Principles of Math 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 a first introduction to some finite mathematical structures, algorithms, and techniques which are important in discrete math, statistics, and computer science. Topics include algebra and equations; power, polynomial, exponential, logarithmic, and root functions; graphing functions and inequalities; solving linear systems of equations; matrices and basic matrix arithmetic and algebra; use of linear programming to model problems; graphical solution methods for linear programming problems; sets and Venn diagrams; basic principles of probability; and basic counting techniques including combinations and permutations. Whenever possible, concepts will be motivated by applications in the information sciences.

MATH 1254 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, 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 come of the basic techniques of the disciple, 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 1403 credits
Algebra and Functions for Business
Prerequisite(s): One of the following: C+ or better in one of Foundations of Mathematics 11 or Precalculus 11; or C or better in one of Principles of Math 11 or MATH 085; or one of Foundations of Mathematics 12 or Precalculus 12.
MATH 140 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.

MATH 1413 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, or MATH 110; or C+ or better in both MATH 094 and 095; or C or better in MATH 140; or 63% or better on the MDPT.
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.

MATH 1524 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 1706 credits
Statistics and Mathematical Methods for Business
Prerequisite(s): Acceptance to the BBA Trades Management, or permission of the Business department
This course is an introduction to the mathematics of finance and to elementary statistics. The mathematics portion of the course covers mathematical applications to retail operations, simple and compound interest, discounts, annuities, financial papers, and depreciation methods. The statistics portion covers descriptive statistics, sampling, probability, estimation, hypothesis testing, regression, and correlation. Emphasis is on applications with the use of relevant computer software.
Credit cannot be obtained for both MATH 170 and MATH 106 or BUS 162. Credit cannot be obtained for MATH 104 after MATH 170, but credit can be obtained for MATH 170 following MATH 104.

MATH 2054 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 as well as to students in an elementary classroom. Fifteen hours of elementary classroom observation is mandatory. 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 2113 credits
Calculus III
Prerequisite(s): MATH 112 with C or better, or MATH 116 with C or better
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 2213 credits
Linear Algebra
Prerequisite(s): MATH 112 with 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 2253 credits
Topics in Discrete Mathematics
Prerequisite(s): MATH 112 with a C+ or higher
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 2353 credits
Mathematical Modeling
Prerequisite(s): MATH 112 or MATH 116
Pre- or corequisite(s): At least one of: MATH 106, MATH 152, MATH 211, MATH 221, or MATH 270
This course introduces the student to the techniques of mathematical modeling: the construction of a mathematical description of a real-world situation, and the analysis of this description. All computation will be done in a CAS (computer algebra system) environment (such as MAPLE), enabling the student to concentrate on creating and criticizing the models.

MATH 2553 credits
Ordinary Differential Equations
Prerequisite(s): MATH 112
Pre- or corequisite(s): MATH 211 and one of MATH 152, MATH 221, PHYS 221.
Most mathematical models of a physical process are in the form of differential equations. This course provides various techniques and ideas in solving ordinary differential equations with an emphasis on applications. Graphing calculators and Maple are used in this course. Topics include first- and second-order linear differential equations, non-linear equations, series solutions, Laplace transform methods, and linear systems.
Note: This course is also offered as ENGR 255. Students can receive credit for only one of MATH 255 and ENGR 255.

MATH 2653 credits
Transition to Advanced Mathematics
Prerequisite(s): MATH 112 with a C+ or higher
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 better prepared to take upper-level mathematics courses.
The mathematical contexts are the elementary theories of sets, integers, and the real numbers, which themselves form an essential background for subsequent courses.
This course is a prerequisite for the mathematics major degree and an important course for anyone studying mathematics.
Note: Students who have credit for MATH 214 may not take MATH 265 for further credit.

MATH 2704 credits
Introduction to Probability and Statistics
Prerequisite(s): MATH 112
An introduction to the theory and practice of statistics for engineering, science, and mathematics students who have experience with calculus. Topics include descriptive statistics, elementary probability theory, expectation and variance of random variables, bionomial, hypergeometric, Poisson, uniform, normal and exponential distributions, sampling distributions, confidence intervals and hypothesis tests for means and proportions, tests of goodness-of-fit and independence, correlation, simple linear regression.

MATH 3023 credits
Analysis of Observational and Experimental Data
Prerequisite(s): MATH 104 with at least a B+, or MATH 106 with at least a B, or MATH 270
This is a practical course on the use and understanding of multiple linear regression and the analysis of variance techniques. The MINITAB software is used throughout the course. Topics covered include the method of least-squares, the analysis of variance table, F tests, indicator variables, matched pairs, randomized block designs, one-way and two-way experimental designs, the comparison of regression lines, and the analysis of covariance. Logistic regression is discussed as time allows. Students complete a group project on a real data set.
Note: Students cannot obtain credit for both MATH 302 and BUS 301 in a BA or BSc degree.

MATH 3083 credits
Linear Programming
Prerequisite(s): MATH 221
Linear programming is a powerful optimization technique which is used in many areas of business, science and engineering. This course provides an introduction to many applications. The simplex method and variations thereof are covered in depth along with duality theory and sensitivity analysis. Students do analysis by hand as well as with the computer.

MATH 3123 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 3153 credits
Applied Regression Analysis
Prerequisite(s): MATH 104 with a B+ or better, or MATH 106 with a B or better, or MATH 270.
This is a practical course on the use and understanding of linear regression analysis. A statistical computer package such as MINITAB (or S-plus or SAS) software is used throughout the course. Topics include the method of least squares, the analysis of variance table, F tests, selection of predictor variables, diagnostics, remedial measures and validation, qualitative predictor variables, the comparison of regression models, the analysis of covariance, nonparametric regression, introduction to nonlinear regression analysis, and logistic regression. Students complete at least one group project using a real data set.
Note: Students cannot obtain credit for both MATH 315 and MATH 302.

MATH 3163 credits
Numerical Analysis
Prerequisite(s): MATH 112, knowledge of a programming language acceptable to the department, and either MATH 221 or MATH 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 3223 credits
Complex Variables
Prerequisite(s): MATH 211
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 3303 credits
Design of Experiments
Prerequisite(s): MATH 270 or MATH 106 with a B or better, or MATH 104 with a B+ or better.
This course discusses the construction and analysis of standard experimental designs. The basic techniques of randomization and blocking, and the use of covariates are reviewed, followed by consideration of the 2k factorial and fractional factorial designs. Repeated measures designs are next discussed, including the split-plot and cross-over varieties. Variance components analysis and response surface methods are covered as time allows.
Emphasis is on the conduct, assumption, implications and rationale of particular designs. The data analysis is implemented using statistical software. Students are expected to produce a report resulting from analyzing data collected from an experiment which they have designed and conducted and which illustrates at least one of the major designs discussed.

MATH 3393 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 3403 credits
Introduction to Analysis
Prerequisite(s): MATH 265
This course provides an introduction to some of the fundamental ideas of mathematical analysis; the subject which forms the rigorous foundation for calculus. Topics include: 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 who have credit for MATH 214 or MATH 320 may not take MATH 340 for further credit.

MATH 3433 credits
Applied Discrete Mathematics
Prerequisite(s): MATH 225 and knowledge of a computing language acceptable to the instructor
This course introduces discrete modeling. Topics covered include generation of combinatorial objects, applications to scheduling, and applications of graphs.

MATH 3453 credits
Modern Geometries
Prerequisite(s): MATH 265, MATH 211, and 221, all with a C or better
This course will study Euclidean and non-Euclidean geometries, such as projective geometry, spherical geometry, and hyperbolic geometry, including transformations, symmetries, and applications.

MATH 3503 credits
Survey Sampling
Prerequisite(s): MATH 106 with at least a B, or MATH 270, or MATH 104 with a B+
This course introduces the theory and practice of survey sampling. The basic theory of simple random sampling, stratified random sampling, ratio estimation, cluster sampling, and systematic sampling is covered, together with the more specialized topics of questionnaire design, estimation of population size, and the random response method for sensitive questions. Students are expected to produce a report resulting from analyzing data collected in a survey which they have designed and conducted and which illustrates at least one of the sample designs discussed during the course.

MATH 3553 credits
Number Theory and Applications
Prerequisite(s): MATH 265
An introduction to the fundamental ideas of number theory, with attention to applications in computation, cryptography and communications.
Topics include primes and gcds, congruence, and applications (hashing functions, check digits), factorization methods and cryptology (ciphers, public key cryptography, etc.) and continued fractions.

MATH 3603 credits
Operations Research I
Prerequisite(s): MATH 211, MATH 221, MATH 308
This course is concerned with the application of mathematical models to problems arising in industry. Operations research was developed during and just after the last world war, and has had amazing success in enabling organizations to be more effective and efficient. The topics covered include: a brief review of linear programming; dynamic and integer programming, scheduling; nonlinear programming, optimization with and without constraints; network models and applications; and PERT and CPM.

MATH 3703 credits
Probability & Stochastic Processes
Prerequisite(s): MATH 211, MATH 270
This course covers the theory of probability and stochastic processes for science and mathematics students who have experience with second-year calculus and elementary probability and statistics. 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, lifetime distributions, Cox's proportional hazard model, Kaplan-Meier estimate of the survival function, and simulation.

MATH 3813 credits
Mathematical Methods I
Prerequisite(s): MATH 211, 312, 255, 221. PHYS 111/112 recommended
This course covers a wide range of mathematical techniques: calculus problem-solving devices; Fourier series, Fourier integrals; the gamma, beta, and error functions; Bessel functions, Legendre, Hermite and Laguerre polynomials, Sturm-Liouville systems; partial differential equations; and calculus of variations.
Note: Credit cannot be obtained for more than one of MATH 381, PHYS 381, or ENGR 257.

MATH 4023 credits
Generalized Linear Models and Survival Analysis
Prerequisite(s): MATH 302 or MATH 315, and MATH 370
The course covers the application of the methods of the linear model analysis developed in MATH 302, MATH 315, and MATH 330 to non-normal data. This includes analysis of contingency tables using log-linear models, analysis of incidence data using Poisson models, analysis of binomial data using various link functions such as logit and probit, analysis of case-control data using logistic models, analysis of matched case-control data using logistic models, analysis of matched case-control data using conditional logistic regression, and analysis of survival data by adjusting for covariates or using Cox's proportional hazard model.

MATH 4103 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 4153 credits
Ordinary Differential Equations II
Prerequisite(s): MATH 211, MATH 214 or MATH 265, MATH 255 and one of MATH 152 or MATH 221
This course will study qualitative properties of differential equations and systems of differential equations. Topics include 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 4203 credits
Empirical and Non-parametric Statistics
Prerequisite(s): MATH 211 and MATH 270
Empirical and non-parametric statistics are used either when little can be assumed about the underlying distribution or when the underlying distribution is very complex. These methods are based on order statistics, rankings, or re-sampling, and are very useful when a relatively quick answer is required.

MATH 4303 credits
Time Series & Forecasting
Prerequisite(s): (MATH 270 and one of MATH 302 or MATH 315) or MATH 370
This course provides an introduction to the basic ideas of time series analysis and to the Box-Jenkins auto-regressive integrated moving-average (ARIMA) family of models in particular. It covers both the theory and applications. Students are expected to complete a group project, analyzing some real-life data in time series.
Note: Students who have credit for MATH 390 may not take MATH 430 for further credit.

MATH 4383 credits
Advanced Linear Algebra
Prerequisite(s): MATH 221 and at least two upper-level Math courses
Techniques and applications of linear algebra. Vector spaces; linear functionals; the singular value decomposition; the generalized inverse; canonical forms; the spectral decomposition.

MATH 4393 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 4403 credits
Fourier Analysis
Prerequisite(s): MATH 255 and one of MATH 320 or MATH 340
Fourier analysis is the study of functions by decomposing them into expansions in trigonometric functions. This can be done on the circle, real line or on groups. These expansions have many applications in mathematics to such areas as ordinary and partial differential equations, signal processing and rapid numerical computations. Topics are: Fourier series and their properties, Fourier transforms, distributions, and Fast Fourier transform.

MATH 4443 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 4453 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 4503 credits
Statistical Distribution Theory
Prerequisite(s): MATH 370
This is a course in mathematical statistics. It is the continuation of MATH 370 in the stream of theoretical statistics, which is designed for students specializing in either mathematics or statistics. Topics include distributions of functions of random variables; transformations of discrete and continuous random variables; beta, t, and F distributions; order statistics; multivariate normal distribution; convergence in distribution and probability; the Law of Large Numbers; the Central Limit Theorem; method of maximum likelihood; confidence intervals; and tests of statistical hypotheses.

MATH 4513 credits
Parametric Statistical Inference
Prerequisite(s): MATH 450
This course is the continuation of MATH 450 in mathematical statistics. It is designed for students specializing in either mathematics or statistics. Topics include method of maximum likelihood, Fisher information, Cramer-Rao lower bound, Neyman-Pearson theorem, uniformly most powerful tests, likelihood ratio tests, sequential probability ratio test, Monte Carlo method, bootstrap procedures, Bayesian inference, and quadratic forms

MATH 4603 credits
Operations Research II (stochastic)
Prerequisite(s): MATH 270, MATH 360
The application of mathematical methods problems in industry and business, allowing for random occurrence. Topics include decisions under uncertainty, decision trees, utility, Bayesian analysis; renewal theory, stochastic inventory control, machine maintenance problems; Markov chains, Chapman-Kolmogorov equations; queuing models; multiserver queues, networks of queues, applications of queuing models; Markov decision processes, applications to inventory control and scheduling problems; simulations, random variables, reduction of variance, number of runs; reliability theory, systems with repair.

MATH 4703 credits
Applied Methods of Multivariate Statistics
Prerequisite(s): MATH 221 and MATH 370
This course is the extension of the linear model methods of MATH 302 and MATH 315 to the multivariate situation. The emphasis of the course is on examination of a range of widely-used multivariate statistical techniques, their relationship with familiar univariate methods and the solution to practical problems. Topics include Hotelling's T^2, the analysis of dispersion, multivariate regression, principal components, factor analysis, canonical correlations, and discriminant analysis. Although theory is discussed, the emphasis is on applications.

MATH 4803 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 4811 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 4883 credits
Selected Topics in Statistics
Prerequisite(s): Four upper-level Mathematics courses, including at least three listed under the statistics option for the BA or BSc degree. 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 statistical technique or application. It will be offered either as an individual reading course or as a seminar, depending upon student and faculty interest. May not be repeated for additional credit.

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