Undergraduate Mathematics Courses

**MATH-100 College Mathematics**

Prerequisites: Placement Test. A sufficient score on the placement exam will result in placement in MATH-101X (Calculus I) or MATH-101 (Calculus I). For students without advanced credit or transfer credit for MATH-101, failure to take the placement exam will result in placement in MATH-100.

Corequisites: None

Minimum Class Standing: None

A study of functions and their algebra and graphs. Special functions of engineering and science are emphasized, including polynomial, trigonometric, and exponential functions and their inverses. Concepts and methods of algebra, trigonometry, and analytic geometry important to calculus are also emphasized. NOTE: Credits for MATH-100 do not apply to degree requirements (except the BBA). Also placement in MATH-100 may delay entry in courses for which calculus is a prerequisite. Terms Offered: All

**MATH-101 Calculus I**

Prerequisites: MATH-100, MATH-100X. or sufficient score on the placement exam

Corequisites: None

Minimum Class Standing: None

An introduction to the theory and techniques of differentiation of polynomial, trigonometric, exponential, logarithmic, hyperbolic, and inverse functions of one variable. Also included are limits, continuity, derivative applications and interpretations. Computer software will be used to aid in understanding these topics. Terms Offered: All

**MATH-101X Calculus I**

Prerequisites: MATH-100, a sufficient score on the placement exam, or permission of the Department Head

Corequisites: None

Minimum Class Standing: None

This course is for students showing a lack of proficiency in algebra and trigonometry on the placement examination. The course contains the same material as MATH-101 but in addition, includes a review of algebraic expressions, trigonometic functions and their inverses, and analytic geometry. Computer software will be used to aid in understanding these topics. Terms Offered: Summer, Fall

**MATH-102 Calculus II**

Prerequisites: MATH-101 or MATH-101X

Corequisites: None

Minimum Class Standing: None

Riemann integration and the Fundamental Theorem of Calculus, including applications to area, volume, etc., and basic methods for conversion of integrals including change of variable, substitutions, partial fractions, integration by parts, improper integrals and numerical integration. Also introduced are sequences and series in one variable with emphasis on Taylor Series. Computer software will be used to aid in understanding these topics. Terms Offered: All

**MATH-102H Calculus II - Honors**

Prerequisites: MATH-101 or MATH-101X, and professor‘s recommendation

Corequisites: None

Minimum Class Standing: None

Honors Calculus II is a deeper, more conceptual, rigorous, and limit based version of Calculus II (MATH-102). It is designed for students with strong mathematical skills. Riemann integration and the Fundamental Theorem of Calculus, including applications to area, volume, etc., and basic methods for conversion of integrals including change of variable, substitutions, partial fractions, integration by parts, improper integrals and numerical integration. Also introduced are sequences and series in one variable with emphasis on Taylor Series. Computer software will be used to aid in understanding these topics. Terms Offered: All

**MATH-203 Multivariate Calculus**

Prerequisites: MATH-102 or MATH-102H

Corequisites: None

Minimum Class Standing: None

A study of polar coordinates, parametric equations, and the calculus of functions of several variables with an introduction to vector calculus. Topics include surface sketching, partial derivatives, gradients, differentials, multiple integrals, cylindrical and spherical coordinates and applications. Computer software will be used to aid in understanding these concepts. Terms Offered: All

**MATH-203H Multivariate Calculus – Honors**

Prerequisites: MATH-102 or MATH-102H, and professor‘s recommendation

Corequisites: None

Minimum Class Standing: None

Honors Multivariate Calculus is an extended, deeper, more conceptual, rigorous, and limit-based version of Multivariate Calculus (MATH-203). The course is designed for students with strong mathematical skills. The topics include parametric equations, polar, Cartesian, cylindrical, and spherical coordinates, vector algebra, equations of lines, planes, and quadratic surfaces, calculus of functional of several variables, unconstrained and constrained optimization problems, multidimensional integrals, change of variables, and elements of vector calculus. Computer software will be used to aid in understanding these topics and for graphical visualization. Terms Offered: All

**MATH-204 Differential Equations and Laplace Transforms**

Prerequisites: MATH-203 or MATH-203H

Corequisites: None

Minimum Class Standing: None

An introduction to the principles and methods for solving first order, first degree differential equations, and higher order linear differential equations. Includes a study of the Laplace transform and its application to the solution of differential equations. Existence and uniqueness theorems for O.D.E.‘s are also discussed. Terms Offered: All

**MATH-204H Differential Equations and Laplace Transform Honors**

Prerequisites: MATH-203H or MATH-203, and professor‘s recommendation

Corequisites: None

Minimum Class Standing: FR 1

Honors Differential Equations and Laplace Transform is an extended, deeper, more conceptual, rigorous version of MATH-204. The course is designed for students with strong mathematical skills. The additional topics include Cauchy-Euler Equation, the Dirac Delta Function, Linear Models: Boundary Value Problems, Systems of Linear Differential Equations, and optional advanced topics, e.g. Power Series Solution and Solutions About Singular Points. Terms Offered: All

**MATH-205 Applied Probability and Statistics**

Prerequisites: MATH-203 or MATH-203H

Corequisites: The student may take MATH-203 as a co-requisite but must have permission from the instructor.

Minimum Class Standing: SOI

The study of the basic concepts and methods of probability and statistics. Topics covered include sample spaces, counting techniques, laws of probability, conditional probability, and dependence and independence. Broad variety of discrete and continuous distributions are studied, including moment generating functions. Functions of random variables are considered. The central limit theorem and sampling distributions are applied to point and interval parameter estimation. Broad aspects of testing statistical hypotheses for a simple population are included. Some applied statistical techniques are practiced with a statistical package. Terms Offered: Winter, Spring

**MATH-305 Numerical Methods and Matrices**

Prerequisites: MATH-204 or MATH-204H

Corequisites: None

Minimum Class Standing: SOII

An introduction to numerical methods including the study of iterative solutions of equations, interpolation, curve fitting, numerical differentiation and integration, and the solution of ordinary differential equations. An introduction to matrices and determinants; application to the solution of linear systems. Terms Offered: All

**MATH-307 Matrix Algebra**

Prerequisites: MATH-101

Corequisites: MATH-102

Minimum Class Standing: None

A study of matrix concepts including such topics as basic algebraic operations, determinants, inversion, solution of systems of linear equations, vector spaces, basis and dimension, eigenvalues, and eigenvectors. Terms Offfered:All

**MATH-308 Abstract Algebra**

Prerequisites: MATH-307 or CS-211 and MATH-101

Corequisites: None

Minimum Class Standing: SOI

Students will learn topics in modern algebra and will practice proof techniques. Topics will include: congruence classes, modular arithmetic, groups, subgroups, normal subgroups, Lagrange‘s theorem, rings, subrings, ideals, quotient rings, isomorphisms and homomorphisms, polynomial arithmetic, fields, divisors, factorization, and proofs of the main theorems. The course is required for mathematics majors and is also useful in cryptography and quantum physics. Terms Offered: Summer, Fall

**MATH-310 Biostatistics I**

Prerequisites: MATH-102 or MATH-102H

Corequisites: None

Minimum Class Standing: SOI

Students will learn methods of biostatistics and its applications in life sciences. Topics include: Descriptive Statistics; Elements of Probability theory; Bayes Rule; Discrete and Continuous Probability distributions; One-sample and two-sample estimation and hypothesis testing; Bayesian inference; Nonparametric Methods; Simple Regression Analysis. Computer packages such as MINITAB will be used for all applications and the analysis of data sets. Terms Offered: All

**MATH-313 Boundary Value Problems**

Prerequisites: MATH-204 or MATH-204H

Corequisites: None

Minimum Class Standing: SOII

An introduction to linear partial differential equations (PDE‘s) and basic techniques of applied mathematics used to solve initial, boundary value problems associated with these equations. Topics include: derivation of some of the fundamental PDE‘s‘ and boundary conditions that arise in science and engineering; Fourier Series; Sturm-Liouville Systems including eigenvalues, eigenfunctions and eigenfunction expansions; the separation of variables techniques; Fourier Transforms. Applications to problems of science and engineering will be given throughout the course. Terms Offered: Summer, Fall

**MATH-317 Advanced Matrix Theory**

Prerequisites: MATH-307

Corequisites: None

Minimum Class Standing: JR

A study of theory and applications of matrix algebra including determinants, rank, linear transformations, characteristic values, functions of matrices, orthogonality, similarity, and other advanced topics. Terms Offered: As Needed

**MATH-321 Real Analysis I**

Prerequisites: MATH-203 or MATH-203H

Corequisites: None

Minimum Class Standing: JR

A more advanced study of functions in one real variable including limits, uniform continuity, differentiation, integration, and sequences and series of functions; topology of R. Terms Offered: As Needed

**MATH-327 Mathematical Statistics I**

Prerequisites: MATH-203 or MATH-203H

Corequisites: None

Minimum Class Standing: JRI

A study of random variables and their distribution functions including expectations, transformations, moment generating functions, stochastic independence, and sampling distribution. Also, a study of order statistics and limiting distributions of sample mean. Terms Offered: Winter, Spring

**MATH-328 Methods of Applied Mathematics**

Prerequisites: MATH-204 or MATH-204H

Corequisites: None

Minimum Class Standing: JRI

Topics from advanced calculus, dimensional analysis and scaling, perturbation and asymptotic methods, calculus of variations and integral equations. Applications of these tools to problems in engineering will be included. Terms Offered: Winter, Spring

**MATH-350 Financial Mathematics**

Prerequisites: MATH-102 or MATH-102H and BUSN-226 or MATH-327 or MATH-408

Corequisites: None

Minimum Class Standing: JRI

The course will provide an understanding of the fundamental concepts of financial mathematics. Definitions of key terms will be studied, including inflation, rates of interest, term structure of interest rates, yield rate, equation of value, accumulation function, discount function, annuity, perpetuity, stocks, bonds, mutual funds. Procedures like determining equivalent measures of interest, discounting, accumulating, amortization will be covered. Modern topics of financial analysis will be introduced, such as yield curves, spot rates, forward rates, duration, convexity, immunization, and short sales. Key terms of financial economics at an introductory level will be provided: derivatives, forwards, futures, short and long positions, call and put options, spreads, collars, hedging, arbitrage, and swaps. Terms Offered: Winter, Spring

**MATH-360 Life Contingencies I**

Prerequisites: MATH-350

Corequisites: None

Minimum Class Standing: JR

This course is an introduction to life insurance mathematics based on a stochastic approach. This course is to develop a student‘s knowledge of the theoretical basis of certain actuarial models and the application of those models to insurance and other financial risks. Definitions of key terms will be studied, including actuarial present value, survival model, life insurance, annuities, and benefit premiums. Terms Offered: Summer, Fall

**MATH-361 Life Contingencies II**

Prerequisites: MATH-360

Corequisites: None

Minimum Class Standing: JRII

This is a continuation of Life Contingencies I. Development is based on a stochastic approach to life insurance models. Definitions of key terms will be studied, including benefit reserves, and multi-life and multiple-decrement models. Terms Offered: Winter, Spring

**MATH-408 Probability and Statistics**

Prerequisites: MATH-203 or MATH-203H

Corequisites: None

Minimum Class Standing: SOII

This is a course in engineering statistics. Fundamentals of probability are introduced together with examples of discrete and continuous random variables. Descriptive and inferential statistics for one and two populations is covered. Simple linear regression, one-way and two-way and ANOVA DOE including factional designs are discussed. Elements of reliability and SPC are covered. The use of statistical software is a necessary part of this course. A brief introduction to MINITAB (a statistical package) is given. Terms Offered: All

**MATH-410 Biostatistics II**

Prerequisites: MATH-310

Corequisites: None

Minimum Class Standing: SOII Design of experiments and data analysis useful in Biostatistics including analysis of variance and covariance, nested designs, multiple regression, logistic regression and log-linear models. Life sciences applications and case-studies. Computer packages such as MINITAB will be used for all applications and the analysis of data sets. Terms Offered: All

**MATH-412 Complex Variables**

Prerequisites: MATH-203 or MATH-203H

Corequisites: None

Minimum Class Standing: SO

An introduction to the theory of complex variables. Includes basic algebra of complex numbers, analytic functions and the Cauchy-Riemann equations, elementary transformations, complex integration, the Cauchy integral formulas, Taylor and Laurent series, and the theory of residues. Terms Offered: As Needed

**MATH-416 Vector Analysis**

Prerequisites: MATH-203 or MATH-203H

Corequisites: None

Minimum Class Standing: SOII

An introduction to vector algebra and calculus including vector products, vector functions, and their differentiation and integration, gradients, line and surface integrals, conservative fields and potentials functions, Green‘s theorem, parametric equations, curvature, and curvilinear coordinates. Terms Offered: Winter, Spring

**MATH-418 Intermediate Differential Equations**

Prerequisites: MATH-204 or MATH-204H, MATH-305

Corequisites: None

Minimum Class Standing: JRI

A study of systems of linear and nonlinear ordinary differential equations (ODE‘s). Systems of linear ODE‘s, matrix methods, variation of parameters, and perturbation methods and boundary layers, phase portraits and stability of nonlinear ODE‘s. Numerical methods for solving systems of ODE‘s will be presented and used to solve physical problems of applied mathematics and engineering. Terms Offered: Summer, Fall

**MATH-420 Mathematical Modeling**

Prerequisites: MATH-204 or MATH-204H, MATH-205, MATH-305

Corequisites: None

Minimum Class Standing: JRI

A study of the process of translating real-world problems into mathematical models. Various methods of formulation and solution of models will be illustrated by practical examples. Terms Offered: Summer, Fall

**MATH-421 Real Analysis II**

Prerequisites: MATH-317, MATH-321

Corequisites: None

Minimum Class Standing: JRII

An introduction to the study of real functions including metric spaces, normed linear spaces, Hilbert Spaces, and linear operators. Terms Offered: Winter, Spring

**MATH-423 Partial Differential Equations**

Prerequisites: MATH-305, MATH-313

Corequisites: None

Minimum Class Standing: JRI

This course is a continuation of MATH-313. Topics include Bessel‘s equation and Legendre‘s equation, boundary value problems in curvilinear coordinate systems, Green‘s functions for ordinary and partial differential equations. Applications to problems of science and engineering will be given throughout the course. Terms Offered: Winter, Spring

**MATH-427 Mathematical Statistics II**

Prerequisites: MATH-327

Corequisites: None

Minimum Class Standing: JRI

A further study of statistics including point and interval estimation, sufficient statistics, Bayes estimates, UMP tests, likelihood ratio tests, goodness of fit tests, an introduction to non-parametric methods. Regression analysis and ANOVA models are included. Terms Offered: Summer, Fall

**MATH-428 Sampling Theory**

Prerequisites: MATH-426

Corequisites: None

Minimum Class Standing: SRI

A study of sampling theory including probability sampling, simple random sampling, sample size estimates, stratified sampling, and cluster sampling. Terms Offered: Winter, Spring

**MATH-438 Data Analysis for Engineers and Scientists**

Prerequisites: IME-332 or MATH-205 or MATH-408

Corequisites: None

Minimum Class Standing: SRI

This course will cover topics in sampling techniques, data analysis and regression, design of experiments, and statistical quality and process control. In this course, the student will be given hands-on experience by combining lectures with laboratory classes involving the use of computers and appropriate statistical packages. The student taking this course is assumed to have taken an introductory course in probability and statistics. Terms Offered: As Needed

**MATH-448 Time Series**

Prerequisites: MATH-327

Corequisites: None

Minimum Class Standing: SRI

This course is designed to provide a working knowledge of time series and forecasting methods as applied in economics, engineering, and the natural and social sciences. Terms Offered: Summer, Fall