# Course Descriptions

### Mathematics Courses (*Statistics Courses)

115 Calculus I 4 cr.
Limits, continuity, and differentiation of algebraic, exponential, logarithmic, trigonometric, and inverse trigonometric functions. Sum, product, quotient and chain rule formulas for differentiation. Logarithmic and implicit differentiation. Linearization and differentials. Indeterminate forms and L’Hospital’s Rule. Graphing using the first and second derivative. Application of the derivative to optimization and related rates problems. Indefinite and definite integrals. Substitution rule for integration. Application of the definite integral to area problems. Credit is not allowed for both MATH 115/104, MATH 115/114, or MATH 115/111. Prerequisite: grade of "C" or better in MATH 105, or evidence of mastery of college algebra skills and trigonometry
116 Calculus II 4 cr.
Applications of integration (areas, volume, work, arc length, surface area), additional techniques of integration, improper integrals, infinite sequences and series, including tests of convergence, power series, Taylor and Maclaurin series. Prerequisite: grade of "C" or better in MATH 114 OR MATH 115.
215 Calculus III 4 cr.
Parametric equations, polar coordinates, calculus of functions of several variables and vector-valued functions, including double and triple integrals using various coordinate systems. Prerequisite: grade of "C" or better in MATH 116.
250 Foundations of Higher Mathematics 3 cr.

An introduction to higher-level mathematics. Topics include mathematical logic, sets, relations, functions, number systems and countability. The course emphasizes mastery of proof writing techniques including conditional, biconditional, contradiction, induction, set-theoretic, and existence and uniqueness proofs. Prerequisite: grade of "C" or better in MATH 116.

301 Introduction to Probability and Statistics I  3 cr.
Univariate and multivariate probability distributions of discrete and continuous random variables, mathematical expectation, limit theorems, random variable transformations, moment generating functions. Prerequisite: grade of "C" or better in MATH 116.
302W Introduction to Probability and Statistics II  3 cr.
Sampling distributions of random variables, confidence intervals, and hypothesis testing for one and two sample settings. ANOVA, simple linear regression, estimation techniques, properties of estimators, likelihood ratio test. Prerequisite: grade of "C" or better in MATH 301.
308 Numerical Analysis 3 cr.
Linear systems, interpolation, functional approximation, numeric differentiation and integration, and solutions to non-linear equations. May be counted as either mathematics or computer science, but not both. Prerequisites: grade of "C" or better in COSC 150/160 and in Math 116.
310 Linear Algebra 3 cr.
Systems of linear equations, matrix operations, determinants, vector spaces and subspaces, linear transformations, change of basis, eigenvalues and eigenvectors, diagonalization, and orthogonality. Prerequisites: grade of "C" or better in MATH 116. Credit is not allowed for both MATH 210 and MATH 310.
311 Number Theory 3 cr.
Divisibility, congruences, quadratic residues, Diophantine equations, and arithmetic functions. Prerequisite: grade of "C" or better in MATH 250.
314 Differential Equations 3 cr.
First-order ordinary differential equations, theory and solutions of higher order linear ordinary differential equations, the Laplace transform, numerical solutions of differential equations, applications to physical sciences and engineering. Prerequisite: grade of "C" or better in MATH 116.
325W Applied Statistics with Regression  3 cr.
TThis course begins with a review of inferential statistics. Emphasis on data collection methods, stating hypotheses, confidence intervals and bootstrapping methods for estimating parameters are introduced. Both traditional and re-sampling methods are demonstrated for testing hypotheses. Additional topics covered are graphical methods for exploring distributions and determining outliers, 1-way and 2- way analysis of variance models using a linear models approach, and linear and multiple regression methods. JMP software is used for demonstrating methods. Prerequisites: grade of "C" or better in MATH 225 or in MATH 301.
330W Fundamentals of Geometry 3 cr.
Euclidean and Non-Euclidean geometry from both the synthetic and metric axiomatic approach. Prerequisite: grade of "C" or better in MATH 250.
335 Biostatistics II * 3 cr.
This course is a continuation of MATH 225 (Introduction to Biostatistics). Topics include two-sample hypothesis testing, analysis of variance, correlation methods, simple linear regression, multiple regression, logistic regression, chi-square tests, and nonparametric statistical procedures. Prerequisite: grade of "C" or better in MATH 225.
340 Problem Solving Seminar 1 cr.
Solution and discussion of problems from the Putnam Examination and other sources. Completion of or concurrent enrollment in MATH 215 or permission of instructor.
350W History of Mathematics 3 cr.
Multicultural survey of the history of mathematics from the development of number systems to the development of calculus. Contributions of ancient Greek and western mathematics are emphasized, but those of Egyptian, Babylonian, Islamic, Hindu, and Chinese cultures are also discussed. Prerequisite: grade of "C" or better in MATH 311.
PHYS 350 Mathematical Methods in Physics 3 cr.
A variety of theoretical methods that are useful for general problem-solving in advanced science and engineering courses: complex numbers and functions of a complex variable, Fourier series and transforms, Laplace transforms, Legendre, Laguerre and Hermite polynomials, calculus of variations, special functions and tensor analysis or other content as determined appropriate in support of upper level physics coursework. Prerequisites: MATH 215, MATH 210 (can be taken concurrently) and MATH 314 (can be taken concurrently).
366 Operations Research 3 cr.
The course will provide an introduction to the background of operations including example problems and a brief history. An extensive discussion of the theory and application of linear programming will follow. Other topics will include nonlinear programming, continuous and discrete probability models, dynamic programming, game theory and transportation and network flow models. Prerequisite: grade of "C" or better in MATH 310.
371 Optimization 3 cr.
Linear programming, transportation problem, network flow, nonlinear convex programming, dynamic programming, geometric programming, game theory, and gradient methods. Prerequisites: grade of “C” or better in MATH 215 or equivalent and MATH 310.
373 Statistical Computing 3 cr.
Generating pseudo-random numbers, Monte Carlo integration, simulation, Bayesian inference, Gibbs sampling, Metropolis sampling, Metropolis-Hastings sampling, the E-M algorithm, multivariate Newton-Raphson maximization. Prerequisites: grade of "C" or better in MATH 302W, and COSC 150 or COSC 160.
390 Internship 1 to 3 cr.
Internship suitably related to the program as determined by the Faculty Advisor and dependent on the approval of the Department. May be repeated for a total of up to three credits. Prerequisites: grade of "C" or better in MATH 215 and in MATH 310.
410 Advanced Linear Algebra 3 cr.
This is a second course in linear algebra that provides an in-depth study of fundamental concepts of the subject. Topics include general vector spaces, eigenvalues and eigenvectors, inner products and orthogonality, the Gram-Schmidt process, QR factorization, singular value decomposition, the Spectral Theorem, and least squares and the generalized inverse. Prerequisites: grade of "C" or better in MATH 250 and MATH 310.
411W Abstract Algebra I 3 cr.
An introduction to algebraic structures with emphasis on groups, including subgroups, abelian and cyclic groups, permutation groups, cosets, and quotient groups, as well as homomorphisms and isomorphisms. Prerequisites: grade of "C" or better in MATH 215, in MATH 250, and in MATH 310.
412W Abstract Algebra II 3 cr.
A deeper examination of algebraic structures including rings, ideals, integral domains, fields, and other selected topics. Prerequisite: grade of "C" or better in MATH 411W.
415W Introduction to Real Analysis I 3 cr.
Properties of real numbers, cardinality, sequences and series, properties of sets, functional limits and continuity. Prerequisites: grade of "C" or better in MATH 215, in MATH 250, and in MATH 310.
416W Introduction to Real Analysis II 3 cr.
A continuation of MATH 415W including differentiation, sequences and series of functions, integration theory and advanced topics in analysis. Prerequisite: grade of "C" or better in MATH 415W.
420 Introduction to Complex Variables 3 cr.
The complex number plane, analytic functions, integration of complex functions, sequences and series, and conformal mappings. Prerequisite: grade of "C" or better in MATH 415W.
423W Topology 3 cr.
Topological spaces, homeomorphisms, connectedness, compactness, regular and normal spaces, metric spaces, convergence, and separation axioms. Prerequisites: grade of "C" or better in MATH 411W or in 415W.
435 Clinical Trials: Desing and Anaylsis 3 cr.
This course covers the basic and advanced elements involved in the design of a clinical trial. Topics include types and properties of clinical trials, ethical issues, randomization procedures, sample size estimation, baseline assessment options, compliance, and dealing with missing data. Statistical topics include linear model analysis, longitudinal data analysis, stratified data analysis, multiple comparisons and multiple endpoints, covariate adjustment, subgroup analyses, adaptive designs, non-inferiority analyses and methods of imputation. Prerequisite: grade of "C" or better in MATH 325 or MATH 525.
445 Prediction and Classification Modeling 3 cr.
Classification rates, ROC curves, cross-validation techniques, modern regression methods, data reduction/principle components, stages of biomarker development, and study design issues in cancer and occupational research. Prerequisite: grade of "C" or better in MATH 325W or in MATH 525W.
491 Selected Topics in Mathematics I 1 cr.
Topics selected in consultation with the advisor.
492 Selected Topics in Math II 2 cr.
Topics selected in consultation with the advisor.
493 Selected Topics in Math III 3 cr.
Topics selected in consultation with the advisor.