 Department of Mathematics

# Mathematics Courses

NOTE: This page is maintained separately from the University Catalog. In case of discrepancy, the content of the University Catalog prevails.

## MATHEMATICS service courses

MATH 105: Fundamentals of Mathematics (3 cr). Integers, rational numbers, exponents, order of operations. Functions in context, and their algebraic and graphical representation. Linear and quadratic equations. Introduction to the graphing calculator.

MATH 113: Mathematics of Finance (3 cr). Simple and compound interest, discounting, annuities, amortization and sinking funds, stocks, bonds, insurance. (Prerequisite: MATH 105 or by placement.)

MATH 115: Topics in Applied Mathematics (3 cr). Topics in the application of elementary mathematics to real world problems: management science, voting schemes, theory of games, population growth, other models. (Prerequisite: MATH 105 or by placement.)

MATH 116: Elementary Statistics (3 cr). An introduction to statistical thinking and its applications to a wide variety of areas. Topics include: statistical and visual methods for summarizing data, basic principles of probability, regression, and fundamentals of hypothesis testing and confidence intervals. Critical examination of the results of a statistical analysis is emphasized. (Prerequisite: MATH 105 or by placement. A student may not earn credit for more than one of these courses: MATH 116, MATH 156, STAT 210.) Course Attribute: Mathematical Perspectives, Quantitative Reasoning Flag

MATH 120: Elementary Functions (3 cr). Graphs and properties of functions, including polynomial functions, exponential functions, logarithmic functions, inverse functions and composition of functions. Applications to real world situations using algebraic, numerical, and graphical methods. (Prerequisite: MATH 105 or by placement.) Course Attribute: Mathematical Perspectives, Quantitative Reasoning Flag

MATH 125: Explorations in Mathematics (3 cr). Exploration of easily accessible, engaging, and thematically connected mathematical ideas as a vehicle to lead students to experiences that are characteristic of the mathematical enterprise. Individual Course Descriptions (Prerequisite: MATH 105 or by placement.) Course Attribute: Mathematical Perspectives

MATH 140: Concepts of Calculus (3 cr). An informal introduction to a study of quantities that change relative to each other and the fundamental concepts of the calculus which measure this change: the derivative and the integral. (Prerequisite: MATH 120 or by placement.) Course Attribute: Mathematical Perspectives

MATH 146: Introductory Biostatistics (3 cr)A first course in statistics, with an emphasis on applications and methods of particular relevance to the biological sciences. Topics include: random sampling procedures, experiments and observational studies, exploratory data analysis, correlation, bootstrapping and resampling methods, the normal distribution, confidence intervals hypothesis tests for proportions and means, chi-square tests, ANOVA. Problems and examples are drawn from fields such as bioinformatics, genetics, ecology, epidemiology, and public health. Cross-listed as STAT 146.

MATH 147: Calculus from an Historical Perspective (3 cr). An overview of concepts from differential and integral calculus through excerpted readings in English translation of original texts which emphasizes connections with developments in science and philosophy. (Prerequisite: MATH 120 or by placement.)

MATH 150: Elements of Calculus I (3 cr). Modeling data with polynomial functions, exponential functions, and logistic functions. Rates of change and the derivative. Application of the derivative including optimization and inflection points. Result of cumulative change and the definite integral. (Prerequisite: MATH 120 or by placement.)

MATH 151: Elements of Calculus II (3 cr). Modeling with trigonometric functions, functions of several variables, contour maps, partial derivatives, and optimization with and without constraints. (Prerequisite: MATH 150.)

MATH 154: Milestones in Mathematics (3 cr). Charts milestones in various branches of mathematics through the reading of original sources: number theory, infinity, Euclidean and non-Euclidean geometry, and algebra are all possible threads of development. (Prerequisite: MATH 120 or by placement.)

MATH 156: General Statistics (3 cr). An introduction to the major concepts and tools used for collecting, analyzing, and making inferences from data. Topics include: graphical displays, correlation, regression, design of experiments, probability, simulation, random sampling, confidence intervals and hypothesis testing. (Prerequisite: MATH 120 or by placement. A student may not earn credit for more than one of these courses: MATH 116, MATH 156, STAT 210. ) Course Attribute: Mathematical Perspectives

MATH 158: General Statistics II (3 cr). A second course in statistics covering various methods of data analysis. Topics include: t-tests, analysis of categorical data, estimation and inference of multiple regression models, Analysis of Variance, and multiple comparisons. The ability to communicate and correctly interpret the results of a statistical data analysis is emphasized. (Prerequisite: MATH 156, or MATH 116 with minimum grade of B.) Course Attribute: Quantitative Reasoning Flag

## MATHEMATICS for ELEMENTARY EDUCATION

MATH 201: Foundations of Arithmetic - ECED (3 cr). Concepts necessary for understanding the structure of arithmetic and its algorithms (with whole numbers, integers, fractions and decimals), number patterns, and introductory probability and statistics. (Restrictions: Must be enrolled in one of these programs: Master of Education, B.S. in Education.) Course Attribute: Mathematical Perspectives

MATH 202: Geometry and Measurement - ECED (3 cr). Concepts necessary for an understanding of basic geometry: shapes in one, two, and three dimensions, scientific measurement and dimensional analysis, congruence and similarity of figures, compass and straightedge constructions, transformations, and coordinate geometry. Use of computer software to explore geometric concepts. (Restrictions: Must be enrolled in one of these programs: Master of Education, B.S. in Education.) Course Attribute: Mathematical Perspectives

MATH 211: Foundations of Arithmetic - MCED (3 cr). Concepts necessary for understanding the structure of arithmetic, its algorithms and properties (with whole numbers, integers, rational and irrational numbers), basic set theory and introductory number theory. (Restrictions: Must be enrolled in one of these programs: Master of Education, B.S. in Education.) Course Attribute: Mathematical Perspectives

MATH 212: Geometry and Measurement - MCED (3 cr). Concepts necessary for an understanding of basic geometry: shapes in one, two, and three dimensions, scientific measurement and dimensional analysis, congruence and similarity of figures, compass and straightedge constructions, transformations, coordinate geometry, conjecture and proof, perspective drawing and introductory trigonometry. Use of computer software to explore geometric concepts. (Restrictions: Must be enrolled in one of these programs: Master of Education, B.S. in Education.) Course Attribute: Mathematical Perspectives

MATH 213: Algebra Concepts - MCED (3 cr). Development of algebraic problem solving, polynomials, linear, quadratic and exponential equations and functions, pattern representation, sequences and series. Use of technology and manipulative materials in the teaching of algebra. (Restrictions: Must be enrolled in one of these programs: Master of Education, B.S. in Education.) Course Attribute: Mathematical Perspectives

MATH 214: Mathematical Problem Solving - MCED (3 cr). Problem solving, drawing from a wide range of school mathematics topics, logic, combinatorics, and basic probability theory. (Prerequisites: MATH 211, MATH 212, MATH 213.) Course Attribute: Mathematical Perspectives

## MATHEMATICS MAJOR

MATH 169: Precalculus (3 cr). This is a study of linear, polynomial, rational, exponential, logarithmic, and trigonometric functions from symbolic, graphical, and numerical perspectives. Topics include algebraic and analytic properties of functions; sums, differences, products, quotients, and composites of functions; inverse functions; and functions as models. (Prerequisite: By placement.)

MATH 170: Calculus I (4 cr). Limits and continuity. Transcendental functions. The derivative, techniques of differentiation, and applications of the derivative. Parametric equations. The definite integral, numerical integration, antiderivatives, and method of substitution. (Prerequisite: MATH 169 or by placement.) Course Attribute: Mathematical Perspectives

MATH 171: Calculus II (4 cr). Numerical integration, applications of the definite integral, techniques of integration, and improper integrals. Taylor polynomials. Sequences and series. Polar coordinates. (Prerequisite: MATH 170.) Course Attribute: Mathematical Perspectives

MATH 220: Calculus III (4 cr). Vectors, lines and planes. Functions of several variables, partial derivatives and applications, gradient and directional derivative. Multiple integrals, line integrals, Green's Theorem. (Prerequisite: MATH 171.) Course Attribute: Mathematical Perspectives

MATH 222: Applied Linear Algebra (3 cr). An introduction to elementary linear algebra with an emphasis on application and interpretation. Topics include systems of linear equations and their solutions, matrix algebra, linear transformations, determinants, inverses, eigenvalues and eigenvectors, orthogonality. Selected applications to physical and social sciences. (Prerequisite: MATH 169 or by placement.)

MATH 225: Foundations of Higher Mathematics (3 cr). Propositional and predicate logic; methods of proof, including direct approaches, contradiction, contraposition, mathematical induction; sequences, recursion, recurrence relations; set theory; functions and relations. Primary emphasis on proof-writing. (Prerequisite: By placement.) Course Attribute: Mathematical Perspectives

MATH 230: Introduction to Ordinary Differential Equations (3 cr). Modeling with ordinary differential equations. Analytical, qualitative, and numerical techniques for first-order equations, first-order nonlinear systems, and linear systems. (Prerequisite: MATH 171.)

MATH 240: Linear Algebra (3 cr). Systems of linear equations, Gaussian elimination, echelon forms, algebraic structure of solutions; vector and matrix arithmetic, invertibility; linear transformations and their matrices; vector spaces and subspaces, bases, coordinates, dimension, rank; change of basis; determinants, Cramer's Rule; eigenvectors and eigenvalues; diagonalization; inner products, the Gram-Schmidt process.(Prerequisite: MATH 225; MATH 230 recommended.)

MATH 256: Introduction to Probability and Statistics (3 cr). Calculus-based introduction to probability and descriptive and inferential statistics. Topics include: numerical and graphical summaries of data, conditional probability, Bernoulli trials, normal distribution, the central limit theorem, estimation, t-tests, chi-square tests, type I and II errors, regression and correlation.(Prerequisite: MATH 171.)

MATH 257: Data Modeling (3 cr). Exploratory data analysis and visualization, logistic regression, estimation and inference of multiple regression models, model selection, Analysis of Variance, multiple comparisons, and experimental design. (Prerequisite: MATH 256.)

MATH 280: Combinatorics (3 cr). An introduction to counting techniques of discrete objects. The enumeration of sets, permutations and combinations, the binomial and multinomial theorem will serve as an appetizer; counting methods including the inclusion-exclusion principle; the pigeonhole principle, generating functions, and recurrence relations will be the main course. Applications of combinatorial techniques and problem solving will be emphasized. [Optional: finite geometries, permutation groups, latin squares, designs, and codes.] (Prerequisite: MATH 225.)

MATH 300: History of Mathematics (3 cr). Some of the highlights in the historical development of mathematics with special attention given to the invention of non-Euclidean geometry and its importance for mathematics and Western thought. (Prerequisites: MATH 220, MATH 240.)

MATH 301: Geometry (3 cr). Axiom systems, models and finite geometries, convexity, transformations, Euclidean constructions, and the geometry of triangles and circles. Introduction to projective and non-Euclidean geometries. (Prerequisite: MATH 225.)

MATH 302: Number Theory (3 cr). Divisibility and primes, linear congruences, quadratic residues and reciprocity. Diophantine equations, multiplicative functions, distribution of primes. (Prerequisite: MATH 240.)

MATH 303: Mathematical Logic (3 cr). Axiomatic development of propositional calculus, functional complete sets of operators, axiomatic development of the first order function calculus, the existential operator, the algebra of logic. (Prerequisite: MATH 225.)

MATH 311: Probability Theory (3 cr). Sample spaces, basic axioms of probability, Bayes' theorem, expectation, common discrete and continuous distributions, moment generating functions, central limit theorem, inequalities, convergence of random variables, and transformations of random variables. (Prerequisite: MATH 171.)

MATH 312: Statistical Inference (3 cr). Maximum likelihood principle, Bayesian estimation, properties of estimators, sufficiency, likelihood ratio tests, chi-square distribution, t distribution, F distribution, power, nonparametrics, bootstrap, and Markov Chain Monte Carlo. (Prerequisite: MATH 256 or MATH 311.)

MATH 316: Cryptology (3 cr). The making and breaking of secret ciphers and codes. Classical ciphers: shift, affine, Vigenère, substitution, Hill, one-time pads, and Enigma. A brief introduction to number theory. Modern methods: RSA algorithm, DES, AES: Rijndael, discrete logarithms and elliptic curves. (Prerequisite: MATH 225.)

MATH 321: Numerical Analysis (3 cr). Accuracy, function evaluation and approximation, systems of linear equations, nonlinear equations, numerical differentiation and integration, and solutions to differential equations. (Prerequisite: CSCI 170 and MATH 171.)

MATH 325: Mathematical Modeling (3 cr). The synthesis, formulation and solution of various problems in applied mathematics and related fields. (Prerequisite: MATH 230.)

MATH 330: Graph Theory (3 cr). Graphs, subgraphs, trees, isomorphism, Eulerian and Hamiltonian paths, planarity, digraphs, connectivity, and chromatic number. Other topics may be included. (Prerequisite: MATH 225.)

MATH 340: Abstract Algebra I (3 cr). Groups, isomorphism, homomorphism, normal subgroups, rings, ideals, fields. (Prerequisites: MATH 225, MATH 240.)

MATH 341: Abstract Algebra II (3 cr). A continuation of MATH 340. Topics may include Boolean algebra, lattice theory, combinational group theory, coding theory, Galois theory, commutative rings. (Prerequisite: MATH 340.)

MATH 360: Elementary Topology (3 cr). Metric spaces, topological spaces, continuity, convergence, compactness, connectedness, and separation axioms. (Prerequisite: MATH 240.)

MATH 370: Real Analysis (3 cr). Rigorous development of calculus of functions of a single variable. The real number system, topology of the real line, continuity, uniform continuity, the derivative, the Riemann integral, sequences and series of real numbers, and uniform convergence. (Prerequisites: MATH 220 and MATH 225.)

MATH 372: Applied Analysis (3 cr). Special functions, orthogonal sets of functions. Sturm-Liouville theory. Partial Differential Equations. Fourier series, integrals and transforms. (Prerequisite: MATH 230.)

MATH 380: Introduction to Complex Variables (3 cr). Complex numbers, analytic functions, complex integration, series representation of analytic functions, the calculus of residues. (Prerequisites: MATH 220 and MATH 225.)

MATH 385: Secondary Mathematics from an Advanced Perspective (3 cr). A capstone course for prospective high school teachers focusing on connections between secondary and undergraduate mathematics. Emphasis on analysis and algebra. The real numbers, sequences and series, countability, concepts of infinity. Functions, logarithms, solving equations, the Fundamental Theorem of Algebra and its consequences. Complex numbers and functions. (Prerequisites: MATH 340 or consent of instructor.)

MATH 391: Mathematics Seminar 1 (1 cr). Juniors (MATH 391) and seniors (MATH 393) meet together in the spring semester. Students will read selections from the mathematical literature, explore how to write mathematics effectively, learn how to use technical word processing tools, practice how to communicate mathematical ideas and give oral presentations. (Restriction: Must be enrolled as a major in mathematics.)

MATH 392: Mathematics Seminar 2 (1 cr). Each senior will meet with a faculty advisor to work on an individual research project. (Restriction: Must be enrolled as a major in mathematics.)

MATH 393: Mathematics Seminar 3 (1 cr). The student will write a paper and give a formal presentation describing the project developed during MATH 392. (Prerequisite: MATH 392; Restriction: Must be enrolled as a major in mathematics.)

MATH 397: Special Study (0-6 cr). Credit by special arrangement. Area to be specified. (Prerequisite: MATH 225.)

## STATISTICS

STAT 146: Introductory Biostatistics (3 cr). A first course in statistics, with an emphasis on applications and methods of particular relevance to the biological sciences. Topics include: random sampling procedures, experiments and observational studies, exploratory data analysis, correlation, bootstrapping and resampling methods, the normal distribution, confidence intervals hypothesis tests for proportions and means, chi-square tests, ANOVA. Problems and examples are drawn from fields such as bioinformatics, genetics, ecology, epidemiology, and public health. Cross-listed as MATH 146.

## ACTUARIAL SCIENCE MAJOR

MACS 101: Introduction to Actuarial Science (3 cr) . The course consists of presentations introducing various topics dealt with by actuaries, weekly lab activities to provide in-depth work with these ideas, and presentations from actuaries regarding their work. Specific topics include mortality tables, interest theory, probability, principles of insurance and reserves. (Prerequisite: MATH 150 or by placement.)

MACS 201: Actuarial Mathematics (3 cr). An introduction to Actuarial Mathematics. Topics include survival distributions and life tables, force of morality, laws of morality, life insurance, life annuities, benefit premiums, and benefit reserves.