Unless otherwise noted, all courses are 3 credits. MATH 1060 Basic Mathematics with Algebra This course covers the arithmetic of whole numbers, signed numbers, fractions, decimals and percents, its primary coverage is polynomial arithmetic, algebraic expressions, factoring, solving equations (linear and quadratic) with applications and graphing. Note:Credits for this Basic Skills course are not applicable toward degree requirements. Prerequisite: None Successful completion of Math Basic Skills requirement is necessary for all the following courses. Successful completion of Math Basic Skills Requirements means obtaining a score of 20 on Basic Skills Math test or grade P in Math 1060. MATH 1090 Mathematical Concepts (This is a UCC - Area 3E course.) This course is intended to provide a wide ranging exposure to mathematical ideas expected of a liberal arts undergraduate. Topics include: Voting, Fair division, Apportionment, Graphs and Networks, Consumer Finance, Statistics and Probability. The course is designed for students not majoring in business, the sciences or math. MATH 1100 Contemporary Mathematics (This is a UCC - Area 3E course.) This course is intended to provide a wide ranging exposure to mathematical ideas expected of a liberal arts undergraduate. Topics include Sets, Logic, Statistics, Probability, Number Systems and Problem Solving. The course is designed for students not majoring in business, the sciences or math. MATH 1110 Algebra and Geometry with Applications This is a course with emphasis on studying practical problems with mathematical models. Topics include: Problem solving, number theory, introduction to functions and modeling, systems of equations and matrices, exponential and logarithmic functions, linear inequalities in two variables and geometry. Prerequisite: Math 1100 MATH 1150 College Algebra A comprehensive study of algebraic functions and their properties. Topics include the real numbers system, exponents and radicals, solving equations and inequalities, functions and their graphs, polynomial functions and rational functions. MATH 1160 Precalculus (This is a UCC - Area 3E course.) A comprehensive study of exponential, logarithmic and trigonometric functions. Topics include function properties, exponential, logarithmic and trigonometric functions (their properties and graphs), solving exponential and logarithmic equations, trigonometric functions (their properties and graphs), trigonometric identities and solving trigonometric equations. Prerequisite: MATH 1150 or by placement with permission from the Department Chairperson. MATH 1170 Business Math (This is a UCC - Area 3E course.)A study of algebraic and transcendental functions, including their properties and graphs with a focus on applications to business. Topics include algebraic fundamentals, equations and inequalities, polynomial functions and graphs, exponential and logarithmic functions and mathematics of finance. MATH 1300 Elementary Statistics (This is a UCC - Area 3E course.) This course studies the development of statistical concepts with applications to various disciplines. Topics include descriptive and inferential statistical techniques. The latter are explained in terms of concepts from probability theory such as normal distribution, t-distribution, sampling theory, estimation, confidence intervals, hypothesis testing, t-test, Chi square test, analysis of variance and regression and correlation. The software package SPSS is used to perform statistical analysis. Not open to science or mathematics majors. MATH 1350 Algebra, Trigonometry, and Functions (4 credits) (This is a UCC - Area 3E course.) A comprehensive study of algebraic and elementary transcendental functions. Topics include: the real number system, solving equations and inequalities, function properties, algebraic functions and their graphs, exponential and logarithmic functions (their properties and graphs), solving exponential and logarithmic equations, trigonometric functions (their properties and graphs) trigonometric identities and solving trigonometric equations. Students may be admitted into the course based on the results of a placement test. MATH 1400 Quantitative Mathematics I An introduction to functions, equations, matrix algebra, linear programming, and mathematics of finance. Topics include Equations and Inequalities, Functions and Graphs, Matrix Algebra, Linear Programming: Graphical Analysis as well as the Simplex Method, and Mathematics of Finance, Markov Chains (optional) MATH 1450 Quantitative Mathematics II This course covers essential ideas of the calculus: functions, limits, continuity, differentiation and applications, antiderivatives and definite integrals. Business applications are stressed. Trigonometry is not required. Prerequisite: MATH 1400 MATH 1600 Calculus I (4 credits) (This is a UCC - Area 3E course.) Limit and continuity of functions, the Intermediate Value Theorem, derivatives, differentiation rules, Rolle's theorem and the Mean Value Theorem, applications of differentiation, antiderivatives, definite integrals and the Fundamental Theorem of Calculus. Prerequisite: Math 1160 or Math 1350 or by placement. MATH 1610 Calculus II (4 credits) Indefinite and definite integrals and their estimation, techniques of integration., improper integrals, L'Hospital's Rule, applications of integration, infinite series, power series and introduction to taylor polynomials and approximations. Prerequisite: MATH 1600 MATH 2000 Logic and Methods of Higher Mathematics An introduction to rigorous reasoning through logical and intuitive thinking. The course will provide logical and rigorous mathematical background for study of advanced math courses. Students will be introduced to investigating, developing, conjecturing, proving and disproving mathematical results. Topics include formal logic, set theory, proofs, mathematical induction, functions, partial ordering, relations and the integers. Prerequisite: MATH 1600 MATH 2010 Calculus III (4 credits) Study of vectors and the Geometry of Space; vector valued functions, differentiation and integration of vector-valued functions; calculus of functions of several variables including partial differentiation and multiple integrals; higher order derivatives and their applications; Vector Fields; Line and Surface integrals. Prerequisite: MATH 1610 MATH 2020 Linear Algebra An introductory course in the theory of linear transformations and vector spaces. Topics include: systems of equations, matrices, determinants, general vector spaces, inner product spaces, eigenvalues and eigenvectors. Prerequisite: MATH 1610 MATH 2120 Survey of Mathematics This course surveys number theory, graph theory and combinatorics, and the history of mathematics. Prerequisite: MATH 1610 MATH 2300 Statistics (4 credits) A rigorous course for math and science majors covering: measures of central tendency, measures of variation, graphical techniques for univariate and bivariate data, correlation and regression, probability, binomial and normal distributions, estimation, confidence interval, testing of hypothesis, contingency tables, analysis of variance, nonparametric methods; use of packages such as SAS, Minitab , etc. is strongly emphasized. Prerequisite: None MATH 3010 Modern Algebra An introduction to groups, isomorphisms, rings, integral domains, fields and polynomial rings. Emphasis is placed on the development of theorems and techniques of proofs using definitions and examples. Prerequisite: MATH 2000 or CS 2600 MATH 3110 Number Theory This is an introductory course in Number Theory for students interested in mathematics and the teaching of mathematics. The course covers basic notions of integers and sequences, divisibility, and mathematical induction. It also covers standard topics such as Prime Numbers; the Fundamental Theorem of Arithmetic; Euclidean Algorithm; the Diophantine Equations; Congruence Equations and their Applications (e.g. Fermat’s Little Theorem); Multiplicative Functions (e.g. Euler’s Phi Function); Application to Encryption and Decryption of Text; The Law of Quadratic Reciprocity. Prerequisite: MATH 2000 MATH 3220 Differential Equations A study of the methods of solution and applications of ordinary differential equations. Topics include: first and second order equations, existence and uniqueness of solutions, separation of variables, exact equations, integrating factors, linear equations, undetermined coefficients, variation of parameters, transform methods, series solutions, systems of equations and elementary numerical methods. Prerequisite: MATH 1610 MATH 3230 Foundations of Geometry Foundations of Geometry presents the different axiomatic approaches to the study of geometry with specific applications to finite, Euclidean, and non-Euclidean geometries with extensive use of constructions to explore ideas, properties, and relationships. Technology will be used throughout the course to encourage these open-ended explorations. The role of different types of proofs will be developed throughout the course. Prerequisites: MATH 1610 and (MATH 2000 or CS 2600) MATH 3240 Probability and Statistics (4 credits) A mathematical treatment of probability as well as statistics. Topics include probability axioms, discrete and continuous sample spaces, random variables, mathematical expectation, probability functions; basic discrete and continuous distribution functions; multivariate random variables. Also covered is Central Limit Theorem, confidence intervals, hypotheses testing and Linear regression. Software such as SAS or Minitab may be used for hypotheses testing and regression problems. Prerequisite: MATH 1610 MATH 3260 Mathematical Models in Finance I (3 credits) A course on the formulation, analysis, and interpretation of advanced mathematical models in finance and interest theory.Technology will be used to give students a hands-on experience in developing and solving their own models. The course will cover the basic fundamentals needed for the second actuarial exam. Applications to "real-world" problems in interest theory, including the development of complex annuity models, will also be studied. Although primary focus will be on the application of financial models developed in Kellison, the mathematical derivation and analysis of the formulae will also be covered. Prerequisite: MATH 2010 (C+ or better) or MATH 2020 (C+ or better) MATH 3320 Statistical Computing Students solve statistical problems on the computer with the help of statistical packages, such as SAS, BMD, Mystat, etc., and learn to interpret the outputs and draw inferences. Topics include analysis of variance with and without interactions, correlation and regression analysis, general linear models, multiple comparisons and analysis of contingency tables. Prerequisite: MATH 3240 MATH 3340 Applied Regression Analysis This is a comprehensive treatment of regression analysis course, statistical topics including: simple linear regression, least square estimates, ANOVA table, F-test, R-square, multiple regression, using dummy variables, selections of the “best subset” of predictor variables, checking model assumptions and Logistic regression. The computer package, SAS, will be used through out the course and applications to real life data will be an integral part of the course. Prerequisite: MATH 3240 MATH 3350 Introduction to Numerical Analysis Treatment of numerical methods including numerical integration, numerical solution of equations and systems of equations, approximation of functions, numerical solution of differential equations, applications and computer implementation of numerical methods. Prerequisite: MATH 2020 MATH 3800 Linear and Nonlinear Optimization Iterative Algorithms, Optimization process and Linear Programming (LP), including the Graphical method and Simplex method. Duality and Sensitivity analysis, LP applications in business and health. Nonlinear Unconstrained problems and various Descent methods. Nonlinear Constrained optimization, including Primal, Penalty, and Barrier methods. Prerequisite: MATH 2020 MATH 3990 Selected Topics (1- 3 credits) A topic not covered by an existing course is offered as recommended by the department and approved by the dean. The number of credits for MATH 3990 may vary from 1 to 3 for a selected topic. MATH 3990 can not be credited more than twice, each on a different topic, towards degree requirements. Prerequisite: Department Chairperson's permission MATH 4010 Applied Algebra A course covering applications of Modern Algebra. Topics include Boolean algebras and applications to switching theory; symmetry groups in three dimensions, monoids and machines, applications of rings, fields, and Galois theory including error-correcting codes. Prerequisite: MATH 3010 MATH 4110 Advanced Discrete Mathematics This is an advanced course in discrete mathematics primarily dealing with discrete dynamical systems, algorithms, combinatorics and Graph Theory. Emphasis is placed on complexity of algorithms, on existence and optimization problems in Graph Theory and on associated algorithms. Prerequisite: MATH 2020 or CS 2600 MATH 4120 Time Series Analysis This is an applied statistical methods course in time series modeling of empirical data observed over time. Prerequisite: MATH 3340 or (MATH 3240 and instructor's permission) MATH 4130 Experimental Design for Statistics For processes of any kind that have measurable inputs and outputs, Design of Experiments (DOE) methods guide you in the optimum selection of inputs for experiments, and in the analysis of results. Full factorial as well as fractional factorial designs are covered – see the course outline for additional details. Software such as SAS or S-Plus will be used for testing and regression problems. Prerequisite: MATH 3240 with at least a C- or the approval by the chairperson of Math Dept MATH 4150 Topics from Applied Mathematics The objective of this course is to give the student an understanding and appreciation of applied mathematics. This will be accomplished by working through a variety of problems from the physical sciences. Emphasis will be on modeling scientific phenomena rather than developing mathematical methods. Basic ideas and concepts will first be illustrated on simple problems, and they will eventually be extended to more complicated systems. Prerequisite: MATH 3220 MATH 4210 Mathematical Statistics A theoretical treatment of statistical topics including: distribution theory, sampling, point and interval estimation, methods of estimation such as maximum likelihood estimation, properties of estimators, Neyman-Pearson Lemma, hypothesis testing, power of a test, and linear models. Prerequisite: MATH 3240 MATH 4220 Complex Analysis Elements of complex analysis. Topics include: complex numbers, analytic functions, Cauchy integral theorem, Cauchy integral formula, power series and conformal mapping. Prerequisite: MATH 2010 MATH 4230 Real Analysis A rigorous approach to the theory of functions of real variables. Topics include: metric spaces, sets, limits, sequences, continuity, uniform continuity, differentiation, Riemann integration, sequences and series of functions, and Riemann-Stieltjes integral. Prerequisite: MATH 2010 MATH 4250 Introduction to Topology This course uses the concepts of set theory, analysis and group theory in a rigorous manner to explore the fundamental mathematical definitions of continuity, homeomorphism, metrics, product topology, compactness, connectedness, the fundamental group and homotopy theory. Prerequisite: MATH 3010 MATH 4270 Mathematical Models in Finance II (3 credits)A course on the mathematical derivation, analysis, and interpretation of advanced mathematical models in finance and interest theory and is a continuation of course MATH3260. Technology will be used to give students a hands-on experience in developing and solving their own models. The course will cover the more advanced topics needed for the second actuarial exam. Applications to "real-world" problems in interest theory, including more complex analysis and applications of the models developed in MATH3260 will be studied. Although primary focus will be on the application of financial models developed in Kellison, the mathematical derivation and analysis of the formulae will also be covered. Prerequisite: MATH 3260 MATH 4300 Derivatives MarketThis course will provide an introduction to financial instruments, including derivatives, and the concept of no-arbitrage as it relates to financial mathematics. Technology will be used to give students a hands-on experience in developing and solving their own models. Applications to "real-world" problems will also be studied. Topics covered will include: General Derivatives, Options, Forwards and Futures, Swaps, Hedging and Investment Strategies.Prerequisite: MATH 1610 and (ECON 2010 or ECON 2020) MATH 4900 Mathematics Seminar (2 credits) (This is a Writing Intensive-WI course.) This is a required course for all mathematics majors and should be taken, if possible, in the junior year. The course will be led by a faculty member and conducted in an inquiry based fashion, with coverage of topics determined by the interests of the student and faculty. Each student will complete a project of study in an area of mathematics or it applications, culminating in a presentation to the faculty and students, and a final paper submitted to the faculty advisor. Prerequisite: Must be registered in a 4000-level mathematics course, or must have successfully completed a 4000-level course. Math 4900 registration form may be downloaded from here. MATH 4990 Independent Study (1- 3 credits) An individual research project under the direction of a faculty member and with the approval of the chairperson. The number of credits for each independent study may vary from 1 to 3 per semester, up to a limit of 6 credits.