Mathematics (MATH)

MATH 100  Problem-Solving Strategies in Mathematics  (3)  

Intensive study of the problem-solving process. Algebraic, patterning, modeling, and geometric strategies are explored. Includes a review of basic algebra skills and concepts necessary for problem solving. Consent of the Department is required. This does not fulfill the Mathematical Arts requirement of the Sophia Program.

MATH 102  Liberal Arts Mathematics  (3)  

Mathematical modeling through the use of graph theory. Topics include graphs, directed graphs, trees, matchings and network flows. Designed primarily for first year college students. Prerequisite: MATH 100 or recommendation of Math Placement Advisor.

MATH 103  Precalculus  (3)  

This course studies polynomial, rational, exponential, logarithmic, and trigonometric functions from the symbolic, numeric, and graphical perspectives. The emphasis on these concepts will provide solid preparation for a college-level calculus course. This does not fulfill the Mathematical Arts requirement of the Sophia Program. Prerequisite: MATH 102 or recommendation of Math Placement Advisor.

MATH 104  Finite Mathematics  (3)  

Set theory, counting techniques, probability, random variables, expected value, variance, standard deviation, and linear programming. Prerequisite: MATH 103 or recommendation of Math Placement Advisor.

MATH 105  Elements of Calculus I  (3)  

Introduction to differential and integral calculus designed primarily for liberal arts students and those in the professional programs. Limits are treated intuitively. Emphasis on applications.

MATH 106  Elements of Calculus II  (3)  

Introduction to differential and integral calculus designed primarily for liberal arts students and those in the professional programs. Limits are treated intuitively. Emphasis on applications. Prerequisite: MATH 105.

MATH 107  Mathematics for Sustainability  (3)  

This course develops and applies mathematical concepts and tools to quantitatively explore sustainability issues. Topics such as industrial agriculture, energy sustainability, population growth, and ecological footprints will be explored from environmental, social, and economic perspectives wherever possible. Mathematical concepts developed in the course are motivated through the study of these topics and allow students to survey several mathematical areas. Particular concepts covered include properties of real numbers, algebraic simplification of expressions, solving equations and inequalities, rates of change, interpretation of numerical information, functions and inverses, modeling, differentiation/integration, qualitative analysis of differential equation models, calculating probabilities, statistical techniques on real data, and graph paths and connectivity.

MATH 108  Elements of Linear Algebra  (3)  

Matrices, systems of equations, determinants, eigenvalues, linear transformations, vector spaces. Emphasis on applications. Prerequisite: MATH 104 or MATH 105.

MATH 110  Modern Geometries  (3)  

Finite geometries. Transformational geometry with an introduction to fractals. Euclidean geometry, including classical constructions. Non-Euclidean geometries, including hyperbolic and/or projective geometry. Prerequisite: MATH 104 or MATH 105.

MATH 113  Survey of Calculus  (4)  

A one semester introduction to differential and integral calculus designed primarily for liberal arts students and those in the professional programs. An emphasis on applications and modeling. Prerequisites: MATH 103 or placement

MATH 114  Introduction to Statistics  (3)  

Introduction to basic sampling and experimental design. Basics of probability, random variables, and probability distributions. Sampling distributions. Estimation and hypothesis testing for means and proportions. Statistical software will be used. Prerequisite: MATH 104 or MATH 105 or equivalent.

MATH 118  Patterns in Mathematics for Elementary Teachers  (3)  

Problem solving and strategies; properties of whole numbers, integers, rational numbers, and real numbers; algorithms and computation; elementary number theory. The course follows the recommendations of the Mathematical Association of America and the National Council of Teachers of Mathematics for the training of elementary teachers. Prerequisite: One Mathematical Arts Sophia Program course.

MATH 131  Calculus I  (4)  

Algebraic and transcendental functions; limits; continuity; derivatives; maxima and minima; concavity; related rates; Taylor polynomials; Mean Value Theorem; anti-differentiation; Riemann sums; the Fundamental Theorem of Calculus; techniques of integration; sequences and series. The course is based on graphical, numerical, and symbolic points of view. Graphing calculators are used throughout the course. Prerequisite: At least four years of high school mathematics.

MATH 132  Calculus II  (4)  

Algebraic and transcendental functions; limits; continuity; derivatives; maxima and minima; concavity; related rates; Taylor polynomials; Mean Value Theorem; anti-differentiation; Riemann sums; the Fundamental Theorem of Calculus; techniques of integration; sequences and series. The course is based on graphical, numerical, and symbolic points of view. Graphing calculators are used throughout the course. Prerequisite: At least four years of high school mathematics. Prerequisite: MATH 131.

MATH 133  Theory and Application of Calculus  (4)  

This course is designed for students who have completed a full year of calculus in high school and have mastered the mechanics of differentiation and integration. The basic concepts of a two-semester college calculus sequence, including limits, derivatives, integrals, sequences and series, will be explored in depth. The emphasis of the course is on understanding the theory of calculus and constructing mathematical models. Prerequisite: A minimum score of 3 on the AP Calculus exam or permission of instructor.

MATH 180  Mathematics of Voting  (1)  

This course in applied math and politics will focus on the mathematics behind voting in both two-party and multi-party systems, comparing systems in the US with those in France and Ireland. Students will explore both implemented and theoretical social choice functions and analyze each, subject to standard criteria. They will develop an understanding for how formal rules and procedures have an impact on policy outcomes and informal institutions such as political parties.

MATH 211  Elementary Number Theory  (3)  

Basic number theoretic concepts are studied, with an emphasis on writing proofs. Divisibility; primes; Euclid’s algorithm and its consequences; linear diophantine equations; residue classes; linear congruences; arithmetic functions. Applications of number theory to computer science (cryptography, complexity of computations). Prerequisite: MATH 118 or MATH 131.

MATH 225  Foundations of Higher Mathematics  (3)  

Set theory, logic, relations, functions, and an introduction to abstract mathematical structures, with an emphasis on reading and writing mathematical proofs. Prerequisite: one calculus course or permission of instructor.

MATH 231  Calculus III  (4)  

Three-dimensional space: parametric equations, lines, planes, vectors, dot product, cross product. Polar coordinates. Vector-valued functions. Functions of several variables: partial derivatives, linear approximation, gradient, directional derivatives, maxima, minima, chain rule. Multiple ntegrals. Vector Calculus (including Green’s Theorem and Stokes’ Theorem). Prerequisite: MATH 132 or MATH 133.

MATH 241  Statistical Applications  (3)  

Sampling studies, design of experiments, hypothesis testing, analysis of variance, regression and correlation, regression modeling, time series. Introduction to operations research: queuing, systems analysis, quality assurance, acceptance sampling. Emphasis on applications to business and economic decision making. Prerequisite: MATH 114 with a grade of “C” or higher (also listed as BUAD 341).

MATH 251  Principles of Operations Research  (3)  

An introduction to Operations Research—quantitative models used in management decision-making. The course will focus on the models as tools with computer software used extensively for problem solving and assignments. Case studies are used. Prerequisite: One year of Calculus or MATH 114 (also listed as BUAD 427).

MATH 252  Financial Mathematics  (3)  

Mathematical theory of interest, annuities, amortization schedules, yield rates, and sinking funds. Prerequisite: Two semesters of calculus or equivalent or permission of the instructor.

MATH 272  Women and Mathematics: Seminar  (3)  

This course has three major components: an overview of the history of mathematics, the lives and contributions of selected women mathematicians throughout history, and the experiences of women in the contemporary mathematical community. In our general exploration of history, we focus on the development of mathematical ideas and the contributions made by various cultures and individuals. Among the historical figures studied in depth are Hypatia, Maria Agnesi, Sophie Germain, Sofia Kovaleskaia, Emmy Noether, Julia Robinson. The course will examine the ways in which the views of the modern mathematical community and the broader society discourage or encourage the participation of women and other under-represented groups in mathematics. Prerequisite: One semester of college-level calculus or equivalent.

MATH 302  Mathematics for Elementary School Teachers  (3)  

Review of basic properties of the real number system. Foundations of Euclidean geometry with additional study of transformational geometry. Elementary probability and statistics. This course meets for two hours of class instruction and has a two-hour laboratory component. Recommendations of MAA and NCTM are continued. Prerequisite: Two MATH courses including MATH 118 with a grade of C or higher in MATH 118.

MATH 326  Linear Algebra and Differential Equations  (4)  

Linear systems; linear independence; matrix algebra; determinants; vector spaces including subspaces, dimension, rank, change of bases; linear transformations; eigenvalues and eigenvectors; inner product; orthogonality; and Gram-Schmidt. An introduction to differential equations, including first order linear, separable, and exact; second order with constant coefficients and variation of parameters, reduction of order, and undetermined coefficients. Applications included. Prerequisites: MATH 231.

MATH 335  Differential Equations II  (3)  

A study of methods for solving higher order linear ordinary differential equations, linear first order systems, and boundary value problems for the heat and wave equations. Analysis of nonlinear systems of first order ordinary differential equations using approximation by linear systems, numerical solutions and phase portraits. The course will use mathematical software to solve differential equations and systems of differential equations symbolically, numerically and graphically. Prerequisite: MATH 326.

MATH 336  Numerical Analysis  (3)  

Computer arithmetic and algorithm convergence. Solutions of equations. Optimization. Numerical linear algebra. Numerical solutions to ordinary differential equations. Numerical differentiation and integration. Error analysis. Prerequisite or corequisite: MATH 326.

MATH 339  Discrete Mathematics  (3)  

Introduction to graph theoretic and combinatoric models: planar graphs; circuits; spanning trees; network flows; counting; generating functions; recurrence relations. Prerequisites: MATH 225 and CPSC 207.

MATH 341  Analysis I  (3)  

Construction of the reals; Sequences; Real valued functions of a single real variable: continuity, uniform continuity, sequences and series of functions, uniform convergence, differentiation, integration. Prerequisites: MATH 225 and MATH 231.

MATH 342  Analysis II  (3)  

Construction of the reals; Sequences; Real valued functions of a single real variable: continuity, uniform continuity, sequences and series of functions, uniform convergence, differentiation, integration. Prerequisite: MATH 341.

MATH 345  Probability  (3)  

A calculus-based approach to probability theory. Topics include probability spaces, classical theory, random variables, discrete and continuous distributions, multivariant distributions, transformations of random variables, random sampling, the law of large numbers, the central limit theorem and moment generating functions. Prerequisite: MATH 231 or equivalent.

MATH 346  Statistics  (3)  

Topics include sampling distributions, estimation, theory of estimators, test of hypotheses, analysis of variance, regression and correlation analysis, time series, experimental design, modeling and decision criteria. The use of statistical analysis in decision problems is stressed. Prerequisite: MATH 345 or equivalent.

MATH 353  Abstract Algebra I  (3)  

Basic algebraic systems: groups, rings, and fields. Homomorphisms and factor groups, rings. Polynomial rings and field extensions. Applications, including symmetry groups and algebraic coding theory. Prerequisite: MATH 225 and MATH 326.

MATH 354  Abstract Algebra II  (3)  

Basic algebraic systems: groups, rings, and fields. Homomorphisms and factor groups, rings. Polynomial rings and field extensions. Applications, including symmetry groups and algebraic coding theory. Prerequisite: MATH 353.

MATH 361  Geometry  (3)  

Historical and formal development of Euclidean and non-Euclidean geometries; role of axiom systems; congruence, parallelism, measurement. Prerequisite: MATH 225.

MATH 372   Stochastic Models  (3)  

Stochastic models of contingent payment, survival, frequency, severity and ruin. Compound distribution models. Emphasis on application to actuarial models. Prerequisite: MATH 345.

MATH 381  Mathematical Modeling  (3)  

In this course, students study the modeling process with application from difference equations, probability, dynamical systems, optimization, and simulation. Students will design, develop, implement, evaluate, and present mathematical models using real data for observable phenomena. Models and issues related to environmental and sustainability studies are emphasized. Prerequisites: MATH 326 and MATH 345.

MATH 438  Mathematical Programming  (3)  

Topics include model building; classical optimization; linear programming; non-linear programming. Prerequisite: MATH 231, MATH 326 and junior or senior status.

MATH 490  Special Topics  (1-3)  

Topics in Mathematics not covered in the regular department offerings. May be repeated with a different topic.

MATH 496  Pro-Seminar  (2)  

Student presentation of selected topics. Prerequisite: Permission of the department chair.

MATH 497  Independent Study  (1-3)  

Provides properly qualified students with an opportunity for independent study and careful consideration from an advanced standpoint of selected topics in undergraduate mathematics. Prerequisite: Permission of the department chair. May be repeated.

MATH 499  Internship  (1-3)  

Professional work experience in mathematics or statistics with a business or organization. May be repeated.