# Mathematics Course Descriptions

## Mathematics Course Descriptions

 Choose a course level 100 level 200 level 300 level 400 level 500 level

### Mathematics - 100 level courses

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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.
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.
MATH 104: Finite Mathematics (3) Set theory, counting techniques, probability, random variables, expected value, variance, standard deviation, and linear programming.
MATH 105-106: Elements of Calculus I, II (3, 3) Introduction to differential and integral calculus designed primarily for liberal arts students. Limits are treated intuitively. Emphasis on applications.  MATH 105 is a prerequisite for MATH 106.
MATH 108: Elements of Linear Algebra (3) Matrices, systems of equations, determinants, eigenvalues, linear transformations, vector spaces.  Emphasis on applications.  Prerequisite: MATH 104 or 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 105.
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 105 or equivalent.
MATH 118: Patterns in Mathematics 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 general education college math course.
MATH 131-132: Calculus I, II (4, 4) Algebraic and transcendental functions; limits; continuity; derivatives; maxima and minima; concavity; related rates; Taylor polynomials; Mean Value Theorem; anti-differentiaion; 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. Graphics calculators are used throughout the course. Prerequisite: At least four years of high school mathematics.  MATH 131 is a prerequisite for MATH 132.
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.

### Mathematics - 200 level courses

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MATH 209 Introduction to Cryptology (3) Introduction to Cryptology is based on mathematical ideas from number theory, probability, and linear algebra.  The course studies various ciphers such as Hill, Vigenere, RSA, DES.  Prerequisite: Either MATH 105, 118, or 131.
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 congruencies; arithmetic functions. Applications of number theory to computer science (cryptography, complexity of computations).  Prerequisite: MATH 118 or 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.  Functions of several variables: partial derivatives, linear approximation, gradient, directional derivatives, maxima, minima, chain rule.  Multiple integrals.  Vector Calculus (including Green's Theorem and Stokes' Theorem).  Prerequisite: MATH 132 or 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.  MATH 241 is also listed as BUAD 341.  Prerequisite: MATH 114 with a grade of "C" or higher.
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.  MATH 251 is also listed as BUAD 427. Prerequisite: One year of Calculus or MATH 114.
MATH 252: Theory of Interest (3) Mathematical theory of interest.  Annuities, Amortization Schedules, Yield rates, and Sinking Funds. Prerequisite: Two semesters of Calculus or equivalent.
MATH 272: History of Mathematics with an emphasis on women's voices (3) This course has 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.

### Mathematics - 300 level courses

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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. Prerequisites: Two MATH courses including MATH 118 with a grade of "C" or higher in MATH 118.
MATH 326: Linear Algebra/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 variations 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. This 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, polynomial interpolation, numerical differentiation and integration. Ordinary differential equations, numerical approximations of solutions to initial value problems. Error analysis. Prerequisite: MATH 132 or 133.
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 341-342: Analysis I, II (3, 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 231.  MATH 341 is a prerequisite for MATH 342.
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 349 Topics in Actuarial Mathematics II (2) 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 353-354: Modern Algebra I, II (3, 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 326.  MATH 353 is a prerequisite for MATH 354.
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 362: Topology (3) Basic concepts of point set topology, including separation axioms, connectedness, compactness and continuous mapping. Prerequisite: MATH 231.
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. Prerequisites: MATH 231, 326, and 345.

### Mathematics - 400 level courses

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MATH 438: Mathematical Programming (3) Topics include model building; classical optimization; linear programming; non-linear programming. Prerequisite: MATH 225, MATH 326, and junior or senior status.
MATH 490: Special Topics (3) Topics in Mathematics not covered in the regular department offerings. May be repeated for credit with a different topic.
MATH 496: Pro-Seminar (2) Student presentation of selected topics. Prerequisite: Consent 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. Consent of the department chair.
MATH 499 Internship in Mathematics (1-3) Professional work experience in mathematics or statistics with a business organization.

### Mathematics - 500 level courses

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MATH 501: Topics in Undergraduate Mathematics 1-3 Workshop in topics of undergraduate mathematics and related pedagogy. Designed for faculty currently teaching or preparing to teach the specified topics. May be repeated for credit. Prerequisite: Appropriate mathematical preparation.
MATH 502: AP Mathematics 2 A survey of the content of the AP Mathematics syllabus. The selection of topics and their applications will be guided by the preparation of the students. Appropriate technology will be used. Instructional technique and design of an AP course will be discussed. Problem-solving sessions are an integral part of the course. May be repeated for up to a maximum of four hours of credit.