Mathematics Course Descriptions

Mathematics Course Descriptions

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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 College General Education requirements in Mathematics.
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 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 108: Elements of Linear Algebra (3) Matrices, systems of equations, determinants, eigenvalues, linear transformations, vector spaces, determinants. 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 115-116: Calculus for the Life Sciences I, II (4, 4) Brief treatment of the real numbers, sets, functions, polynomials and graphs. Differential and integral calculus with special emphasis on the exponential and logarithmic functions and on ordinary differential equations. The last section of the course is equivalent to a three-credit course in statistics including use of statistical software. Motivating examples and exercises will be taken from the biological applications when possible. Not adequate preparation for MATH 231.
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 college mathematics 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 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 calculus, 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.

Mathematics - 200 level courses

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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.
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. 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: A year of Calculus or MATH 114.  (Also listed as BUAD 427)
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: Women and Mathematics: Seminar (2) The life, times and work of the notable women from Hypatia to Noether. Recent history of American women in mathematics. The societal and cultural influences which cause women to leave mathematics at all levels. Students in turn assume leadership of discussion. Prerequisite: two college mathematics courses above MATH 102.

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. The course meets for an additional required one-hour laboratory weekly. 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 225 and 231, or permission.
MATH 332: 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 ir 133.
Math 335: Differential Equations II (3) This course studies methods for solving higher order linear ordinary differential equations, linear first order systems, and boundary value problems for the heat and wave equations. It analyzes 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 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 225and 231.
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 its equivalent.
MATH 353-354: Modern Algebra I, II (3, 3) Basic algebraic systems: groups, rings, and fields. Homomorphisms and factor groups, rrings.  Polynomial rings and field extensions.  Applications, including symmetry groups and algebraic coding theory. Prerequisites: MATH 225 and 326.
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 382: Modeling Applications (1) The examination, analysis, and preparation of a variety of mathematical models of real-world phenomena from economics, science and industry. Discrete, continuous, and statistical models are included. May be repeated for credit. Only one hour may be used for the mathematics major. Prerequisites: MATH 345 and invitation by the department.

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: 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 495, 496: Pro-Seminar I, II (2, 2) Student presentation of selected topics. Prerequisite: Consent of the department chair.
MATH 497: Independent Study (1-2) 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.

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.