
Mathematics Courses 
MS 111Q  Finite Mathematics
(4 Credits) An introduction to various areas of modern mathematics. Topics include matrices, graph theory, linear systems, probability, Markov processes, and statistics. Applications of the mathematics introduced are given in areas such as archaeology and communication networks. MS 112Q  Mathematical Game Theory (4 Credits) An introduction to mathematical game theory, including combinatorial games, games of chance, and matrix games. Topics include game trees, base two arithmetic, values of games, probability, expected values, matrices, domination, and mixed and pure strategies. MS 113Q/113P  Chaos and Fractals in Nature (4 Credits) This course will investigate chaotic behavior in physical systems and use mathematics to describe that behavior. Some of the first evidence of chaotic behavior in nature came from a study of a mathematical model of the earth's climate. Since then, it has been discovered that chaotic behavior ocrs in many physical systems, including chemical and biological systems. Fractals have turned out to be a very valuable way to describe chaotic systems geometrically. MS 114Q  Elementary Graph Theory (4 Credits) A gentle introduction to graph theory and discrete math, with an emphasis on understanding the major results and using them to do applications from various fields. Topics include: connectivity, planarity, adjacency matrices, Eulerian and Hamiltonian graphs, trees, isomorphism, duality, coloring problems, directed graphs, matching problems and network flows. MS 115Q  Great Ideas in Mathematics (4 Credits) A survey of mathematics from the Ancient Greeks to the modern day through looking at its great ideas and theorems. Topics vary, but may include the Pythagorean theorem and Euclidean geometry, number theory, Cardano's solution of the cubic, Newton's discovery of the calculus, mathematical modeling, abstraction and proof, and probability and statistics. MS 116Q  Introduction to Cryptology (4 Credits) This course gives an historical overview of Cryptology and the mathematics behind it. Cryptology is the science of making (and breaking) secret codes. From the oldest recorded codes (taken from hieroglyphic engravings) to the modern encryption schemes necessary to secure information in a global community, Cryptology has become an intrinsic part of our culture. This course will examine not only the mathematics behind Cryptology, but its cultural and historical impact. Topics will include: matrix methods for securing data, substitutional ciphers, transpositional codes, Vigenere ciphers, Data Encryption Standard (DES), and public key encryption. The mathematics encountered as a consequence of the Cryptology schemes studied will include matrix algebra, modular arithmetic, permutations, statistics, probability theory and elementary number theory. MS 122Q  Calculus for Business Decisions (4 Credits) This course covers the tools necessary to apply the science of decisionmaking in the business environment. Students working in teams give oral and written presentations on key projects taken from realworld business problems. Quantitative reasoning topics include: graphing functions, demand, revenue, cost, profit, trend lines, differentiation, optimization and integration. Students integrate the use of technology with excel spreadsheets, powerpoint presentations, and software packages. Prerequisite: DS 280 and MIS 191. MS 125Q  Introduction to Mathematical and Statistical Modelling (4 Credits) An introduction to some mathematical techniques used to explore, model and analyze phenomena in the sciences. Topics include: probability, statistics, regression and linear systems. MS 130  Calculus I with Review, part 1 (4 Credits) This course is intended for students planning to take a calculus course. Topics include exponents, factoring, solving equations and inequalities, graphs, functions, linear and quadratic functions, exponential and logarithmic functions, and systems of linear equations. MS 131Q  Calculus I with Review, part 2 (4 Credits) Designed for students who enter Stetson with insufficient precalculus background for the standard sequence. THe combination of MATH 130 and MATH 131 covers the same calculus material as MATH 141 (Calculus I), including limits, continuity, differentiation and applications of derivatives, antidfferentiation, the definite integral and the Fundamental Theorem of Calculus, and includes a review of precalculus material including trigonometry, with an emphasis on applications in the sciences. Prerequisite: MATH130 MS 141Q  Calculus I with Analytic Geometry (4 Credits) A first calculus course designed for majors in mathematics and the physical sciences. Topics include limits, continuity, differentiation, applications of derivatives, antidifferentiation, the definite integral, and the fundamental theorem of calculus. Prerequisite: MS101. MS 142Q  Calculus II with Analytic Geometry (4 Credits) The continuation of MATH 141Q. Topics include techniques of integration, applications of integration, differential equations, sequences and series, power series, and Taylor's theorem. Prerequisite: MATH 141Q or MATH 131Q. MS 211Q  Linear Algebra (4 Credits) An introduction to the theory and applications of linear systems. Topics include matrix operations, solving linear systems by elimination, basis and dimension, linear transformations, eigen values and eigen vectors, and general vector spaces. Prerequisite: MATH 141 MS 221Q  An Introduction to Logic and Proof (4 Credits) This course prepares the student to confront the elements of advanced theoretical mathematics: to understand mathematical statements, to read and write proofs, and to appreciate the processes of mathematical creation. Topics include elementary logic, set theory, functions, relations, and induction. Prerequisite: MS142. MS 243Q  Calculus III with Analytic Geometry (4 Credits) An introduction to the calculus of more than one variable. Topics include vectors, parametric equations, polar coordinates, partial differentiation, multiple integration and vector fields. Prerequisite: MATH 142Q MS 301  Number Theory (4 Credits) This course studies the elementary properties of integers, including divisibility, factorization, and primality. Topics include diophantine equations, congruences, the Chinese Remainder Theorem, divisibility tests, theorems of Fermat, Wilson and Euler, residue classes, quadratic residues, quadratic reciprocity, continued fractions, multiplicative functions, and applications to cryptography. MS 301  Real Analysis I (4 Credits) A rigorous study of some concepts in calculus. Topics include basic topology, limits and continuity, and sequences. MS 305  Introduction to Abstract Algebra (3 Credits) A onesemester introduction to the basic algebraic structures with emphasis on developing computational skills within these structures. Groups, permutations, integers modulo n, cosets, the Lagrange theorem, grouphomomorphisms, rings, polynomials, integral domains, fields, real and complex number fields. MS 312  Advanced Linear Algebra (4 Credits) A continuation of MATH 211Q, this course is an axiomatic theory of vector spaces. Topics include general vector spaces, inner product spaces, linear mappings, the RankNullity theorem, representations of mappings, dual spaces and diagonalization. MS 321  Cryptology (4 Credits) An introduction to the concepts and practices of cryptology. Topics include: symmetrickey and publickey ciphers, hash functions, digital signatures, and other security primitives. Relevant areas of mathematics will include probability theory, number theory and abstract algebra. Prerequisite: MS320. MS 321  Ordinary Differential Equations (4 Credits) An introduction to the study of equations involving derivatives. Topics include: first and second order differential equations, existence and uniqueness of solutions, separation of variables, variation of parameters, linear and nonlinear systems, solution by generalized eigenvectors, phase portraits, linearization, numerical methods, potential functions, gradient systems, limit cycles and chaotic systems, and mathematical modeling with differential equations. MS 331  Combinatorics and Graph Theory (4 Credits) An introduction to the theory and applications of graph theory. Topics include basic graph theory, Eulerian and Hamiltonian graphs, trees, planarity, duality, graph coloring, graph algorithms, and various practical applications. MS 335  Geometry (3 Credits) This course may be either a survey course covering several topics in geometry or an indepth treatment of one area. Topics include: Halberd's foundations of Euclidean geometry, nonEuclidean geometries, projective geometry, metric of affine geometry, finite geometries. MS 341  Mathematical Modeling and Computer Simulation (4 Credits) An introduction to the development of mathematical models., and the use of computers toward that goal. Topic include: model construction, regression, emperical modeling, difference equations and dynamical systems, probabilistic modeling, and Monte Carlo simulation. (Crosslisted as CSCI 341) Prerequisite: CSCI 141 MS 351  Operations Research (4 Credits) An introduction to deterministic optimization. Topics may include linear programming and the simplex method, integer programming, goal programming, the transportation problem, network analysis, dynamic programming, and game theory. MS 361  Numerical Analysis (4 Credits) A study and analysis of common numerical methods used in applied mathematics. Topics include solutions of nonlinear equations, the solutions of systems of linear equations, interpolation, numerical integration, and the numerical solution of differential equations. Prerequisite: CSCI141. Crosslisted as CSCI 361. MS 371  Probability (4 Credits) An introduction to the study of randomness. Topics include discrete and continuous probability distributions, conditional probability, independence, combinatorial probability, expected value and variance, and laws of large numbers. Prerequisite: MS203. MS 372  Mathematical Statistics (4 Credits) A theoretical introduction to statistics, including point estimation, confidence intervals and hypothesis test. Topics include goodness of fit tests, contingency tables, regression, correlation, analysis of variance, nonparametric tests and use of the t, F, Z and chisquared distributions to draw inferences about means and variances of one or two populations. Emphasis is on deriving the statistical tests in addition to using them to draw statistical conclusions. Prerequisite: MS371. MS 385  Independent Study (4 Credits) MS 390  Special Topics in Mathematics (4 Credits) May be repeated for credit. MS 397  Internship in Mathematics (4 Credits) MS 401  Real Analysis I (4 Credits) A rigorous study of the theory of Calculus. Topics include: basic topology, sequences, functions, limits, continuity and differentiation. MS 402  Real Analysis II (4 Credits) The continuation of MATH 401. Topics include differentiation, integration, infinite series, and convergence of functions. Prerequisite: MATH 401. MS 411  Complex Analysis (4 Credits) A detailed study of the complex number system and complex functions. Topics include harmonic functions, complex differentiation and integration, the Cauchy integral formula, Taylor and Laurent series, residues and poles, and conformal mappings. MS 422  Partial Differential Equations (4 Credits) A study of partial differential equations, their solutions and application. Topics covered include Fourier series, separation of variables, boundary value problems, existence and uniqueness of solutions, method of characteristics, numerical solutions and applications including the heat equation, wave equation, and Laplace's equation. Prerequisite: MATH 321. MS 431  Topology (4 Credits) A rigorous study of pointset topology, including topics such as open and closed sets, subspaces, continuity and convergence, separation axioms, connectedness, compactness, and product spaces. MS 441  Abstract Algebra I (4 Credits) A study of group theory, examples and applications. Topics include: subgroups, homomorphisms, direct products, factor groups, the Sylow theorems, free groups and select applications. MS 497  Preparation for Senior Research (1 Credits) Fall semester. Students will select a mathematical topic and present a research proposal for the following semester in MS498. Students may have to do a literature search or learn computer software to facilitate the research process. The student will then present a research proposal to the faculty. MS 498  Senior Project I (4 Credits) Spring semester. Students will do a research project on the topic selected the previous semester in MS497. The students will present their results in an oral presentation, and in a final paper. Prerequisite: MS497. 