Course Catalog 2008-2009
Associate Professor Jessen T. Havill, Chair
Professors Daniel D. Bonar, Todd H. Feil, Michael D. Westmoreland; Associate Professors Lewis D. Ludwig, Matthew Neal; Assistant Professor Sarah Crown; Visiting Instructor/Assistant Professor Laura D. Bosley; Visiting Instructor Timothy DeGenero; Academic Secretary Dee Ghiloni
The Mathematics curriculum is designed so that students will have a sound theoretical understanding of mathematics and an understanding of a variety of applications of mathematics. The study of mathematics is a challenging activity that sharpens logical reasoning and improves problem solving skills.
Students interested in Mathematics or the Natural Sciences should take 123-124 followed by 222 and 231 by the end of the sophomore year. Prospective math majors or minors should also take 210 the first semester of the sophomore year.
For research opportunities in mathematics see the Oak Ridge Science Semester described at www.orss.denison.edu. Summer research opportunities may also be available on campus.
Students interested in taking only one or two courses in Mathematics should choose 102, 121, or 123.
B.A. Degree in Mathematics. The core courses consist of Mathematics 123, 124, 222, 210 and 231. The minimum requirements for a B.A. in mathematics are the core plus Computer Science 171, either Mathematics 321 or 332, one course in discrete mathematics (331 or 337), one course in continuous mathematics (329 or 357), and two additional courses chosen from 242 and all 300-level courses.
B.S. Degree in Mathematics. The B.S. requirements consist of the core courses, CS 171, the real analysis sequence (321-322), the abstract algebra sequence (332-333), one course in discrete mathematics (331 or 337), one course in continuous mathematics (329 or 357), and two additional courses chosen from 242 and all 300-level courses.
A minor in Mathematics consists of 123, 124, 210, 222, 231 and two mathematics courses chosen from 242 and 300-level courses.
It is recommended that a B.A. candidate in Mathematics consider a second major or a strong minor. Economics would be a reasonable second major or minor for students planning to go into business or into an MBA program following graduation. Computer Science would also be a strong second major or minor.
Students who intend to pursue graduate study in mathematics should take a B.S. major.
Elements of Statistics (MATH-102). An introduction to statistical reasoning and methodology. Topics include exploratory data analysis, elementary probability, a standard normal-theory approach to estimation and hypothesis testing and simple linear regression. Not open for credit to students who have taken Psychology 370. 4
Essentials of Calculus (MATH-121). A one-semester introduction to single-variable differential and integral calculus and selected topics in multi-variable calculus. Emphasis is given to applications from the biological and social sciences. (123 may be taken after this course, but only 2 of the 4 credits count toward graduation) (Offered each semester) 4
Calculus I (MATH-123). An introduction to single variable calculus. Topics include limits, derivatives, integrals, applications of calculus, indeterminate forms, sequences and series. Prerequisite: Placement or 121. 4
Calculus II (MATH-124). This course is a continuation of Math 123 with an emphasis on mathematical models of the real world and the extremely useful and beautiful concept of infinite sums of numbers. It also includes an introduction to the language of higher dimensional mathematics which is necessary for the study of multivariable problems. Topics include: integration techniques, differential equations, probability models, sequences, series, power series, vectors, basic theory and solutions of linear systems of equations, matrix algebra, eigenvectors, and systems of differential equations with applications to the physical science, social sciences and game theory. (Offered each semester) 4
Introductory Topics in Mathematics (MATH-199). A general category used only in the evaluation of transfer credit. 1-4
Topics in Mathematics (MATH-200). (Also listed under Computer Science offerings.) 1
Introduction to Proof Techniques (MATH-210). An introduction to proof writing techniques. Topics will include logic and proofs, set theory, relations and functions, cardinality and mathematical induction. 4
Calculus III (MATH-222). Multiple variable calculus together with a rigorous review of beginning calculus. Prerequisite: 124 or consent. (Offered each semester) 4
Linear Algebra and Differential Equations (MATH-231). An introduction to linear algebra and differential equations: matrix algebra and real vector spaces, bases, dimension and subspaces. First-order and second-order differential equations and methods of their solution with applications. Linear systems of differential equations. Prerequisite: 124. (Offered each semester) 4
Applied Statistics (MATH-242). Statistics is the science of reasoning from data. This course will introduce you to the fundamental concepts and methods of statistics, including calculus-based probability. Topics include experimental design, data collection, and the scopes of conclusion, sampling, the application of probability models to statistical analyses, hypothesis testing, and regression analysis. Prerequisite: Math 124. (Offered every spring) 4
Intermediate Topics in Mathematics (MATH-299). A general category used only in the evaluation of transfer credit. 1-4
Advanced Analysis I (MATH-321). Thorough analysis of limits, continuity, differentiation, integration and uniform convergence of infinite series. Prerequisites: 210, 222, 231. 4
Advanced Analysis II (MATH-322). Vector calculus and differential geometry. Prerequisites: 210, 222, 231. 4
Complex Analysis (MATH-329). An introduction to complex numbers, analytic functions, derivatives, singularities, integrals, Taylor series, Laurent Series, conformal mappings, residue theory, analytic continuation. Cauchy-Riemann Equations, Cauchy's Theorem, Cauchy Integral Formula, Big and Little Picard Theorems, Riemann Mapping Theorem, Rouche's Theorem. Prerequisite: Math 222. 4
Combinatorics (MATH-331). The basic ideas of sets and functions are used to explore the three basic problems in combinatorics: the counting problem, the existence problem, and the optimization problem. Topics may include: combinatorial proof, the principle of inclusion-exclusion, induction, generating functions, recurrence relations, the Pigeonhole principle, Ramsey theory, basic graph theory, shortest path problems, minimum spanning tree problems, transversal theory, and graph coloring. Prerequisite: Math 210. 4
Abstract Algebra I (MATH-332). The study of abstract vector spaces and introduction to the structure and properties of groups, rings and fields. Prerequisites: Math 210, Math 231. 4
Abstract Algebra II (MATH-333). A continuation of Math 332. A continued study of the structures of groups, rings and fields, with focus on substructures and quotient structures. Prerequisite: Math 332. 4
Theory of Computation (MATH-334). (Also listed under Computer Science offerings.) This course is a study of formal languages and their related automata. Turing machines, unsolvable problems and NP-complete problems. Prerequisite: CS 171 and MATH 210. 4
Operations Research (MATH-337). This course involves mathematical modeling of real-world problems and the development of approaches to find optimal (or nearly optimal) solutions to these problems. Topics include: Modeling, Linear Programming and the Simplex Method, the Karush-Kuhn Tucker conditions for optimality, Duality, Network Optimization, and Nonlinear Programming. Prerequisite: Math 231. 4
Probability (MATH-341). The probability is developed by studying combinatorics, probability models, moment generating functions, limit theorems and conditional probability. Topics in statistical decision theory and inference are then examined: classical and Bayesian estimation, hypotheses testing and the general linear model. Prerequisite: 124. 4
Methods of Applied Mathematics (MATH-357). A study of some of the basic methods used in applications of mathematics to physics, engineering, and economics, focusing on continuous models. Topics include vector calculus, differential forms, Fourier series, Fourier transforms, orthogonal sets of functions, solution and theory of partial differential equations, power series solutions of ordinary differential equations, and distributions. Possible physical applications include signal processing, quantum mechanics, electricity and magnetism, heat flow, fluid flow and sound waves. Prerequisites: 222 and 231. 4
Directed Study (MATH-361). 1-4
Directed Study (MATH-362). 1-4
Independent Study (MATH-363). 1-4
Independent Study (MATH-364). 1-4
Advanced Topics in Mathematics (MATH-399). A general category used only in the evaluation of transfer credit. 1-4
Advanced Mathematical Topics (MATH-400). 4