Course Catalog 2009-2010
Associate Professor Matthew Neal, Chair
Professors Daniel D. Bonar, Todd H. Feil, Michael D. Westmoreland; Associate Professors Lewis D. Ludwig, Matthew Neal; Assistant Professor Sarah Crown; Visiting Instructor Timothy DeGenero; Academic Administrative Assistant 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 should take 123-124 followed by 222 and 231 by the end of the sophomore year. Prospective mathematics 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 Math 102, 121, or 123.
Bachelor of Arts Degree. 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 110 or 111, 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 either 242 or 275 and all 300-level courses, excluding 361-362 and 363-364.
Bachelor of Science Degree. The B.S. requirements consist of the core courses, CS 110 or 111, 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 either 242 or 275 and all 300-level courses, excluding 361-362 and 363-364. A year long senior research project may count as one elective.
A minor in Mathematics consists of 123, 124, 210, 222, 231 and two mathematics courses chosen from either 242 or 275 and all 300-level courses, excluding 361-362 and 363-364.
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 pursue a Bachelor of Science degree.
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 and applications of calculus to the natural and social sciences. Prerequisite: Placement or Math 121. 4
Calculus II (MATH-124). Further study of single and multivariable calculus including an introduction to differential equations and linear algebra with applications to the natural and social sciences. (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.) 4
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. Prerequisite: Math 124. 4
Technical Communication I (MATH-215). This course aims to enhance mathematics and computer science students' proficiency and comfort in orally communicating content in their disciplines. Students will present three talks during the semester on substantive, well-researched themes appropriate to their status in their major. Prerequisite: Math 210 or CS 271. 1
Calculus III (MATH-222). Multivariable calculus including the following topics: vectors and geometry, parametrized curves and surfaces, partial derivatives and integrals of multivariable functions and vector calculus with applications to the natural and social sciences. Prerequisite: Math 124 or consent. (Offered each semester) 4
Linear Algebra and Differential Equations (MATH-231). Further study of linear algebra and differential equations (together with infinite sequences and series) with applications to the natural and social sciences. Prerequisite: Math 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
Elementary Graph Theory (MATH-275). Graphs are mathematical structures that are used to model a great variety of phenomena ranging from the internet to social networks to phylogenetic clusters, In this class, we will study the mathematical properties of graphs and develop algorithms to solve many common graph problems. Prerequisite: CS 174 or Math 210. 4
Intermediate Topics in Mathematics (MATH-299). A general category used only in the evaluation of transfer credit. 1-4
Technical Communication II (MATH-315). This course is a capstone experience in oral and written communication for mathematics and computer science majors. Students will research a substantive topic, write a rigorous expository article, and make a presentation to the department. Prerequisite: Math/CS 215. Corequisite: a 300-400 level mathematics or computer science course. 1
Advanced Analysis I (MATH-321). Thorough analysis of limits, continuity, differentiation, integration and uniform convergence of infinite series. Prerequisites: Math 210, 222, 231. 4
Advanced Analysis II (MATH-322). Vector calculus and differential geometry. Prerequisites: Math 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, 231. 4
Abstract Algebra II (MATH-333). A continuation of Math 332. A continued study of the structures of groups, rings and fields, and other topics in abstract algebra. Prerequisite: Math 332. 4
Theory of Computation (MATH-334). This course is a study of formal languages and their related automata. Turing machines, unsolvable problems and NP-complete problems. Prerequisites: CS 110 or CS 111 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. Applications include but are not limited to statistical decision theory and inference. Prerequisite: Math 124. 4
Methods of Applied Mathematics (MATH-357). A stud of some of the basic methods and modeling techniques used in applications to the natural and social sciences, focusing on continuous models. Possible topics include vector calculus, differential forms, Fourier series, Fourier transforms, orthogonal sets of functions, solution and theory of partial differential equations, non-linear optimization, dynamical systems and probability models. Prerequisites: Math 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