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### Mathematics Courses

1001 Basic Mathematics Review of basic mathematical concepts including the properties and operations of whole numbers, fractions, decimals, and integers; percents; ratios and proportions; basic geometry; and graph interpretation.

1002 Basic Algebra Review of basic algebraic skills. Topics include operations with polynomials, solving equations and inequalities, factoring polynomials, operations with rational expressions, graphing linear equations, solving systems of equations, and square roots. Prerequisite: Passing the arithmetic section of the mathematics proficiency examination or permission of the instructor.

1106 Finite Mathematics With Applications Insight into the way mathematicians approach problems in other disciplines, through the study of the following topics with applications: lines, matrices, linear programming, counting techniques, discrete probability, graph theory, and game theory. The course is designed primarily for non-Mathematics majors. Prerequisites: Mathematics 1001 or passing the arithmetic portion of the mathematics proficiency test, Mathematics 1002 or passing the algebra portion of the mathematics proficiency exam. Natural Science and Mathematics. Quantitative Reasoning.

1107 College Algebra and Trigonometry The basic concepts of algebra and trigonometry needed for the study of calculus. Included are properties of exponents; solving equations and inequalities; graphing; properties of polynomial, exponential, logarithmic, and trigonometric functions. Prerequisites: Mathematics 1001 or passing the arithmetic portion of the mathematics proficiency test, Mathematics 1002 or passing the algebra portion of the mathematics proficiency test. Natural Science and Mathematics. Quantitative Reasoning.

1109 Discrete Mathematics An introduction to mathematical reasoning, discrete structures, and foundations of algorithm analysis. Possible topics include propositional and predicate logic, proof techniques including mathematical induction, recurrences, sets, relations, pigeonhole principle, combinatorics, graphs, discrete probability, and number theory. Prerequisites: Computer Science 1106. Quantitative Reasoning. Cross-listed with Computer Science 1109.

1117 Calculus I Initial study of limits, derivatives and integrals; review of trigonometric functions; differentiation techniques and formulas applied to rational and trigonometric functions; applications of derivatives including curve sketching; extrema and rate problems; definition of the integral; elementary applications of integrals. Prerequisite: Mathematics 1107 or placement by the Department. Natural Science and Mathematics. Quantitative Reasoning.

1118 Calculus II Further study of the trigonometric, exponential, and logarithmic functions and their derivatives, methods of integration; parametric equations; polar coordinates; sequences, infinite series, and power series. Prerequisite: Mathematics 1117 or placement by the Department. Natural Science and Mathematics. Quantitative Reasoning

2210 Numerical Methods An introduction to numerical methods for solving problems from calculus and linear algebra, including the solution of a single nonlinear equation, the solution of linear systems, interpolation and approximation, differentiation and integration, and the solution of eigenvalue problems. Prerequisites: Computer Science 1106, Mathematics 1118. Cross-listed with Computer Science 2210. Offered in 2005-2006 and alternate years.

2218 Linear Algebra A study of the theory of finite-dimensional vector spaces, linear transformations, matrices, determinants, inner products, and eigenvalues. Prerequisites: Mathematics 1117 or 1118 or placement by the Department. Natural Science and Mathematics. Quantitative Reasoning.

2219 Calculus III A study of functions of several variables. Topics include partial derivatives, directional derivatives, multiple integrals, the structure of Euclidean n-space, En, functions from Em to En, line and surface integrals, Green's and Stokes' Theorems. Prerequisites: Mathematics 1118 or placement by the Department. Natural Science and Mathematics. Quantitative Reasoning.

2224 Fundamentals of Mathematics A transition course from the technical problem solving of the calculus courses to the rigorous theorem proving courses of advanced mathematics. Introductions to logic and set theory, including the algebra of sets, functions, and relations, with examples from number theory, analysis and abstract algebra. Prerequisite: Mathematics 1118 or permission of the Department. Natural Science and Mathematics. Quantitative Reasoning.

2242 Mathematical Structures I An introduction to selected topics in mathematics, including sets and operations involving sets, numbers and numeration, operations and algorithms involving whole numbers, integers, rational numbers, and algebra. This course does not count toward the major in Mathematics, and is open to those students preparing to teach in the elementary education. This course does not meet the National Science and Mathematics requirement. Prerequisites: Mathematics 1001 or passing the arithmetic portion of the mathematics proficiency test, Mathematics 1002 or passing the algebra portion of the mathematics proficiency test.

3304 Differential Equations Linear differential equations with applications in the physical, biological, and social sciences; series solutions; systems of linear differential equations; approximation methods; the Laplace transform; Fourier series; the heat equation. Prerequisite: Mathematics 1118. Offered in 2005-2006 and alternate years.

3305 Introduction to Mathematical Analysis A treatment of the theory of elementary calculus including functions limits, sequences, series, uniform continuity, derivatives and Riemann integration, topological properties of the real numbers. Prerequisite: Mathematics 2224.

3310 History of Mathematics A study of the development of mathematics from primitive counting systems to modern mathematics, with particular emphasis on the 17th century. Prerequisites: Mathematics 1117 and 2224. Offered in 2005-2006 and alternate years.

3312 Real Analysis A study of the convergence of sequences and series of functions; polynomial approximation; interchange of limit processes; the Lebesgue integral. Prerequisite: Mathematics 3305. Offered as needed.

3314 Theory of Computation This course studies the abstract models of machines and languages recognized by them, and introduces the concept of computability. This course not only serves as the theoretical foundation of computer science, but also has wide application to programming languages, linguistics, natural language processing, compiler design, and software design. Topics include finite automata and regular languages, pushdown automata and context-free grammars, grammar transformations and normal forms, Turing machines and computable functions, and unsolvable problems including the halting problem. Prerequisite: Computer Science/Mathematics 1109 or Mathematics 2224. Recommended: Computer Science 2217. Cross-listed with Computer Science 3314.

3316 Complex Analysis An introductory course in the theory of functions of a complex variable; properties of analytic functions, classical integral theorems, Taylor and Laurent expansions, and applications. Prerequisite: Mathematics 2219 and 3305 are recommended.

3322 Fundamental Concepts of Geometry The foundations and evolution of geometry; selected topics from Euclidean and non-Euclidean geometries, projective geometry, affine geometry; studies in the nature of proof and famous geometric problems. Prerequisites: Mathematics 1117 and 2224. Offered in 2005-2006 and alternate years.

3323 Probability A study of sample spaces, counting techniques, discrete and continuous random variables and related moments; binomial, Poisson, normal and other probability distributions; Chebychev inequality, central limit theorem. Prerequisite: Mathematics 1118, Mathematics 2219 is recommended.

3324 Mathematical Statistics A systematic treatment of statistics from a theoretical point of view; sampling distributions, decision theory, estimation, hypothesis testing, modeling, and applications. Prerequisite: Mathematics 3323. Offered as needed.

3328 Operations Research A survey of topics from Operations Research: linear programming, computer applications using the Simplex Algorithm, dynamic programming, inventory control, queuing problems, network analysis, and game theory. Prerequisites: Computer Science 1106, Mathematics 3323, Mathematics 3324 or 3335 is strongly recommended. Offered as needed.

3335 Stochastic Processes A study of Markov Chains, stable distributions for regular chains, absorption probabilities, computer simulations, Poisson process, and birth-death process. Prerequisite: Mathematics 3323. Offered as needed.

3336 Number Theory An introduction to the theory of numbers: divisibility, primes, unique factorization, congruences, Euler's phi-function, Fermat's and Wilson's theorems, quadratic reciprocity, perfect numbers and applications to Diophantine equations. Prerequisite: Mathematics 2224. Offered in 2005-2006 and every third year.

3342 Mathematical Structures II A continuation of an introduction to selected topics in mathematics. This course includes the development of the following topics: algebra, geometry, measurement, statistics, and probability. This course does not count toward the major in Mathematics, and is open to those students preparing to teach in elementary school. This course does not meet the National Science and Mathematics requirement. Prerequisites: Mathematics 1001 or passing the arithmetic portion of the mathematics proficiency test, Mathematics 1002 or passing the algebra portion of the mathematics proficiency test, Mathematics 2242.

3391; 3392; 4491; 4492 Mathematics Problems Seminar Consideration of problems chosen from diverse areas of mathematics and mathematical ideas outside of a course context. The problems considered vary from year to year.

4406 Abstract Algebra A presentation of the theory of groups, rings, and fields through a study of topics selected from: homomorphisms, isomorphism theorems, Lagrange's theorem, the Sylow theorems, principal ideal domains, Euclidean domains, unique factorization domains, polynomial rings over a field, construction with straight edge and compass, and finite fields. Prerequisite: Mathematics 2224. Offered in 2005-2006 and alternate years.

4409 Topology An introduction to the basic notions of topological spaces, which are the foundation for analysis and calculus. Topics include basic set theory, the axioms and specific examples of topological spaces, connectedness and compactness, separation axioms, continuous function, and homotopy theory. Offered as needed.

4494 Capstone Experience in Mathematics All senior Mathematics majors will read an expository paper in one of the mathematics journals and make written oral reports on the topic discussed in the article. The article will be chosen in consultation with a member of the Department of Mathematics and Computer Science. Offered in the fall semester.

2265; 3365; 4465 Special Topics In Mathematics The study of a selected topic in the discipline. Different topics are chosen for each offering, based on students' interests and needs.

2295; 3395; 4495 Internships in Mathematics Supervised field experiences in appropriate settings, usually off-campus, designed to assist students in acquiring and using skills and knowledge of the discipline unique to the selected topic.

2298; 3398; 4498 Independent Studies In Mathematics Directed study planned and conducted with reference to the needs of students who are candidates for departmental honors. Qualified students who are not candidates for such honors but who desire to do independent studies are also admitted with permission of the Department.

Lewis Hall of Science 114, McDaniel College, Westminster, Maryland 21157-4390; Phone: 410-857-2470, Fax: 410-386-4624.