Page 85 of Albion College Departments and Courses Catalog by Albion College Michigan

First-order differential equations and numerical algorithms of Euler and Runge-Kutta. Linear algebraic systems, Gaussian elimination, rowechelon form matrix algebra, inverses and determinants. Vector spaces, subspaces, linear independence, bases, span, dimension, linear mappings and function spaces. Second and higher-order linear differential equations. Eigenvectors, eigenvalues and spectral decomposition methods. First-order linear differential systems, including solutions methods using matrix exponentials. Applications focus on problems in physics, chemistry, biology, economics and engineering. Additional topics may include nonlinear dynamical systems, stability theory, transform theory and power series solutions. Mason. 299 Colloquium in Mathematics and Computer Science (1/4) Fall, Spring Prerequisite: Mathematics 143 or Computer Science 173. Selected topics in mathematics and computer science as presented by students, departmental faculty and visiting speakers. Requirements include written summaries of each presentation and a paper on a mathematics/computer science topic of personal interest. Same as Computer Science 299. Staff. 309 Mathematical Statistics (1) Fall Prerequisite: Mathematics 236 or 245. A mathematical study of probability distributions, random sampling, and topics selected from statistical theory: estimation, hypothesis testing and regression. Anderson. 310 Applied Mathematical Statistics (1) Spring Prerequisite: Mathematics 309. A continuation of Mathematics 309. In-depth studies of regression analysis, analysis of variance, experimental design and nonparametric statistics. Covers topics pertinent to actuarial mathematics. Offered in alternate years. Anderson. 316 Numerical Analysis (1) Fall Prerequisites: Mathematics 236 or 247 and Computer Science 171. Methods of obtaining numerical solutions to mathematical problems. Stresses the implementation and error analysis of algorithms. Topics include solution of non-linear equations, systems of equations, interpolating polynomials, numerical integration and differentiation, numerical solution to ordinary differential equations, and curve fitting. Offered in alternate years. Same as Computer Science 316. Mason. 326 Operations Research (1) Spring Prerequisites: Mathematics 236 or 247, and Mathematics 245. An introduction to computational methods in mathematical modeling including linear programming and Markov chains. Applications in business, economics and systems engineering. Knowledge of probability is helpful. Offered in alternate years. Same as Computer Science 326. Mason. 331 Real Analysis (1) Spring Prerequisites: Mathematics 245 and either 236 or 239. A study of the concepts underlying calculus of a single variable: The completeness property of the real number system, convergence, continuity, properties of elementary functions, the derivative and the Riemann integral. Bollman. 335 Abstract Algebra (1) Fall Prerequisites: Mathematics 236 and 239. Properties of the integers, real number system and other familiar algebraic entities are viewed abstractly in structures such as groups, semigroups, rings and fields. Homomorphisms and isomorphisms (functions compatible with the algebraic operations) illuminate the underlying similarities among these structures. Students will develop their skills in mathematical writing and presentations. Messer. 342 Geometry (1) Spring Prerequisites: Mathematics 143 and 239. The logical foundation of Euclidean geometry, including the axiom systems of Euclid and Hilbert, and their philosophical implications. An introduction to hyperbolic, elliptic and projective geometry. Employs software such as Geometers Sketchpad to illustrate cours e topics. Bollman. 345 History of Mathematics (1) Fall Prerequisite: Mathematics 141. A study of the history and evolution of mathematical ideas and their significance, from approximately 3500 B.C.E. to the present. Topics include number systems, arithmetic, Euclidean and non-Euclidean geometry, algebra, calculus, probability, number theory and applied mathematics. Offered in alternate years. Bollman. 360 Mathematical Modeling (1) Spring Prerequisites: Mathematics 247 and Computer Science 171. An introduction to analytical methods in mathematical modeling, including nonlinear optimization, dynamical systems and random processes. Applications in physics, biology, economics and systems engineering. Knowledge of probability and statistics is helpful. Same as Computer Science 360. Mason. 380 Mathematical Physics (1) Spring Same as Physics 380. Staff. Page 5 of 6 Albion College Catalog 2006-2007 Mathematics 5/10/2006 http://www.albion.edu/academics/catalog/departments/math.asp

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