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2003-2004 UAF Catalog Course Descriptions |
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Mathematics Math placement information is in the front of this catalog in the Undergraduate: Applying for Admission section. No student will be permitted to enroll in a course having prerequisites if a grade lower than a C is received in the prerequisite course. Developmental Mathematics DEVM
050
(3
Credits)
Fall,
Spring DEVM 052 (2 Credits) Fall Alternative Approaches to Math: Basic College Math (2+0) Basic college mathematics: operations with percents, decimals, fractions and signed numbers, translating word problems, introduction to algebra and geometry, using alternative teaching styles. (Prerequisites: Appropriate placement test scores.) DEVM 060 (3 Credits) Fall, Spring Elementary Algebra (3+0) First year high school algebra. Evaluating and simplifying algebraic expressions, solving first degree equations and inequalities, integer exponents, polynomials, factoring, rational expressions, equations and graphs of lines. Also available via Independent Learning. (Prerequisite: DEVM 050 or placement.) DEVM 061 (1 Credit) Independent Learning Only Review of Elementary Algebra Designed to assist students in reviewing material covered by DEVM 060. Individuals who have not previously taken an elementary algebra course are recommended to enroll in DEVM 060. DEVM 062 (3 Credits) Fall, Spring Alternative Approaches to Math: Elementary Algebra (3+0) Algebraic topics. Includes operations with polynomial expressions, first- and second-degree equations, graphing, integral and relational exponents, and radicals using alternative teaching styles. (Prerequisites: DEVM 050/052 or appropriate placement test scores.) DEVM 063 (2 Credits) Fall Applied Math I: Alternative Approaches to Elementary Algebra (1+3) Elementary algebra, using an alternative teaching style; how skills are used in the work place; problem solving in a hands-on environment; evaluations, factoring, graphing, simplifying, estimating, solving first-degree equations, integer exponents and polynomials. Applied Math I and II will prepare students for DEVM 105. (Prerequisites: DEVM 050, appropriate placement test scores or permission of instructor.) DEVM 064 (2 Credits) Spring Applied Math II: Alternative Approaches to Elementary Algebra (1+3) Elementary algebra, using an alternative teaching style; how skills are used in the work place; problem solving in a hands-on environment; evaluations, factoring, graphing, simplifying, estimating, solving first-degree equations, integer exponents and polynomials. Applied Math I and II will prepare students for DEVM 105. (Prerequisites: DEVM 060, DEVM 063 or permission of instructor.) DEVM 065 (1 - 3 Credits) Fall, Spring Mathematics Lab (0+3 - 9) Designed to assist students in reviewing and reinforcing course concepts covered by DEVM 050, 060 and 105. Consists of instruction which may include lab instruction, individual student work or group work. Recommended for students who need more time and help to master the material in Developmental Math courses. (Prerequisite: Placement.) DEVM 071 (1 Credit) Independent Learning Only Review of Intermediate Algebra Course reviews material covered by DEVM 105. Individuals who have not taken an intermediate algebra course on the high-school level are recommended to enroll in DEVM 105. DEVM 081 (1 Credit) Independent Learning Only Review of Basic Geometry High school geometry without formal proofs. Topics include basic definitions, measurement, parallel lines, triangles, polygons, circles, area, solid figures and volume. (Prerequisite: DEVM 060.) DEVM 082 (1 Credit) Fall, Spring Hands-On Geometry (1+0) Basic concepts and uses of geometry. Emphasis on "hands-on" and applied problems. (Prerequisite: A solid knowledge of arithmetic -- no algebra required.) DEVM 105 (3 Credits) Fall, Spring Intermediate Algebra (3+0) Second year high school algebra. Operations with rational expressions, radicals, rational exponents, logarithms, inequalities, quadratic equations, linear systems, functions, Cartesian coordinate system and graphing. Also available via Independent Learning. (Prerequisite: DEVM 060 or placement.) DEVM 106 (3 Credits) Fall, Spring Alternative Approaches to Math: Intermediate Algebra (3+0) Algebraic topics. Includes .exponents, radicals, graphing, systems of equations, quadratic equations and inequalities, logarithms and exponentials, and complex numbers using alternative teaching styles. (Prerequisites: DEVM 060/062 or appropriate placement test scores. This course satisfies elective credit only.) MATHEMATICS MATH
107X
(3
Credits)
Fall,
Spring MATH 108 (2 - 3 Credits) Fall, Spring Trigonometry (2 - 3+0) m A study of the trigonometric functions. Also available via Independent Learning. (Prerequisite: MATH 107X or placement or concurrent enrollment in MATH 107X.) MATH 131X (3 Credits) Fall, Spring Concepts and Contemporary Applications of Mathematics (3+0) m Applications of mathematics in modern life including applications of graph theory in management science; uses of probability and statistics in industry, government and science; and applications of geometry to engineering and astronomy. Problem solving emphasized. Also available via Independent Learning. (Prerequisites: DEVM 105 or 106 or placement; or high school geometry and algebra II.) MATH 161X (3 Credits) Fall, Spring Algebra for Business and Economics (3+0) m Functions of one and several variables with attention to linear, polynomial, rational, logarithmic, and exponential relationships. Geometric progressions as applied to compound interest and present value. Linear systems of equations and inequalities. Note: No credit may be earned for more than one of MATH 107X or 161X. (Prerequisites: DEVM 105 or 106; or two years of high school algebra and MATH 161X placement or higher.) MATH 200X (4 Credits) Fall, Spring MATH 201X (4 Credits) Fall, Spring MATH 202X (4 Credits) Fall, Spring Calculus (4+0) m Techniques and application of differential and integral calculus, vector analysis, partial derivatives, multiple integrals, and infinite series. Note: No credit may be earned for more than one of MATH 200X, 262X or 272X. MATH 200X, 201X and 202X also available via Independent Learning. (Prerequisites: MATH 107X and 108 or placement for MATH 200X; MATH 200X for MATH 201X; MATH 201X for MATH 202X.) MATH 205 (3 Credits) Fall Mathematics for Elementary School Teachers I (3+1) m Elementary set theory, numeration systems, and algorithms of arithmetic, divisors, multiples, integers, introduction to rational numbers. Emphasis on classroom methods. Also available via Independent Learning. (Prerequisite: MATH 107X or placement. Restricted to B.A.S. and B.A. Elementary Education degree students; others by permission of instructor.) MATH 206 (3 Credits) Spring Mathematics for Elementary School Teachers II (3+1) m A continuation of MATH 205. Real number systems and subsystems, logic, informal geometry, metric system, probability, and statistics. Emphasis on classroom methods. Also available via Independent Learning. (Prerequisite: MATH 205.) MATH 215 (2 Credits) Spring Introduction to Mathematical Proofs (2+0) m Emphasis on proof techniques with topics including logic, sets, relations, equivalence induction, number theory, graph theory and congruence classes. In addition, a rigorous treatment of topics from calculus could be given. (Prerequisites: MATH 200X, 201X or concurrent with 201X or instructor permission.) MATH 262X (4 Credits) Fall, Spring Calculus for Business and Economics (4+0) m Ordinary and partial derivatives. Maxima and minima problems, including the use of Lagrange multipliers. Introduction to the integral of a function of one variable. Applications include marginal cost, productivity, revenue, point elasticity of demand, competitive/complementary products, consumer's surplus, etc. Note: No credit may be earned for more than one of MATH 200X, 262X or 272X. (Prerequisite: MATH 161X.) MATH 272X (3 Credits) Fall Calculus for Life Sciences (3+0) m Differentiation and integration with applications to the life sciences. Note: No credit may be earned for more than one of MATH 200X, 262X or 272X. (Prerequisites: MATH 107X and 108.) MATH 302 (3 Credits) Fall, Spring Differential Equations (3+0) Nature and origin of differential equations, first order equations, and solutions, linear differential equations with constant coefficients, systems of equations, power series solutions, operational methods, and applications. (Prerequisite: MATH 202X.) MATH 305 (3 Credits) Alternate Spring Geometry (3+0) Topics selected from such fields as Euclidean and non-Euclidean plane geometry, affine geometry, projective geometry, and topology. (Prerequisite: MATH 202X or permission of instructor. Next offered: 2003 - 04.) MATH 306 (3 Credits) Alternate Spring Introduction to the History and Philosophy of Mathematics (3+0) Includes a detailed study of certain important periods of history as examined by such thinkers as Plato, B. Russell, D. Hilbert, L.E.J. Brouwer and K. Godel. For students of mathematics, science, history and philosophy. (Prerequisite: MATH 202X or permission of instructor. Next offered: 2004-05.) MATH 307 (3 Credits) Fall Discrete Mathematics (3+0) Logic, counting, sets and functions, recurrence relations graphs and trees. Additional topics chosen from probability theory. (Prerequisite: MATH 201X or permission of instructor.) MATH 308 (3 Credits) Spring Abstract Algebra (3+0) Theory of groups, rings and fields. (Prerequisite: MATH 215 or permission of instructor. Recommended: MATH 307 and/or MATH 314.) MATH 310 (3 Credits) Fall Numerical Analysis (3+0) Direct and iterative solutions of systems of equations, interpolation, numerical differentiation and integration, numerical solutions of ordinary differential equations, and error analysis. (Prerequisite: MATH 302 or MATH 314 or permission of instructor. A knowledge of programming is desirable.) MATH 314 (3 Credits) Fall, Spring Linear Algebra (3+0) Linear equations, finite dimensional vector spaces, matrices, determinants, linear transformations, and characteristic values. Inner product spaces. (Prerequisite: MATH 201X.) MATH 371 (3 Credits) Alternate Fall Probability (3+0) Probability spaces, conditional probability, random variables, continuous and discrete distributions, expectation, moments, moment generating functions, and characteristic functions. (Prerequisite: MATH 202X. Next offered: 2004-05.) MATH 401W (3 Credits) Fall MATH 402 (3 Credits) Spring Advanced Calculus (3+0) A rigorous treatment of one and several dimensional calculus. Includes mappings from n-space and their continuity, differentiability and integrability properties as well as sequences and series. (Prerequisites: ENGL 111X; MATH 215 and 202X for MATH 401; MATH 401 for MATH 402.) MATH 404W (3 Credits) As Demand Warrants Topology (3+0) Introduction to topology, set theory, open sets, compactness, connectedness, product spaces, metric spaces and continua. (Prerequisites: ENGL 111X; MATH 202X and 215. Recommended: MATH 314 and/or 308.) MATH 408 (3 Credits) Alternate Spring Mathematical Statistics (3+0) Distribution of random variables and functions of random variables, interval estimation, point estimation, sufficient statistics, order statistics, and test of hypotheses including various criteria for tests. (Prerequisites: MATH 371 and STAT 200. Next offered: 2004-05.) MATH 412 (3 Credits) Alternate Spring Differential Geometry (3+0) Introduction to the differential geometry of curves, surfaces, and Riemannian manifolds. Basic concepts covered include the Frenet-Serret apparatus, surfaces, first and second fundamental forms, geodesics, Gauss curvature and the Gauss-Bonnet Theorem. Time permitting topics such as minimal surfaces, theory of hypersurfaces and/or tensor analysis may be included. (Prerequisites: MATH 314 and 401; or permission of instructor. Next offered: 2004-05.) MATH 421 (4 Credits) Fall Applied Analysis (4+0) Vector calculus, including gradient, divergence, and curl in orthogonal curvilinear coordinates, ordinary and partial differential equations and boundary value problems, and Fourier series and integrals. (Prerequisite: MATH 302.) MATH 422 (3 Credits) Spring Introduction to Complex Analysis (3+0) Complex functions, including series, integrals, residues, conformal mapping, and applications. May be taken independently of MATH 421. (Prerequisite: MATH 302.) MATH 460W,O (3 Credits) Alternate Fall Mathematical Modeling (3+0) Analysis, construction, and interpretation of mathematical models. Applications to the physical, biological, and social sciences. Topics selected from combinatorics, probability, statistics, perturbation, numerical analysis, and differential equations. Students develop a modeling project. (Prerequisites: COMM 131X or 141X; ENGL 111X; MATH 201X. Recommended: One or more of MATH 302, 314, STAT 300, 401; and some programming experience. Next offered: 2003-04.) MATH 490O (1 Credit) Spring Senior Seminar (1+0) Advanced topics selected from areas outside the usual undergraduate offerings. A substantial level of mathematical maturity is assumed. (Prerequisites: COMM 131X or 141X; MATH 308 or 401.) MATH 600 (1 Credit) Fall, Spring Teaching Seminar (1+0) Fundamentals of teaching mathematics in a university setting. Topics may include any aspect of teaching; university regulations, class and lecture organization, testing, book selection, teaching evaluations, etc. Specific topics will vary on the basis of student and instructor interest. Individual classroom visits will also be used for class discussion. May be repeated for credit. (Prerequisite: Graduate standing.) MATH 608 (3 Credits) As Demand Warrants Partial Differential Equations (3+0) First and second order differential equations, boundary value problems, and existence and uniqueness theorems. Green's functions, and principal equations of mathematical physics. (Prerequisite: MATH 422 or permission of instructor.) MATH 611 (3 Credits) Fall MATH 612 (3 Credits) Spring Mathematical Physics (3+0) (Cross-listed with PHYS 611 and PHYS 612) Advanced consideration of such topics as transform methods, asymptotic methods, Green's function, Sturm-Liouville theory, conformal mapping, and calculus of variations with applications to problems arising in physics. (Prerequisite: MATH 422 or permission of instructor.) MATH 615 (3 Credits) Alternate Spring Applied Numerical Analysis (3+0) Review of numerical differentiation and integration, and the numerical solution of ordinary differential equations. Main topics to include the numerical solution of partial differential equations: curve fitting, splines, and the approximation of functions. Supplementary topics such as the numerical method of lines, the fast Fourier transform, and finite elements may be included as time permits and interest warrants. (Prerequisites: CS 201, MATH 310, 314, 421, 422 or permission of instructor. Next offered: 2003 - 04.) MATH 621 (3 Credits) Alternate Fall Advanced Applied Analysis (3+0) Topics covered may include conformal mapping, Fourier, Laplace, and Z transforms and impulse functions with applications to solving differential equations which arise in science and engineering. Other topics as time permits include asymptotic expansions, local analysis, O.D.E.'s and special functions. (Prerequisites: MATH 421 and 422; or permission of instructor. Next offered: 2004-05.) MATH 630 (3 Credits) As Demand Warrants Advanced Linear Algebra (3+0) Vector spaces over arbitrary fields primary, rational and Jordan canonical forms, invariant subspace decompositions and multilinear algebra. (Prerequisites: MATH 308 and MATH 314.) MATH 631 (4 Credits) Alternate Fall Theory of Modern Algebra I (4+0) Rigorous development of groups, rings and fields. Introduction to category theory, module theory, homological algebra and Galois Theory. (Prerequisites: MATH 308 and graduate standing or permission of instructor. Next offered: 2004-05.) MATH 632 (3 Credits) Alternate Fall Theory of Modern Algebra II (3+0) Advanced topics taken from group theory, category theory, ring theory, homological algebra and field theory. (Prerequisite: MATH 631.) Next offered: 2003-04. MATH 641 (4 Credits) Alternate Fall Real Analysis I (4+0) General theory of Lebesgue measure and Lebesgue integration on the real line. Convergence properties of the integral. Introduction to the general theory of measures and integration. Differentiation, the product measures, and an introduction to LP spaces. (Prerequisites: MATH 401-402 or permission of instructor.) Next offered: 2003-04. MATH 642 (3 Credits) Alternate Fall Real Analysis II (3+0) Theory of abstract measures and integration. Signed and vector-valued measures. The fundamental theorems of functional analysis: open mapping, closed graph, Hahn-Banach, uniform boundedness, Banach-Alaoglu, etc. Lebesgue-Stieljies integration. Probability spaces and distributions. Applications and special topics to be selected on the basis of instructor and student interest. (Prerequisite: MATH 641. Next offered: 2004-05.) MATH 645 (4 Credits) Alternate Spring Complex Analysis (4+0) Analytic functions, power series, Cauchy integral theory, Residue Theorem. Basic topology of the complex plane and the structure theory of analytic functions. The Riemann mapping theorem. Infinite products. (Prerequisite: Math 641 or permission of instructor. Next offered: 2003 - 04.) MATH 651 (4 Credits) Alternate Spring Topology (4+0) Treatment of the fundamental topics of point-set topology. Separation axioms, product and quotient spaces, convergence via nets and filters, compactness and compactifications, paracompactness, metrization theorems, countability properties, and connectedness. Set theory as needed for examples and proof techniques. (Prerequisites: MATH 401-402 or MATH 404 or permission of instructor. Next offered: 2004-05.) MATH 655 (3 Credits) Alternate Fall Algebraic Topology (3+0) Fundamentals of algebraic topology with applications to topology and geometry. The fundamental group, covering spaces, axiomatic homology, and singular homology. (Prerequisites: MATH 308 and MATH 401-402 and MATH 404 or permission of instructor.) Next offered: 2003-04. MATH 660 (3 Credits) Alternate Spring Advanced Mathematical Modeling (3+0) Examination of models and procedures reflecting problems arising in the physical and social sciences. Derivation of model equations and methods for solution. Heat conduction problems, random walk processes, simplification of equations, dimensional analysis and scaling, perturbation theory, and a discussion of self-contained modules that will illustrate the principal modeling ideas. Students will develop a modeling project as part of the course requirements. (Prerequisite: Permission of instructor. Next offered: 2004-05.) MATH 661 (3 Credits) Alternate Fall Optimization (3+0) (Cross-listed with CS 661) Linear and nonlinear programming, simplex method, duality and dual simplex method, post-optimal analysis, constrained and unconstrained nonlinear programming, Kuhn-Tucker conditions. Applications to management, physical, and life sciences. Computational work with the computer. (Prerequisites: Knowledge of calculus, linear algebra, and computer programming. Next offered: 2004-05.) MATH 663 (3 Credits) Alternate Spring Applied Combinatorics and Graph Theory (3+0) A study of combinatorial and graphical techniques for complexity analysis including generating functions, recurrence relations, theory of counting, planar directed and undirected graphs, and applications to NP complete problems. (Prerequisites: MATH 307 and 314. Next offered: 2003 - 04.) |
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