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1999-2000 UAF Catalog

Course Descriptions


Degrees and Programs Index

Mathematics

No student will be permitted to enroll in a course having prerequisites if a grade lower than C is received in the prerequisite course.

DEVELOPMENTAL MATHEMATICS

DEVM 050 (3 Credits) Fall, Spring
Pre-Algebra (3+0)
Operations with whole numbers, fractions, decimals, percents and ratios, signed numbers, evaluation of algebraic expressions and evaluation of simple formula. Metric measurement system and geometric figures. Also available via Independent Learning.
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 tailored to the specific cultural backgrounds of the students. (Prerequisites: Appropriate placement test scores. Students must meet federal eligibility requirements.)
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)
Elementary algebra. Algebraic equations, first-degree equations, polynomials, factoring, integral exponents and rational expressions using alternative teaching styles tailored to the specific cultural backgrounds of the students. (Prerequisites: DEVM 050 or appropriate placement test scores. Students must meet federal eligibility requirements.)
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 070. (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 070. (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 070. 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 070 (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 071 (1 Credit) Independent Learning Only
Review of Intermediate Algebra
Course reviews material covered by DEVM 070. Individuals who have not taken an intermediate algebra course on the high-school level are recommended to enroll in DEVM 070.
DEVM 072 (3 Credits) Fall, Spring
Alternative Approaches to Math: Intermediate Algebra (3+0)
Intermediate algebra. Exponents, radicals, graphing, systems of equations, quadratic equations, inequalities and complex numbers using alternative teaching styles tailored to specific cultural backgrounds of the students. (Prerequisites: DEVM 060 or appropriate placement test scores. Students must meet federal eligibility requirements.)
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.)

MATHEMATICS

MATH 107X (3 Credits) Fall, Spring
Functions for Calculus (3+0) m
A study of algebraic, logarithmic, and exponential functions, together with selected topics from algebra. Note: No credit may be earned for more than one of MATH 107X or 161. Also available via Independent Learning. (Prerequisites: Two years of high school algebra and MATH 107X placement or higher.)
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 107 or concurrent registration 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. (Prerequisites: High school geometry and algebra II.)
MATH 132 (3 Credits) As Demand Warrants
Concepts of Mathematics (3+0) m
Mathematical thought and history for students with a limited mathematical background. Mathematical reasoning rather then formal manipulation. Topics may include number theory, topology, set theory, geometry, algebra and analysis. (Prerequisites: MATH 131X.)
MATH 161 (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 161. (Prerequisites: Two years of high school algebra and MATH 161 placement or higher.)
MATH 181 (3 Credits) As Demand Warrants
Finite Math (3+0)
Topics in matrix theory including Markov chains, linear programming, simplex method. Partitions, binomial and multinomial theorems, counting techniques, probability and finite stochastic processes. May be used as a prerequisite for STAT 200. (Prerequisite: DEVM 070 or placement.)
MATH 200X (4 Credits) Fall, Spring
MATH 201X

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 200, 262 or 272. MATH 200X and 201 also available via Independent Learning. (Prerequisites: MATH 107X, 108.)
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. Materials fee: $10.00. Also available via Independent Learning. (Prerequisites: MATH 131 or MATH 107. Restricted to B.Ed. 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. Materials fee: $10.00. 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 200, 201 or concurrent with 201 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 200, 262 or 272. (Prerequisite: MATH 161.)
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 200, 262 or 272. (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 202.)
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 202 or permission of instructor. Next offered: 1999 - 2000.)
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 202 or permission of instructor. Next offered: 2000-01.)
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 201 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 permission of instructor. A knowledge of FORTRAN or BASIC 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 201.)
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. Materials fee: $5.00. (Prerequisite: MATH 202. Next offered: 2000-01.)
MATH 401W (3 Credits) Fall
MATH 402W

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: MATH 215 and 202 for MATH 401; MATH 401 for MATH 402.)
MATH 404W,O (3 Credits) As Demand Warrants
Topology (3+0)
Introduction to topology, set theory, open sets, compactness, connectedness, product spaces, metric spaces and continua. (Prerequisites: MATH 202 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. Materials fee: $5.00. (Prerequisites: MATH 371 and STAT 200. Next offered: 2000-01.)
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. Corequisite: MATH 402 or permission of instructor. Next offered: 2000-01.)
MATH 421 (4 Credits) Fall
Applied Analysis I (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. Materials fee: $10.00. (Prerequisite: MATH 302.)
MATH 422 (4 Credits) Spring
Applied Analysis II (4+0)
Complex functions, including series, integrals, residues, and conformal mapping. Applications to potential theory and the boundary-value problems of mathematical physics. May be taken independently of MATH 421. Materials fee: $10.00. (Prerequisite: MATH 302.)
MATH 460W,O (3 Credits) 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. Materials fee: $10.00. (Prerequisite: MATH 201. Recommended: One or more of MATH 302, 314, STAT 300, 401; and some programming experience.)
MATH 490O (1 Credit) Fall
Senior Seminar (1+0)
Advanced topics selected from areas outside the usual undergraduate offerings. A substantial level of mathematical maturity is assumed. (Prerequisites: At least one of 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

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 consent 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, MATH 314, MATH 421, MATH 422 or consent of the instructor.) Next offered: 1999 - 2000.
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 421-422 or MATH 604 or permission of instructor. Next offered: 2000-01.)
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: 2000-01.)
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: 1999 - 2000.
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 the instructor.) Next offered: 1999 - 2000.
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: 2000-01.)
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 consent of the instructor.) Next offered: 1999 - 2000.
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: 2000-01.)
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: 1999 - 2000.
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: Consent of instructor. Next offered: 2000-01.)
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: 2000-01.)
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. (Prerequisite: Consent of instructor.) Next offered: 1999 - 2000.

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