2006-2007 UAF Catalog


Course descriptions index


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. A $42 per semester fee for computer facilities will be assessed for one or more CS, STAT and MATH 310, 460 and 660 courses. This fee is in addition to any lab/materials fees.

Developmental Mathematics

DEVM 050  3 Credits
Pre-Algebra
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. (Prerequisites: Appropriate placement test scores.) (3 + 0) Offered Fall, Spring


DEVM 051  1 Credit
Math Skills Review
Develops and reviews basic mathematical terminology, theory and operations as outlined by the Alaska State Mathematics Standards. Mathematics topics focus on reviewing the six basic "strands" of mathematical content: Numeration, Measurement, Estimation and Computation, Function and Relationship, Geometry, and Statistics and Probability. Approaches to problem solving will emphasize the process of mathematical thinking, communication and reasoning. It is an appropriate course for those preparing for the High School Qualifying exam in Alaska or those needing a review of basic math skills in preparation for a math placement test at UAF. May be repeated for a total of three credits. (1 + 0) Offered As Demand Warrants


DEVM 052  2 Credits
Alternative Approaches to Math: Basic College Math
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.) (2 + 0) Offered Fall


DEVM 060  3 Credits
Elementary Algebra
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: Grade of C or better in DEVM 050 or appropriate placement test scores.) (3 + 0) Offered Fall, Spring


DEVM 061  1 Credit
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. Independent Learning Only


DEVM 062  3 Credits
Alternative Approaches to Math: Elementary Algebra
Algebraic topics. Includes operations with polynomial expressions, first- and second-degree equations, graphing, integral and relational exponents, and radicals using alternative teaching styles. (Prerequisites: Grade of C or better in DEVM 050 or appropriate placement test scores.) (3 + 0) Offered Fall, Spring


DEVM 063  2 Credits
Applied Math I: Alternative Approaches to Elementary Algebra
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.) (1 + 3) Offered As Demand Warrants


DEVM 064  2 Credits
Applied Math II: Alternative Approaches to Elementary Algebra
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.) (1 + 3) Offered As Demand Warrants


DEVM 065  1-3 Credits
Mathematics Skills
Designed to assist students in reviewing and reinforcing course concepts covered by DEVM 050, 060, 062, 105 and 106. Consists of instruction which may include individual student work or group work. Recommended for students who need more time and help to master the material in Developmental Math courses. May be repeated. (Prerequisite: Placement.) (1-3+0) Offered Fall, Spring


DEVM 071  1 Credit
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. Independent Learning Only


DEVM 081  1 Credit
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. Available via Independent Learning Only. (Prerequisite: DEVM 060.)


DEVM 082  1 Credit
Hands-On Geometry
Basic concepts and uses of geometry. Emphasis on "hands-on" and applied problems. (Prerequisite: A solid knowledge of arithmetic—no algebra required.) (1 + 0) Offered Fall, Spring


DEVM 105  3 Credits
Intermediate Algebra
Second year high school algebra. Operations with rational expressions, radicals, rational exponents, logarithms, inequalities, quadratic equations, linear systems, functions, Cartesian coordinate system and graphing. To matriculate to MATH 107X from DEVM 105 a grade of B or higher is required. Also available via Independent Learning. (Prerequisite: Grade of C or better in DEVM 060, DEVM 062 or appropriate placement test scores.) (3 + 0) Offered Fall, Spring


DEVM 106  4 Credits
Intensive Intermediate Algebra
Algebraic topics. Includes .exponents, radicals, graphing, systems of equations, quadratic equations and inequalities, logarithms and exponentials, and complex numbers using alternative teaching styles. (Prerequisites: Grade of C or better in DEVM 060, 062, DEVM 105 or appropriate placement test scores. This course satisfies elective credit only.) (4.5 + 0) Offered Fall, Spring

Mathematics

MATH 103X  3 Credits
Concepts and Contemporary Applications of Mathematics (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.) (3 + 0) Offered Fall, Spring


MATH 107X  4 Credits
Functions for Calculus (m)
A study of algebraic, logarithmic and exponential functions, sequences and series, conic sections, and, as time allows, systems of equations, matrices and counting methods. A brief review of basic algebra is given the first week to prepare students for the rigor expected in this course. The primary purpose of this course, in conjunction with MATH 108, is to prepare students for calculus. Note: Credit may be earned for taking MATH 107X or MATH 116X, but not for both. Also available via Independent Learning. (Prerequisites: a grade of B or better in DEVM 105 or a C or better in DEVM 106; or two years of high school algebra and MATH 107X placement or higher.) (4.5 + 0) Offered Fall, Spring


MATH 108  2-3 Credits
Trigonometry (m)
A study of the trigonometric functions. Also available via Independent Learning. (Prerequisite: MATH 107X or placement or concurrent enrollment in MATH 107X.) (2-3 + 0) Offered Fall, Spring


MATH 161X  3 Credits
Algebra for Business and Economics (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: Credit may be earned for taking MATH 107X or MATH 116X, but not for both. (Prerequisites: DEVM 105 or 106; or two years of high school algebra and MATH 161X placement or higher.) (3 + 0) Offered Fall, Spring


MATH 200X  4 Credits
Calculus (m)
Limits including those with indeterminate form, continuity, tangents, derivatives of polynomial, exponential, logarithmic nd trigonometric functions including product, quotient and chain rules, and the mean value theorem. Applications of derivatives including graphing functions and rates of change. Antiderivatives, Newton's method, definite and indefinite integrals, methods for substitution in integrals and the Fundamental Rule of Calculus. Applications of integrals include areas, distances, and volumes. Note: No credit may be earned for more than one of MATH 200X, 262X or 272X. Also available via Independent Learning. (Prerequisites: MATH 107X and 108 or placement for MATH 200X.) (4 + 1) Offered Fall and Spring


MATH 201X  4 Credits
Calculus (m)
Techniques and applications of integration. Integration of trigonometric functions, volumes including those using slicing, arc-length, integration by parts, trigonometric substitutions, partial fractions, hyperbolic functions and improper integrals. Numeric integration including Simpson's rule, first order differential equations with applications to population dynamics and rates of decay, sequences, series, tests for convergence including comparison and alternating series tests, conditional convergence, power series, Taylor series, polar coordinates including tangent lines and areas, and conic sections. Also available via Independent Learning. (Prerequisites: MATH 200X or placement in MATH 201X.) (4 + 0) Offered Fall and Spring


MATH 202X  4 Credits
Calculus (m)
Partial derivatives and multiple integration (double and triple). Vectors, parametric curves, motion in three dimensions, limits, continuity, chain rule, tangent planes, directional derivatives, optimization, Lagrange multipliers, integrals in polar coordinates, parametric surfaces, Jacobians, line integrals, Green's Theorem, surface integrals and Stokes' Theorem. Also available via Independent Learning. (Prerequisites: MATH 201X.) (4 + 0) Offered Fall and Spring


MATH 205  3 Credits
Mathematics for Elementary School Teachers I (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, MATH 161X or placement. Restricted to B.A.S. and B.A. Elementary Education degree students; others by permission of instructor.) (3 + 1) Offered Fall


MATH 206  3 Credits
Mathematics for Elementary School Teachers II (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.) (3 + 1) Offered Spring


MATH 215  2 Credits
Introduction to Mathematical Proofs (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 permission of instructor.) (2 + 0) Offered Spring


MATH 262X  4 Credits
Calculus for Business and Economics (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.) (4 + 0) Offered Fall, Spring


MATH 272X  3 Credits
Calculus for Life Sciences (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.) (3 + 0) Offered Fall


MATH 302  3 Credits
Differential Equations
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.) (3 + 0) Offered Fall, Spring


MATH 305  3 Credits
Geometry
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: 2005-06.) (3 + 0) Offered Alternate Spring


MATH 306  3 Credits
Introduction to the History and Philosophy of Mathematics
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: 2006-07.) (3 + 0) Offered Alternate Spring


MATH 307  3 Credits
Discrete Mathematics
Logic, counting, sets and functions, recurrence relations graphs and trees. Additional topics chosen from probability theory. (Prerequisite: MATH 201X or permission of instructor.) (3 + 0) Offered Fall, Spring


MATH 308W  3 Credits
Abstract Algebra
Theory of groups, rings and fields. (Prerequisites: ENGL 111X; ENGL 211X or 213X; MATH 215 or permission of instructor. Recommended: MATH 307 and/or MATH 314.) (3 + 0) Offered Spring


MATH 310  3 Credits
Numerical Analysis
Direct and iterative solutions of systems of equations, interpolation, numerical differentiation and integration, numerical solutions of ordinary differential equations and error analysis. Materials fee: $42. (Prerequisite: MATH 302 or MATH 314 or permission of instructor. A knowledge of programming is desirable.) (3 + 0) Offered Fall


MATH 314  3 Credits
Linear Algebra
Linear equations, finite dimensional vector spaces, matrices, determinants, linear transformations and characteristic values. Inner product spaces. (Prerequisite: MATH 201X.) (3 + 0) Offered Fall, Spring


MATH 371  3 Credits
Probability
Probability spaces, conditional probability, random variables, continuous and discrete distributions, expectation, moments, moment generating functions and characteristic functions. (Prerequisite: MATH 202X. Next offered: 2006-07.) (3 + 0) Offered Alternate Fall


MATH 401W  3 Credits
MATH 402  3 Credits
Advanced Calculus
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; ENGL 211X or ENGL 213X; or permission of instructor; MATH 215 and 202X for MATH 401; MATH 401 for MATH 402.) (3 + 0) 401W Offered Fall, 402 Offered Spring


MATH 404  3 Credits
Topology
Introduction to topology, set theory, open sets, compactness, connectedness, product spaces, metric spaces and continua. (Prerequisites: MATH 202X and 215. Recommended: MATH 314 and/or 308.) (3 + 0) Offered As Demand Warrants


MATH 408  3 Credits
Mathematical Statistics
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: 2006-07.) (3 + 0) Offered Alternate Spring


MATH 412  3 Credits
Differential Geometry
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: 2006-07.) (3 + 0) Offered Alternate Spring


MATH 421  4 Credits
Applied Analysis
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.) (4 + 0) Offered Fall


MATH 422  3 Credits
Introduction to Complex Analysis
Complex functions, including series, integrals, residues, conformal mapping and applications. May be taken independently of MATH 421. (Prerequisite: MATH 302.) (3 + 0) Offered Spring


MATH 460  3 Credits
Mathematical Modeling
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: $42. (Prerequisites: MATH 201X. Recommended: One or more of MATH 302, 314, STAT 300, 401; and some programming experience.) (3 + 0) Offered Alternate Fall


MATH 490O  1 Credit
Senior Seminar
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.) (1 + 0) Offered Spring


MATH 600  1 Credit
Teaching Seminar
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.) (1 + 0) Offered Fall, Spring


MATH 608  3 Credits
Partial Differential Equations
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.) (3 + 0) Offered As Demand Warrants


MATH 611  3 Credits
MATH 612  3 Credits
Mathematical Physics
(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.) (3 + 0) 611 Offered Fall, 612 Offered Spring


MATH 615  3 Credits
Applied Numerical Analysis
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: 2006-07.) (3 + 0) Offered Alternate Spring


MATH 621  3 Credits
Advanced Applied Analysis
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: 2006-07.) (3 + 0) Offered Alternate Fall


MATH 630  3 Credits
Advanced Linear Algebra
Vector spaces over arbitrary fields primary, rational and Jordan canonical forms, invariant subspace decompositions and multilinear algebra. (Prerequisites: MATH 308 and MATH 314.) (3 + 0) Offered As Demand Warrants


MATH 631  4 Credits
Theory of Modern Algebra I
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: 2006-07.) (4 + 0) Offered Alternate Fall


MATH 632  3 Credits
Theory of Modern Algebra II
Advanced topics taken from group theory, category theory, ring theory, homological algebra and field theory. (Prerequisite: MATH 631.) Next offered: 2005-06. (3 + 0) Offered Alternate Fall


MATH 641  4 Credits
Real Analysis
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.) (4 + 0) Offered Alternate Fall


MATH 642  3 Credits
Real Analysis II
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: 2006-07.) (3 + 0) Offered Alternate Fall


MATH 645  4 Credits
Complex Analysis
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.) (4 + 0) Offered Alternate Spring


MATH 651  4 Credits
Topology
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: 2006-07.) (4 + 0) Offered Alternate Spring


MATH 655  3 Credits
Algebraic Topology
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.) (3 + 0) Offered Alternate Fall


MATH 660  3 Credits
Advanced Mathematical Modeling
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. Materials fee: $42. (Prerequisite: Permission of instructor. Next offered: 2006-07.) (3 + 0) Offered Alternate Spring


MATH 661  3 Credits
Optimization
(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: 2006-07.) (3 + 0) Offered Alternate Fall


MATH 663  3 Credits
Applied Combinatorics and Graph Theory
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.) (3 + 0) Offered Alternate Spring


Catalog Index | Class Schedule | Admissions

Send comments or questions to the UAF Admissions Office.
Last modified April 8, 2011 by Marketing and Communications Web Developer.