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