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 $20 per semester fee will be assessed for one or more MATH and STAT courses to support the math tutorial lab and specialized software. 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 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, ABUS 155 or appropriate placement scores. Prerequisite
courses and/or placement exams must be taken within one calendar year prior to
commencement of the course.) (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. (Prerequisite: Grade
of C or better in DEVM 050, ABUS 155 or appropriate placement scores.
Prerequisite courses and/or placement exams must be taken within one calendar
year prior to commencement of the course.) (3 + 0) Offered Fall,
Spring

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 050, ABUS 155 or appropriate placement scores. Prerequisite courses and/or
placement exams must be taken within one calendar year prior to commencement of
the course.) (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.
(Prerequisite: Grade of C or better in DEVM 050, ABUS 155 or appropriate
placement scores. Prerequisite courses and/or placement exams must be taken
within one calendar year prior to commencement of the course. 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 society. Topics include
voting systems, probability and statistics and applications of graph theory in
management sciences. 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 the first week
prepares students for the rigor expected. 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 161X, 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 161X, 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 and 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 and 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
may be included. (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 and MATH 215 or permission of instructor. Next
offered: 2007-08.) (3 + 0) Offered Alternate Spring

MATH 306 3
Credits

Introduction to the History and Philosophy of Mathematics

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: 2008-09.) (3 + 0) Offered
Alternate Spring

MATH 307 3
Credits

Discrete Mathematics

(Cross-listed with CS 307)

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 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: 2008-09.) (3 + 0) Offered Alternate Fall

MATH 401W 3
Credits

MATH 402 3
Credits

Advanced Calculus

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) MATH 401W Offered Fall, MATH 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 405.) (3 + 0) Offered As
Demand Warrants

MATH 405W 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 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 200X. Next offered: 2008-09.)
(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:
2008-09.) (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

An introduction to mathematical modeling using differential
or difference equations. Emphasis is on formulating models and interpreting
qualitative behavior such models predict. Examples will be taken from a variety
of fields, depending on the interest of the instructor. 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.)
Next offered: 2007-08. (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 405 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

Mathematical Physics I

(Cross-listed with PHYS 611)

Mathematical tools and theory for classical and modern
physics. Core topics: linear algebra including eigenvalues, eigenvectors and
inner products, infinite dimensional spaces. Infinite series. Hilbert spaces
and generalized functions. Complex analysis, including Laurent series and
contour methods. Applications to problems arising in physics. Selected
additional topics, which may include operator and spectral theory, groups, tensor
fields and hypercomplex numbers. (Prerequisites: MATH 302, MATH 314, MATH
421/422 or permission of instructor.) (3 + 0) Offered Fall

MATH 612 3
Credits

Mathematical Physics II

(Cross-listed with PHYS 612)

Continuation of Mathematical Physics I; mathematical tools
and theory for classical and modern physics. Core topics: classical solutions
to the principal linear partial differential equations of electromagnetism,
classical and quantum mechanics. Boundary value problems and Sturm-Liouville theory. Green's
functions and eigenfunction expansions. Integral transforms. Orthogonal polynomials
and special functions. Applications to problems arising in physics. Selected
additional topics, which may include integral equations and Hilbert-Schmidt
theory, perturbation methods, probability theory. (Prerequisites: PHYS/MATH 611
or equivalent or permission of instructor.) (3 + 0) 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: 2008-09.)
(3 + 0) Offered Alternate Spring

MATH 617 3
Credits

Functional Analysis

Study of Banach and Hilbert spaces and continuous linear maps
between them. Linear functionals and the Hahn-Banach theorem. Compact
operators, self adjoint operators, and their spectral properties. Weak topology
and its applications. (Prerequisites: MATH 314, 401 or equivalent.
Recommendations: MATH 422, 641 or equivalent. Next offered: 2008-09.)
(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 314 and MATH 405.) (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 405 and graduate standing or permission of
instructor. Next offered: 2008-09.) (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: 2007-08.) (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 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: 2008-09.) (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 401-402, MATH 404 and MATH
405 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: 2008-09.) (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: 2008-09.) (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