Mathematics and Statistics
Department Overview
The number of new fields in which professional mathematicians find employment grows continually. This department prepares students for a variety of careers, including in industry, government and education, at both the undergraduate and graduate levels. In addition to the major programs, the department provides a number of service courses in support of other programs within the university. Current and detailed information on mathematics degrees and course offerings is available from the department. The department maintains a math lab that is available for assistance to all students studying mathematics at the baccalaureate level.
B.A., B.S., Mathematics
Two concentrations are available:

Mathematics

Statistics
Minimum Requirements for Mathematics Bachelor's Degrees: 120 credits
Learn more about the bachelor’s degree in mathematics, including an overview of the program, career opportunities and more.
Accelerated B.S./M.S., Mathematics
The combined Bachelor of Science in Mathematics and Master of Science in Mathematics program allows dedicated mathematics students to complete two degrees in a compressed time frame (typically, five years instead of six), while still maintaining the rigor and content of both degrees.
Minimum Requirements for Accelerated Mathematics B.S./M.S. Degrees: 138 credits
Learn more about the bachelor’s degree in mathematics, including an overview of the program, career opportunities and more.
Learn more about the master’s degree in mathematics, including an overview of the program, career opportunities and more.
Accelerated B.S., Mathematics/M.S., Statistics and Data Science
The combined Bachelor of Science in Mathematics with a concentration in Statistics and Master of Science in Statistics and Data Science program allows dedicated statistics students to complete two degrees in a compressed time frame (typically, five years instead of six), while still maintaining the rigor and content of both degrees. Students will receive a B.S. in Mathematics with a concentration in Statistics, and an M.S. in Statistics and Data Science.
Minimum Requirements for Accelerated Math B.S./Statistics and Data Science M.S. Degrees: 138 credits
Learn more about the bachelor’s degree in mathematics, including an overview of the program, career opportunities and more.
Learn more about the master’s degree in statistics and data science, including an overview of the program, career opportunities and more.
M.S., Ph.D., Mathematics
The number of new fields in which professional mathematicians find employment grows continually. This department prepares students for careers in industry, government and education.
The Master of Science in Mathematics prepares students for Ph.D. work, in addition to providing a terminal degree for those planning to enter industry or education. The aim of the Ph.D. program is to provide the student with the expertise to accomplish significant research in applied or pure mathematics, as well as to provide a broad and deep professional education.
In addition to the major programs, the department provides a number of service courses in support of other programs within the university. Current and detailed information on mathematics degrees and course offerings is available from the department.
Minimum Requirements for Mathematics Degrees: M.S.: 30 credits; Ph.D.: 18 thesis credits
Learn more about the master’s degree in mathematics, including an overview of the program, career opportunities and more.
M.S., Statistics and Data Science
Statistics is a collection of methods and theories used to make decisions or estimate unknown quantities from incomplete information. Statistical techniques are useful, for example, in estimating plant, animal and mineral abundances; forecasting social, political and economic trends; planning field plot experiments in agriculture; performing clinical trials in medical research; and maintaining quality control in industry. Employment opportunities are excellent for statisticians in many of these areas.
The Master of Science in Statistics and Data Science builds upon UAF’s strength in the sciences and our setting in Alaska by introducing a strong quantitative alternative or supplement to existing programs. The curriculum is built around four statistics core courses and flexibility in the selection of elective courses. The core courses are designed to blend mathematical statistics coursework typical of most M.S. programs in statistics with real applications. We believe this blending provides a substantial improvement in the graduate’s skills.
Graduates of this program could be labeled quantitative biologists, biometricians, quantitative geologists, geostatisticians, or mathematical statisticians depending upon their specific course work. In addition, this program prepares individuals for Ph.D.level work in statistics or their area of application.
Minimum Requirements for Statistics and Data Science M.S.: 30 credits
Learn more about the master’s degree in statistics and data science, including an overview of the program, career opportunities and more.
Graduate Certificate, Applied and Computational Mathematics
The graduate certificate in applied and computational mathematics is equivalent to most of a year of coursework done by graduate students in this area. The certificate encourages a more indepth study of mathematics beyond the undergraduate level. The focus is on mathematics that is useful in the sciences and engineering, especially on techniques that can be applied in computer programs. Furthermore, it provides students with a credential recognizing their additional mathematical expertise.
The certificate is ideal for current graduate students in disciplines other than mathematics who seek greater exposure to mathematical ideas and techniques. It is most suitable for students in the sciences and engineering. It is not suitable for students already enrolled in the M.S. in mathematics or Ph.D. in mathematics programs.
Minimum Requirements for Applied and Computational Mathematics Graduate Certificate: 12 credits
Graduate Certificate, Statistics
Statistics is a collection of methods and theories used to make decisions or estimate unknown quantities from incomplete information. Statistical techniques are useful, for example, in estimating plant, animal and mineral abundances; forecasting social, political and economic trends; planning field plot experiments in agriculture; performing clinical trials in medical research; and maintaining quality control in industry. Employment opportunities are excellent for statisticians in many of these areas.
As a postbaccalaureate program, the certificate in statistics is equivalent to a full year of graduate statistics courses and is ideal for current graduate students in disciplines other than statistics (especially the sciences). The graduate certificate in statistics encourages a more indepth study of statistics and provides students a credential recognizing their quantitative expertise.
Graduates of this program could be labeled quantitative biologists, biometricians, quantitative geologists, geostatisticians, or mathematical statisticians depending upon their specific course work. In addition, this program prepares individuals for Ph.D.level work in statistics or their area of application.
Minimum Requirements for Statistics Graduate Certificate: 12 credits.
Programs
Degrees
 B.A., Mathematics
 B.S., Mathematics
 Accelerated B.S./M.S., Mathematics
 Accelerated B.S., Mathematics/M.S., Statistics and Data Science
 M.S., Mathematics
 M.S., Statistics and Data Science
 Ph.D., Mathematics
Graduate Certificates
Minors
Courses
Mathematics (MATH F113+)
MATH F113X Numbers and Society (m)
3 Credits
Offered Fall, Spring and Summer
Numbers and patterns are present in every aspect of daily life. We use mathematical concepts and tools to understand what numbers and patterns can tell us. Topics may include the mathematics of voting; dividing things fairly; determining efficient routes and schedules; modeling population growth; understanding financial mathematics; and introductory cryptography.
Prerequisites: An appropriate score on the math placement test, or a grade of B or better in MATH F055, MATH F062 or MATH F068.
Attributes: UAF GER Mathematics Req
Lecture + Lab + Other: 3 + 0 + 0
MATH F122X Essential Precalculus with Applications (m)
3 Credits
Offered Fall and Spring
A study of various classes of functions, exploring their numeric, algebraic and graphical aspects. Function classes include linear, quadratic, rational, exponential and logarithmic. This course is appropriate for students in programs relating to business and economics or life sciences or students intending to take MATH F230X.
Prerequisites: Appropriate placement score, MATH F105, MATH F105N or MATH F105J.
Special Notes: Credit may be earned for MATH F151X or MATH F122X, but not for both.
Attributes: UAF GER Mathematics Req
Lecture + Lab + Other: 3 + 0 + 0
MATH F151X College Algebra for Calculus (m)
4 Credits
Offered Fall and Spring
Study of algebraic, logarithmic and exponential functions; systems of equations; applications.
Prerequisites: Appropriate score on the math placement test, B or better in MATH F105, B or better in MATH F105J or C or better in MATH F105N.
Special Notes: Credit may be earned for MATH F151X or MATH F122X, but not for both; Only eight credits total may be earned from MATH F151X, MATH F152X and MATH F156X.
Attributes: UAF GER Mathematics Req
Lecture + Lab + Other: 4.5 + 0 + 0
MATH F152X Trigonometry (m)
3 Credits
Offered Fall and Spring
A study of trigonometric functions including graphing, identities, inverse trigonometric functions, solving equations and polar coordinates; applications.
Prerequisites: MATH F151X (may be taken concurrently) or placement.
Special Notes: Only eight credits total may be earned from MATH F151X, MATH F152X and MATH F156X.
Attributes: UAF GER Mathematics Req
Lecture + Lab + Other: 3 + 0 + 0
MATH F156X Precalculus (m)
4 Credits
Offered Fall and Spring
Various classes of functions and their graphs are explored numerically, algebraically and graphically. Function classes include polynomial, rational, exponential, logarithmic and trigonometric. Skills and concepts needed for calculus are emphasized. This class is intended for students intending to take MATH F251X.
Prerequisites: Placement into MATH F156X.
Special Notes: Only eight credits total may be earned from MATH F151X, MATH F152X and MATH F156X.
Attributes: UAF GER Mathematics Req
Lecture + Lab + Other: 4 + 1 + 0
MATH F186 Applied Engineering Mathematics
4 Credits
Offered Fall
Fundamental mathematics topics appearing in first and secondyear engineering classes. All content is taught within the context of an engineering application. Specific topics include applications of algebra, trigonometry, vectors, sinusoids, linear systems, complex numbers, derivatives and integrals.
Prerequisites: Appropriate score on the math placement test and high school trigonometry; or MATH F151X and MATH F152X; or MATH F156X.
Crosslisted with ES F186.
Lecture + Lab + Other: 4 + 1 + 0
MATH F211 Mathematics for Elementary School Teachers (m)
3 Credits
Offered Fall
Elementary set theory, numeration systems, and algorithms of arithmetic, divisors, multiples, integers and introduction to rational numbers. Emphasis on classroom methods. Restricted to Elementary Education majors; others by permission of instructor.
Prerequisites: MATH F122X; or MATH F151X; or MATH F156X; or placement.
Lecture + Lab + Other: 3 + 1 + 0
MATH F212 Mathematics for Elementary School Teachers II (m)
3 Credits
Offered Spring
A continuation of MATH F211. Real number systems and subsystems, logic, informal geometry, metric system, probability and statistics. Emphasis on classroom methods.
Prerequisites: MATH F211.
Lecture + Lab + Other: 3 + 1 + 0
MATH F230X Essential Calculus with Applications in the Life Sciences
3 Credits
Offered Fall and Spring
An introduction to the key ideas of differential and integral calculus, emphasizing applications in the life sciences. This course emphasizes a solid conceptual understanding, along with calculation techniques for basic applications. MATH F230X cannot serve as a prerequisite for MATH F252X.
Prerequisites: MATH F122X or MATH F151X or MATH F156X or appropriate score on the math placement test.
Special Notes: Credit cannot be earned for both MATH F230X and MATH F251X.
Attributes: UAF GER Mathematics Req
Lecture + Lab + Other: 3 + 0 + 0
MATH F251L Calculus I Recitation
0 Credit
Offered Fall and Spring
Recitation section for Calculus I. Activities may include worksheets, quizzes and problem sessions associated with corresponding lecture material from MATH F251X, with an emphasis on prerequisite support.
Corequisites: MATH F251X.
Attributes: UAF GER Mathematics Req
Lecture + Lab + Other: 0 + 2 + 0
MATH F251X Calculus I (m)
4 Credits
Offered Fall and Spring
A first course in singlevariable calculus. Topics include limits; continuity and differentiation of functions; applications of the derivative to graphing, optimization, and rates of change; definite and indefinite integration; and the Fundamental Theorem of Calculus.
Prerequisites: Appropriate score on the math placement test; or MATH F151X and MATH F152X; or MATH F156X; or ES/MATH F186.
Corequisites: MATH F251L.
Special Notes: Credit may not be earned for both MATH F251X and MATH F230X.
Attributes: UAF GER Mathematics Req
Lecture + Lab + Other: 4 + 0 + 0
MATH F252L MATH F252X Recitation
0 Credit
Offered Fall and Spring
Corequisites: MATH F252X.
Attributes: UAF GER Mathematics Req
Lecture + Lab + Other: 0 + 0 + 0
MATH F252X Calculus II (m)
4 Credits
Offered Fall and Spring
Further topics in singlevariable calculus, including techniques of integration; applications of integration; convergence of sequences and series; parameterized curves; and polar coordinates.
Prerequisites: MATH F251X.
Corequisites: MATH F252L.
Attributes: UAF GER Mathematics Req
Lecture + Lab + Other: 4 + 1 + 0
MATH F253X Calculus III (m)
4 Credits
Offered Fall and Spring
Multivariable calculus. Topics include vectors in 2 and 3dimensions; differential calculus of functions of several variables; multiple integration; vector calculus, including Green's and Stokes' Theorem; and applications.
Prerequisites: MATH F252X.
Attributes: UAF GER Mathematics Req
Lecture + Lab + Other: 4 + 0 + 0
MATH F265 Introduction to Mathematical Proofs (m)
3 Credits
Offered Spring
Emphasis on proof techniques with topics including logic, sets, cardinality, relations, functions, equivalence, induction, number theory, congruence classes and elementary counting. In addition, a rigorous treatment of topics from calculus or a selection of additional topics from discrete mathematics may be included.
Prerequisites: MATH F252X (may be taken concurrently).
Lecture + Lab + Other: 3 + 0 + 0
MATH F302 Differential Equations
3 Credits
Offered Fall and Spring
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.
Prerequisites: MATH F253X.
Lecture + Lab + Other: 3 + 0 + 0
MATH F305 Geometry
3 Credits
Offered Spring Evennumbered Years
Topics selected from such fields as Euclidean and nonEuclidean plane geometry, affine geometry, projective geometry, and topology.
Prerequisites: MATH F265; MATH F314.
Recommended: MATH F253X.
Lecture + Lab + Other: 3 + 0 + 0
MATH F307 Discrete Mathematics
3 Credits
Offered Spring
Logic, counting, sets and functions, recurrence relations, graphs and trees. Additional topics chosen from probability theory.
Prerequisites: MATH F252X.
Lecture + Lab + Other: 3 + 0 + 0
MATH F314 Linear Algebra
3 Credits
Offered Fall and Spring
Linear equations, finite dimensional vector spaces, matrices, determinants, linear transformations and characteristic values. Inner product spaces.
Prerequisites: MATH F252X.
Lecture + Lab + Other: 3 + 0 + 0
MATH F316 Introduction to the History of Mathematics
3 Credits
Offered Spring Oddnumbered Years
Important periods in the history of mathematics, including mathematics of Ancient Babylon, Mesopotamia, Greece, China and India, medieval Europe, the Middle East and the Renaissance; the development of geometry, algebra and calculus. Other areas in the development of mathematics will be studied as time permits.
Prerequisites: MATH F253X; MATH F265 (may be taken concurrently).
Lecture + Lab + Other: 3 + 0 + 0
MATH F320 Topics in Combinatorics
3 Credits
Offered Fall Oddnumbered Years
Introduction to some fundamental ideas of combinatorics. Topics selected from such fields as enumerative combinatorics, generating functions, set systems, recurrence relations, directed graphs, matchings, Hamiltonian and Eulerian graphs, trees and graph colorings.
Prerequisites: MATH F265.
Lecture + Lab + Other: 3 + 0 + 0
MATH F321 Number Theory
3 Credits
Offered Fall Evennumbered Years
Number theory investigates the properties of the integers, one of the most basic of mathematical sets. Seemingly naive numbertheoretic questions stimulated much of the development of modern mathematics! Topics may include classical areas such as primality, congruences, quadratic reciprocity and Diophantine equations, and more recent applications, such as cryptography.
Prerequisites: MATH F265.
Lecture + Lab + Other: 3 + 0 + 0
MATH F371 Probability
3 Credits
Offered Fall Oddnumbered Years
Probability spaces, conditional probability, random variables, continuous and discrete distributions, expectation, moments, moment generating functions and characteristic functions.
Prerequisites: MATH F253X.
Lecture + Lab + Other: 3 + 0 + 0
MATH F401 Introduction to Real Analysis
3 Credits
Offered Fall
Completeness of the real numbers and its consequence, convergence of sequences and series, limits and continuity, differentiation, the Riemann integral.
Prerequisites: WRTG F111X; WRTG F211X, WRTG F212X, WRTG F213X or WRTG F214X; MATH F253X; MATH F265.
Lecture + Lab + Other: 3 + 0 + 0
MATH F404 Introduction to Topology
3 Credits
Offered Fall Evennumbered Years
Introduction to topological spaces, set theory, open sets, compactness, connectedness, product spaces, metric spaces and continua.
Prerequisites: MATH F253X; MATH F265.
Recommended: MATH F314 and/or MATH F405.
Lecture + Lab + Other: 3 + 0 + 0
MATH F405 Abstract Algebra
3 Credits
Offered Spring
Theory of groups, rings and fields.
Prerequisites: WRTG F111X; WRTG F211X, WRTG F212X, WRTG F213X or WRTG F214X; MATH F265.
Recommended: MATH F307 and/or MATH F314.
Lecture + Lab + Other: 3 + 0 + 0
MATH F408 Mathematical Statistics
3 Credits
Offered Spring Evennumbered Years
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 F371; STAT F200X or STAT F300.
Lecture + Lab + Other: 3 + 0 + 0
MATH F410 Introduction to Complex Analysis
3 Credits
Offered Fall Oddnumbered Years
Complex functions including series, integrals, residues, conformal mapping and applications.
Prerequisites: MATH F253X.
Lecture + Lab + Other: 3 + 0 + 0
MATH F412 Differential Geometry
3 Credits
Offered Spring Oddnumbered Years
Introduction to the differential geometry of curves, surfaces, and Riemannian manifolds. Basic concepts covered include the FrenetSerret apparatus, surfaces, first and second fundamental forms, geodesics, Gauss curvature and the GaussBonnet Theorem. Time permitting, topics such as minimal surfaces, theory of hypersurfaces and/or tensor analysis may be included.
Prerequisites: MATH F314; MATH F401.
Lecture + Lab + Other: 3 + 0 + 0
MATH F426 Numerical Analysis
3 Credits
Offered Fall
Direct and iterative solutions of systems of equations, interpolation, numerical differentiation and integration, numerical solutions of ordinary differential equations, and error analysis.
Prerequisites: MATH F302 or MATH F314.
Recommended: Knowledge of programming.
Lecture + Lab + Other: 3 + 0 + 0
MATH F430 Topics in Mathematics
3 Credits
Offered Fall Evennumbered Years
An elective course in mathematics for majors. Topics will vary from year to year and may be drawn from mathematical biology, numerical linear algebra, graph theory, logic, or other areas of mathematics. May be repeated with permission of instructor for a total of nine credits.
Prerequisites: MATH F265.
Lecture + Lab + Other: 3 + 0 + 0
MATH F432 Introduction to Partial Differential Equations
3 Credits
Offered Spring Oddnumbered Years
Analysis and solution of partial differential equations. Initial and boundary value problems for parabolic, hyperbolic and elliptic types. Solution methods include separation of variables and Fourier transform.
Prerequisites: MATH F302.
Lecture + Lab + Other: 3 + 0 + 0
MATH F460 Mathematical Modeling
3 Credits
Offered Spring Evennumbered Years
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.
Prerequisites: COM F131X or COM F141X; MATH F252X; WRTG F111X; WRTG F211X, WRTG F212X, WRTG F213X or WRTG F214X.
Recommended: one or more of MATH F302, MATH F314, MATH F401, MATH F426, STAT F300 or some programming experience.
Lecture + Lab + Other: 3 + 0 + 0
MATH F490 Senior Seminar
3 Credits
Offered Spring
Advanced topics selected from areas outside the usual undergraduate offerings. A substantial level of mathematical maturity is assumed.
Prerequisites: COM F131X or COM F141X; at least one of MATH F401 or MATH F405; senior standing.
Lecture + Lab + Other: 3 + 0 + 0
MATH F600 Teaching Seminar
1 Credit
Offered Fall
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.
Prerequisites: Graduate standing.
Lecture + Lab + Other: 1 + 0 + 0
MATH F614 Numerical Linear Algebra
3 Credits
Offered Fall Oddnumbered Years
Algorithms and theory for stable and accurate computation using matrices and vectors on computers. Matrix factorizations, direct and iterative methods for solving linear systems, least squares, eigenvalue and singular value decompositions. Practical implementation and application of algorithms.
Prerequisites: MATH F314.
Recommended: MATH F401 or MATH F432.
Lecture + Lab + Other: 3 + 0 + 0
MATH F615 Numerical Analysis of Differential Equations
3 Credits
Offered Spring Oddnumbered Years
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 F201; MATH F314; MATH F410; MATH F426; MATH F432.
Lecture + Lab + Other: 3 + 0 + 0
MATH F617 Functional Analysis
3 Credits
Offered Spring Evennumbered Years
Study of Banach and Hilbert spaces, and continuous linear maps between them. Linear functionals and the HahnBanach theorem. Applications of the Baire Category theorem. Compact operators, self adjoint operators, and their spectral properties. Weak topology and its applications.
Prerequisites: MATH F314; MATH F401.
Recommended: MATH F410; MATH F641.
Lecture + Lab + Other: 3 + 0 + 0
MATH F631 Algebra I
4 Credits
Offered Fall Evennumbered Years
Rigorous development of groups, rings and fields.
Prerequisites: MATH F405.
Lecture + Lab + Other: 4 + 0 + 0
MATH F632 Algebra II
3 Credits
Offered Spring Oddnumbered Years
Advanced topics which may be chosen from group theory, Galois theory, commutative or noncommutative algebra, algebraic geometry, homological algebra or other areas.
Prerequisites: MATH F631.
Lecture + Lab + Other: 3 + 0 + 0
MATH F641 Real Analysis
4 Credits
Offered Fall Oddnumbered Years
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 F401.
Lecture + Lab + Other: 4 + 0 + 0
MATH F645 Complex Analysis
4 Credits
Offered Spring Evennumbered Years
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.
Prerequisites: MATH F641.
Lecture + Lab + Other: 4 + 0 + 0
MATH F651 Topology
4 Credits
Offered Spring Oddnumbered Years
Treatment of the fundamental topics of pointset 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 F401 or MATH F404.
Lecture + Lab + Other: 4 + 0 + 0
MATH F658 Topics in Geometry
3 Credits
Offered Fall Evennumbered Years
Elective topics in geometry. Recent offerings include configurations of points and lines; topology and differential geometry of surfaces; polyhedra and polytopes.
Prerequisites: Linear algebra; geometry; undergraduate real analysis; undergraduate abstract algebra.
Lecture + Lab + Other: 3 + 0 + 0
MATH F660 Advanced Mathematical Modeling
3 Credits
Offered Spring Evennumbered Years
The mathematical formulation and analysis of problems arising in the physical, biological, or social sciences. The focus area of the course may vary, but emphasis will be given to modeling assumptions, derivation of model equations, methods of analysis, and interpretation of results for the particular applications. Examples include heat conduction problems, random walk processes, molecular evolution, perturbation theory. Students will develop a modeling project as part of the course requirements.
Prerequisites: Permission of instructor.
Lecture + Lab + Other: 3 + 0 + 0
MATH F661 Optimization
3 Credits
Offered Fall Evennumbered Years
Linear and nonlinear programming, simplex method, duality and dual simplex method, postoptimal analysis, constrained and unconstrained nonlinear programming, KuhnTucker conditions. Applications to management, physical and life sciences. Computational work with the computer.
Prerequisites: Knowledge of calculus, linear algebra and computer programming.
Lecture + Lab + Other: 3 + 0 + 0
MATH F663 Graph Theory
3 Credits
Offered Fall Oddnumbered Years
A survey of modern techniques in graph theory; topics may include graphs and digraphs, trees, spanning trees, matchings, graph connectivity, graph coloring, planarity, cycles, and extremal problems.
Prerequisites: MATH F314; MATH F320.
Lecture + Lab + Other: 3 + 0 + 0
MATH F665 Topics in Graduate Mathematics
3 Credits
Offered As Demand Warrants
Elective courses in graduate mathematics offered by faculty on a rotating basis. Topics may include, but are not limited to, graph theory, glaciology modeling, general relativity, mathematical biology, Galois theory and numerical linear algebra. May be repeated for credit with permission of instructor.
Lecture + Lab + Other: 3 + 0 + 0
MATH F692 Seminar
16 Credits
Lecture + Lab + Other: 0 + 0 + 0
MATH F698 Nonthesis Research/Project
16 Credits
Lecture + Lab + Other: 0 + 0 + 0
MATH F699 Thesis
19 Credits
Lecture + Lab + Other: 0 + 0 + 0
Statistics (STAT)
STAT F200X Elementary Statistics (m)
3 Credits
Offered Fall and Spring
Introduction to concepts and applications of elementary statistical methods. Topics include sampling and data analysis, descriptive statistics, elementary probability, probability and sampling distributions, confidence intervals, hypothesis testing, correlation, and simple linear regression.
Prerequisites: Appropriate placement score; or a grade of B or better in MATH F105 or MATH F105N or in all three of MATH F105G and MATH F105H and MATH F105J; or grade of C or better in a math course numbered F122 or above.
Attributes: UAF GER Mathematics Req
Lecture + Lab + Other: 3 + 0 + 0
STAT F300 Statistics
3 Credits
Offered Fall and Spring
A calculusbased course emphasizing applications. Topics include probability, joint and conditional probability, expectation and variance, parameter estimation (method of moments and maximum likelihood), one and two sample hypothesis tests, simple linear regression and oneway analysis of variance.
Prerequisites: MATH F230X or MATH F251X or placement.
Lecture + Lab + Other: 3 + 0 + 0
STAT F401 Regression and Analysis of Variance
4 Credits
Offered Fall and Spring
Multiple regression including multiple and partial correlation, extra sum of squares principle, indicator variables, polynomial models, model selection, and assessment of underlying assumptions. Analysis of variance and covariance for multifactor studies in completely random and randomized complete block designs, multiple comparisons and orthogonal contrasts. Matrix concepts are taught as needed.
Prerequisites: STAT F200X or STAT F300.
Corequisites: STAT F401L.
Lecture + Lab + Other: 3 + 3 + 0
STAT F401L STAT F401 Laboratory
0 Credit
Offered Fall and Spring
Computer laboratory section for STAT F401 Regression and Analysis of Variance. Activities may include case studies involving the application of lecture topics and methods in R software.
Corequisites: STAT F401.
Lecture + Lab + Other: 0 + 3 + 0
STAT F402 Scientific Sampling
3 Credits
Offered Fall
Sampling methods, including simple random, stratified and systematic and one and twostage cluster sampling; estimation procedures, including ratio and regression methods; special area and point sampling procedures; optimum allocation. Adaptive and probability sampling; bootstrapping and basic markandrecapture.
Prerequisites: STAT F200X or STAT F300.
Lecture + Lab + Other: 3 + 0 + 0
STAT F454 Statistical Consulting Seminar
1 Credit
Offered Spring
Introduction to statistical consulting and data analysis. Emphasis on interaction with researchers and identification of scientific and statistical issues relevant to the research problem. Includes regular class meetings as well as supervised meetings with researchers. Designed to combine mathematical statistics with applications from a variety of fields.
Prerequisites: MATH F408; STAT F200X or STAT F300; STAT F401.
Stacked with STAT F654.
Special Notes: Students from any field of study with strong quantitative skills are encouraged to enroll.
Lecture + Lab + Other: 1 + 0 + 0
STAT F461 Applied Multivariate Statistics
3 Credits
Offered Spring Evennumbered Years
Estimation and hypothesis testing, multivariate normality and its assessment, multivariate one and two sample tests, confidence regions, multivariate analysis of variance, discrimination and classification, principal components, factor analysis, clustering techniques and graphical presentation. Statistical computing packages utilized in assignments.
Prerequisites: STAT F401.
Lecture + Lab + Other: 3 + 0 + 0
STAT F602 Experimental Design
3 Credits
Offered Fall Evennumbered Years
Constructing and analyzing designs for experimental investigations; completely randomized, randomized block and Latinsquare designs, splitplot design, incomplete block design, confounded factorial designs, nested designs, treatment of missing data, comparison of designs.
Prerequisites: STAT F401.
Lecture + Lab + Other: 3 + 0 + 0
STAT F605 Spatial Statistics
3 Credits
Offered Spring Evennumbered Years
Stochastic processes and variograms. Geostatistics including kriging and spatial design of experiments. Point processes including model selection and Kfunctions. Lattice process models and image analysis. Computerintensive statistical methods.
Prerequisites: STAT F401; MATH F251X; MATH F252X; MATH F253X.
Lecture + Lab + Other: 3 + 0 + 0
STAT F611 Time Series
3 Credits
Offered Spring Oddnumbered Years
An applied course in time series and repeated measure analysis. Autoregression and moving average models. Estimation of parameters and tests. Prediction. Spectral analysis. Analysis of repeated measures data.
Prerequisites: STAT F401.
Lecture + Lab + Other: 3 + 0 + 0
STAT F621 Nonparametric Statistics and Machine Learning
3 Credits
Offered Fall Oddnumbered Years
A survey course in nonparametric statistical techniques. Distributionfree methods for small samples including sign, rank and randomization tests and bootstrapping. Modern techniques including kernel density estimation, survival analysis, spline regression and generalized additive models. Classification methods including regression trees, support vector machines and neural net models.
Prerequisites: STAT F401.
Lecture + Lab + Other: 3 + 0 + 0
STAT F631 Categorical Data Analysis
3 Credits
Offered Fall Oddnumbered Years
Statistical methods designed for count and categorical data. Contingency tables. Logistic and related models. Loglinear models. Repeated categorical responses. Survival data.
Prerequisites: STAT F401.
Lecture + Lab + Other: 3 + 0 + 0
STAT F641 Bayesian Statistics
3 Credits
Offered Fall Evennumbered Years
Bayes' Rule, Bayesian models for univariate data, prior selection (conjugate and nonconjugate, noninformative and objective priors). Single parameter and multiparameter models. Hierarchical, general linear and mixed models. Study of posterior simulation techniques including Markov chain Monte Carlo. Model validation and model selection. Emphasis on applications, using modern statistical software packages.
Prerequisites: MATH F252X; (MATH F371 and MATH F408) or STAT F651.
Lecture + Lab + Other: 3 + 0 + 0
STAT F651 Statistical Theory I
3 Credits
Offered Fall
Probability and distribution of random variables. Conditional probability and stochastic independence. Distributions of functions of random variables. Expected values. Limiting distributions. Distributions derived from the normal distribution. Designed to combine mathematical statistics with applications from a variety of fields.
Prerequisites: MATH F253X; MATH F314; previous statistics course.
Special Notes: Students from any field of study with strong quantitative skills are encouraged to enroll.
Lecture + Lab + Other: 3 + 0 + 0
STAT F652 Statistical Theory II
3 Credits
Offered Spring Oddnumbered Years
Data reduction concepts, including sufficiency, ancillarity, completeness. Point estimation and interval estimation of parameters. Bootstrapping. Hypothesis testing, including the NeymanPearson paradigm and likelihood ratio tests. Asymptotic properties of estimators. Bayesian inference. Designed to combine mathematical statistics with applications from a variety of fields.
Prerequisites: STAT F651.
Special Notes: Students from any field of study with strong quantitative skills are encouraged to enroll.
Lecture + Lab + Other: 3 + 0 + 0
STAT F653 Statistical Theory III: Linear Models
3 Credits
Offered Spring Evennumbered Years
Best linear unbiased estimation in the general linear model, GaussMarkov theory and applications, maximum likelihood estimation for linear models, multivariate normal distributions, linear regression and analysis of variance, weighted regression, robust and nonlinear regression and generalized linear models. Designed to combine mathematical statistics with applications from a variety of fields.
Prerequisites: STAT F651 or MATH F371; MATH F253X; MATH F314.
Special Notes: STAT F401 or equivalent course in applied linear regression modeling is strongly recommended.
Lecture + Lab + Other: 3 + 0 + 0
STAT F654 Statistical Consulting Seminar
1 Credit
Offered Spring
Introduction to statistical consulting and data analysis. Emphasis on interaction with researchers and identification of scientific and statistical issues relevant to the research problem. Includes regular class meetings as well as supervised meetings with researchers. Designed to combine mathematical statistics with applications from a variety of fields.
Prerequisites: MATH F408; STAT F200X or STAT F300; STAT F401.
Stacked with STAT F454.
Special Notes: Students from any field of study with strong quantitative skills are encouraged to enroll.
Lecture + Lab + Other: 1 + 0 + 0
STAT F661 Sampling Theory
3 Credits
Offered Fall
Statistical theory for sampling and sample surveys. Choice of method, power and sample size considerations, treatment of sampling and nonsampling biases. Sampling methods based on detectability. Adaptive sampling. Spatial sampling. Mark and recapture methods. The jackknife, the bootstrap and resampling plans.
Prerequisites: STAT F200X; STAT F401.
Lecture + Lab + Other: 3 + 0 + 0
STAT F671 Statistical Computing
3 Credits
Offered Spring Oddnumbered Years
Topics in statistical programming which may include Advanced R, program design, parallel processing, object oriented programming, functions, environments, debugging, loops and their replacements, C++ in R and code optimization. Optimizers, linear programming, random number generators including MCMC. Web applications. Writing R packages. Reproducible research. Text mining and relational databases.
Prerequisites: STAT F401; MATH F251X or MATH F230X; Knowledge of basic R highly recommended.
Lecture + Lab + Other: 3 + 0 + 0
STAT F692 Seminar
16 Credits
Lecture + Lab + Other: 0 + 0 + 0
STAT F692P Seminar
16 Credits
Lecture + Lab + Other: 0 + 0 + 0
STAT F698 Nonthesis Research/Project
16 Credits
Lecture + Lab + Other: 0 + 0 + 0
Mathematics Faculty
Elizabeth Allman
Professor of Mathematics
Mathematical biology, computational algebra, algebraic statistics
esallman@alaska.edu
9074742479
Chapman 308B
Troth Yeddha' Campus
Sergei Avdonin
Professor of Mathematics
Nonharmonic Fourier series, partial differential equations, control theory, inverse problems
s.avdonin@alaska.edu
9074745023
Chapman 304A
Troth Yeddha' Campus
Leah Berman
Department Chair and Professor of Mathematics
Configurations and discrete geometry
lwberman@alaska.edu
9074747123
Chapman 102
Troth Yeddha' Campus
Latrice Bowman
Term Associate Professor of Mathematics
Online learning, masterybased mathematics, gateway math success
lnbowman@alaska.edu
9074745427
Chapman 210B
Troth Yeddha' Campus
Ed Bueler
Professor of Mathematics
Numerical analysis and partial differential equations
elbueler@alaska.edu
9074747332
Chapman 306C
Troth Yeddha' Campus
Jill Faudree
Professor of Mathematics
Combinatorics and graph theory
jrfaudree@alaska.edu
9074747385
Chapman 306B
Troth Yeddha' Campus
John Gimbel
Professor of Mathematics
Graph theory, combinatorics, order
jggimbel@alaska.edu
9074746102
Chapman 304C
Troth Yeddha' Campus
James Gossell
Term Assistant Professor of Mathematics
Combinatorics and commutative algebra
jegossell@alaska.edu
9074742767
Chapman 301D
Troth Yeddha' Campus
David Maxwell
Professor of Mathematics
Partial differential equations, geometric analysis, mathematical physics
damaxwell@alaska.edu
9074741196
Chapman 308C
Troth Yeddha' Campus
John Rhodes
Professor of Mathematics
Mathematical biology and algebraic statistics
j.rhodes@alaska.edu
9074745445
Chapman 208B
Troth Yeddha' Campus
Tony Rickard
Professor of Mathematics Education
Problemsolving, curriculum development, multicultural and rural education
adrickard@alaska.edu
9074745374
Chapman 301B
Troth Yeddha' Campus
Alexei Rybkin
Professor of Mathematics
Completely integrable partial differential equations and nonlinear water wave systems
arybkin@alaska.edu
9074746002
Chapman 304B
Troth Yeddha' Campus
Gordon Williams
Professor of Mathematics
Discrete geometry, especially abstract polytopes, convex polytopes and tilings
giwilliams@alaska.edu
9074742756
Chapman 306D
Troth Yeddha' Campus
Statistics Faculty
Ron Barry
Professor of Statistics
Experimental design and spatial statistics
rpbarry@alaska.edu
9074747226
Chapman 201C
Troth Yeddha' Campus
Scott Goddard
Associate Professor of Statistics
Bayesian testing and variable selection
sdgoddard@alaska.edu
9074745514
Chapman 201E
Troth Yeddha' Campus
Julie McIntyre
Professor of Statistics
Measurement error models and nonparametric statistics
jpmcintyre@alaska.edu
9074747772
Chapman 201D
Troth Yeddha' Campus
Margaret Short
Associate Professor of Statistics
Bayesian spatial and spatiotemporal statistical modeling
mshort18@alaska.edu
9074745249
Chapman 201B
Troth Yeddha' Campus