Professors: Gregory T. Adams, Thomas Cassidy, Ulrich Daepp (Chair), George R. Exner, Michael R. Frey, Pamela B. Gorkin, Paul J. McGuire, Howard Smith
Associate Professors: Carmen O. Acuña, M. Lynn Breyfogle, Peter A. Brooksbank, Emily Dryden, James E. Hutton, Peter McNamara, Linda B. Smolka, Karl A. Voss
Assistant Professors: Jodi Black, KB Boomer, Gabrielle Flynt, Sharon A. Garthwaite, Alex J. Rice (visiting), Adam Piggott, Nathan C. Ryan, Bonnie B. Smith (visiting), Stephen Wang
Instructor: Amy M. Donner (visiting)
The student is expected to have completed courses in modern abstract algebra, real analysis (advanced calculus) beyond calculus of several variables, linear algebra, and probability. Those courses are prerequisite to advanced courses required for the M.A. and M.S. degrees.
Students must demonstrate proficiency in real analysis and either abstract algebra or probability. Proficiency is demonstrated by means of a preliminary exam or by auditing the relevant course with a grade of B or better on the final exam.
It is not possible to obtain the M.A. or M.S. degree in summers alone because the required courses of the M.A. or M.S. degree are offered only during the fall and spring semesters.
After having been admitted, candidates will confer with their academic adviser in the department of mathematics no later than the day of graduate enrollment. A tentative program of courses will be prepared; candidates may select programs with concentrations in pure mathematics, applied mathematics, or statistics.
Final approval of a candidate’s program rests with the department’s Graduate Committee. Granting of the master’s degree is dependent on the student’s having:
- passed the preliminary examination or audited the corresponding courses with a grade of B or better on the final examination;
- completed MATH 609 or MATH 646, MATH 645, MATH 662 , and either five approved electives or four approved electives and a master’s thesis under the direction of a faculty member in the mathematics department;
- passed a comprehensive oral examination;
- presented a mathematical talk in the Student Colloquium lecture series. The final decision as to whether or not the student is to be recommended for a degree rests with the department’s Graduate Committee. Every graduate student is expected to attend regularly the functions of Pi Mu Epsilon, the Bucknell chapter of the Mathematical Association of America, and the lectures given by local or visiting mathematicians and, upon occasion, to contribute to these programs.
603. Probability (I and II; 3, 0)
Elementary probability, random variables, moments, central limit theorem, conditional expectation, statistical distributions derived from the normal distribution. Probability simulations and applications from various fields.
604. Mathematical Statistics (AI or AII; 3, 0)
Point and interval estimation, hypothesis testing, Fisher's likelihood theory, frequentist versus Bayesian approach, computational statistics. Prerequisite: permission of the instructor.
605. Statistical Modeling (AI or AII; 3, 0)
Regression and analysis of (co)variance. Model diagnosis and remediation. Model selection, multicollinearity, logistic regression. R or SAS will be used. Prerequisite: permission of the instructor.
607. Statistical Design of Scientific Studies (II; 3, 0)
Experiments, observational studies. Completely randomized, block, mixed models, crossed, nested design. Simple random, stratified, cluster sampling. Estimation procedures, sample size calculations. Uses R or SAS.
609. Real Analysis II (AI or AII; 3, 0)
Continuation of MATH 608. Integration theory and advanced topics in analysis. Prerequisite: MATH 608.
611. Theory of Numbers (AI or AII; 3, 0)
Classical number theory in an algebraic setting. Topics include unique factorization, Diophantine equations, and linear and quadratic congruences. Advanced topics from algebraic or analytic number theory. Prerequisite: permission of the instructor.
619. Topics in Advanced Mathematics (AI or AII; R; 3, 0)
Special topics, to be selected from algebra, analysis, geometry, statistics, applied mathematics, etc.
633. Topology (AI or AII; 3, 0)
Topological spaces, connectedness, compactness, continuity, separation, and countability axioms. Metric, product, function, and uniform spaces. Prerequisite: permission of the instructor.
635. Geometry (I; 3, 0)
Historical and axiomatic foundations of geometry. Euclidean and non-Euclidean geometries. Prerequisite: permission of the instructor.
643. Numerical Analysis (I; 3, 2)
Floating point arithmetic, development of computational algorithms and error estimates for root approximation, interpolation and approximation by polynomials, numerical differentiation and integration, cubic splines, least-squares, linear systems; lab component. Prerequisite: permission of the instructor.
645. Linear Algebra (AI or AII; 3, 0)
Systems of linear equations, determinants, vector spaces, canonical forms for linear transformations and matrices, bilinear forms, inner product spaces, applications to such other areas as geometry, differential equations, linear programming. Prerequisite: permission of the instructor.
646. Abstract Algebra II (AI or AII; 3, 0)
Advanced topics in group theory including solvable groups, field theory and Galois theory.
650. Methods in Applied Mathematics (AI or AII; 3, 0)
Techniques drawn from partial differential equations, transform methods, Fourier and complex analysis, and variational calculus. Prerequisite: permission of the instructor.
658. Topics in Operations Research (AI or AII; 3, 0)
Mathematical and statistical techniques in operations research. Queueing theory. Additional topics may include simulation, forecasting, non-linear programming, inventory models. Methods and applications drawn from various fields. Prerequisite: permission of the instructor.
662. Complex Analysis (AI or AII; 3, 0)
Limits, analytic functions, integrals including contour integrals. Cauchy's Integral Theorem, entire functions and singularities. Prerequisite: permission of the instructor.
678. Seminar (I or II; R; 2, 0) Half course.
Seminar based on topics from algebra, analysis, topology, differential equations, statistics, or applied mathematics; topics selected according to demand or interest. Prerequisite: permission of the instructor.
691. 692. Reading and Research (I or II; R; 2-8, 0) Half to two courses.
Reading and research in various topics for qualified graduate students. Prerequisite: permission of the instructor.