Mathematics (MATH)
Graduate Studies
570-577-1343
www.bucknell.edu/Math
Professors: George R. Exner, Ph.D. Michigan. Michael R. Frey, Ph.D. North Carolina. Pamela B. Gorkin, Ph.D. Michigan State. Paul J. McGuire, Ph.D. Indiana. Howard Smith, Ph.D. Cardiff, Wales.
Associate Professors: Carmen O. Acuña, Ph.D. Massachusetts. Gregory T. Adams, Ph.D. Indiana. Lynn Breyfogle, Ph.D. Western Michigan. Thomas Cassidy, Ph.D. Oregon. Ulrich Daepp, Ph.D. Michigan State. James E. Hutton, Ph.D. Cornell. Karl A. Voss (Chair), Ph.D. Yale.
Assistant Professors: Karen Boomer, Ph.D. Pennsylvania State University. Peter A. Brooksbank, Ph.D. Oregon. Emily Dryden, Ph.D. Dartmouth. Sharon Garthwaite, Ph.D. Wisconsin. Peter McNamara, Ph.D. MIT. Nathan Ryan, Ph.D. Dartmouth. Linda B. Smolka, Ph.D. Pennsylvania State University.
Admission Requirements
- 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.
Program Description
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.
Courses Offered
604. Mathematical Statistics (AI or II; 3, 0)
Point and interval estimation, hypothesis testing, theory of least squares and its relation to the design and analysis of experiments. Prerequisite: a course in probability.
605. Linear Statistical Models I (AI or II; 3, 0)
Regression and analysis of (co)variance. Model diagnosis and remediation. Generalized linear models and nonlinear regression. Multicollinearity and ridge regression. Use of advanced statistical software.
607. Statistical Design of Scientific Studies (II; 3, 0)
Sampling, design of experiments and observational studies. Includes completely randomized, block, factorial, and nested designs. Simple random stratified, systematic, and cluster sampling. Estimation procedures and sample size calculations. Prerequisite: a course in statistics.
609. Introduction to Real Analysis II (AI or II; 3, 0)
Integration theory and advanced topics in analysis.
611. Theory of Numbers (AI or II; 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: a course in abstract algebra.
617. Statistics for the Biological Sciences (I; 3, 0)
Exploratory data analysis, design of experiments and inference emphasizing applications in biology and environmental science. Includes multiple linear regression, analysis of variance, categorical data analysis, nonparametric statistics. Not available to graduate students in the mathematics department.
619. Topics in Advanced Mathematics (I or II; R; 3, 0)
Special topics, to be selected from algebra, analysis, geometry, statistics, etc.
633. Topology (AI or II; 3, 0)
Topological spaces, connectedness, compactness, continuity, separation and countability axioms. Metric, product, function, and uniform spaces.
635. Geometry (I; 3, 0)
Historical axiomatic foundations of geometry. Euclidian and non-Euclidean geometries.
643. Numerical Analysis (I; 3, 0)
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. Prerequisites: a course in multivariable calculus and a course in programming.
645. Linear Algebra (AI or II; 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: an introductory course in linear algebra.
646. Modern Algebra (AI or II; 3, 0)
Advanced topics in group theory including solvable groups, field theory, Galois theory. Prerequisite: a course in abstract algebra.
650. Methods in Applied Mathematics (AI or II; 3, 0)
Techniques drawn from partial differential equations, transform methods, Fourier and complex analysis, and variational calculus. Prerequisite: a course in differential equations.
658. Topics in Operations Research (AI orII; 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: a course in probability or permission of the instructor.
662. Introduction to Complex Analysis (AI or II; 3, 0)
Limits, analytic functions, integrals including contour integrals. Cauchy’s Integral Theorem, entire functions and singularities. Prerequisite: a course in multivariable calculus.
678. Seminar (AI or II; R; 2, 0) One-half course credit
Informal seminar in various topics as the need arises. Topics may deal with algebra, analysis, topology, differential equations, statistics, or applied mathematics. Prerequisite: permission of the instructor.
691 and 692. Reading and Research (I or II or S; 2-8, 0) One-half to two courses
Reading and research in various topics for qualified graduate students.
