Mathematics (M.S.)
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Degree Offered: |
M.S. |
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Director: |
Karpechina |
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Phone: |
(205) 934-2154 |
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E-mail: |
This email address is being protected from spambots. You need JavaScript enabled to view it. |
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Web site: |
Faculty
Blokh, Alexander, Professor of Mathematics, 1992, Ph.D. (Kharkov State); Dynamical Systems
Chernov, Nikolai, Professor of Mathematics, 1994, M.S., Ph.D. (Moscow State, Russia) ; Dynamical Systems, Ergodic Theory
Dale, Louis, Professor of Mathematics; Vice President for Equity and Diversity, 1973, B.A. (Miles), M.S. (Atlanta), Ph.D. (Alabama); Ring Theory
Hutchison, Jeanne S., Assistant Professor of Mathematics, 1970, B.S. (Creighton), M.A., Ph.D. (California-Los Angeles)
Johnson, Walter, Instructor of Mathematics, 2002, B.S.EE. (Auburn), M.A.Ed. (UAB); Introductory Math Curriculum Director
Jung, Paul, Assistant Professor of Mathematics, 2011, Ph.D. (University of California System: Los Angeles); Probability Theory and Statistical Mechanics
Karpeshina, Yulia, Professor of Mathematics, 1995, M.S., Ph.D. (Saint Petersburg, Russia); Partial Differential Equations and Mathematics Physics
Knowles, Ian W., Professor of Mathematics, 1979, B.Sc. (Adelaide), M.Sc., Ph.D. (Flinders-South Australia); Ordinary and Partial Differential Equations, Numerical Analysis
Kravchuk, Elena, Instructor of Mathematics, 2002, M.S. (Donetsk State – Ukraine), Ph.D. (NASU, Donetsk – Ukraine)
Lewis, Roger T., Professor Emeritus of Mathematics, 1975, A.B. (Tennessee), M.S. (Florida Institute of Technology), Ph.D. (Tennessee); Differential Equations, Spectral Theory
Li, JunFang, Assistant Professor of Mathematics, 2008, B.S. (Wuhan), M.A., Ph.D. (Oklahoma); Geometric Analysis and Non-linear Partial Differential Equations
Mayer, John C., Professor of Mathematics; Associate Chair, Department of Mathematics, 1984, B.A. (Randolph-Macon), M.A., Ph.D. (Florida); Topology, Continuum Theory, Dynamical Systems, Mathematics Education
Navasca, Carmeliza, Assistant Professor of Mathematics, 2012, B.A.(University of California at Berkeley), Ph.D. (University of California at Davis); Multilinear Algebra, Control Theory, Optimization, Data Mining
Nkashama, Mubenga N., Professor of Mathematics, 1989, B.S., M.S. (National University of Zaire), Ph.D. (Catholic University of Louvain, Belgium); Differential Equations, Dynamical Systems, Nonlinear Functional Analysis
Oversteegen, Lex G., Professor of Mathematics, 1980, Kandidaat, Doctorandus (Amsterdam), Ph.D. (Wayne State); Topology, Continuum Theory, Dynamical Systems
O’Neil, Peter V., Professor Emeritus of Mathematics, 1978, B.S. (Fordham), M.S., Ph.D. (Rensselaer Polytechnic Institute); Graph Theory, Combinatorics
Saito, Yoshimi, Professor Emeritus of Mathematics, 1983, B.A., M.A., Ph.D. (Kyoto, Japan); Scattering Theory, Differential Equations
Shterenberg, Roman G., Associate Professor of Mathematics, 2007, M.S., Ph.D (St. Petersburg State University – Russia); Mathematical Physics, Spectral Theory, Inverse Problems, Partial Differential Equations, Non-linear Partial Differential Equations
Simányi, Nándor, Professor of Mathematics, 1999, M.S., Ph.D. (Rolánd Eötvös - Hungary), Dr.M.S. (Hungarian Academy of Sciences); Dynamical Systems With Some Algebraic Flavour
Stansell, Laura R., Instructor of Mathematics, 2007, B.S. (Berry), M.S. (Southern Mississippi), M.S. (UAB)
Starr, Shannon, Assistant Professor of Mathematics, 2012, B.A.(University of California at Berkeley), Ph.D. (University of California at Davis); Mathematical Physics and Probability
Stocks, Douglas R., Associate Professor Emeritus of Mathematics, 1969, B.A., M.A., Ph.D. (Texas)
Stolz, Günter, Professor of Mathematics, 1994, Ph.D. (Frankfurt, Germany); Spectral Theory, Mathematical Physics
Vaughan, Loy O. Jr., Associate Professor of Mathematics, 1969, B.A. (Florida State), M.S., Ph.D. (Alabama)
Ward, James R. Jr., Professor Emeritus of Mathematics, 1989, B.A., M.A., Ph.D. (South Florida); Differential Equations, Nonlinear Analysis, Dynamical Systems
Weikard, Rudi, Professor of Mathematics; Chair, Department of Mathematics, 1990, Ph.D. (Technical University of Braunschweig, Germany); Ordinary and Partial Differential Equations, Mathematical Physics
Weinstein, Gilbert, Associate Professor of Mathematics, 1991, B.A. (Haifa, Israel), M.Ph., Ph.D. (Syracuse); Partial Differential Equations, General Relativity, Differential Geometry
Zeng, Yanni, Associate Professor of Mathematics, 1997, B.S., M.S. (Zhongshan, China), Ph.D. (New York); Nonlinear Analysis, Applied Partial Differential Equations
Zou, Henghui, Associate Professor of Mathematics, 1994, B.S. (Xiangtan, P.R.C.), M.S. (Peking, P.R.C.), Ph.D. (Minnesota); Nonlinear Partial Differential Equations, Nonlinear Analysis
Program Information
Mathematics has always been divided into a pure and an applied branch. However, these have never been strictly separated. The M.S. program in mathematics stresses the interconnection between pure mathematics and its diverse applications.
Areas of Specialization
The student must choose a primary and a secondary specialization from a list of areas determined by the expertise of the faculty. As soon as the student is ready to choose specialization areas, he or she should contact the mathematics graduate program director, who will nominate a graduate study committee for the student. Courses offered to meet degree requirements must be approved by the mathematics graduate program director and the student's graduate study committee.
Degree Requirements
Plan I (Thesis)
The student must complete 30 semester hours approved by the mathematics graduate program director and the student's graduate study committee. The grade in each course has to be a B or better. A minimum of 24 hours must be on the 600 level or above. See Course Descriptions for which courses at the 500 level may not be counted toward the M.S. degree. In addition the following specific requirements must be met:
- at least 9 hours must be in the primary area of specialization,
- at least 6 hours must be in the secondary area of specialization,
- at least 9 hours must be outside the primary area,
- at most 6 hours of research may be included in the 30-hour requirement,
- a thesis must be completed, and
- an examination must be passed on material in the primary area of specialization (the exam may be written, oral, or both, at the discretion of the student's graduate study committee).
The student's performance in all respects must be approved by the graduate program director and the student's graduate study committee.
Plan II (Nonthesis)
The student must complete 30 semester hours approved by the mathematics graduate program director and the student's graduate study committee. The grade in each course has to be a B or better. A minimum of 24 hours must be on the 600 level or above. See Course Descriptions for which courses at the 500 level may not be counted toward the M.S.degree. In addition, the following specific requirements must be met:
- at least 12 hours must be in the primary area of specialization,
- at least 6 hours must be in the secondary area of specialization,
- at least 9 hours must be outside the primary area,
- no research may be included in the 30-hour requirement,
Two examinations must be passed on material in the two areas of specialization. (The exams may be written, oral, or both, at the discretion of the student's graduate study committee.)
Additional Information
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Each semester |
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Deadline for All Application Materials to be in the Graduate School Office: |
Six weeks before term begins |
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Number of Evaluation Forms Required: |
Three |
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Entrance Tests |
GRE (TOEFL and TWE also required for international applicants whose native language is not English.) |
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Comments |
None |
For detailed information, contact Dr. Ioulia Karpechina, Mathematics Graduate Program Director, UAB Department of Mathematics, CH 493B, 1300 University Boulevard, Birmingham, Alabama 35294-1170.
Telephone 205-934-2154
E-mail This email address is being protected from spambots. You need JavaScript enabled to view it.
Web http://www.uab.edu/mathematics/
Course Descriptions
All courses carry 3 hours of credit unless otherwise noted. A course may count as a prerequisite only if it was completed with a grade of B or better. The instructor can waive any prerequisite. Courses numbered below 520 and 540-541 may not be counted toward a graduate degree in mathematics.
501. History of Mathematics I. Development of mathematical principles and ideas from an historical viewpoint, and their cultural, educational and social significance; earliest origins through Newton and Leibnitz. Prerequisite: Undergraduate level MA 125 Minimum Grade of C or Undergraduate level MA 142 Minimum Grade of C.
502. History of Mathematics II. Development of mathematical principles and ideas from an historical viewpoint, and their cultural, educational and social significance; Newton and Leibnitz through early 20th century. Prerequisite: MA 501 Minimum grade of B or MA 311 Minimum grade of B.
511. Integrating Math Ideas. This course will integrate ideas from algebra, geometry, probability, and statistics. Emphasis will be on using functions as mathematical models, becoming fluent with multiple representations of functions, and choosing the most appropriate representations for solving a specific problem. Students will be expected to communicate mathematics verbally and in writing through small group, whole group, and individual interactions.
512. Connect Ma to SC and Tech. This course will extend the idea of functions as mathematical models introduced in MA 511 and extend the families of functions that are used as models. Specific models from the earth, life, and physical sciences will be introduced. The role of probability and statistics in model-building will be emphasized. Students will be expected to communicate mathematics verbally and in writing through small group, whole group, and individual interactions.
513. Patterns, Functions & Algebraic Reasoning. Problem solving experiences, inductive and deductive reasoning, patterns and functions, some concepts and applications of geometry for elementary and middle school teachers. Topics include linear and quadratic relations and functions and some cubic and exponential functions. Number sense with the rational number system including fractions, decimals and percents will be developed in problem contexts. An emphasis will be on developing algebraic thinking and reasoning. Recommended that 2 years of high school algebra or MA102 has been completed before taking course.
514. Geometry & Proportional Reasoning. Problem solving experiences, inductive reasoning, concepts and applications of geometry and proportional reasoning for elementary and middle school teachers. Topics include analysis of one, two and three dimensional feature of real objects, ratio and proportionality, similarity and congruence, linear, area, and volume measurement, and the development of mathematically convincing arguments. An emphasis will be on developing thinking and reasoning.
515. Probabilistic & Statistics Reasoning. Descriptive and inferential statistics, probability, estimation, hypothesis testing. Reasoning with probability and statistics is emphasized.
516. Numerical Reasoning. Develop understanding of numbers and improve numerical reasoning skills specifically with regard to place value, number relationships that build fluency with basis facts, and computational proficiency; developing a deep understanding of numerous diverse computational algorithms; mathematical models to represent fractions, decimals and percents, equivalencies and operations with fractions, decimals and percents; number theory including order of operations, counting as a big idea, properties of numbers, primes and composites, perfect, abundant and significant numbers, and figurate numbers; inductive and deductive reasoning with numbers.
517. Extending Algebraic Reasoning. Extending algebraic and functional reasoning to polynomials, rational, exponential, and logarithmic functions; problem-solving involving transfer among representations (equation, graph, table); proof via symbolic reasoning, contradiction, and algorithm; interpretation of key points on graphs (intercepts, slope, extrema); develop facility and efficiency in manipulating symbolic representations with understanding; appropriate use of technology and approximate versus exact solutions; functions as models. Prerequisite: MA 313.
519. Special Topics for Teachers. With permission of instructor, may be used as continuation of any of MA 513 through 518. May be repeated for credit when topics vary.
534. Algebra I: Linear. Abstract vector spaces, subspaces, dimension, bases, linear transformations, matrix algebra, matrix representations of linear transformations, determinants. Prerequisites: MA 142 or permission of instructor.
535. Algebra II: Abstract. Groups, homomorphisms, quotient groups, isomorphism theorems, rings and ideals, integral domains, fields. As time permits, Galois theory, semigroups, modules, or other areas of algebra may be included. Prerequisites: MA 534 or permission of instructor.
540. Advanced Calculus I. Introduction to the real numbers; sequences and series of real numbers; functions and continuity; differentiation. This course is taught as a do-it-yourself course and will meet 4 hours per week. Prerequisites: Admission to the graduate program or permission of instructor.
541. Advanced Calculus II. Integration; sequences and series of functions; uniform vs. pointwise convergence; some elementary and special functions. This course is taught as a do-it-yourself course and will meet 4 hours per week. Prerequisites: Admission to the graduate program or permission of instructor.
544. Vector Analysis. Review and applications of multiple integrals, Jacobians and change of variables in multiple integrals; line and surface integrals; theorems of Green, Gauss, and Stokes with application to the physical sciences; computation in spherical and cylindrical coordinates. Prerequisite: MA 244.
545. Complex Analysis. Analytic functions, complex integration and Cauchy's theorem, Taylor and Laurent series, calculus of residues and applications, conformal mappings. Prerequisite: MA 244.
553. Transforms. Theory and applications of Laplace and Fourier transforms. Prerequisite: MA 252.
554. Intermediate Differential Equations. Topics from among Frobenius series solutions, Sturm-Liouville systems, nonlinear equations, and stability theory. Prerequisite: MA 252.
555, 556. Partial Differential Equations I, II. Classification of second-order partial differential equations, background on eigenfunction expansions and Fourier series, solution of the wave equation, reflection of waves, solution of the heat equation in bounded and unbounded media, Laplace's equation, Dirichlet and Neumann problems. Prerequisite: MA 252.
560. Scientific Programming. This course is designed to provide the computational skills needed to attempt serious scientific computational tasks. Computers and floating point arithmetic; the GNU/Linux operating system and an introduction to the complied programming languages FORTRAN (including FORTRAN 95) and C++ in the context of solving systems of linear equations and differential equations arising from practical situations; use of debuggers and other debugging techniques, and profiling; use of callable subroutine packages like LAPACK and differential equation routines; parallel programming a Beowulf system with MPI; introduction to Matlab.
561. Modeling with PDE. Practical examples of partial differential equations; derivation of partial differential equations from physical laws; introduction to MATLAB and its PDE Toolbox, and other PDE packages such as FEMLAB using practical examples; brief discussion of finite difference and finite element solution methods; introduction to continuum mechanics and classical electrodynamics; parallel programming using MPI and the mathematics department Beowulf system; specialized modeling projects in topics such as groundwater modeling, scattering of waves, medical and industrial imaging, fluid mechanics, and acoustic and electromagnetic applications.
562. Intro to Stochastic Defferential Equations. Stochastic differential equations arise when random effects are introduced into the modeling of physical systems. Topics include Brownian motion and Wiener processes, stochastic integrals and the Ito calculus, stochastic differential equations, and applications to financial modeling, including option pricing.
563, 564. Operations Research I, II. Mathematical techniques and models with application in industry, government, and defense. Topics usually chosen from dynamic, linear, and nonlinear programming, decision theory; Markov chains, queuing theory, inventory control, simulation, network analysis, and selected case studies. Prerequisite: MA 243.
565. PDE: Finite Difference Methods. Review of difference methods for ordinary differential equations including Runge-Kutta, multistep, adaptive stepsizing, and stiffness; finite difference versus finite element; elliptic boundary value problems, iterative solution methods, self-adjoint elliptic problems; parabolic equations including consistency, stability, and convergence, Crank-Nicolson method, method of lines; first order hyperbolic systems and characteristics, Lax- Wendroff schemes, method of lines for hyperbolic equations.
567. Gas Dynamics. Euler s equations for in viscid flows, rotation and vorticity, Navier-Stok
568, 569. Numerical Analysis I, II. Integrals, interpolation, rational approximation, numerical solution of ordinary differential equations, iterative solution of algebraic equations in single variable, least squares. Gaussian elimination for solution of linear equations. Prerequisites: MA 252 and either MA 263 or CS 210.
570, 571. Differential Geometry I, II. Theory of curves and surfaces: Frenet formulas for curves, first and second fundamental forms of surfaces. Global theory; abstract surfaces, manifolds, Riemannian geometry. Prerequisite: MA 244.
572. Geometry I. The axiomatic method; Euclidean geometry including Euclidean constructions, basic analytical geometry, transformational geometry, and Klein s Erlanger Program; introduction to fractal geometry. Course integrates intuition/ exploration and proof/explanation.
573. Geometry II. Analytical geometry, Birkhoff s axioms, and the complex plane; structure and representation of Euclidean isometries; plane symmetries; non- Euclidean (hyperbolic) geometry and non-Euclidean transformations; fractal geometry; algorithmic geometry. Course integrates intuition/exploration and proof/explanation. Project and report or oral presentation required.
574, 575. Introduction to Topology I, II. Separable metric spaces, basis and sub-basis, continuity, compactness, completeness, Baire category theorem, countable products, general topological spaces, Tychonov theorem. Prerequisite: MA 244.
585. Probability. Probability spaces, combinatorics, conditional probabilities and independence, Bayes rule, discrete and continuous distributions, mean value and variance, moment generation function, joint distributions, correlation, Central Limit Theorem, Law of Large Numbers, random walks, Poisson process. Prerequisite: Undergraduate level MA126 Minimum Grade of C.
586. Mathematical Statistics. Confidence intervals, hypothesis testing, analysis of variance and co-variance, maximum likelihood estimates, linear regression, tests of fit, robust estimates and tests. Prerequisite: MA 485 Minimum grade of B or MA 585 Minimum grade of B.
587. Advanced Probability. Foundation of probability, conditional probabilities, and independence, Bayes theorem, discrete and continuous distributions, joint distributions, conditional and marginal distributions, convolution, moments and moment generation function, multivariable normal distribution and sums of normal random variables, Markov chains. Prerequisite: MA 485 Minimum grade of B or MA 585 Minimum grade of B. 3 hours.
590-591. Math Seminar. Topics vary; may be repeated for credit. Prerequisites vary with topics. 1-3 hours.
592-597. Special Topics in Mathematics. These courses cover special topics in mathematics and the applications of mathematics. May be repeated for credit when topics vary. Prerequisites vary with topics. 1, 2, or 3 hours.
598-599. Research in Mathematics. Topics vary; may be repeated for credit. Prerequisites vary with topics. 1-3 hours.
610. Introduction to Set Theory. Set theory, products, relations, orders and functions, cardinal and ordinal numbers, transfinite induction, axiom of choice, equivalent statements.
631. Linear Algebra. Vector spaces and their bases; linear transformations; eigenvalues and eigenvectors; Jordan canonical form; multilinear algebra and determinants; norms and inner products. Prerequisites: Admission to graduate program or permission of instructor.
632. Abstract Algebra. Propositional and predicate logic; set, relations, and functions; the induction principle; Groups, in particular symmetry groups, permutations groups, and cyclic groups; cosets and quotient groups; group homomorphisms; rings, integral domains, and fields; ideals and rings homomorphisms; factorization; polynomial rings. Prerequisites: Admission to graduate program or permission of instructor.
642. Calculus of Several Variables. Functions of several variables; total and partial derivatives; the implicit function theorem, integration of different forms; Stokes’ Theorem. Prerequisites: A grade of at least B in MA 441/541 or permission of instructor.
645. Real Analysis I. Abstract measures and integration; positive Borel measures; Lp spaces. Prerequisites: A grade of at least B in MA 642 or permission of instructor.
646. Real Analysis II. Complex measures and the Radon-Nikodym theorem; differentiation; integration on product spaces and Fubini theorem. Prerequisites: A grade of at least B in MA645 or permission of instructor.
648. Complex Analysis. The algebraic and topological structure of the complex plane, analytic functions, Cauchy's integral theorem and integral formula, power series, elementary functions and their Riemann surfaces, isolated singularities, residues, the Laurent expansion, the Riemann mapping. Prerequisite: A grade of at least B in MA 642 or permission of instructor.
650. Differential Equations. Separable, linear, and exact first-order equations; existence and uniqueness theorems; continuous dependence of solutions on data and initial conditions; first order systems and higher order equations; stability for two-dimensional linear systems; higher order linear systems; boundary value problems; stability theory. Prerequisites: A grade of at least B in MA 630 or permission of instructor.
655. Partial Differential Equations. This course covers first order partial differential equations, elliptic equations, parabolic equations, and hyperbolic equations. The prerequisites for this class are MA 642, or MA 650, or permission of the instructor.
660. Numerical Linear Algebra. Vectors and matrix norms; the singular value decomposition; stability; condition numbers and error analysis; QR factorization; LU factorization; least squares problems; computation of eigenvalues and eigenvectors; iterative methods. Prerequisites: A grade of at least B in MA 630 or permission of instructor.
661. Modeling with PDE. Practical examples of partial differential equations; derivation of partial differential equations from physical laws; introduction to MATLAB and its PDE Toolbox, and other PDE packages such as FEMLAB using practical examples; brief discussion of finite difference and finite element solution methods; introduction to continuum mechanics and classical electrodynamics; parallel programming using MPI and the mathematics department Beowulf system; specialized modeling projects in topics such as groundwater modeling, scattering of waves, medical and industrial imaging, fluid mechanics, and acoustic and electromagnetic applications.
663-664. Operations Research I-II. Mathematical optimization techniques. Formulation, solution, and analysis of problems arising from business, engineering, and science. Prerequisite: MA 244.
665. Partial Differential Equations: Finite Difference Method. Review of difference methods for ordinary differential equations including Runge-Kutta, multi-step, adaptive step-sizing, and stiffness; finite difference versus finite element; elliptic boundary value problems; iterative solution methods, self-adjoint elliptic problems; parabolic equations including consistency, stability, and convergence, Crank-Nicolson method, method, method of lines; first order hyperbolic systems and characteristics Lax-Wendroff schemes, methods of lines for hyperbolic equations.
668, 669. Numerical Analysis I, II. Integrals, interpolation, rational approximation, numerical solution of ordinary differential equations, iterative solution of algebraic equations in single variable, least squares. Gaussian elimination for solution of linear equations. Prerequisites: MA 252 and either MA 263 or CS 210.
670. Topology I. Definition of topologies; closure; continuity; product topology; metric spaces. Prerequisites: A grade of at least B in MA 630 or permission of instructor.
671. Topology II. Connectedness; completeness and compactness (in particular in metric spaces); countability and separation axioms; Tychonoff’s theorem; homotopy; partitions of unity. Prerequisites: A grade of at least B in MA 670 or permission of instructor.
675. Differential Geometry. Local and global theory of curves and surfaces: Fenchel’s theorem; the first and second fundamental forms; surface area; Bernstein’s theorem; Gauss theorema egregium; local intrinsic geometry of surfaces; Riemannian surfaces; Lie derivatives; covariant differentiation; geodesics; the Riemann curvature tensor; the second variation of arclength; selected topics in the global theory of surfaces. Prerequisites: A grade of at least B in MA 642 or permission of instructor.
687. Advanced Probability. Foundation of probability, conditional probabilities, and independence, Bayes theorem, discrete and continuous distributions, joint distributions, conditional and marginal distributions, convolution, moments and moment generation function, multivariable normal distribution and sums of normal random variables, Markov chains. Prerequisite: MA 485 Minimum grade of B or MA 585 Minimum grade of B. 3 hours.
690, 691. Mathematics Seminar. This course covers special topics in mathematics and the applications of the mathematics. May be repeated for credit when topics vary. Prerequisites vary with topics.
691-697. Special Topics in Mathematics. These courses cover special topics in mathematics and the applications of mathematics. May be repeated for credit when topics vary. Prerequisites vary with topics. 1, 2, or 3 hours.
698. Nonthesis Research. Prerequisite: Permission of instructor. 1-6 hours.
699. Thesis Research. Prerequisite: Admission to candidacy and permission of instructor. 1-6 hours
