Graduate School Bulletin - Spring 2005

MATHEMATICS

The Department of Mathematics grants the M.A., M.S., and Ph.D. degrees. There are no specific course prerequisites for admission; however, two semesters of advanced calculus, and at least one semester each of algebra and topology are suggested. Both the M.A. and M.S. degrees are 30-credit-hour programs, offered under either Plan A or Plan B. The department also offers an M.S. in Applied Mathematics which requires 36 hours.

The Master of Arts degree, featuring a core program that emphasizes mathematical structures, is designed for prospective community college teachers and for students contemplating studies at the Ph.D. level.

The Master of Science degree, through an emphasis on the applications of mathematics and the acquisition of computational skills, focuses on careers in business, industry, and government.

The Master of Science in Applied Mathematics is a more intensive program intended to develop the skills needed to apply mathematics to real world problems. The degree requires 18 hours in mathematics, 12 hours in computer science and/or statistics, and a 6-hour minor, for a total of 36 hours.

The doctorate is a research degree granted on the basis of broad mathematical knowledge and exhibited creative ability. Course work leading to the doctorate is available in the areas of algebra, analysis (classical and modern), applied mathematics, optimization, numerical analysis, differential equations, and topology. A comprehensive examination is required of each student.

Admission Requirements

The graduate programs in mathematics do not have formal admission requirements other than those of the Graduate School. Admission, however, is competitive. The admission committee reviews transcripts and letters of recommendation seeking evidence of mastery in proof-based mathematics (such as analysis, topology, and modern algebra), the ability to craft mathematical proofs, and general mathematical maturity.

Degree Requirements

In order to be admitted to candidacy for the Ph.D. degree, a student must pass a proficiency examination in one foreign language chosen from French, German or Russian, complete studies in a minor field (either inside or outside the department) and successfully complete the comprehensive examinations. Subsequent work becomes highly specialized through seminars, independent study, and finally, work on a dissertation which penetrates in depth some field of particular interest. Areas in which members of the faculty have active research projects include algebraic topology, group theory, ring theory, algebraic geometry, number theory, complex variables, rational approximation, operator theory, partial differential equations, continuum mechanics, numerical analysis, algebraic combinatorics and optimization.

The ability to communicate mathematics is an increasingly important professional qualification. The department requires all students to complete a teaching or research assignment during each semester of their enrollment in a graduate mathematics program. Students will be assigned to teach courses at the early undergraduate level. Entering students will normally be assigned three semester hours, and continuing ones will normally teach 6 semester hours. With the approval of the Director of Graduate Studies, a student may substitute an equivalent research effort for the teaching activity.

GRADUATE COURSES

MA 415G GRAPH THEORY (SAME AS CS 415G) (3)

MA 416G PRINCIPLES OF OPERATIONS RESEARCH I (SAME AS CS 416G) (3)

MA 417G PRINCIPLES OF OPERATIONS RESEARCH II (SAME AS STA 417G) (3)

MA 432G METHODS OF APPLIED MATHEMATICS I (3)

MA 433G INTRODUCTION TO COMPLEX VARIABLES (3)

MA 471G ADVANCED CALCULUS I (3)

MA 472G ADVANCED CALCULUS II (3)

MA 481G DIFFERENTIAL EQUATIONS (3)

MA 483G INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS (3)

MA 485G FOURIER SERIES AND BOUNDARY VALUE PROBLEMS (SAME AS ME 585) (3)

MA 501 SEMINAR IN SELECTED TOPICS (3)

MA 502 SEMINAR IN SELECTED TOPICS (3)

MA 503 COMBINATORICS (3)

MA 506 METHODS OF THEORETICAL PHYSICS I (SAME AS PHY 506) (3)

MA 507 METHODS OF THEORETICAL PHYSICS II (SAME AS PHY 507) (3)

MA 515 MATHEMATICAL PROGRAMMING AND EXTENSIONS (SAME AS STA 515) (3)

MA 522 MATRIX THEORY AND NUMERICAL LINEAR ALGEBRA I (SAME AS CS 522) (3)

MA 527 APPLIED MATHEMATICS IN THE NATURAL SCIENCES I (SAME AS ME 527) (3)

MA 532 ORDINARY DIFFERENTIAL EQUATIONS (3)

MA 533 PARTIAL DIFFERENTIAL EQUATIONS (3)

MA 537 NUMERICAL ANALYSIS (SAME AS CS/EGR 537) (3)

MA 551 TOPOLOGY I (3)

MA 561 MODERN ALGEBRA I (3)

MA 565 LINEAR ALGEBRA (3)

MA 570 MULTIVARIATE CALCULUS (3)

MA 575 PRINCIPLES OF ANALYSIS (3)

MA 611 INDEPENDENT WORK IN MATHEMATICS (3-9)

MA 613 PROBLEMS SEMINAR IN OPERATIONS RESEARCH (SAME AS EE/STA 619) (3)

MA 614 ENNUMERATIVE COMBINATORICS (3)

MA 616 NUMERICAL TECHNIQUES FOR NONLINEAR OPTIMIZATION (3)

MA 617 MARKOVIAN DECISION PROBLEMS (3)

MA 618 COMBINATORICS AND NETWORKS (3)

MA 622 MATRIX THEORY AND NUMERICAL LINEAR ALGEBRA II (SAME AS CS 622) (3)

MA 625 NUMERICAL METHODS FOR DIFFERENTIAL EQUATIONS (3)

MA 628 APPLIED MATHEMATICS IN THE NATURAL SCIENCES II (3)

MA 630 MATHEMATICAL FOUNDATIONS OF STOCHASTIC PROCESSES AND CONTROL THEORY I (3)

MA 633 THEORY OF PARTIAL DIFFERENTIAL EQUATIONS (3)

MA 641 DIFFERENTIAL GEOMETRY (3)

MA 642 DIFFERENTIAL GEOMETRY (3)

MA 651 TOPOLOGY II (3)

MA 654 ALGEBRAIC TOPOLOGY I (3)

MA 655 ALGEBRAIC TOPOLOGY II (3)

MA 661 MODERN ALGEBRA II (3)

MA 667 GROUP THEORY (3)

MA 671 FUNCTIONS OF A COMPLEX VARIABLE I (3)

MA 672 FUNCTIONS OF A COMPLEX VARIABLE II (3)

MA 676 ANALYSIS I (3)

MA 677 ANALYSIS II (3)

MA 681 FUNCTIONAL ANALYSIS I (3)

MA 682 FUNCTIONAL ANALYSIS II (3)

MA 714 TOPICS IN DISCRETE MATHEMATICE (SUBTITLE REQUIRED) (3)

MA 715 SELECTED TOPICS IN OPTIMIZATION (3)

MA 721 SELECTED TOPICS IN NUMERICAL ANALYSIS (3)

MA 732 SELECTED TOPICS IN DIFFERENTIAL AND INTEGRAL EQUATIONS (3)

MA 748 MASTER'S THESIS RESEARCH (0)

MA 749 DISSERTATION RESEARCH (0)

MA 751 SELECTED TOPICS IN TOPOLOGY (3)

MA 752 SELECTED TOPICS IN TOPOLOGY (3)

MA 761 HOMOLOGICAL ALGEBRA (3)

MA 764 SELECTED TOPICS IN ALGEBRA (3)

MA 765 SELECTED TOPICS IN ALGEBRA (3)

MA 768 RESIDENCE CREDIT FOR MASTER'S DEGREE (1-6)

MA 769 RESIDENCE CREDIT FOR DOCTOR'S DEGREE (0-12)

MA 772 SELECTED TOPICS IN THE THEORY OF COMPLEX VARIABLES (3)

MA 773 SELECTED TOPICS IN ANALYSIS (3)

MA 777 MATHEMATICAL SEMINAR (3)

MA 778 MATHEMATICAL SEMINAR (3)

The Graduate School | UK Research | University of Kentucky | An Equal Opportunity University