Chair: Robert Feinerman (Gillet Hall, Room 211).
Adviser: Charles Berger (Gillet Hall, Room 101A; 718-960-8868)
Department Faculty and Staff: Distinguished Professors: Adam Koranyi, Victor Pan; Professors: Charles Berger, Robert Feinerman, Melvin Fitting, Nancy Griffeth, Michael Handel, Nicholas Hanges, Leon Karp, Linda Keen, Joseph Lewittes, Richard Mosak, Melvyn B. Nathanson, Esther Phillips, Robert Schneider, Zoltan Szabo; Associate Professors: Yves Jean, Gwang Jung, Julian Laderman, Nikola Lakic, John C. Mineka, Christina Sormani, Katherine St. John; Assistant Professors: Calin Diaconu, David Fisher, Yiannis Petridis, Rhys Rosholt; Lecturer: David J. Rothchild; Instructors:Brian Murphy; Director of Mathematics Laboratory and Computer Services: Robert Sutliff; Systems and Network Administrator: Etina Bueno
The Department of Mathematics and Computer Science offers the following graduate degree programs: Master of Science in Computer Science, Master of Arts in Mathematics, and Master of Arts for Secondary School Teachers of Mathematics. The Department also offers courses in the Program in Mathematics Education for Intermediate School Teachers, which is administered by the Department of Middle and High School Education.
The Computer Science program is offered for (a) recent graduates who wish to continue their studies while beginning their professional careers; (b) individuals presently employed in computer-related fields who wish to qualify for advanced career opportunities or training; and (c) individuals who seek a career change.
Admission Requirements
Degree Requirements
Students must complete the following requirements for the M.S. Program in Computer Science:
The Master of Arts Program in Mathematics is offered for (a) students who may eventually work toward a doctorate in mathematics; (b) those who seek the M.A. as a terminal degree; (c) graduates of the M.A. Program for Secondary School Teachers of Mathematics seeking additional graduate mathematics credits and who wish the structure of a formal degree program and the credential of a pure mathematics master's degree; (d) qualified students who wish to take individual graduate mathematics courses.
Admission Requirements
Degree Requirements
The requirements for the M.A. Degree in Mathematics are as follows:
MAT 582, 601, 602, 603, 604, and 615 may not be used toward this degree.
The Department of Mathematics and Computer Science offers courses designed to meet the needs of students in the Program for Secondary School Teachers of Mathematics.
Admission Requirements
Degree Requirements
Students in this program are required to complete from 21 to 24 credits in mathematics, as well as 6 to 9 credits in middle and high school education. Candidates for the degree are required to pass a comprehensive examination based on four courses, including at least one course each in algebra, analysis, and geometry.
MAT 601: Secondary School Mathematics from an Advanced Standpoint. 3 hours, 3 credits. This course will cover topics chosen from the theory of arithmetic, logic, probability, and geometry that are of particular interest to teachers of secondary school mathematics.
MAT 602: Introduction to Number Theory and Modern Algebra I. 3 hours, 3 credits. Topics from number theory that have special relevance to the intermediate school program will be considered. These include prime numbers, unique factorization, congruences, Diophantine equations, and Fermat's theorem. Abstract algebra, including equivalence relations and some group theory, will be interwoven in the development, but the primary emphasis is on the number systems that could be considered in the intermediate schools.
MAT 603: Introduction to Number Theory and Modern Algebra II. 3 hours, 3 credits. Further study of the topics in MAT 602. Also, rational numbers, rings, integral domains, fields, ordered fields. PREREQ: MAT 602.
MAT 604: Application of the Real and Complex Number Systems. 3 hours, 3 credits. A study of irrational numbers, the algebraic properties of the complex numbers and polynomials over the integers, rationals, and reals through a concrete, nonabstract approach. Applications in the theory of equations and inequalities.
*Courses preceded by an asterisk are not expected to be offered in 2007-2009.
MAT 582: Statistics for Students in Biological, Health, and Social Sciences. 4 hours, 4 credits. (Open to all graduate students except those in the education or M.A. programs in graduate mathematics.) Topics in statistics, with emphasis on needs of students in fields other than mathematics. The topics will include methods of central tendency and variability, probability theory, sampling, normal distribution, and large sample theory, t-test and small sample theory, chisquare test, correlation and regression, analysis of variance, and nonparametric methods. Statistical analysis using a computer package.
MAT 613: Theory of Numbers. 4 hours, 4 credits. Euclid's algorithm and the fundamental theorems on divisibility; prime numbers and congruences; the theorems of Fermat, Euler, and Wilson; quadratic residues and reciprocity law, algebraic numbers, Pythagorian triples, other diophantine equations, Fermat's L.A.S.T. Theorem, Pell's equation and continued fractions, the distribution of prime numbers, and advanced topics.
MAT 615: Modern Algebra. 3 hours, 3 credits. (May not be taken for credit by non-education students.)Modern algebraic techniques with a view to applications of solvability of equations, geometric problems, and number theoretic problems. An emphasis will be placed on extensive examples and illustrations. PREREQ: An undergraduate course in modern algebra or Departmental permission.
*MAT 616: Algebra. 4 hours, 4 credits. Group theory, including finitely generated Abelian groups, Sylow's theorem(s), simple groups, solvable groups. Ring theory, including integral domains, Euclidean rings. Field theory, including finite field extensions, Galois theory. PREREQ: One course in modern algebra.
MAT 630: Basic Concepts of Geometry. 3 hours, 3 credits. Elementary geometry from an advanced standpoint.
MAT 634: Introduction to Geometries. 3 hours, 3 credits. Geometry as the study of properties deduced from a set of axioms. Brief introduction to non-Euclidean geometrics, synthetic projective geometry. Geometry as the study of invariants of a transformation group: analytic projective geometry and its subgeometries. PREREQ: Elements of linear algebra.
MAT 636: Non-Euclidean Geometrics. 4 hours, 4 credits. Hyperbolic and elliptic geometry, with some trigonometry and calculus; circular models of the hyperbolic and elliptic planes; surfaces of constant curvature; and historical background of attempts to prove Euclid's parallel postulate. Spherical Geometry and Great Circles.
MAT 637: Topics in Discrete Mathematics. 60 hours, 4 credits. Topics chosen from: probability, combinatorics, decision making, game theory, graph theory, recurrence relations, linear programming, statistical inference, probability. Problem solving using mathematical modeling. PREREQ: Two semesters of calculus.
MAT 640: Topology and Analysis I. 3 hours, 3 credits. (May not be taken for credit by noneducation students.) Basic topics in continuity, compactness, and connectedness. Applications to simply stated but not trivial topological problems related to the geometry of mappings of segments, curves, circles, and disks. PREREQ: One semester of advanced calculus or instructor's permission.
*MAT 641: Topology and Analysis II. 3 hours, 3 credits. (May not be taken for credit by noneducation students.) Continuation of the study of continuity, compactness, and connectedness with applications to n-dimensional Euclidean space. PREREQ: MAT 640 (Topology and Analysis I).
MAT 655: Exploring Mathematics Using Technology. 3 hours (15 lecture, 30 lab), 2 credits. Use of tools of technology (such as Computer Algebra systems and graphing calculators) to explore ideas, concepts, and techniques in various areas of mathematics, such as calculus and probability. PREREQ: Two semesters of calculus.
MAT 661: History of Mathematics. 4 hours, 4 credits. Historical development of mathematics through the calculus. The mathematics of Babylonian, Egyptian, Hindu, Greek, Arabic, Inca, and Chinese civilizations; some modern developments; contributions of diverse cultures; applications to secondary school teaching.
MAT 670: Foundations of Mathematics. 3 hours, 3 credits. Sets, logic, nature of mathematical proof, and number systems.
MAT 681: Probability. 4 hours, 4 credits. Probability models, combinatorial problems, random variables, expectation and variance, binomial, normal and Poisson variables, law of large numbers, central-limit theorem, markov chains, and selected additional topics.
MAT 711: Topics in Algebra. 4 hours, 4 credits. Topics chosen from: semigroups with operators, homomorphisms, ring and field extensions, modules and ideals, right and left vector spaces over division rings, linear transformations, and rings of linear transformations, Galois theory, matrix groups, nilpotent groups, centers, exponential maps, Lie algebras. PREREQ: One course each in linear and modern algebra.
*MAT 715: Advanced Linear Algebra. 4 hours, 4 credits. Vector spaces, linear transformations, bilinear quadratic forms, tensors, forms and wedge products, finite and infinite dimensional linear algebra, eigenvalues, eigenvectors, introduction to Hilbert Spaces and eigenfunctions, all studied from an abstract, proof-oriented approach. PREREQ: One course in linear algebra.
*MAT 719: Special Topics in Algebra. 3 hours, 3 credits. (May be reelected for credit as often as the topic changes.)
*MAT 733: Differential Geometry. 4 hours, 4 credits. Curves in E3, curvature, torsion, fundamental existence theorem for space curves, geometry of a surface, inverse and implicit function theorems, Gauss curvature, and Minimal Surfaces. PREREQ: One course each in advanced calculus and linear algebra.
MAT 734: Calculus on Manifolds. 4 hours, 4 credits. Inverse and Implicit Function Theorems, Manifolds, Differential Forms, Fubini's Theorem, Partition of Unity, Integration on Chains, Stokes' and Green's Theorems, and an introduction to Riemannian geometry. PREREQ: One course each in linear algebra and advanced calculus.
*MAT 739: Special Topics in Geometry. 3 hours, 3 credits. (May be reelected for credit as often as the topic changes.)
*MAT 741: Topology. 4 hours, 4 credits. Sets, functions, metric spaces, topological spaces, neighborhoods, continuity, homeomorphisms, connectedness, compactness, homotopy, fundamental group, universal covers, Invariance of Domain Theorem. PREREQ: One course each in modern algebra and advanced calculus.
*MAT 742: General Topology. 3 hours, 3 credits. Topological spaces, continuous functions, separation, properties, induced topological structures, compactness, and metrization. PREREQ: MAT 741 (Topology) or equivalent.
*MAT 743: Algebraic Topology. 3 hours, 3 credits. Homology theory, complexes, and homotopy. Fixed-point theorems. PREREQ: MAT 741 (Topology) or equivalent, plus one course in modern algebra.
MAT 751: Theory of Functions of a Real Variable. 4 hours, 4 credits. Real number system, metric and Banach spaces; applications; the Lebesgue integral; measurable sets and functions; Lp spaces and Hilbert spaces; measure spaces and Daniell integral; Riemann-Stieltjes integral; Radon-Nikodym theorem; and Stone-Weierstrass theorem. PREREQ: A one semester course in advanced calculus.
MAT 753: Theory of Functions of a Complex Variable I. 4 hours, 4 credits. Algebra and geometry of complex numbers, analytic functions, Taylor and Laurent Series, Abel's Limit Theorem, meromorphic functions, residue calculus, Cauchy integral theorem and applications, classification of functions by singularities, analytic continuation, linear transformations, the cross ratio, conformal mapping, the Riemann Sphere. PREREQ: One semester of advanced calculus.
*MAT 754: Theory of Functions of a Complex Variable II. 3 hours, 3 credits. Selected topics in the theory of functions of a complex variable. PREREQ: One first course in complex variables.
MAT 755: Ordinary Differential Equations. 4 hours, 4 credits. First Order, Second Order, and Higher Order Linear Equations, Series Solutions, the Laplace Transform, Systems of First Order Linear Equations, Numerical Methods, Nonlinear Differential Equations and Stability, Existence and Uniqueness Theorems. PREREQ: One course each in linear algebra and advanced calculus.
MAT 756: Partial Differential Equations. 4 hours, 4 credits. First order equations and characteristics, Laplace's Equation, Green's functions, Heat Equation and Fundamental Solutions, Wave Equation and Domains of Dependence and Influence, Wave Propogation, Elliptic, Hyperbolic and Parabolic Equations, Maximum Principal, Existence and Uniqueness. PREREQ: One course each in linear algebra and advanced calculus.
MAT 759: Special Topics in Analysis. 3 hours, 3 credits. (May be reelected for credit as often as the topic changes.)
MAT 771: Mathematical Logic I. 4 hours, 4 credits. Development of the propositional calculus and the predicate calculus, with special emphasis on their mathematical aspects and applications. Semantics, axiom systems, and tableau systems will be presented, and Godel's completeness theorem will be proven .Further topics will be selected from computer implementation, model theory, and incompleteness/undecidability. PREREQ: One course in either modern algebra or set theory.
*MAT 772: Mathematical Logic II. 3 hours, 3 credits. Advanced topics in computability, first order theories, higher-order logics, semantics, model theory, set theory, analytic methods in proof theory, Gentzen systems, and cut elimination. PREREQ: MAT 771 (Mathematical Logic I).
MAT 775: Set Theory. 4 hours, 4 credits. Axiomatic approach to the theory of sets. Relations, functions, the axiom of choice, ordinal numbers, well-ordering, Zorn's lemma, cardinal numbers and transfinite arithmetic, transfinite induction. PREREQ: Any two courses chosen from linear algebra, modern algebra, or advanced calculus
MAT 782: Mathematical Statistics. 4 hours, 4 credits. Fundamental concepts of statistics. Point estimation, maximum likelihood estimators, hypothesis testing, confidence regions, t-test, analysis of variance, non-parametric tests, chi-square goodness-of-fit tests, correlation, regression analysis, and selected additional topics. PREREQ: A course in probability.
*MAT 785: Introduction to Applied Mathematics. 3 hours, 3 credits. Sets of orthogonal functions; Bessel's inequality, Parseval's theorem; Fourier series, convergence criteria; the Fourier integral; Laplace's equation, Bessel functions, Legendre functions, spherical harmonics; and calculus of variations. PREREQ: One course in advanced calculus.
*MAT 786: Computer Applications to Mathematics and Science I. 4 hours, including lab, 3 credits. Rapid introduction to high-level language, such as Fortran or PL/1. Use of scientific packages discussed. Projects on the College computer of a moderately advanced nature in scientific and mathematical fields will be tailored for the students. Some efficient techniques for these projects taught. PREREQ: Three courses in calculus or instructor's permission.
*MAT 787: Computer Applications to Mathematics and Science II. 4 hours, including lab, 3 credits. Study of areas where time and storage limitations are imposed on the programmer. Uses of trees and heaps in sorting, and data organization discussed. Off-line and on-line algorithms compared and investigated as to time versus space considerations. Optimization of mathematical calculations and methods, such as graph theory, fast arithmetic, and matrix manipulation presented. Students of the class shall determine more specific topics on the College computer. PREREQ: MAT 786 or instructor's permission.
MAT 789: Special Topics in Applied Mathematics. 3 hours, 3 credits. (May be reelected for credit as often as the topic changes.)
*Courses preceded by an asterisk are not expected to be offered in 2007-2009.
*CMP 605: BASIC and Computer Assisted Instruction. 3-4 hours, 3-4 credits. Introduction to programming in BASIC on a microcomputer. Standard methods of computer-assisted instruction: drills, tests, tutorials, and demonstrations. Management topics such as scorekeeping and record-keeping. Examples will be taken from a cross-section of disciplines. PREREQ: This course is intended for teachers with little or no programming background. No particular math background is required. Note: Students taking this course for 4 credits will be required to do an extra major project.
*CMP 607: LOGO and Computer Assisted Instruction. 3-4 hours, 3-4 credits. Introduction to programming in LOGO on a microcomputer. LOGO graphics techniques. Standard methods of computer-assisted instruction: drills, tests, tutorials, and demonstrations. Discovery approach to geometry. PREREQ: This course is intended for teachers with little or no programming background. No particular math background is required. Note: Students taking this course for 4 credits will be required to do an extra major project.
*CMP 609: Programming in Pascal. 4 hours, 4 credits. An intensive introductory course in structured programming using the language Pascal on microcomputers. This course is intended for people wishing to teach Pascal at the high school level.
CMP 683: Numerical Analysis. 4 hours, 4 credits. Topics in numerical analysis chosen from number systems, error analysis, linear equations and matrices, differentiation and integration, nonlinear equations, interpolation and approximation, and ordinary and partial differential equations. PREREQ: Linear Algebra and one year of programming.
CMP 685: Computability Theory. 4 hours, 4 credits. Mathematical formulation of computability theory and abstract machine theory. Finite-state machines and Turing machines; Church's Thesis; recursive functions and recursively enumerable sets; unsolvability and the halting problem.
CMP 692: Programming Languages. 4 hours, 4 credits. A study of programming languages from abstract and concrete points of view. Syntax, semantics; data objects and typing; control structures; scope of names; storage classes; binding times; parameter passing, value, reference, name, value-replace; and procedures, side-effects, recursion, serial reusability, reentrancy. PREREQ: Assembly Language Programming.
CMP 695: Survey of Computer Hardware. 4 hours, 4 credits. A survey of currently available computer equipment, together with some historical context. CPU's, microcomputers, minicomputers, large computers, super computers. Computer architecture, hierarchical storage, virtual storage and relocation, caches. Peripheral devices, storage systems, I/O channels. Communication hardware.
CMP 697: Operating Systems. 4 hours, 4 credits. A study of the functions and implementation of operating systems for various sizes and types of computers. Processor, storage, and device management. Paging algorithms, thrashing. File systems, concurrency, deadlocking, semaphores, and synchronization. PREREQ: Assembly Language Programming.
CMP 717: Video Game Programming. 4 hours, 4 credits. General game architecture, asynchronous input, animated sprites, action oriented A.I., collision detection, scrolling, sound clips, 3D graphics. Student projects involving development of several video games, both individually and in teams. PREREQ: CMP 338 and a strong foundation in object-oriented programming techniques. PREREQ/COREQ: MAT 226 or its equivalent. NOTE: Students should expect to devote a great deal of time working both individually and in teams to produce several video games written in Java. This is a "Programming Intensive" course.
CMP 731: Systems Analysis and Design. 4 hours, 4 credits. Examination of the stages of a computer system life cycle with a structured approach: problem definition, feasibility study, analysis, design, implementation, and maintenance. Techniques employed include data flow diagrams, data dictionaries, system flowcharts, cost/benefit analysis, decision tables, Warnier/Orr diagrams, HIPO charts, PERT, and the critical path method.
CMP 737: Software Engineering. 4 hours, 4 credits. Structured coding techniques and coding style will be considered: single entry-single exit constructs, modularity (coupling, cohesion), data encapsulation, data abstraction, generic facilities, and type checking. Verification, validation, and testing techniques will be studied: static analysis, unit testing, input-output assertions, weakest precondition, structured induction, and symbolic execution.
CMP 738: Communicating Robots. 4 hours, 4 credits. Techniques and principles for building communicating robots; programming on resource-limited systems, designing communications protocols, and testing distributed algorithms. Project to involve building a robot to work/compete with other robots. PREREQ: CMP 338 or its equivalent.
CMP 743: Principles of Communications Networks. 4 hours, 4 credits. Digital and analog communication, system architectures and connection-oriented and connectionless service. The OSI model as a conceptual framework, and actual communication models and their protocols. Selected contemporary topics, such as communications security and the World Wide Web. PREREQ: A course in operating systems.
CMP 747: Linear Programming and Operations Research. 4 hours, 4 credits. Theory and application of linear techniques. Convex sets and polyhedrons. The simplex method and the revised simplex method. Procedures to handle degeneracy. Duality theory and the dual simplex method. Elements of inventory and queueing theory. Industrial applications in scheduling and production control. Khachian's algorithm. PREREQ: One course in linear algebra.
CMP 758: Data Base Systems. 4 hours, 4 credits. Introduction to use and design of database systems. Topics include: levels of extraction and views of data; data models, entity relationship, hierarchical, network, and relational data organization; data dependencies, normal forms; design algorithms; distributed data bases; query languages.
CMP 761: Analysis of Algorithms. 4 hours, 4 credits. Techniques for the design and comparison of algorithms. Several models of computation will be considered. Topics chosen from: searching and sorting algorithms, algorithms on graphs, products involving polynomials and matrices, arithmetic complexity, fast Fourier transform, and NP-complete problems. PREREQ: A course in linear algebra and a course in data structures.
CMP 762: Automata Theory. 4 hours, 4 credits. Finite automata and related devices, the Chomsky hierarchy of formal grammars, equivalence of generative grammar characterizations of languages with recognition by restricted classes of machines, normal forms, computational complexity, intractable problems.
CMP 765: Artificial Intelligence. 4 hours, 4 credits. Topics in artificial intelligence from the areas of problem solving, pattern recognition, speech recognition, and natural language processing. Representations and search methods in artificial intelligence. Computer implementation. PREREQ: A course in data structures.
CMP 767: Computer Graphics. 4 hours, 4 credits. Theory and applications of computer graphics. Graphics devices, line and circle drawing algorithms, two-dimensional transformations, clipping and windowing, interactive devices such as light pens and graphics tablets, three-dimensional graphics. PREREQ: A course in linear algebra and one year of programming in a high-level language.
CMP 768: Simulation and Modeling. 4 hours, 4 credits. An introduction to continuous and discrete simulation. System modeling, probabilistic methods, simulation languages. Simulation examples from science, industry, and computer systems. PREREQ: One course in data structures.
CMP 770: Compiler Construction. 4 hours, 4 credits. Modern techniques of compiler design and construction. Topics from Lexical analysis, preprocessing. Grammars and their specifications, parsing techniques. General considerations about top-down and bottom-up parsers. Recursive descent, predictive parsing. LALR (1) grammars and parsers. Error recovery. Intermediate languages and intermediate code generation. Optimization techniques, flow analysis, value numbering, constant propagation, linear test replacement, hoisting, dead-code elimination. Storage mapping, register coloring, spilling. Code generation. PREREQ: Data structures.
CMP 773: Image Processing. 4 hours, 4 credits. Image representation and display. Histograms, point, algebraic, and geometric operations on the image. Image compression. Edge detection. Measurement and classification of images. An introduction to three-dimensional image processing. PREREQ: A course in linear algebra.
CMP 774: Ecommerce Technologies. 4 hours, 4 credits. Advanced Java enabling technologies for developing distributed Ecommerce applications. Topics to include: Introduction to J2EE, Remote Method Invocations (R.M.I.), Java Server Page (J.S.P.), Servlet, Java Database Connectivity (J.D.B.C.), Java A.P.I.'s and tools for X.M.L. and X.S.L.T., Design Patterns and Architectural issues, and Case Studies. Discussion of Web services, including Simple Object Access Protocol (S.O.A.P.), Web Service Definition Language (W.S.D.L.), and Universal Description Discovery and Integration (U.D.D.I.), as well as building Web services based on the advanced Java technologies. PREREQ: Object Oriented Programming.
CMP 775: Combinatorial and Graph Algorithms. 4 hours, 4 credits. A study of some elementary and advanced combinatorial and graph algorithms, including dynamic programming, greedy methods, spanning and transversing graphs, shortest paths, maximum flow, matching and convex hulls. PREREQ: Course in data structures.
CMP 776: Parallel Algorithms and Architecture. 4 hours, 4 credits. Survey of parallel computer architecture and models of parallel computation. Design of parallel algorithms. Examples of specific parallel algorithms for searching and sorting and for numerical, algebraic, and combinatorial computations. PREREQ: A course in data structures.
CMP 788: Topics in Computer Science. 4 hours, 4 credits. (May be reelected for credit as the topic changes.) Advanced, in-depth studies of specialized topics of current interests in computer science. PREREQ: Dependent on topic (see instructor).
CMP 793: Independent Study. 1 hour, 1 credit (may be repeated up to a maximum of 3 credits). Program of individual study of various topics in computer science, under the guidance and supervision of a member of the Department. PREREQ: Graduate advisor's permission.
CMP 798: Independent Study in Computer Science. 4 hours, 4 credits. (May be reelected for credit with graduate adviser's permission.) Program of individual study of various topics in computer science, under the guidance and supervision of a member of the Department. PREREQ: Graduate adviser's written permission.
CMP 799: Master's Thesis Research. 4 hours, 4 credits. Preparation for the M.S. thesis under the guidance of a faculty thesis adviser. PREREQ: Permission of a faculty thesis adviser and the graduate adviser.
*Courses preceded by an asterisk are not expected to be offered in 2007-2009.
*MAT 792: Seminar. 3 hours, 3 credits. (To be taken in the final semester of the M.A. program.)Designed to give candidates for the M.A. an introduction to the methods and literature of mathematical research.
MAT 793: Independent Study. 1 credit.(May be reelected for credit with the graduate adviser's permission.)Planned program of individual study of various topics in mathematics, under the guidance and supervision of a member of the Department. PREREQ: Graduate adviser's written permission.
MAT 794: Independent Study. 1 credit. (May be reelected for credit with the graduate adviser's permission.) Planned program of individual study of topics in mathematics, under the guidance and supervision of a member of the Department. PREREQ: Adviser's written permission.
MAT 795: Independent Study. 2 credits. (May be reelected for credit with graduate adviser's permission.) Planned program of individual study of topics in mathematics, under the guidance and supervision of a member of the Department. PREREQ: Adviser's written permission.
MAT 796: Independent Study. 2 credits. (May be reelected for credit with graduate adviser's permission.) Planned program of individual study of various topics in mathematics, under the guidance and supervision of a member of the Department. PREREQ. Adviser's written permission.
MAT 797: Independent Study. 3 credits. (May be reelected for credit with graduate adviser's permission.) Planned program of individual study of various topics in mathematics, under the guidance and supervision of a member of the Department. PREREQ: Graduate adviser's permission.
MAT 798: Independent Study. 3 credits. (May be reelected for credit with graduate adviser's permission.) Planned program of individual study of various topics in mathematics, under the guidance and supervision of a member of the Department. PREREQ: Graduate adviser's permission.