Department of
MATHEMATICS

COLLEGE OF ARTS AND SCIENCES

Departmental Programs

The Department of Mathematics offers bachelors, masters and doctoral degrees. At the undergraduate level there are degree programs in mathematics and actuarial science. (See also "Program in Actuarial Science," this General Bulletin .) Within the degree program in mathematics there are degree options in mathematics and applied mathematics.

State of Florida Common Course Prerequisites

The State of Florida has identified common course prerequisites for these University degree programs. These prerequisites are lower-level courses that are required for preparation for the University major prior to a student receiving a baccalaureate degree from The Florida State University. They may be taken either at a community college or in a university lower-division program. It is preferred that these common course prerequisites be completed in the freshman and sophomore years.
The following lists the common course prerequisites or approved substitutions necessary for each degree program:

Mathematics

1. Three (3) semester hours of COP XXXX (computer language: Pascal, FORTRAN, C, C+, or C++);
   
2. MAC X311;
   
3. MAC X312;
   
4. MAC X313;
   
5. Successful completion of two laboratory-based science courses for respective science majors: BSC XXXX/XXXXL or CHM XXXX/XXXXL or PHY XXXX/XXXXL.
   

Actuarial Science

1. Three (3) Semester hours of COP XXXX (computer language: FORTRAN, C, C+, C++, or Pascal)
   
2. MAC X311;
   
3. MAC X312;
   
4. MAC X313;
   
5. ECO X013 and ECO X023.
   

Students are encouraged to complete the courses ACG X021, MAP X302 and STA X122 in their first two years.
A grade of "C-" or better is required in all courses to be counted towards the degrees.

Requirements

Please review all college-wide degree requirements summarized in the "College of Arts and Sciences" section of this General Bulletin .
The bachelor of arts (BA) degree in mathematics or actuarial science can be obtained by completion of the bachelor of science (BS) degree requirements plus additional courses required by the University as set forth in the "Undergraduate Degree Requirements" section of this General Bulletin .
Students are strongly encouraged to complete MAC 2311 and two other courses listed as State of Florida Common Course Prerequisites for the appropriate program before applying for the major.
Students should complete the State of Florida Common Course Prerequisites, including the physics and economics requirements, during the first two college years. Students who expect to transfer to pursue the degree program in actuarial science at The Florida State University after one or more years at another college should note the advisability of completing any possible courses equivalent to: ACG X021, STA X122, MAP X302.
A directed program different from those listed below may be followed by a student with a specialized objective in mathematics, provided that the program is advocated by the student's faculty advisor and approved by the chair of the department before the student has enrolled in any 4000-level courses.
A student who expects to continue on to doctoral work in mathematics is encouraged to complete the foreign language requirement in French, German, or Russian.
Mathematics courses at the 4000-level applied toward the mathematics, applied mathematics, or actuarial science major must be taken at The Florida State University unless specifically exempted by the chair on written request.

Second Majors

A student may complete majors in mathematics and actuarial science or in applied mathematics and actuarial science by completing all of the prerequisite and degree requirements for each selected program.

Academic Performance

A grade of "C-" or better is required in all courses to be counted toward these degrees. A student who has accumulated more than five grades below "C-" (including grades of U) in mathematics or computer science courses taken for college credit at The Florida State University or elsewhere, whether repeated or not, will not be permitted to continue as a major in the department.

Baccalaureate Degree in Mathematics

Courses required for both degree options in mathematics are MAS 3105, STA 4442, and a course that exhibits proficiency in a scientific computer programming language. Courses in C, C++, FORTRAN, or PASCAL will provide this background. Successful completion of MAD 3703 will also suffice.
Major in Mathematics. In addition to the State of Florida Common Course Prerequisites and the courses above, the student will complete PHY 2048C or some other approved calculus-based natural or social science course and will complete the courses MAP 2302; MGF 3301; MAS 4302; MAA 4224 or 4226; and three of the following, of which at least two must be at the 4000 level: MAA 4227, 4402; MAD 2104, 3105, 3703, 4704; MAP 4103, 4153, 4180, 4202, 4216, 4331, 4341, 4342; MAS 4106, 4203, 4303; MAT 4934; MHF 4302, 4303; MTG 4302, 4303. At least one of the sequences following, or an approved substitution, must be included: MAA 4226-4227, MAD 3703-4704, MAP 4341-4342, MAS 4302-4303 and MTG 4302-4303 must be completed. The course CGS 3410 is recommended.
A student intending to do graduate work in pure mathematics should take MAA 4227 and MAS 4303. MAA 4402 and MTG 4302 are also recommended.
Major in Applied Mathematics. In addition to the State of Florida Common Course Prerequisites and the courses above, the student will complete PHY 2048C (PHY 2049C is highly recommended) and the courses MAD 3703; MAP 2302, 4103 and 4341; CGS 3410; and three of the following: MAA 4224 or 4226, 4227, 4402; MAD 4704; MAP 4153, 4180, 4202, 4216, 4331, 4342; MAS 4106; MAT 4934.

Baccalaureate Degree in Actuarial Science

In addition to the State of Florida Common Course Prerequisites, there are interdisciplinary degree requirements. The student should obtain information about updates in program requirements from the academic advisor in the Department of Mathematics. This assures the best preparation in this professional program by allowing for a timely response to recommendations of the actuarial professional societies. Representative requirements include: MAS 3105; MAP 4170, 4175; STA 4322 and 4442; STA 4203 or 4853; actuarial tutorials; and three of the following: MAA 4224 or 4226; MAD 3703; MAP 2302, 4341; MAS 4106; MAD 2104 or MGF 3301; STA 2122. The student must also take the following courses in business and economics: ACG 2021, FIN 3403 and 4504, RMI 3011; also required are at least two of the following courses: ECO 4101, 4401, 4421; RMI 4115, 4135, 4224, 4292; FIN 4514. These courses will satisfy the requirements for a minor in business.

Honors in the Major

The Department of Mathematics offers honors in the major designed to introduce the student to the process of independent and original research. For requirements and other information, see the "University Honors Program and Honor Societies" section of this General Bulletin .

Minor

Information concerning acceptable minors is available from the departmental office. The required computer science, physics, and statistics courses are collateral and may be counted toward a minor in the appropriate department.

Requirements for a Minor in Mathematics

A minor in mathematics consists of twelve (12) semester hours in courses with prefixes MAA, MAC, MAD, MAP, MAS, MAT, MGF, MHF, MTG, but not including any of the courses MAC 1XXX, 2233 or MGF 1XXX. A grade of "C-" or better must be earned in each course counted toward the minor.

Prerequisite Courses

Before taking any mathematics course, the student must complete with a grade of "C-" or better each course prerequisite to that course.Moreover, a student who earns a "C-" or better in a course with one or more stated or implied prerequisites may not subsequently earn credit in the prerequisite course(s). For example, a student who has earned a "C-" or better in MAC 2312 may not subsequently enroll in MAC 1105, 1114, 1140, or 2311.
Credit Note 1. In exception to the preceding paragraph, a transfer student may take MAC 1105 for credit even though the student has a "C-"or better in a transfer course that has been equated to a course for which MAC 1105 is prerequisite, provided the student has taken the AMP (Advanced Mathematics Placement) test and has not yet satisfied the Area I liberal studies requirement in mathematics.
Credit Note 2. In cases in which a student has earned a "D+", "D", or "D-" in a course and subsequently takes a similar course at the same level, the hours toward graduation for the first course will be disallowed as soon as the student passes the second course. These cases are: MAC 2233 after MAC 2311; MAC 2311 after MAC 2233; MAC 1141 after MAC 1140; MAC 1140 after MAC 1141.

Definition of Prefixes

MAA - Mathematics: Analysis
MAC - Mathematics: Calculus/Precalculus
MAD - Mathematics: Discrete
MAE - Mathematics: Education
MAP - Mathematics: Applied
MAS - Mathematics: Algebraic Structures
MAT - Mathematics
MGF - Mathematics: General/Finite
MHF - Mathematics: History/Foundations
MTG - Mathematics: Topology and Geometry
OCP - Oceanography: Physical

Undergraduate Courses

ISC 3121. Science, Technology, and Society (3).
and
SCE 4939r . Seminar in Contemporary Science, Mathematics, and Science Education (1).
Note: For descriptions of the above courses see interdisciplinary science courses in the "College of Arts and Sciences" section of this General Bulletin .
MAC 1105. College Algebra (3). Recommended background: two years of high school algebra. On basis of test scores the student may be required to take a community college course before MAC 1105. Review of algebraic operations, equations and inequalities; functions and functional notation; graphs; inverse functions; linear, quadratic, rational function; absolute value; radicals; exponential and logarithmic functions; system of equations and inequalities; applications.
MAC 1114. Analytic Trigonometry (2). Prerequisite: MAC 1105. Trigonometric functions, inverse trigonometric functions and their graphs; identities and conditional equations; solution of triangles; trigonometric form of complex numbers; DeMoivres theorem and nth roots; introduction to plane vectors.
MAC 1140. Precalculus Algebra (3). Prerequisite: MAC 1105 or appropriate score on a mathematics placement examination. May be taken concurrently with MAC 1114. Credit must be reduced to two (2) hours for students having a grade of "C-" or better in MAC 1141. (See Credit Note 2 above.) Functions and graphs, with emphasis on higher degree polynomial, rational, exponential, and logarithmic functions; systems of equations; solution of linear systems, matrix methods, determinants; sequences and series, induction, and the binomial theorem. Applications, approximation, and methods of proof.
MAC 1147. Precalculus Algebra/Trigonometry (5). Prerequisite: MAC 1105 or appropriate score on a mathematics placement examination. Credit must be reduced to four (4) hours for students who took MAC 1141 and received a grade of "C-" or better. This is a one-semester course encompassing the topics of MAC 1140 (Precalculus Algebra) and MAC 1114 (Analytic Trigonometry). See the topics for MAC 1140 and MAC 1114 for the topics in MAC 1147.
MGF 1106. Mathematics for Liberal Arts I (3). Recommended background: two years of high school algebra. Course is not intended for students whose programs require precalculus or calculus courses. Set theory; symbolic logic; counting principles; permutations and combinations; probability; statistics; geometry; applications and history of mathematics.
MGF 1107. Mathematics for Liberal Arts II (3). Recommended background: two years of high school algebra. Topics will include financial mathematics; linear and exponential growth; numbers and number systems; history of mathematics; elementary number theory; voting techniques; graph theory; game theory; geometry; and computer applications.
MGF 1214. Environmental Mathematics (3). Recommended background: two years of high school algebra. An elementary introduction to mathematical models useful in understanding and solving environmental problems. The H.T. Odum energy diagrams for energy flows provide visual models that are translated into flow equations, which can then be solved by ordinary calculators.
MAC 2233. Calculus for Business (3). Prerequisites: Appropriate score on a mathematics placement examination or MAC 1105 or 1140 (or former course MAC 1141). Not open to students who have credit in MAC 2311 with a grade of "C-" or better. (See Credit Note 2 above.) Limits, continuity, first and higher derivatives, and the differential, with applications to graphing, rates of change, and optimization methods; techniques of integration and applications; introduction to multivariate calculus.
MAC 2311. Calculus with Analytic Geometry I (4). Prerequisites: MAC 1147, or MAC 1140 and 1114; or appropriate score on a mathematics placement examination. Polynomial, trigonometric, exponential and logarithmic functions; first and second derivatives and their interpretations; definition and interpretation of the integral; differentiation rules; implicit differentiation; applications of the derivative; antiderivatives; fundamental theorem of calculus. This course must must be taken for reduced credit by students with prior credit for college calculus.
MAC 2312. Calculus with Analytic Geometry II (4). Prerequisite: MAC 2311 or MAC 2483. or appropriate score on a mathematics placement examination. Techniques of integration; applications of integration; series and Taylor series; differential equations. This course must must be taken for reduced credit by students with prior credit for some of the content.
MAC 2313. Calculus with Analytic Geometry III (5). Prerequisite: MAC 2312. Functions of several variables and their graphical representations; vectors; partial derivatives and gradients; optimization; multiple integration; polar, spherical, and cylindrical coordinate systems; curves; vector fields; line integrals; flux integrals; divergence theorem and Stokes' theorem. This course must be taken for reduced credit by students with prior credit for some of the content; see or call department for details.
MAC 2483. Biocalculus (4). Prerequisites: MAC 1114, 1140. Functions as biological models; properties of functions; recurrence relations; sequences, convergence; exponential, logarithmic and trigonometric functions; definite and indefinite integrals; derivatives and partial derivatives; the chain rule and other rules for differentiation; fundamental theorem of calculus; continuous probability distributions, means and variances; biological applications.
MAD 2104. Discrete Mathematics I (3). Prerequisite: MAC 1140. Mathematical techniques of definition and proof, with application to discrete domains; formal logic; elementary combinatorics; digraphs and relations; graphs, trees, and multigraphs; applications.
MAP 2302. Ordinary Differential Equations (3). Prerequisite: MAC 2312. Not open to students having credit in MAP 3305. Differential equations of the first order, linear equations of the second, systems of first order equations, power series solutions, Laplace transforms, numerical methods.
MAD 3105. Discrete Mathematics II (3). Prerequisite: MAD 2104. Techniques of definition and logical argument as applied in several areas of discrete mathematics; counting techniques, permutations, combinations; recurrence relations, graph and network algorithms.
MAD 3107. Mathematics in Computing (5). Prerequisite: MAC 1140. Topics covered include: set theory, symbolic logic, partial functions, algorithms, data types, binary and n-ary relations, recursion, mathematical proofs and mathematical induction.
MAD 3401. Introductory Numerical Analysis (3). Prerequisites: MAC 2312; competence in a programming language suitable for numeric computations. Polynomial interpolation, data fitting, solutions to nonlinear equations, numerical integration, and differentiation. Not open to mathematics majors.
MAD 3703. Numerical Analysis I (3). Prerequisites: MAC 2312; MAS 3105; FORTRAN or PASCAL or C. Root finding, interpolation and polynomial approximation, numerical differentiation and integration, direct and iterative methods for systems of linear equations.
MAP 3305. Engineering Mathematics I (3). Prerequisite: MAC 2313 or MAC 2312 with a grade of B or better. Not open to students having credit in MAP 2302. Ordinary differential equations, Laplace transform. Linear algebra: determinants, matrices, eigenvalues and eigenvectors. Systems of first-order differential equations.
MAP 3306. Engineering Mathematics II (3). Prerequisites: MAC 2313; MAP 2302 or 3305. Not open to students having credit in MAP 4341. Fourier series and Fourier transforms, solution of partial differential equations by separation of variables.
MAS 3105. Applied Linear Algebra I (4). Prerequisite: MAC 2312. Gaussian elimination, vector spaces, least squares problems, determinants, eigenvalues and eigenvectors, linear transformations, applications.
MAS 3301. Introduction to Modern Algebra (3). Prerequisites: MAC 2312; MAD 2104 or MAS 3105. Groups, permutations and symmetries, rings, integral domains, properties of the integers, fields and rational numbers. Mathematics majors must take MAS 4302 instead.
MAT 3711. Introduction to Symbolic Computation (3). Prerequisite: MAC 2312. Generalities of programs for symbolic computation; programming mathematics; elementary computer algebra: manipulating polynomials, Groebner bases; elementary computer analysis; integration techniques.
MAT 3930r. Special Topics in Mathematics (1-3). May be repeated to a maximum of twelve (12) semester hours.
MGF 3301. Introduction to Advanced Mathematics (3). Prerequisite: MAC 2312. An introduction to the methods of mathematics through such a variety of classical and modern topics as set theory, algebra, real number topology and graph theory. Axioms and proofs will be emphasized throughout.
MAA 4224. Introduction to Analysis I (3). Prerequisites: MAC 2313; MAS 3105; MGF 3301. A rigorous treatment of elementary calculus. Topics include the completeness of the real numbers, sequences and series, limits and continuity, derivatives, integrals, the Fundamental Theorem of Calculus, and sequences and series of functions.
MAA 4226, 4227. Advanced Calculus I, II (3, 3). Prerequisites: MAC 2313; MAS 3105; MGF 3301. Functions, sequences, limits; continuity, uniform continuity; differentiation; integration; convergence, uniform convergence. For strong students with advisor approval only.
MAA 4402. Complex Variables (3). Prerequisite: MAC 2313. Analytic functions, Cauchy-Riemann conditions; complex integration, Cauchys theorem and integral formula; power series, analytic continuation, Riemann surfaces; residues and applications; conformal mapping.
MAD 4704. Numerical Analysis II (3). Prerequisites: MAD 3703; MAP 2302. Approximation theory, numerical solution of nonlinear systems, boundary value problems and initial value problems for ordinary differential equations.
MAE 4813. Number Systems (4). Principles and operations related to finite and infinite subsets of the real numbers are investigated, compared, and contrasted with an emphasis on understanding. Open to preservice or in-service teachers only.
MAE 4815. Elements of Algebra (3). The algebra of sets and the algebra of real numbers are studied. Concepts rather than rote manipulations are emphasized. Open to prospective teachers or to in-service teachers only.
MAE 4816. Elements of Geometry (3). A variety of traditional and innovative geometric topics are explored via a hands on approach. Topics include congruence, similarity, Pythagorean triples, and areas of curvilinear figures. Open to teachers or to prospective teachers only.
MAE 4874. Fundamental Principles of Algebra (2). Prerequisite: A 2000 level course in mathematics or two years experience in teaching secondary school mathematics. Not open to students majoring in mathematics.
MAE 4878. Introduction to Applications of Mathematics for Teachers (2). Prerequisite: A 2000 level course in mathematics or two years experience in teaching high school mathematics. Not open to students majoring in mathematics.
MAP 4103. Mathematical Modeling (3). (S/U grade only.) Prerequisites: MAP 2302; MAS 3105; PHY 2048C. Application of mathematics to real life situations, construction of mathematical models, use of elementary and advanced mathematical methods, and case studies.
MAP 4153. Vector Calculus with Introduction to Tensors (3). Prerequisite: MAC 2313. Vector calculus: gradient, divergence, curl; differential operators in orthogonal curvilinear coordinates. Line, surface, and volume integrals; Stokes and Greens theorems. Subscript notation, Cartesian tensors; applications.
MAP 4170. Introduction to Actuarial Mathematics (4). Corequisites: MAC 2313; STA 4442. Amount function, dollar-weighted and time-weighted rates, force of interest; special annuity types, bonds, capitalization and applications. Survival theory: force of mortality and death curve, analytical functions of mortality, contingent payments; continuous and discrete single premium models.
MAP 4175. Actuarial Models (4). Prerequisites: MAP 4170; recommended: STA 4322. Survival probabilities; mortality laws, table construction, and contingent payments and annuities; premium principles and reserves for continuous, discrete and semi-continuous insurance products; multiple decrement theory (competing risks) and application to pension plans; pricing and nonforfeiture models.
MAP 4180. Game Theory and Applications (3). Prerequisites: MAC 2313; MAS 3105; MAP 2302; STA 4442. Solution concepts for noncooperative games. Nash equilibrium. Selection criteria. Evolutionary stable strategies. Cooperative games in strategic form. Characteristic function games. The prisoners dilemma. Applications.
MAP 4202. Optimization (3). Prerequisites: MAC 2313; MAD 3703; MAS 3105. Linear programming, unconstrained optimization, searching strategies, equality and inequality constrained problems.
MAP 4216. Calculus of Variations (3). Prerequisites: MAP 2302; MAA 4226. Fundamental problems, weak and strong extrema, necessary and sufficient conditions, Hamilton-Jacobi theory, dynamic programming, control theory and Pontryagins maximum principle.
MAP 4341. Elementary Partial Differential Equations I (3). Prerequisites: MAC 2313; MAP 2302 or 3305. Separation of variables, Fourier Series, Sturm-Liouville problems, multidimensional initial boundary value problems, nonhomogeneous problems, Bessel functions and Legendre polynomials.
MAP 4342. Elementary Partial Differential Equations II (3). Prerequisite: MAP 4341. Solution of first-order quasi-linear partial differential equations, classification and reduction to normal form of linear second-order equations, Greens function, infinite domain problems, the wave equation, radiation condition, spherical harmonics.
MAS 4106. Applied Linear Algebra II (3). Prerequisites: MAC 2313; MAS 3105. Positive definite matrices, matrix computation, linear programming and game theory. Applications.
MAS 4203. Theory of Numbers (3). Prerequisite: MAS 3301 or 4302; or consent of the instructor. The Euclidean algorithm; congruencies, quadratic residues, the law of quadratic reciprocity, and an elementary discussion of arithmetic functions and distribution of primes.
MAS 4302, 4303. Introduction to Abstract Algebra I, II (3, 3). Prerequisite: MAS 3105; MGF 3301. Groups, permutation groups, subgroups, group homomorphisms, structure of groups, rings, ideals, ring homomorphisms, rings of quotients, polynomials, factorization, fields, field extensions.
MAT 4906r. Directed Individual Study (1-4). May be repeated to a maximum of twelve (12) semester hours.
MAT 4931r. Special Topics in Mathematics (1-3). May be repeated to a maximum of six (6) semester hours when subject matter changes.
MAT 4934r. Honors Work (3). May be repeated to a maximum of nine (9) semester hours.
MAT 4945r. Internship in Actuarial Science (1-3). (S/U grade only.) Prerequisite: Instructor approval. Supervised internships individually assigned to accommodate students professional development in the actuarial field. May be repeated for a maximum of three (3) semester hours.
MHF 4302. Mathematical Logic I (3). Prerequisite: MAS 3301 or consent of instructor. Propositional and predicate logic, models. Godels completeness theorem and related theorems.
MTG 4212. College Geometry (3). Prerequisites: MAC 2312; MAS 3105. Fundamental topics in geometry from an advanced viewpoint, primarily designed for teachers and prospective teachers of mathematics.
MTG 4302. Elementary Topology I (3). Prerequisites: MAC 2313; MGF 3301. Topological spaces, metric spaces, connectedness, compactness, separation properties, topology of the plane, product spaces.
MTG 4303. Elementary Topology II (3). Prerequisite: MTG 4302. Function spaces, Hilbert space, quotient spaces, continua, paracompactness and metrizability, nets and filters, the fundamental group.

Graduate Courses

MAA 5306, 5307. Advanced Calculus I, II (3, 3).
MAA 5406, 5407. Theory of Functions of a Complex Variable I, II (3, 3).
MAA 5506. Functional Analysis I (3).
MAA 5616, 5617. Measure and Integration I, II (3, 3).
MAD 5305. Graph Theory (3).
MAD 5420. Numerical Optimization (3).
MAD 5708. Numerical Analysis II (3).
MAD 5738, 5739. Numerical Solution of Partial Differential Equations I, II (3, 3).
MAD 5745. Spectral Methods for Partial Differential Equations (3).
MAD 5757. High Order Finite Difference Methods for Computational Acoustics and Fluid Dynamics (3).
MAP 5177. Actuarial Models (3).
MAP 5207. Optimization (3).
MAP 5217. Calculus of Variations (3).
MAP 5345. Elementary Partial Differential Equations I (3).
MAP 5346. Elementary Partial Differential Equations II (3).
MAP 5395. Finite Element Methods (3).
MAP 5423. Complex Variables, Asymptotic Expansions, and Integral Transforms (3).
MAP 5431. Introduction to Fluid Dynamics (3).
MAP 5441. Perturbation Theory (3).
MAP 5485. Introduction to Mathematical Biophysics (3).
MAP 5486. Mathematical Bioeconomics (3).
MAP 5512. Hydrodynamic Stability (3).
MAP 5513. Wave Propagation Theory (3).
MAP 5601. Introduction to Financial Mathematics (3).
MAP 5611. Introduction to Computational Finance (3).
MAS 5307, 5308. Groups, Rings, and Vector Spaces I, II (3, 3).
MAS 5311, 5312. Abstract Algebra I, II (3, 3).
MAS 5331r, 5332r. Algebraic Structures I, II (3, 3).
MAT 5907r. Directed Individual Study (1-4). (S/U grade only.)
MAT 5911r. Supervised Research (1-9). (S/U grade only.)
MAT 5920r. Colloquium (0). (S/U grade only.)
MAT 5932r. Selected Topics in Mathematics (1-3).
MAT 5941. Internship in College Teaching (1-3). (S/U grade only.)
MAT 5945r. Internship in Financial Mathematics (1-3). (S/U grade only.)
MAT 5946r. Supervised Teaching (1-9). (S/U grade only.)
MHF 5206. Foundations of Mathematics (3).
MHF 5306. Mathematical Logic I (3).
MHF 5307. Mathematical Logic II (3).
MTG 5326, 5327. Topology I, II (3, 3).
MTG 5346, 5347. Algebraic Topology I, II (3, 3).
MTG 5376r. Topological Structures I (3).
OCP 5253. Fluid Dynamics: Geophysical Applications (3).
MAA 6416r. Advanced Topics in Analysis (3).
MAA 6939r. Advanced Seminar in Analysis (1). (S/U grade only.)
MAD 6408r. Advanced Topics in Numerical Analysis (3).
MAD 6939r. Advanced Seminar in Scientific Computing (1). (S/U grade only.)
MAP 6316r. Advanced Topics in Differential Equations (3).
MAP 6434r. Advanced Topics in Hydrodynamics (3).
MAP 6437r. Advanced Topics in Applied Mathematics (3).
MAP 6939r. Advanced Seminar in Applied Mathematics (1). (S/U grade only.)
MAS 6396r, 6397r. Advanced Topics in Algebra I, II (3, 3).
MAS 6939r. Advanced Seminar in Algebra (1). (S/U grade only.)
MAT 6908r. Directed Individual Study (1-4). (S/U grade only.)
MTG 6396r. Advanced Topics in Topology (3).
MTG 6939r. Advanced Seminar in Topology (1). (S/U grade only.)
For listings relating to graduate course work for thesis, dissertation, and masters and doctoral examinations and defense, consult the Graduate Bulletin .

MATHEMATICS
EDUCATION:
see Curriculum and Instruction