## Department of

## Mathematics

### College of Arts and Sciences

**Web Page:** http://www.math.fsu.edu/

**Interim Chair:** Phillip Bowers; **Associate Chair: **Bellenot; **Associate Chair for Graduate Studies: **Bowers; **Director of Pure Mathematics:** Aldrovandi; **Director of Applied and Computational Mathematics: **Gallivan; **Director of Financial Mathematics:** Kercheval; **Director of Biomathematics: **Bertram; **Coordinator of Basic Mathematics: **Blackwelder; **Coordinator of Graduate Teaching Assistants: **Kirby;** Coordinator of Actuarial Science:** Paris; **Professors: **Aluffi, Bellenot, Bertram, Bowers, S., Cogan Fenley, Gallivan, Heil, Huckaba, Hurdal, Hussaini, Kercheval, Klassen, Mio, Muslimani, Nolder, Okten, Sussman, Tam, van Hoeij, Wang; **Associate Professors:** Agashe, Aldrovandi, Kim, Magnan, Oberlin, Petersen; **Assistant Professors:** Ballas, Bauer, Fahim, Jain, Lee, Moore, Reznikov, Vo, Zhu;** Research Associate in Mathematics:** Boyd; **Teaching Faculty III**: Blackwelder, Dodaro, Grigorian, Kirby, LeNoir, Paris, Wooland; **Teaching Faculty II:** Ewald, Harris; **Teaching Faculty I:** Hollingsworth, Maltby; **Professors Emeriti:** Blumsack, Bryant, Case, Gilmer, Heerema, Kopriva, Kreimer, Mesterton-Gibbons, Mott, Nichols, Quine, Summers, Wright; **Courtesy Professors: **Absil,** **Beaumont, Chen, Croicu, le Dimet, Erlebacher, M. Fenley, Fusaro, Gan, Gunzburger, Marcolli, Mascagni, Mathelin, Moorer, Navon, Peterson, Tabak, Tang, van Dooren, Xiaoqiang Wang

The Department of Mathematics (http://www.math.fsu.edu) offers programs of study leading to the Bachelor of Science (BS) and Bachelor of Arts (BA) degrees, the Master of Science (MS) and Master of Arts (MA) degrees, and the Doctor of Philosophy (PhD) degree. (For details of the master's and doctoral degrees, see the *Graduate Bulletin*.) A combined degree plan may be developed for a strong undergraduate, especially one entering with advanced credit. This allows a student to earn both a bachelor's and a master's degree in about five years. A degree in mathematics can be regarded as the central component of a liberal education, or as preparation for professional study in another field or mathematics graduate study. Students can also look forward to employment in an industrial or financial firm, a governmental agency, or teaching in a secondary, college, or university institution; the Actuarial Science program is professionally oriented toward the insurance and financial sectors.

The department has a widely recognized research faculty, all of whom teach undergraduate students. Under the direction of a faculty member, selected students may choose to pursue an individual research project under Honors in the Major. For all students, the University provides Internet access, course Web pages and communications, and access to a number of leading databases, including the Mathematical Review. The department operates its own network of computers and computer labs. Faculty and students in the department have access to a variety of mathematical software, which is used in courses and in research. For additional information, see the departmental Web site.

The department offers opportunities for its majors to participate in learning activities outside the classroom. The** Mathematics Society at Florida State University** provides a venue in which undergraduate students and faculty meet monthly to share interests and enjoy an accessible lecture by a faculty member or a distinguished visitor. **Future Seminole Actuaries** benefits from a first-rate professional relationship with actuarial employers; actuaries from government, insurance, and consulting firms often visit the department to describe the field and interview students for summer internships and employment. The students share experiences about summer internships and prepare for actuarial examinations; well-placed graduates of the program help current students. The department fields a team for the **William Lowell Putnam Examination**, a nationwide competition among mathematics students conducted annually by the Mathematical Association of America. A Fall seminar is held for students to become familiar with Putnam-style problems and to hone their skills at solving them. Each year, the national mathematics honorary society, **Pi Mu Epsilon**,** **inducts students of high academic achievement in mathematics. Founded nationally in 1914, Florida State University began the Florida Beta chapter in 1956. All of these activities offer opportunities to socialize while learning.

## Departmental Programs

There are five majors leading to the bachelor's degree: applied and computational mathematics, pure mathematics, biomathematics, mathematics/FSU-Teach, and actuarial science (please consult the "Program in Actuarial Science" section of this *General Bulletin*). In any of these majors, students who intend to pursue graduate work in higher mathematics are encouraged to include appropriate mathematics sequences. Under the direction of a faculty member, a student may pursue a flexible major program to fit particular interests or an individual research project under honors in the major.

## Combined BS/MS Degrees

This program in mathematics is built on the department's four majors at the graduate level: (pure) mathematics, applied and computational mathematics, biomathematics, and financial mathematics. With the sharpened focus of university experience, a student from any of the department's four undergraduate options might discover mathematical interests to pursue in any one of the graduate options.

This program allows the motivated and focused student in either the mathematics or the actuarial science program to complete credit hours that can apply to both a bachelor's and master's degree. The student can take up to twelve graduate credit hours as an undergraduate that can then be dual-counted towards a master's degree, if they are accepted to the graduate program. In order to be eligible, a student must have a 3.0 GPA and the proper prerequisites for the course they intend to take.

## 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 one grade below a "C–" (including grades of U) in the calculus sequence MAC 2311, MAC 2312, MAC 2313 at Florida State University or elsewhere, whether repeated or not, will not be permitted to continue as a major in the department. A student who has accumulated three or more grades below "C–" (including grades of U) in any mathematics course or collateral course taken for college credit at Florida State University or elsewhere, whether repeated or not, will not be permitted to continue as a major in the department. For all math majors, collateral courses include COP 3014 or ISC 3313, PHY 2048C, STA 4321. For biomathematics, it includes the collateral biology, chemistry, and physics courses. For actuarial science, it includes the collateral courses with prefixes ACG, ECO, FIN, RMI, or STA. For FSU-Teach, it includes the collateral coursework with prefixes BSC, HIS, MAT, RED, SMT, or TSL.

## Computer Skills Competency

All undergraduates at Florida State University must demonstrate basic computer skills competency prior to graduation. As necessary computer competency skills vary from discipline to discipline, each major determines the courses needed to satisfy this requirement. Undergraduate majors in actuarial science, applied mathematics, biomathematics, mathematics, and mathematics/FSU-Teach satisfy this requirement by earning a grade of "C–" or higher in COP 3014 or ISC 3313.

## State of Florida Common Program Prerequisites

The state of Florida has identified common program prerequisites for this University degree program. Specific prerequisites are required for admission into the upper-division program and **must** be completed by the student at either a community college or a state university prior to being admitted to this program.** Students may be admitted into the University without completing the prerequisites, but may not be admitted into the program.**

At the time this document was published, some common program prerequisites were being reviewed by the state of Florida and may have been revised. Please visit https://dlss.flvc.org/admin-tools/common-prerequisites-manuals for a current list of state-approved prerequisites.

The following lists the common program prerequisites or their substitutions, necessary for admission into these upper-division degree programs:

### Mathematics

- COP XXXX: one scientific programming course for three credit hours designed for computer science majors
- MAC X311
- MAC X312
- MAC X313
- BSC XXXX/XXXXL or CHM XXXX/XXXXL or GLY XXXX/XXXXL or PHY XXXX/XXXXL: one laboratory based science course for four credit hours designed for science majors
- MAP X302

**Note: **A "C" grade or better in all coursework is required for admission.

### Actuarial Science

- COP XXXX: one scientific programming course for three credit hours designed for computer science majors
- ECO X013
- ECO X023
- MAC X311
- MAC X312
- MAC X313

**Note: **A "C" grade or better in all coursework is required for admission.

### FSU-Teach Mathematics

- COP XXXX: one scientific programming course for three credit hours designed for computer science majors
- MAC X311
- MAC X312
- MAC X313
- BSC XXXX/XXXXL or CHM XXXX/XXXXL or PHY XXXX/XXXXL or GLY XXXX/XXXXL: one laboratory based science course for four credit hours designed for science majors
- MAP X302
- SMT X043
- SMT X053

**Note: **A "C" grade or better in all coursework is required for admission. Transfer students will be able to take SMT X043 and SMT X053 when admitted to upper division.

## Requirements

Please review all college-wide degree requirements summarized in the "College of Arts and Sciences" chapter of this *General Bulletin*. The student should also obtain, from the departmental office and Web site, revisions to the degree guidelines since this printing.

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" chapter of this *General Bulletin*.

Students should complete the state of Florida common program prerequisites, including the physics (all the Mathematics majors) or the economics (Actuarial Science majors) requirements, during the first two college years. Actuarial Science majors should also complete the accounting course during the first two college years. Note that all majors have a computing requirement that can be used as the computing prerequisite course, but not vice versa.

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 any departmental major must be taken at Florida State University unless specifically exempted by the chair on written request.

In order to obtain final graduation clearance from the Department of Mathematics, all majors must complete an exit survey.

## 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 Office and Honor Societies" chapter of this *General Bulletin*.

## FSU-Teach Program in Teaching Mathematics

For those interested in teaching mathematics, FSU-Teach is an innovative approach to teacher education that involves collaboration between scientists, mathematicians and education faculty at Florida State University. In FSU-Teach, students will develop deep science or mathematics knowledge and the knowledge, skill, and experience needed to be an effective science or math teacher. The program will pay for tuition for the first two courses, and work study positions with scientists, mathematicians and local schools are available. For more information, see our Web site: http://fsu-teach.fsu.edu/.

## Second Majors

Students may double major in actuarial science and any of the four mathematics majors (pure, applied/computational, biomedical or Math/FSU-Teach) by completing all of the prerequisite and degree requirements for each selected program. A student may also complete a second major in another department. The flexible plan major is particularly appropriate for students in other majors who seek deeper mathematics study, or students in mathematics who have interdisciplinary interests. Mathematics has no restrictions on the number of hours that can overlap with another major.

## Requirements for a Minor in Mathematics

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

## Baccalaureate Degree in Mathematics

Courses required for each of the degree options in mathematics are MAP 2302 and MAS 3105. The student must exhibit proficiency in a scientific computer programming language, and must also satisfy the University's computer skills competency requirement. Students will normally complete COP 3014 or ISC 3313 to satisfy both those requirements, although the former may be shown by courses in C, C++, FORTRAN, Java, or another approved higher-level language. STA 4321 is required. Representative requirements for the four mathematics major options follow. Students should refer to the departmental Web site (http://www.math.fsu.edu) or the departmental office (*208 LOV*) for the most current information.

**Major in Mathematics. **In addition to the state of Florida common program prerequisites and the courses above, the student will complete PHY 2048C and will complete the courses MAS 4302; MAA 4224 or 4226; and four 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, 4341, 4342; MAS 4106, 4203, 4303; MAT 4934; MGF 3301; MHF 4302; MTG 4302. At least one of the sequences following, or an approved substitution, must be included: MAA 4226-4227, MAA 4402 and MTG 4302, MAD 3703-4704, MAP 4341-4342, or MAS 4302-4303. Additional computer languages are recommended.

A student intending to do graduate work in pure mathematics should take MAA 4226-4227 and MAS 4302-4303 as well as MAA 4402 and MTG 4302.

**Major in Applied Mathematics. **In addition to the state of Florida common program prerequisites and the courses above, the student will complete PHY 2048C (PHY 2049C is highly recommended) and the courses MAD 3703; MAP 4103 and 4341; and three of the following: MAA 4224 or 4226, 4227, 4402; MAD 4704; MAP 4153, 4180, 4202, 4216, 4342; MAS 4106; MAT 4934.

**Major in Biomathematics. **This modern major can lead to employment in the area of biological applications, to medical school, or to graduate school in mathematical biology or the sciences. In addition to the state of Florida common program prerequisites, the student will complete collateral science courses including BSC 2010, 2010L, 2011; CHM 1045C, 1045L; PHY 2048C; and at least one upper-division course on a list of such courses, typically PCB 3063. No additional minor is required. MAP 2480 and MAP 4481 are required, along with additional elective requirements; students should consult the departmental office or the Web site for exact elective requirements.

**Major in Mathematics/FSU-Teach.** A new mathematics major for students in the FSU-Teach program. In addition to what was mentioned above (i.e. the state of Florida common program prerequisites, COP 3014, MAP 2302, MAS 3105, and STA 4321), the student will complete PHY 2048C and a course in each of four mathematical areas of Analysis, Algebra, Geometry and Modeling and two additional electives (one at the 3000 level or above). The courses acceptable for each mathematical area are: for Algebra: MAS 3301, MAS 4203 or MAS 4302; for Analysis: MAA 4402, MAA 4224 or MAA 4226; for Geometry: MTG 4212; for Modeling: MAP 4103, MAP 4175, MAP 4180 or MAP 4481; and for electives: MAA 4227, MAD 2104, MAD 3105, MAP 4170, MAP 4153, MAP 4202, MAP 4216, MAP 4341, MAS 4106, MAS 4303, MGF 3301, MHF 4302, MTG 4302 or additional courses from the Algebra, Analysis, Geometry, and/or Modeling groups. The FSU-Teach educational courses are a collateral major and can count as the minor for the Mathematics/FSU-Teach option.

**Note: **In order to obtain final graduation clearance from the Department of Mathematics, all majors must complete an exit survey.

## Baccalaureate Degree in Actuarial Science

In addition to the state of Florida common program prerequisites, there are interdisciplinary degree requirements. Representative requirements include: MAP 4170, 4175, COP 3014 or equivalent; and four repetitions of actuarial tutorial MAT 4930r. STA 4321 is required.

The student must also take the following courses in business and economics: ACG 2021; ECO 2013 or 3203, and ECO 2023 or 3101; FIN 3403 and 4504; RMI 3011. These courses satisfy the requirements for a minor in business, and no additional minor is required.

**Note: **For the most recent information concerning course requirements for this program, please refer to http://www.math.fsu.edu.

Additional requirements include a total of six courses from three course groups. Students must complete:

- Two courses chosen from MAP 2302, MAP 4176, and MAS 3105.
- At least one course chosen from MAA 4224, 4226, 4227; MAD 3703; MAP 4341; MAS 4106; STA 4203, 4322, 4853.
- At least one of the following courses: ECO 3101, 3203, 4401, 4421; FIN 4514; RMI 4115, 4135, 4224, 4292.

## Minor or Second Major

Information concerning acceptable minors and second majors for students majoring in a department program 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.

## 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.

**Credit Note 3. **Credit cannot be obtained for both MAD 2104 and MGF 3301.

## Definition of Prefixes

**MAA**—Mathematics: Analysis

**MAC**—Mathematics: Calculus and Precalculus

**MAD**—Mathematics: Discrete

**MAE**—Mathematics Education

**MAP**—Mathematics Applied

**MAS**—Mathematics: Algebraic Structures

**MAT**—Mathematics

**MGF**—Mathematics: General and Finite

**MHF**—Mathematics: History and Foundations

**MTG**—Mathematics: Topology and Geometry

**OCP**—Physical Oceanography

## Undergraduate Courses

**MAA ****4224. ****Introduction to Analysis I (3)**. Prerequisites: MAC 2313, MAS 3105, and prior experience with mathematical proofs (MGF 3301, MAD 2104 or other proving experience). Not open to students with credit in MAA 4226. This course is 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. Students intending graduate study in mathematics should take MAA 4226.

**MAA ****4226. ****Advanced Calculus I (3)**. Prerequisites: MAC 2313, MAS 3105, and prior experience with mathematical proofs (MGF 3301, MAD 2104 or other proving experience). This course covers functions, sequences, limits; continuity, uniform continuity; differentiation; integration; convergence, uniform convergence. For strong students with advisor approval only.

**MAA ****4227. ****Advanced Calculus II (3)**. Prerequisite: MAA 4226. This course is a continuation of MAA 4226.

**MAA ****4402. ****Complex Variables (3)**. Prerequisite: MAC 2313. This course covers analytic functions, Cauchy-Riemann conditions; complex integration, Cauchy's theorem and integral formula; power series, analytic continuation, Riemann surfaces; residues and applications; conformal mapping.

**MAA ****4934r. ****Topics in Analysis (1-3)**. Prerequisite: Instructor permission. Special topics course. May be repeated to a maximum of twelve semester hours. May be repeated within the same semester.

**MAC ****1105. ****College Algebra (3)**. Prerequisite: MAT 1033 with a grade of "C–" or better or a suitable mathematics examination placement score. Recommended background: two years of high school algebra. This course is a 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. On basis of test scores the student may be required to take a community college course before MAC 1105.

**MAC ****1114. ****Analytic Trigonometry (2)**. Prerequisite: MAC 1105. This course covers trigonometric functions, inverse trigonometric functions and their graphs; identities and conditional equations; solution of triangles; trigonometric form of complex numbers; DeMoivre's theorem and nth roots; introduction to plane vectors.

**MAC ****1140. ****Precalculus Algebra (3)**. Prerequisite: MAC 1105 or suitable mathematics examination placement score. This course covers functions and graphs, especially 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. The course also explores applications, approximation, and methods of proof. May be taken concurrently with MAC 1114.

**MAC ****1147. ****Precalculus Algebra/Trigonometry (5)**. Prerequisite: MAC 1105 or suitable mathematics examination placement score. This course 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.

**MAC ****2233. ****Calculus for Business (3)**. Prerequisite: MAC 1105. This course covers 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. Not open to students who have credit in MAC 2311 with a grade of "C–" or better.

**MAC ****2311. ****Calculus with Analytic Geometry I (4)**. Prerequisites: MAC 1147; or MAC 1140 and MAC 1114; or suitable mathematics examination placement score. This course covers 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; anti-derivatives; fundamental theorem of calculus. This course must be taken for reduced credit by students with prior credit for some of the content.

**MAC ****2312. ****Calculus with Analytic Geometry II (4)**. Prerequisite: MAC 2311 or suitable mathematics examination placement score. This course covers techniques of integration; applications of integration; series and Taylor series; differential equations. This course 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. This course covers 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.

**MAD ****2104. ****Discrete Mathematics I (3)**. Prerequisite: MAC 2311 or COP 3014 and MAC 1140. Recommended prerequisite: MAC 2311. This course covers techniques of definition and logical argument, sets and functions, propositional logic, introduction to graphs and relations, and applications. Mathematics majors should take MGF 3301 instead of MAD 2104.

**MAD ****3105. ****Discrete Mathematics II (3)**. Prerequisite: MAD 2104 or MGF 3301. Recommended prerequisite: MAC 2311. This course covers techniques of definition and logical argument, graphs and diagraphs, relations, Boolean algebra, and applications.

**MAD ****3703. ****Numerical Analysis I (3)**. Prerequisites: MAC 2312 with a grade of "B–" or better or MAC 2313 with a grade of "C–" or better, MAS 3105, and competence in a programming language suitable for numeric computations, such as C, C++, Fortran, Java, or Python. This course covers root finding, interpolation and polynomial approximation, numerical differentiation and integration, direct and iterative methods for systems of linear equations.

**MAD ****4704. ****Numerical Analysis II (3)**. Prerequisites: MAD 3703 and MAP 2302. This course covers approximation theory, numerical solution of nonlinear systems, boundary value problems and initial value problems for ordinary differential equations.

**MAD ****4934r. ****Topics in Discrete or Computational Mathematics (1–3)**. Prerequisite: Instructor permission. Special topics course. May be repeated to a maximum of twelve semester hours. May be repeated within the same semester.

**MAE ****4816. ****Elements of Geometry (3)**. This course explores a variety of traditional and innovative geometric topics via a hands on approach. Topics include congruence, similarity, Pythagorean triples, and areas of curvilinear figures. Not open to students majoring in mathematics.

**MAE ****4874. ****Fundamental Principles of Algebra (2)**. Prerequisites: A 2000-level course in mathematics or two years experience in teaching secondary school mathematics. This course is not open to students majoring in mathematics.

**MAP ****2302. ****Ordinary Differential Equations (3)**. Prerequisite: MAC 2312 with a grade of "B–" or better or MAC 2313 with a grade of "C–" or better. This course covers differential equations of the first order, linear equations of the second, systems of first order equations, power series solutions, Laplace transforms, numerical methods. Not open to students having credit in MAP 3305.

**MAP ****2480. ****Biocalculus Computer Laboratory (1)**. Prerequisite: MAC 2311. This computer laboratory applies calculus methods and mathematical programming software to assist students in solving problems from biology, medicine, and psychology.

**MAP ****3305. ****Engineering Mathematics I (3)**. Prerequisite: MAC 2313 or MAC 2312 with a grade of "B–" or better. This course covers ordinary differential equations, Laplace transform, and linear algebra: determinants, matrices, eigenvalues, and eigenvectors. Not open to students having credit in MAP 2302.

**MAP ****3306. ****Engineering Mathematics II (3)**. Prerequisites: MAC 2313 and MAP 2302 or MAP 3305. This course offers Fourier series and Fourier transforms, introduction to partial differential equations. Not open to students having credit in MAP 4341.

**MAP ****4103. ****Mathematical Modeling (3)**. (S/U grade only.) Prerequisites: MAC 2313, MAP 2302, MAS 3105, and PHY 2048C. This course covers the 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. This course covers vector calculus: gradient, divergence, curl; differential operators in orthogonal curvilinear coordinates; line, surface, and volume integrals; Stokes' and Green's theorems; subscript notation, Cartesian tensors; and applications.

**MAP ****4170. ****Introduction to Actuarial Mathematics (4)**. Prerequisite: MAC 2312. This course covers amount function, dollar-weighted and time-weighted rates, force of interest; special annuity types, bonds, capitalization, and applications. Yield curves, spot rates, forward rates, duration, convexity, and immunization and additional financial concepts.

**MAP ****4175. ****Actuarial Models (4)**. Prerequisites: MAP 4170 and STA 4321. This course covers single- and multiple-life survival analysis; mortality laws, deterministic methods, and contingent payments and annuities; premium principles and reserves for continuous, discrete, and semi-continuous insurance products; multiple decrement theory (competing risks) and applications.

**MAP ****4176. ****Advanced Actuarial Models, Credibility, and Simulation (4)**. Prerequisite: MAP 4175. This course covers claim frequency models, individual loss models, aggregate loss models, multiple-life and multiple-death decrement survival models, multiple-state transition models, credibility theory, and simulation.

**MAP ****4180. ****Game Theory and Applications (3)**. Prerequisites: MAC 2313, MAS 3105, MAP 2302, and STA 4321. This course covers 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, and MAS 3105. This course covers linear programming, unconstrained optimization, searching strategies, equality and inequality constrained problems.

**MAP ****4216. ****Calculus of Variations (3)**. Prerequisites: MAP 2302 and MAA 4226 or MAA 4224 or MAP 4341. This course covers 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 and MAP 2302 or MAP 3305. This course covers 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. This course covers solution of first-order quasi-linear partial differential equations, classification and reduction to normal form of linear second-order equations, Green's function, infinite domain problems, the wave equation, radiation condition, spherical harmonics.

**MAP ****4481. ****Mathematical Modeling in Biology (3)**. Prerequisite: MAC 2312. Recommended prerequisite: MAP 2480. This course is an introduction to the use of mathematical models in biology. Linear and nonlinear difference and ordinary differential equations, linear stability analysis, phase plane analysis. Applications may include population biology, infectious diseases, chemical kinetics, and physiology.

**MAP ****4934r. ****Topics in Applied Mathematics (1–3)**. Prerequisite: Instructor permission. Special topics course. May be repeated to a maximum of twelve semester hours. May be repeated within the same semester.

**MAS ****3105. ****Applied Linear Algebra I (4)**. Prerequisite: MAC 2312. This course covers Gaussian elimination, vector spaces, least squares problems, determinants, eigenvalues and eigenvectors, linear transformations, applications.

**MAS ****3301. ****Introduction to Modern Algebra (3)**. Prerequisites: MAC 2312 and MAS 3105. This course covers groups, permutations and symmetries, rings, integral domains, properties of the integers, fields and rational numbers. Mathematics majors other than FSU-Teach must take MAS 4302 instead.

**MAS ****4106. ****Applied Linear Algebra II (3)**. Prerequisites: MAC 2313 and MAS 3105. This course covers positive definite matrices, matrix computation, linear programming and game theory. Applications.

**MAS ****4203. ****Theory of Numbers (3)**. Prerequisites: MAS 3105 and prior experience with mathematical proofs (MGF 3301, MAD 2104, or other proving experience). This course covers the Euclidean algorithm; congruencies, quadratic residues, the law of quadratic reciprocity, and an elementary discussion of arithmetic functions and distribution of primes.

**MAS ****4302. ****Introduction to Abstract Algebra I (3)**. Prerequisites: MAS 3105 and prior experience with mathematical proofs (MGF 3301, MAD 2104 or other proving experience). This course covers groups, permutation groups, subgroups, group homomorphisms, structure of groups, rings, ideals, ring homomorphisms, rings of quotients, polynomials, factorization, fields, field extensions.

**MAS ****4303. ****Introduction to Abstract Algebra II (3)**. Prerequisite: MAS 4302. This course is a continuation of MAS 4302.

**MAS ****4934r. ****Topics in Algebra (1–3)**. Prerequisite: Instructor permission. Special topics course. May be repeated to a maximum of twelve semester hours. May be repeated within the same semester.

**MAT ****3503. ****Functions and Modeling (3)**. Prerequisite: MAC 2312. This course includes group and individual activities designed to strengthen knowledge of, and connections among, topics in secondary and college mathematics. Problem-solving; gathering and analyzing data; and modeling using linear, polynomial, and trigonometric functions, and parametric and polar equations are also explored. Students discuss and present work in class, and make use of various technologies.

**MAT ****3711. ****Introduction to Symbolic Computation (3)**. Prerequisite: MAC 2312. This course covers the 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 within the same term to a maximum of twelve semester hours.

**MAT ****4906r. ****Directed Individual Study (1–4)**. May be repeated within the same term to a maximum of thirty semester hours.

**MAT ****4930r. ****Special Topics in Mathematics (1–3)**. (S/U grade only.) May be repeated to a maximum of twelve semester hours.

**MAT ****4931r. ****Special Topics in Mathematics (1–3)**. May be repeated to a maximum of six semester hours when subject matter changes.

**MAT ****4934r. ****Honors Work (3)**. May be repeated to a maximum of nine semester hours.

**MAT ****4945r. ****Undergraduate Professional Internship (1–3)**. (S/U grade only.) Prerequisite: Instructor permission. This course is a supervised internship individually assigned to accommodate the student's professional development in an area of application (e.g., actuarial science; industrial applications). May be repeated to a maximum of three semester hours.

**MGF ****1106. ****Mathematics for Liberal Arts I (3)**. Prerequisite: MAT 1033 with a grade of "C–" or better or a suitable mathematics examination placement score. This course covers set theory; symbolic logic; counting principles; permutations and combinations; probability; statistics; geometry; applications and history of mathematics. Recommended background: two years of high school algebra. Course is not intended for students whose programs require precalculus or calculus courses.

**MGF ****1107. ****Topics in Practical Finite Mathematics (3)**. Prerequisites: MAT 1033 with a grade of "C–" or better or a suitable mathematics examination placement score. Recommended background: Two years of high school algebra. This course covers 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)**. This course is 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. Recommended background: two years of high school algebra.

**MGF ****3301. ****Introduction to Advanced Mathematics (3)**. Prerequisite: MAC 2312. This course is 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 are emphasized throughout. Not open to students who have received credit for MAD 2104.

**MHF ****4302. ****Mathematical Logic I (3)**. Prerequisite: MGF 3301 or instructor permission. This course covers propositional and predicate logic, models, as well as Godel's completeness theorem and related theorems.

**MTG ****4212. ****College Geometry (3)**. Prerequisites: MAC 2312 and MAS 3105. This course examines fundamental topics in geometry from an advanced viewpoint, primarily designed for teachers and prospective teachers of mathematics.

**MTG ****4302. ****Elementary Topology I (3)**. Prerequisite: MAC 2313 and prior experience with mathematical proofs (MGF 3301, MAD 2104 or other proving experience). This course examines topological spaces, metric spaces, connectedness, compactness, separation properties, topology of the plane, and product spaces.

**MTG ****4303. ****Elementary Topology II (3)**. Prerequisite: MTG 4302. This course examines function spaces, Hilbert space, quotient spaces, continua, paracompactness and metrizability, nets and filters, and the fundamental group.

**MTG ****4934r. ****Topics in Topology or Geometry (1–3)**. Prerequisite: Instructor permission. Special topics course. May be repeated to a maximum of twelve semester hours. May be repeated within the same semester.

## Graduate Courses

**MAA **** 5306. **Advanced Calculus I (3).

**MAA **** 5307. **Advanced Calculus II (3).

**MAA **** 5406. **Theory of Functions of a Complex Variable I (3).

**MAA **** 5407. **Theory of Functions of a Complex Variable II (3).

**MAA **** 5616. **Measure and Integration I (3).

**MAA **** 5617. **Measure and Integration II (3).

**MAA **** 5721. **Computer Analysis (3).

**MAA **** 5932. **Topics in Analysis (1–3).

**MAD **** 5305. **Graph Theory (3).

**MAD **** 5403. **Foundations of Computational Mathematics I (3).

**MAD **** 5404. **Foundations of Computational Mathematics II (3).

**MAD **** 5420. **Numerical Optimization (3).

**MAD **** 5427. **Numerical Optimal Control of Partial Differential Equations (3).

**MAD **** 5738. **Numerical Solution of Partial Differential Equations I (3).

**MAD **** 5739. **Numerical Solution of Partial Differential Equations II (3).

**MAD **** 5745. **Spectral Methods for Partial Differential Equations (3).

**MAD **** 5757. **High Order Finite Difference Methods for Computational Acoustics and Fluid Dynamics (3).

**MAD **** 5932r. **Topics in Computational Mathematics (1–3).

**MAP **** 5107. **Mathematical Modeling (3).

**MAP **** 5165. **Methods of Applied Mathematics I (3).

**MAP **** 5177. **Actuarial Models (3).

**MAP **** 5178. **Advanced Actuarial Models, Credibility, and Simulation (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. **Computational Methods in Biology (3).

**MAP **** 5513. **Wave Propagation Theory (3).

**MAP **** 5601. **Introduction to Financial Mathematics (3).

**MAP **** 5611. **Introduction to Computational Finance (3).

**MAP **** 5615. **Monte Carlo Methods in Financial Mathematics (3).

**MAP **** 5932r. **Topics in Applied Mathematics (1–3).

**MAS **** 5307. **Groups, Rings, and Vector Spaces I (3).

**MAS **** 5308. **Groups, Rings, and Vector Spaces II (3).

**MAS **** 5311. **Abstract Algebra I (3).

**MAS **** 5312. **Abstract Algebra II (3).

**MAS **** 5331r. **Algebraic Structures I (3).

**MAS **** 5332r. **Algebraic Structures II (3).

**MAS **** 5731. **Computer Algebra (3).

**MAS **** 5932r. **Topics in Algebra (1–3).

**MAT **** 5907r. **Directed Individual Study (1–4). (S/U grade only.)

**MAT **** 5911r. **Supervised Research (1–5). (S/U grade only.)

**MAT **** 5921r. **Graduate Mathematics Colloquium (1). (S/U grade only.)

**MAT **** 5932r. **Selected Advanced Topics (1–3).

**MAT **** 5933r. **Special Topics in Mathematics (1– 3). (S/U grade only.)

**MAT **** 5939. **Graduate Seminar (1).

**MAT **** 5941. **Internship in College Teaching (1–3). (S/U grade only.)

**MAT **** 5945r. **Graduate Professional Internship (1–3). (S/U grade only.)

**MAT **** 5946r. **Supervised Teaching (1–5). (S/U grade only.)

**MHF **** 5206. **Foundations of Mathematics (3).

**MHF **** 5306. **Mathematical Logic I (3).

**MTG **** 5326. **Topology I (3).

**MTG **** 5327. **Topology II (3).

**MTG **** 5346. **Algebraic Topology I (3).

**MTG **** 5347. **Algebraic Topology II (3).

**MTG **** 5376r. **Topological Structures I (3).

**MTG **** 5932r. **Topics in Geometry (1–3).

**OCP **** 5256. **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 **** 6434r. **Advanced Topics in Hydrodynamics (3).

**MAP **** 6437r. **Advanced Topics in Applied Mathematics (3).

**MAP **** 6621. **Financial Engineering I (3).

**MAP **** 6939r. **Advanced Seminar in Applied Mathematics (1). (S/U grade only.)

**MAS **** 6396r. **Advanced Topics in Algebra I (3).

**MAS **** 6939r. **Advanced Seminar in Algebra (1). (S/U grade only.)

**MAT **** 6908r. **Directed Individual Study (1–4). (S/U grade only.)

**MAT **** 6932r. **Advanced Topics in Mathematics (1–3).

**MAT **** 6933r. **Selected Advanced Topics (1–3). (S/U grade only.)

**MAT **** 6939r. **Advanced Graduate Seminar (1). (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 coursework for thesis, dissertation, and master's and doctoral examinations and defense, consult the *Graduate Bulletin*.