## Program Information

The Department of Mathematics offers the degrees of Doctor of Philosophy, Master of Science, and the Master of Arts in Teaching and Master of Science in Teaching, each with a major in mathematics. Complete descriptions of the minimum requirements for these degrees are provided in the Graduate Degrees section of this catalog.

The Department has an accelerated bachelor’s/master’s program designed for superior undergraduate students who have the ability to pursue such a plan of study leading to the Master of Science degree. The main feature of the program is that up to 12 semester hours of approved graduate level mathematics courses may be used as dual credit for both the undergraduate and the graduate degree. All other requirements for both the bachelor’s degree and the master’s degree must be met. For admission requirements for this program, see the undergraduate coordinator.

There are opportunities for concentrated study in a number of specific areas of pure and applied mathematics at both the master’s and doctoral levels. The faculty directs studies and research in algebra, number theory, analysis, geometry, topology, logic and set theory, differential equations, dynamical systems, probability theory, optimization, combinatorial theory, biomathematics, and imaging.

In addition to the requirements of the Graduate School, the minimum prerequisite for admission to the program of graduate studies in mathematics is the completion, with an average grade of B or better, of at least 24 credits of undergraduate mathematics, including a full year of calculus and three semesters of appropriate work beyond the calculus. The most appropriate courses for this purpose are advanced calculus, linear algebra and abstract algebra. Students lacking part of the requirements will be required to make up the deficiency early in their graduate work.

Prerequisites to individual courses should be determined before registration by consultation with the instructor concerned. Some of the courses listed are offered only as needed. Since times of offering courses are estimated a year in advance, certain changes may be made if needs are known by the Department.

Students pursuing the master’s degree in mathematics must pass two comprehensive written examinations, one in algebra and one in analysis or prepare and provide an oral defense of a thesis on original research conducted under the supervision of a faculty adviser. Students pursuing the Master of Arts in Teaching or the Master of Science in Teaching degree must prepare a teaching portfolio and pass an oral examination. Each of these programs normally requires two years for completion.

The requirements for a doctoral degree include 36 hours of 6000-level course work in mathematics; no hours of teaching, colloquium, dissertation, or individual work will count toward this requirement. To become a candidate for the doctoral degree, the student must pass a comprehensive preliminary examination with written and oral components administered by the Department. The doctoral student must also pass a reading knowledge examination in one of the following foreign languages: French, German, or Russian. The dissertation is an important requirement for the doctoral degree in mathematics. The topic for the dissertation may be chosen from a number of areas of current research in pure and applied mathematics.

Details concerning all requirements for graduate degrees in mathematics may be obtained by writing the Mathematics Department Graduate Selection Committee or consulting the Department website, http://www.math.ufl.edu.

## Degrees Offered with a Major in Mathematics

- Doctor of Philosophy
- without a concentration
- concentration in Imaging Science and Technology
- concentration in Quantitative Finance

- Master of Arts in Teaching
- Master of Science
- Master of Science in Teaching

Requirements for these degrees are given in the Graduate Degrees section of this catalog.

## Mathematics Courses

Code | Title | Credits |
---|---|---|

MAA 5104 | Advanced Calculus for Engineers and Physical Scientists I | 3 |

MAA 5105 | Advanced Calculus for Engineers and Physical Scientists II | 3 |

MAA 5228 | Modern Analysis I | 3 |

MAA 5229 | Modern Analysis II | 3 |

MAA 5404 | Introduction to Complex Variables for Engineers and Physical Scientists | 3 |

MAA 6406 | Complex Analysis I | 3 |

MAA 6407 | Complex Analysis II | 3 |

MAA 6616 | Analysis I | 3 |

MAA 6617 | Analysis II | 3 |

MAA 7526 | Advanced Topics in Functional Analysis I | 3 |

MAA 7527 | Advanced Topics in Functional Analysis II | 3 |

MAD 6206 | Combinatorial Theory I | 3 |

MAD 6207 | Combinatorial Theory II | 3 |

MAD 6406 | Numerical Linear Algebra | 3 |

MAD 6407 | Numerical Analysis | 3 |

MAD 7396 | Topics in Combinatorial Theory I | 3 |

MAD 7397 | Topics in Combinatorial Theory II | 3 |

MAE 6940 | Supervised Teaching | 1-5 |

MAE 6943 | Internship in College Teaching | 3 |

MAP 5304 | Intermediate Differential Equations for Engineers and Physical Scientists | 3 |

MAP 5345 | Introduction to Partial Differential Equations | 3 |

MAP 5489 | Modeling in Mathematical Biology | 3 |

MAP 6208 | Numerical Optimization | 3 |

MAP 6327 | Applied Differential Equations I | 3 |

MAP 6356 | Partial Differential Equations I | 3 |

MAP 6357 | Partial Differential Equations II | 3 |

MAP 6375 | Numerical Partial Differential Equations | 3 |

MAP 6376 | Finite Element Method | 3 |

MAP 6467 | Stochastic Differential Equations and Filtering Theory I | 3 |

MAP 6468 | Stochastic Differential Equations and Filtering Theory II | 3 |

MAP 6472 | Probability and Potential Theory I | 3 |

MAP 6473 | Probability and Potential Theory II | 3 |

MAP 6487 | Biomathematics Seminar I | 3 |

MAP 6488 | Biomathematics Seminar II | 3 |

MAP 6505 | Mathematical Methods of Physics and Engineering | 3 |

MAP 6506 | Mathematical Methods of Physics and Engineering II | 3 |

MAP 6941 | Internship in Applied Mathematics | 1-5 |

MAP 7436 | Seminar in Applied Mathematics I | 3 |

MAP 7437 | Seminar in Applied Mathematics II | 3 |

MAS 5311 | Introductory Algebra I | 3 |

MAS 5312 | Introductory Algebra II | 3 |

MAS 6331 | Algebra I | 3 |

MAS 6332 | Algebra II | 3 |

MAS 7215 | Theory of Numbers I | 3 |

MAS 7216 | Theory of Numbers II | 3 |

MAS 7396 | Advanced Topics in Algebra I | 3 |

MAS 7397 | Topics in Algebra II | 3 |

MAT 6905 | Individual Work | 3 |

MAT 6910 | Supervised Research | 1-5 |

MAT 6932 | Special Topics in Mathematics | 3 |

MAT 6971 | Research for Master's Thesis | 1-15 |

MAT 7979 | Advanced Research | 1-12 |

MAT 7980 | Research for Doctoral Dissertation | 1-15 |

MHF 5107 | Introduction to Set Theory | 3 |

MHF 5207 | Foundations of Mathematics | 3 |

MHF 6306 | Mathematical Logic I | 3 |

MTG 5316 | Introduction to Topology I | 3 |

MTG 5317 | Introduction to Topology II | 3 |

MTG 5411 | Introduction to Fractal Geometry | 3 |

MTG 5412 | Introduction to Dynamical Systems and Chaos | 3 |

MTG 6256 | Differential Geometry I | 3 |

MTG 6257 | Differential Geometry II | 3 |

MTG 6346 | Topology I | 3 |

MTG 6347 | Topology II | 3 |

MTG 6401 | Ergodic Theory and Dynamical Systems I | 3 |

MTG 6402 | Ergodic Theory and Dynamical Systems II | 3 |

MTG 7396 | Advanced Topics in Topology I | 3 |

## Mathematics Departmental Courses

Code | Title | Credits |
---|---|---|

MAA 5104 | Advanced Calculus for Engineers and Physical Scientists I | 3 |

MAA 5105 | Advanced Calculus for Engineers and Physical Scientists II | 3 |

MAA 5228 | Modern Analysis I | 3 |

MAA 5229 | Modern Analysis II | 3 |

MAA 5404 | Introduction to Complex Variables for Engineers and Physical Scientists | 3 |

MAA 6406 | Complex Analysis I | 3 |

MAA 6407 | Complex Analysis II | 3 |

MAA 6616 | Analysis I | 3 |

MAA 6617 | Analysis II | 3 |

MAA 7526 | Advanced Topics in Functional Analysis I | 3 |

MAA 7527 | Advanced Topics in Functional Analysis II | 3 |

MAD 6206 | Combinatorial Theory I | 3 |

MAD 6207 | Combinatorial Theory II | 3 |

MAD 6406 | Numerical Linear Algebra | 3 |

MAD 6407 | Numerical Analysis | 3 |

MAD 7396 | Topics in Combinatorial Theory I | 3 |

MAD 7397 | Topics in Combinatorial Theory II | 3 |

MAE 6940 | Supervised Teaching | 1-5 |

MAE 6943 | Internship in College Teaching | 3 |

MAP 5304 | Intermediate Differential Equations for Engineers and Physical Scientists | 3 |

MAP 5345 | Introduction to Partial Differential Equations | 3 |

MAP 5489 | Modeling in Mathematical Biology | 3 |

MAP 6208 | Numerical Optimization | 3 |

MAP 6327 | Applied Differential Equations I | 3 |

MAP 6356 | Partial Differential Equations I | 3 |

MAP 6357 | Partial Differential Equations II | 3 |

MAP 6375 | Numerical Partial Differential Equations | 3 |

MAP 6376 | Finite Element Method | 3 |

MAP 6467 | Stochastic Differential Equations and Filtering Theory I | 3 |

MAP 6468 | Stochastic Differential Equations and Filtering Theory II | 3 |

MAP 6472 | Probability and Potential Theory I | 3 |

MAP 6473 | Probability and Potential Theory II | 3 |

MAP 6487 | Biomathematics Seminar I | 3 |

MAP 6488 | Biomathematics Seminar II | 3 |

MAP 6505 | Mathematical Methods of Physics and Engineering | 3 |

MAP 6506 | Mathematical Methods of Physics and Engineering II | 3 |

MAP 6941 | Internship in Applied Mathematics | 1-5 |

MAP 7436 | Seminar in Applied Mathematics I | 3 |

MAP 7437 | Seminar in Applied Mathematics II | 3 |

MAS 5311 | Introductory Algebra I | 3 |

MAS 5312 | Introductory Algebra II | 3 |

MAS 6331 | Algebra I | 3 |

MAS 6332 | Algebra II | 3 |

MAS 7215 | Theory of Numbers I | 3 |

MAS 7216 | Theory of Numbers II | 3 |

MAS 7396 | Advanced Topics in Algebra I | 3 |

MAS 7397 | Topics in Algebra II | 3 |

MAT 6905 | Individual Work | 3 |

MAT 6910 | Supervised Research | 1-5 |

MAT 6932 | Special Topics in Mathematics | 3 |

MAT 6971 | Research for Master's Thesis | 1-15 |

MAT 7979 | Advanced Research | 1-12 |

MAT 7980 | Research for Doctoral Dissertation | 1-15 |

MHF 5107 | Introduction to Set Theory | 3 |

MHF 5207 | Foundations of Mathematics | 3 |

MHF 6306 | Mathematical Logic I | 3 |

MTG 5316 | Introduction to Topology I | 3 |

MTG 5317 | Introduction to Topology II | 3 |

MTG 5411 | Introduction to Fractal Geometry | 3 |

MTG 5412 | Introduction to Dynamical Systems and Chaos | 3 |

MTG 6256 | Differential Geometry I | 3 |

MTG 6257 | Differential Geometry II | 3 |

MTG 6346 | Topology I | 3 |

MTG 6347 | Topology II | 3 |

MTG 6401 | Ergodic Theory and Dynamical Systems I | 3 |

MTG 6402 | Ergodic Theory and Dynamical Systems II | 3 |

MTG 7396 | Advanced Topics in Topology I | 3 |

MTG 7397 | Advanced Topics in Topology II | 3 |

## mathematics (PHD)

SLO 1 Knowledge

Describes and explains advanced knowledge of at least one chosen specialty and conducts research in it.

SLO 2 Skills

Communicates mathematical thinking through clear and compelling arguments to faculty, peers and others.

SLO 3 Professional Behavior

Teaches mathematical courses in a professional manner, assessing the appropriate level of presentation for the students, creating an atmosphere conducive to learning, and supporting student-teacher interactions for active learning

## Mathematics (MAT)

SLO 1 Knowledge

Demonstrates content knowledge relevant to mathematics teaching

SLO 2 Skills

Communicates mathematics effectively through prior organization of material, effective use of the blackboard or other presentation media, compelling choice of illustrative examples, and emphasis on methods of solving problems rather than on presenting solutions

SLO 3 Professional Behavior

Prepares for lessons; arrives on time; conducts themselves appropriately

## Mathematics (MS)

SLO 1 Knowledge

Depth: Either solves problems in two areas from algebra/analysis/applied/topology or conducts research in mathematics at the master's level

SLO 2 Skills

Writes extended mathematical prose to the precision required by the discipline and supports mathematical arguments with logical reasoning

SLO 3 Professional Behavior

Teaches mathematical courses in a professional manner, assessing the appropriate level of presentation for the students, creating an atmosphere conducive to learning, and supporting student-teacher interactions for active learning

## Mathematics (MST)

SLO 1 Knowledge

Describes and explains content knowledge relevant to mathematics and teaching

SLO 2 Skills

Communicates mathematics effectively through prior organization of material, effective use of the blackboard or other presentation media, compelling choice of illustrative examples, and emphasis on methods of solving problems rather than on presenting solutions

SLO 3 Professional Behavior

Prepares for lessons; arrives on time; conducts themselves appropriately