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Mathematics

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  • Overview
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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

Course List
Code Title Credits
MAA 5104Advanced Calculus for Engineers and Physical Scientists I3
MAA 5105Advanced Calculus for Engineers and Physical Scientists II3
MAA 5228Modern Analysis I3
MAA 5229Modern Analysis II3
MAA 5404Introduction to Complex Variables for Engineers and Physical Scientists3
MAA 6406Complex Analysis I3
MAA 6407Complex Analysis II3
MAA 6616Analysis I3
MAA 6617Analysis II3
MAA 7526Advanced Topics in Functional Analysis I3
MAA 7527Advanced Topics in Functional Analysis II3
MAD 6206Combinatorial Theory I3
MAD 6207Combinatorial Theory II3
MAD 6406Numerical Linear Algebra3
MAD 6407Numerical Analysis3
MAD 7396Topics in Combinatorial Theory I3
MAD 7397Topics in Combinatorial Theory II3
MAE 6940Supervised Teaching1-5
MAE 6943Internship in College Teaching3
MAP 5304Intermediate Differential Equations for Engineers and Physical Scientists3
MAP 5345Introduction to Partial Differential Equations3
MAP 5489Modeling in Mathematical Biology3
MAP 6208Numerical Optimization3
MAP 6327Applied Differential Equations I3
MAP 6356Partial Differential Equations I3
MAP 6357Partial Differential Equations II3
MAP 6375Numerical Partial Differential Equations3
MAP 6376Finite Element Method3
MAP 6467Stochastic Differential Equations and Filtering Theory I3
MAP 6468Stochastic Differential Equations and Filtering Theory II3
MAP 6472Probability and Potential Theory I3
MAP 6473Probability and Potential Theory II3
MAP 6487Biomathematics Seminar I3
MAP 6488Biomathematics Seminar II3
MAP 6505Mathematical Methods of Physics and Engineering3
MAP 6506Mathematical Methods of Physics and Engineering II3
MAP 6941Internship in Applied Mathematics1-5
MAP 7436Seminar in Applied Mathematics I3
MAP 7437Seminar in Applied Mathematics II3
MAS 5311Introductory Algebra I3
MAS 5312Introductory Algebra II3
MAS 6331Algebra I3
MAS 6332Algebra II3
MAS 7215Theory of Numbers I3
MAS 7216Theory of Numbers II3
MAS 7396Advanced Topics in Algebra I3
MAS 7397Topics in Algebra II3
MAT 6905Individual Work3
MAT 6910Supervised Research1-5
MAT 6932Special Topics in Mathematics3
MAT 6971Research for Master's Thesis1-15
MAT 7979Advanced Research1-12
MAT 7980Research for Doctoral Dissertation1-15
MHF 5107Introduction to Set Theory3
MHF 5207Foundations of Mathematics3
MHF 6306Mathematical Logic I3
MTG 5316Introduction to Topology I3
MTG 5317Introduction to Topology II3
MTG 5411Introduction to Fractal Geometry3
MTG 5412Introduction to Dynamical Systems and Chaos3
MTG 6256Differential Geometry I3
MTG 6257Differential Geometry II3
MTG 6346Topology I3
MTG 6347Topology II3
MTG 6401Ergodic Theory and Dynamical Systems I3
MTG 6402Ergodic Theory and Dynamical Systems II3
MTG 7396Advanced Topics in Topology I3

Mathematics Departmental Courses

Course List by Depts
Code Title Credits
MAA 5104Advanced Calculus for Engineers and Physical Scientists I3
MAA 5105Advanced Calculus for Engineers and Physical Scientists II3
MAA 5228Modern Analysis I3
MAA 5229Modern Analysis II3
MAA 5404Introduction to Complex Variables for Engineers and Physical Scientists3
MAA 6406Complex Analysis I3
MAA 6407Complex Analysis II3
MAA 6616Analysis I3
MAA 6617Analysis II3
MAA 7526Advanced Topics in Functional Analysis I3
MAA 7527Advanced Topics in Functional Analysis II3
MAD 6206Combinatorial Theory I3
MAD 6207Combinatorial Theory II3
MAD 6406Numerical Linear Algebra3
MAD 6407Numerical Analysis3
MAD 7396Topics in Combinatorial Theory I3
MAD 7397Topics in Combinatorial Theory II3
MAE 6940Supervised Teaching1-5
MAE 6943Internship in College Teaching3
MAP 5304Intermediate Differential Equations for Engineers and Physical Scientists3
MAP 5345Introduction to Partial Differential Equations3
MAP 5489Modeling in Mathematical Biology3
MAP 6208Numerical Optimization3
MAP 6327Applied Differential Equations I3
MAP 6356Partial Differential Equations I3
MAP 6357Partial Differential Equations II3
MAP 6375Numerical Partial Differential Equations3
MAP 6376Finite Element Method3
MAP 6467Stochastic Differential Equations and Filtering Theory I3
MAP 6468Stochastic Differential Equations and Filtering Theory II3
MAP 6472Probability and Potential Theory I3
MAP 6473Probability and Potential Theory II3
MAP 6487Biomathematics Seminar I3
MAP 6488Biomathematics Seminar II3
MAP 6505Mathematical Methods of Physics and Engineering3
MAP 6506Mathematical Methods of Physics and Engineering II3
MAP 6941Internship in Applied Mathematics1-5
MAP 7436Seminar in Applied Mathematics I3
MAP 7437Seminar in Applied Mathematics II3
MAS 5311Introductory Algebra I3
MAS 5312Introductory Algebra II3
MAS 6331Algebra I3
MAS 6332Algebra II3
MAS 7215Theory of Numbers I3
MAS 7216Theory of Numbers II3
MAS 7396Advanced Topics in Algebra I3
MAS 7397Topics in Algebra II3
MAT 6905Individual Work3
MAT 6910Supervised Research1-5
MAT 6932Special Topics in Mathematics3
MAT 6971Research for Master's Thesis1-15
MAT 7979Advanced Research1-12
MAT 7980Research for Doctoral Dissertation1-15
MHF 5107Introduction to Set Theory3
MHF 5207Foundations of Mathematics3
MHF 6306Mathematical Logic I3
MHF 6307Mathematical Logic 23
MTG 5316Introduction to Topology I3
MTG 5317Introduction to Topology II3
MTG 5411Introduction to Fractal Geometry3
MTG 5412Introduction to Dynamical Systems and Chaos3
MTG 6256Differential Geometry I3
MTG 6257Differential Geometry II3
MTG 6346Topology I3
MTG 6347Topology II3
MTG 6401Ergodic Theory and Dynamical Systems I3
MTG 6402Ergodic Theory and Dynamical Systems II3
MTG 7396Advanced Topics in Topology I3
MTG 7397Advanced Topics in Topology II3

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

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