# Mathematics

## Admission

For admission into the M.S., M.A., or Ph.D. degree programs, applicants must have a bachelor’s degree from an approved institution and should have an undergraduate foundation in mathematics equivalent to that of a major in mathematics at the University of South Carolina. At a minimum, this should include a course in abstract algebra (equivalent to MATH 546) and one in advanced calculus (equivalent to MATH 554). A one year sequence in each is desirable. A minimum B (3.0) average in all college-level math courses is required for full admission. Applicants who do not have this preparation may be conditionally admitted and placed in such undergraduate courses as necessary to strengthen their backgrounds.

Applicants should submit an official transcript from each school or college previously attended, at least two letters of recommendation from persons familiar with their abilities in mathematics, and an official report of scores achieved on the GRE. A GRE score of at least 700 on the quantitative portion is expected. Applicants whose native language is not English are also required to submit a satisfactory score on the iBT TOEFL exam. The minimum score for admission to the program is 88. A minimum iBT TOEFL score of 100 is required for consideration for a teaching assistantship; there are also minimum levels for each sub-category (listening, speaking, reading, writing), which can be viewed on the departmental website. The GRE Mathematics Subject Exam is not required, but a strong score enhances the probability of admission with assistantship and the possibility of a supplemental fellowship.

For admission to the M.M. or M.A.T. degree programs, applicants must have a bachelor’s degree from an approved institution and have completed multivariable calculus (Calculus III, equivalent to MATH 241). Further, it is desirable that they have completed six credit hours in mathematics beyond multivariable calculus. At least a B (3.0) average for all college level mathematics courses is expected. Applicants with background deficiencies may be admitted on a conditional basis and placed in certain dual undergraduate/graduate courses to strengthen their foundation. Course work below the 500-level can not be used toward these degrees. Applicants should submit an official transcript from each school or college previously attended, at least two letters of recommendation from persons familiar with their abilities in mathematics, and a report of scores achieved on the GRE. A combined GRE score of 1000 is expected, with at least 550 on the quantitative portion.

Application materials should be submitted as much as possible online at http://www.gradschool.sc.edu/apply.htm, or be mailed to:

The Graduate School

University of South Carolina

Columbia, SC 29208

## Courses

**MATH 511**

**- Probability**

**(3 Credits)**

**Prerequisite or Corequisite:**C or better in MATH 241.

**Cross-listed course:**STAT 511

**MATH 514**

**- Financial Mathematics I**

**(3 Credits)**

**Prerequisites:**C or better in MATH 241.

**Cross-listed course:**STAT 522

**MATH 515**

**- Financial Mathematics II**

**(3 Credits)**

**Cross-listed course:**STAT 523

**MATH 520**

**- Ordinary Differential Equations**

**(3 Credits)**

**Prerequisites:**C or better in MATH 344 or MATH 544.

**MATH 521**

**- Boundary Value Problems and Partial Differential Equations**

**(3 Credits)**

**Prerequisites:**C or better in MATH 520 or in both MATH 241 and MATH 242.

**MATH 522**

**- Wavelets**

**(3 Credits)**

**Prerequisites:**C or better in MATH 344 or MATH 544.

**MATH 523**

**- Mathematical Modeling of Population Biology**

**(3 Credits)**

**Prerequisites:**C or better in MATH 142, BIOL 301, or MSCI 311 recommended.

**MATH 524**

**- Nonlinear Optimization**

**(3 Credits)**

**Prerequisites:**C or better in MATH 241 and one of MATH 344 or MATH 544.

**MATH 525**

**- Mathematical Game Theory**

**(3 Credits)**

**Prerequisites:**C or better in MATH 300 and in either MATH 344 or MATH 544.

**MATH 526**

**- Numerical Linear Algebra**

**(4 Credits)**

**Prerequisites:**C or better in MATH 142.

**MATH 527**

**- Numerical Analysis**

**(3 Credits)**

**Prerequisites:**C or better in MATH 520 or in both MATH 242 and MATH 344.

**Cross-listed course:**CSCE 561

**MATH 528**

**- Mathematical Foundation of Data Science and Machine Learning**

**(3 Credits)**

**Prerequisites:**C or better in MATH 344 or MATH 544.

**MATH 529**

**- Introduction to Deep Neural Networks**

**(3 Credits)**

**Prerequisites:**C or better in MATH 344 or MATH 544.

**MATH 531**

**- Foundations of Geometry**

**(3 Credits)**

**Prerequisites:**C or better in MATH 300.

**MATH 532**

**- Modern Geometry**

**(3 Credits)**

**Prerequisites:**C or better in MATH 300.

**MATH 533**

**- Elementary Geometric Topology**

**(3 Credits)**

**Prerequisites:**C or better in MATH 241 and MATH 300.

**MATH 534**

**- Elements of General Topology**

**(3 Credits)**

**Prerequisites:**C or better in MATH 241 and MATH 300.

**MATH 540**

**- Modern Applied Algebra**

**(3 Credits)**

**Prerequisites:**MATH 300.

**MATH 541**

**- Algebraic Coding Theory**

**(3 Credits)**

**Prerequisites:**C or better in MATH 300 and in either of MATH 344 or MATH 544.

**MATH 544**

**- Linear Algebra**

**(3 Credits)**

**Prerequisites:**C or better in MATH 241 and MATH 300.

**MATH 546**

**- Algebraic Structures I**

**(3 Credits)**

**Prerequisites:**C or better in MATH 300 and 544.

**MATH 547**

**- Algebraic Structures II**

**(3 Credits)**

**Prerequisites:**C or better in MATH 546.

**MATH 548**

**- Geometry, Algebra, and Algorithms**

**(3 Credits)**

**Prerequisites:**C or better in MATH 300 and in one of MATH 344 or MATH 544.

**MATH 550**

**- Vector Analysis**

**(3 Credits)**

**Prerequisites:**C or better in MATH 241.

**MATH 551**

**- Introduction to Differential Geometry**

**(3 Credits)**

**Prerequisites:**C or better in MATH 241 and MATH 300.

**MATH 552**

**- Applied Complex Variables**

**(3 Credits)**

**Prerequisites:**C or better in MATH 241.

**MATH 554**

**- Analysis I**

**(3 Credits)**

**MATH 555**

**- Analysis II**

**(3 Credits)**

**Prerequisites:**C or better in MATH 554.

**MATH 561**

**- Introduction to Mathematical Logic**

**(3 Credits)**

**Prerequisites:**C or better in MATH 300.

**MATH 562**

**- Theory of Computation**

**(3 Credits)**

**Prerequisites:**C or better in CSCE 350 or MATH 300.

**Cross-listed course:**CSCE 551

**MATH 570**

**- Discrete Optimization**

**(3 Credits)**

**Prerequisites:**C or better in MATH 300 and in one of MATH 544 or MATH 344.

**MATH 574**

**- Discrete Mathematics I**

**(3 Credits)**

**Prerequisites:**C or better in MATH 300.

**MATH 575**

**- Discrete Mathematics II**

**(3 Credits)**

**MATH 576**

**- Combinatorial Game Theory**

**(3 Credits)**

**Prerequisites:**C or better in MATH 300 or MATH 374.

**MATH 580**

**- Elementary Number Theory**

**(3 Credits)**

**Prerequisites:**C or better in MATH 300.

**MATH 587**

**- Introduction to Cryptography**

**(3 Credits)**

**Prerequisites:**C or better in CSCE 145 or MATH 241, and at least one of CSCE 355, MATH 300, or MATH 374.

**Cross-listed course:**CSCE 557

**MATH 599**

**- Topics in Mathematics**

**(1-3 Credits)**

**MATH 602**

**- An Inductive Approach to Geometry**

**(3 Credits)**

**Prerequisites:**C or better in MATH 122 or MATH 141 or equivalent.

**MATH 603**

**- Inquiry Approach to Algebra**

**(3 Credits)**

**Prerequisites:**C or higher in MATH 122 or MATH 141 or equivalent.

**MATH 650**

**- AP Calculus for Teachers**

**(3 Credits)**

**Prerequisites:**current secondary high school teacher certification in mathematics and a C or better in at least 6 hours of calculus.

**MATH 700**

**- Linear Algebra**

**(3 Credits)**

**MATH 701**

**- Algebra I**

**(3 Credits)**

**MATH 701I**

**- Foundations of Algebra I**

**(3 Credits)**

**Prerequisites:**MATH 241 or equivalent.

**MATH 702**

**- Algebra II**

**(3 Credits)**

**Prerequisites:**MATH 701.

**MATH 702I**

**- Foundations of Algebra II**

**(3 Credits)**

**Prerequisites:**MATH 701I or equivalent.

**MATH 703**

**- Analysis I**

**(3 Credits)**

**MATH 703I**

**- Foundations of Analysis I**

**(3 Credits)**

**Prerequisites:**MATH 241 or equivalent.

**MATH 704**

**- Analysis II**

**(3 Credits)**

**MATH 704I**

**- Foundations of Analysis II**

**(3 Credits)**

**Prerequisites:**MATH 703I or equivalent.

**MATH 705**

**- Analysis III**

**(3 Credits)**

**MATH 708**

**- Foundations of Computational Mathematics I**

**(3 Credits)**

**Prerequisites:**MATH 554 or equivalent upper level undergraduate course in Real Analysis.

**MATH 709**

**- Foundations of Computational Mathematics II**

**(3 Credits)**

**MATH 710**

**- Probability Theory I**

**(3 Credits)**

**Cross-listed course:**STAT 810

**MATH 711**

**- Probability Theory II**

**(3 Credits)**

**Cross-listed course:**STAT 811

**MATH 712I**

**- Probability and Statistics**

**(3 Credits)**

**MATH 720**

**- Applied Mathematics I**

**(3 Credits)**

**MATH 721**

**- Applied Mathematics II**

**(3 Credits)**

**Prerequisites:**MATH 720.

**MATH 722**

**- Numerical Optimization**

**(3 Credits)**

**MATH 723**

**- Differential Equations**

**(3 Credits)**

**MATH 724**

**- Differential Equations II**

**(3 Credits)**

**Prerequisites:**MATH 723.

**MATH 725**

**- Approximation Theory**

**(3 Credits)**

**Prerequisite or Corequisite:**MATH 703.

**MATH 726**

**- Numerical Differential Equations I**

**(3 Credits)**

**MATH 727**

**- Numerical Differential Equations II**

**(3 Credits)**

**Prerequisites:**MATH 726.

**MATH 728**

**- Selected Topics in Applied Mathematics**

**(3 Credits)**

**MATH 729**

**- Nonlinear Approximation**

**(3 Credits)**

**Prerequisites:**MATH 703.

**MATH 730**

**- General Topology I**

**(3 Credits)**

**MATH 731**

**- General Topology II**

**(3 Credits)**

**MATH 732**

**- Algebraic Topology I**

**(3 Credits)**

**MATH 733**

**- Algebraic Topology II**

**(3 Credits)**

**MATH 734**

**- Differential Geometry**

**(3 Credits)**

**Prerequisites:**MATH 550.

**MATH 735**

**- Lie Groups**

**(3 Credits)**

**MATH 736I**

**- Modern Geometry**

**(3 Credits)**

**Prerequisites:**MATH 241 or equivalent.

**MATH 737**

**- Introduction to Complex Geometry**

**(3 Credits)**

**Prerequisite or Corequisite:**MATH 701.

**MATH 738**

**- Selected Topics in Geometry and Topology**

**(3 Credits)**

**MATH 739**

**- Introduction to Complex Geometry II**

**(3 Credits)**

**Prerequisites:**MATH 737.

**MATH 741**

**- Algebra III**

**(3 Credits)**

**Prerequisites:**MATH 702.

**MATH 742**

**- Representation Theory**

**(3 Credits)**

**Prerequisites:**MATH 702.

**MATH 743**

**- Lattice Theory**

**(3 Credits)**

**Prerequisites:**MATH 740.

**MATH 744**

**- Matrix Theory**

**(3 Credits)**

**Prerequisites:**MATH 700.

**MATH 746**

**- Commutative Algebra**

**(3 Credits)**

**Prerequisites:**MATH 701.

**MATH 747**

**- Algebraic Geometry**

**(3 Credits)**

**Prerequisites:**MATH 701.

**MATH 748**

**- Selected Topics in Algebra**

**(3 Credits)**

**MATH 750**

**- Fourier Analysis**

**(3 Credits)**

**MATH 751**

**- The Mathematical Theory of Wavelets**

**(3 Credits)**

**Prerequisites:**MATH 703.

**MATH 752**

**- Complex Analysis**

**(3 Credits)**

**MATH 752I**

**- Complex Variables**

**(3 Credits)**

**Prerequisites:**MATH 241 or equivalent.

**MATH 754**

**- Several Complex Variables**

**(3 Credits)**

**MATH 755**

**- Applied Functional Analysis**

**(3 Credits)**

**Prerequisites:**MATH 703.

**MATH 756**

**- Functional Analysis I**

**(3 Credits)**

**Prerequisites:**MATH 704.

**MATH 757**

**- Functional Analysis II**

**(3 Credits)**

**Prerequisites:**MATH 704.

**MATH 758**

**- Selected Topics in Analysis**

**(3 Credits)**

**MATH 760**

**- Set Theory**

**(3 Credits)**

**MATH 761**

**- The Theory of Computable Functions**

**(3 Credits)**

**MATH 762**

**- Model Theory**

**(3 Credits)**

**MATH 764**

**- Quantum Information**

**(3 Credits)**

**MATH 768**

**- Selected Topics in Foundations of Mathematics**

**(3 Credits)**

**MATH 770**

**- Discrete Optimization**

**(3 Credits)**

**MATH 774**

**- Discrete Mathematics I**

**(3 Credits)**

**MATH 775**

**- Discrete Mathematics II**

**(3 Credits)**

**Prerequisites:**MATH 774.

**MATH 776**

**- Graph Theory I**

**(3 Credits)**

**MATH 777**

**- Graph Theory II**

**(3 Credits)**

**Prerequisites:**MATH 776.

**MATH 778**

**- Selected Topics in Discrete Mathematics**

**(3 Credits)**

**MATH 780**

**- Elementary Number Theory**

**(3 Credits)**

**MATH 780I**

**- Theory of Numbers**

**(3 Credits)**

**Prerequisites:**MATH 241 or equivalent.

**MATH 782**

**- Analytic Number Theory I**

**(3 Credits)**

**MATH 783**

**- Analytic Number Theory II**

**(3 Credits)**

**MATH 784**

**- Algebraic Number Theory**

**(3 Credits)**

**MATH 785**

**- Transcendental Number Theory**

**(3 Credits)**

**Prerequisites:**MATH 580.

**MATH 788**

**- Selected Topics in Number Theory**

**(3 Credits)**

**MATH 790**

**- Graduate Seminar**

**(1 Credit)**

**MATH 791**

**- Mathematics Pedagogy I**

**(0-1 Credits)**

**MATH 792**

**- Mathematics Pedagogy II**

**(0-1 Credits)**

**Prerequisites:**Satisfactory grade in MATH 791.

**MATH 797**

**- Mathematics into Print**

**(3 Credits)**

**MATH 798**

**- Directed Readings and Research**

**(1-6 Credits)**

**MATH 799**

**- Thesis Preparation**

**(1-9 Credits)**

**MATH 890**

**- Graduate Seminar**

**(1-3 Credits)**

**MATH 899**

**- Dissertation Preparation**

**(1-12 Credits)**