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Department of Mathematical Sciences
383 Bryan Building

Mathematics Major (BA or BS)BA RequirementsBS RequirementsSecondary Teacher LicensureMathematics Second MajorMathematics MinorAccelerated ProgramComputer Science Major (BS)Computer Science MinorComputer Science CoursesMathematics CoursesStatistics Courses

Paul F. Duvall, Professor and Head of Department

Professor J.Vaughan; Associate Professors Blanchet-Sadri, Gentry, Herr, Kissling, Landman, Lea, Long, Ludwig, Sadri, T. Vaughan, Wang; Assistant Professors Byrd, Fabiano, Love; Instructor Kilgariff; Lecturers Blackmon, Bradley, Carter, Keith, Koehler, Montgomery, O'Connor, Sallez, Sen, Shelton, Vruwink, Weigel

The Department of Mathematical Sciences offers undergraduate programs leading to the BA and BS degrees in Mathematics and the BS degree in Computer Science. The BS degree in Computer Science is accredited by the Computer Science Accreditation Commission of the Computing Sciences Accreditation Board. It also offers graduate programs leading to the MA or MEd degrees in Mathematics (with specialities available in pure mathematics, applied mathematics, or applied statistics), and the MS degree in Computer Science.

Mathematics and Computer Science are excellent majors for the student whose immediate objective is to acquire a strong liberal arts education. The goal of all of the Department's programs is to produce students who are both technically competent and sufficiently well grounded in theory that they can contribute to fundamental research in their chosen specialty. To give a professional direction to the student's liberal arts education, the mathematics major may elect a concentration in statistics or computer science, or seek secondary teacher certification. Students seeking secondary teacher licensure should see "Teacher Education Programs", Part 7. The Department of Mathematical Sciences can also help students design a plan of study emphasizing special interests, such as applied mathematics or computer systems analysis.

There are many opportunities for the undergraduate majors in the mathematical sciences in industry, government, business, and secondary school teaching. An undergraduate major in the mathematical sciences also provides excellent preparation for graduate studies in many areas, including actuarial sciences, computer science, economics, engineering, law, mathematics, operations research and statistics. The majors can be specialized to allow preparation for any of these goals.

The department offices, classrooms, and study areas are located in the Bryan Building. Students have access to computing facilities including personal computer laboratories, and workstations. The campus is fully networked locally. The University is an Internet node, and students and faculty have access to the Internet's many features.

 

Mathematics Major (Bachelor of Arts and Bachelor of Science)

Required: 122 semester hours

 

College of Arts and Sciences Liberal Education Requirements (CLER) (54-55 hours)

All students must meet the All-University Liberal Education Requirements (AULER). The College of Arts and Sciences, however, has established liberal education requirements for its programs which, while including those of AULER, contain additional requirements in several categories. Therefore, students following this program should adhere to the College requirements. Please note that students who satisfy the College Liberal Education Requirements (CLER) will also satisfy the All-University Liberal Education Requirements (AULER). See College requirements and courses meeting AULER/CLER requirements.

Major Requirements

The mathematics major must complete courses as specified below, and must maintain a grade point average of at least 2.0 in MAT/CSC/STA courses required for the major.

It is strongly recommended that students planning to pursue graduate study in Mathematics include at least two courses from MAT 591, 592, 595, 596, and two other courses from MAT 514, 515, 516, 517, 518, 531, 532, 540, 541, 542, 545, 546, 549, 556, 591, 592, 595, 596.

Requirements for the Bachelor of Arts

A. MAT 191, 292, 293, 310, 311, 394

B. Two 500-level courses chosen from the following list*: Any MAT course (excluding 503, 504, 505, 513); CSC 523, 524, 553, 555; STA 551, 552, 573, 574, 575
*Students seeking secondary teacher licensure must take one course from list B and must take the three courses MAT 504, 505, and 513.

C. Six additional hours chosen from the following list:

  • Any MAT course 200-level or above (excluding 220, 303, 304, 503, 504, 505)
  • CSC 322, 523, 524, 553, 555
  • STA 271, 351, 352, 551, 552, 573, 574, 575

D. CSC 130 or 230

E. PHY 211, 212 and 251, 252 labs, or PHY 291, 292, and 251, 252 labs; or CHE 103 and 104 (with required CHE 110 lab); or CHE 111, 112, 114, and 115; or BIO 111 and 112

Requirements for the Bachelor of Science

There are four concentrations in the Bachelor of Science degree:

  • Pure Mathematics,
  • Applied Mathematics,
  • Computer Science, and
  • Statistics.

Students must select a concentration.

Pure Mathematics Concentration

1. Required Core Courses (21 hours): MAT 191, 292, 293, 310, 311, 394, 395

2. Three courses chosen from the following (9 hours): MAT 514, 515, 517, 518, 519, 531, 532, 540, 591, 592, 595, 596

3. Three additional courses chosen from the following (9 hours): any MAT course 200-level or above (excluding 220, 303, 304, 503, 504, 505); CSC 322, 523, 524, 553, 555; STA 271, 351, 352, 551, 552, 573, 574, 575

4. CSC 130 or 230

5. PHY 291, 292 and 251, 252 labs; or CHE 111, 112, 114, 115; or BIO 111, 112

Applied Mathematics Concentration

1. Required Core Courses (27 hours): MAT 191, 292, 293, 310, 311, 390, 394, 395; STA 351

2. Two courses chosen from the following (6 hours): MAT 515, 522, 531, 532, 540, 545, 546, 549, 556, 595, 596; CSC 523, 524; STA 551, 552

3. Two additional courses chosen from the following (6 hours): any MAT course 200-level or above (excluding 220, 303, 304, 503, 504, 505); CSC 322, 523, 524, 553, 555; STA 271, 352, 551, 552, 573, 574, 575

4. CSC 130 or 230

5. PHY 291, 292 and 251, 252 labs; or CHE 111, 112, 114, 115; or BIO 111, 112

6. Two additional courses chosen from the following (5-7 hours): ECO 301, 319, 351; PHY 323, 325, 523, 525; CHE 242, 461, 462; CSC 261, 322, 330, 523, 524, 529, 539, 553, 555, 561; STA 352, 551, 552, 573, 574, 575

Computer Science Concentration

1. Required Core Courses (24 hours): MAT 191, 253, 292, 293, 310, 311, 394, 395

2. Two 500-level courses chosen from the following (6 hours): any MAT course (excluding 503, 504, 505, 513); CSC 523, 524, 553, 555; STA 551 552, 573, 574, 575

3. Three additional courses chosen from the following (9 hours): any MAT course 200-level or above (excluding 220, 303, 304, 503, 504, 505); CSC 322, 523, 524, 553, 555; STA 271, 351, 352, 551, 552, 573, 574, 575

4. Required CSC courses: CSC 130, 230, 330; one of CSC 261, 339, 340; two 500-level CSC courses (if not already taken in (2) or (3) above)

5. PHY 291, 292 and 251, 252 labs; or CHE 111, 112, 114, 115; or BIO 111, 112

Statistics Concentration

1. Required Core Courses (21 hours): MAT 191, 292, 293, 310, 311, 394, 395

2. Required Statistics Courses (18 hours): STA 351 or 551; STA 352 or 552; STA 573, 574; two additional statistics courses at or above the 200-level (excluding STA 571 and 572) and chosen with the advice and consent of the department

3. CSC 130 or 230

4. PHY 291, 292 and 251, 252 labs; or CHE 111, 112, 114, 115; or BIO 111, 112

 

Secondary Teacher Licensure

 

Students seeking secondary teacher licensure must satisfy the requirements for the B.A. or B.S. degree and must include in their program:

CSC 322 or MAT 390; STA 271 or 351; MAT 504, 505, 513; one course chosen from: MAT 514, 515, 516, 517, 518, 519, 520, 521, 531,540, 549, 595, 596.

Also see "Teacher Education Programs," Part 7.

 

Mathematics as a Second Major

Requirements for a Second Major in Mathematics are the sambas for the Mathematics Major.

 

Mathematics Minor

The minor in mathematics consists of at least 15 hours of work, chosen as follows:

1. MAT 191, 292

2. MAT 310 or 353

3. Six additional hours at the 200-level or above consisting of any MAT, CSC, or STA courses that count toward the mathematics major.

NOTE: All minor programs must be approved by the Department of Mathematical Sciences.

 

Accelerated Masters Program for Undergraduates:
BA or BS in Mathematics and MA or MEd in Mathematics

The Department of Mathematical Sciences offers an accelerated program that permits the exceptionally well qualified student to receive an undergraduate degree in mathematics (BA or BS) within a four year period and a Masters degree in mathematics (MA or MEd) in an additional year.

A thorough knowledge of calculus is necessary for much of the advanced work required to complete the undergraduate degree. Because of this, it is unlikely that a student would be able to complete the accelerated program without having AP calculus credit. Advanced Placement credit in other areas would also be helpful in order to reduce the number of required undergraduate hours; see courses for which AP credit is available.

Most mathematics courses depend on previous knowledge and have significant prerequisites. It is therefore very important that students identify themselves as potential candidates for the accelerated program early in their academic careers in order to receive appropriate advising. Although formal admission to the accelerated program does not occur until the student achieves junior status, proper advising must take place as early as possible so that appropriate coursework can be chosen in the correct sequence. This is particularly important with respect to mathematics courses so that the student will be ready to begin advanced work in mathematics suitable for the masters degree as soon as possible.

Students in the accelerated program must meet all requirements for the respective degree received. No coursework may be counted toward more than one degree. Requirements for the undergraduate degrees are listed on pp. 104-105. The MA in mathematics requires 30 hours of graduate level mathematics including a thesis; the MEd in mathematics requires 33 hours at the graduate level including 24 hours in mathematics and 9 hours in education. Specific requirements for the MA and MEd are listed in The Graduate School Bulletin (link at bottom).

 

Computer Science Major (Bachelor of Science)

Required: 122 semester hours

 

The BS degree in Computer Science is accredited by the Computer Science Accreditation Commission of the Computing Sciences Accreditation Board.

College of Arts and Sciences Liberal Education Requirements (CLER) (54-55 hours)

All students must meet the All-University Liberal Education Requirements (AULER). The College of Arts and Sciences, however, has established liberal education requirements for its programs which, while including those of AULER, contain additional requirements in several categories. Therefore, students following this program should adhere to the College requirements. Please note that students who satisfy the College Liberal Education Requirements (CLER) will also satisfy the All-University Liberal Education Requirements (AULER). See College requirements and courses meeting AULER/CLER requirements.

Major Requirements

1. CSC 130, 230, 261, 312, 330, 339, 340, 553, 561, 562

2. CSC Electives: 12 hours, selected from any CSC course at the 500-level (except 553, 561, 562); PHY 512, PHY 513.

Supporting Discipline Requirements

1. MAT 191, 253, 292, 293, 353; STA 271

2. One of MAT 515, 531, 532, 541, 542, 556, STA 551, 552

Science Requirements

1. PHY 291, 292 and 251, 252 labs, or CHE 111, 112, 114, 115. (These courses also fulfill the College physical science, laboratory science, and unrestricted science requirements.)

2. At least 4 hours of science courses selected from any course carrying credit toward a biology, chemistry, or physics major, excluding PHY 512 and 513. (Only BIO 111 or 112 fulfills the College life science requirement as well as this requirement.)

Students must maintain a grade point average of at least 2.0 in the core courses, required electives, and required supporting discipline courses.

Because computer science courses change rapidly, it is recommended that the sequence 130, 230, 330 be completed within four (4) consecutive semesters.

 

Computer Science Minor

The minor in computer science consists of at least 15 hours of work, chosen as follows:

1. MAT 253

2. CSC 130, 230, 330

3. One of CSC 261, 339, 340

The Computer Science Minor requires 3 to 4 semesters to complete.

NOTE: All minor programs must be approved by the Department of Mathematical Sciences.

 

Computer Science Courses (CSC)

Courses For Undergraduates

101 Introduction to Computer Concepts (3:3).

Introduction to computers and computing. Topics cover impact of computers on society, ethical issues, hardware, and software applications. (FA,SP)

130 Introduction to Computer Science (3:3).

  • Pr. acceptable score on the mathematics placement test or a grade of at least C in MAT 119.

Programming in a high-level language. Emphasis on problem analysis, problem-solving techniques, and software design principles and techniques. (FA,SP)

230 Elementary Data Structures and Algorithms (3:3).

  • Pr. grade of at least C in 130.

Advanced syntax of high level language taught in CSC 130. Emphasis on modularization and abstraction. Big-O analysis of algorithms. Design and use of abstract data types with various implementations. (FA,SP)

237 Programming Language Laboratory (1 to 3; 1 to 3).

  • May be taken twice for credit with permission of the Department Head.

Syntax and use of a programming language. Language covered announced at preregistration.

261 Computer Organization and Assembly Language (3:3).

  • Pr. grade of at least C in 230 and in MAT 253.

CPU, memory, I/O devices, digital logic design, psw. Number representations and machine language. Assembly language instruction types, registers, addressing, arithmetic, instruction format, opcodes, pseudo-opcodes, assembler directives, system calls, and macros. (FA)

312 Ethics in Computer Science (1:1).

  • Pr. grades of at least C in 230 and in MAT 253.
  • Grade: Pass/Not Pass (P/NP).

Historical and social context of computing, ethical responsibilities of the computing professional, intellectual property rights, and risks and liabilities. (SP)

322 Linear Programming (3:3).

  • Pr. grade of at least C in MAT 310.

Covers simplex computational procedure, minimum feasible solutions, artificial-basis technique, slack variables, perturbation techniques, cycling, parametric objective and dual problems, sensitivity analysis, and decomposition algorithms.

330 Advanced Data Structures (3:3).

  • Pr. grades of at least C in 230 and in MAT 253.

Static and dynamic data structures emphasizing binary trees and graphs. Advanced programming techniques. Advanced sorting and searching algorithms. Hashing techniques. Performance analysis. Methods of developing large applications programs. (FA,SP)

339 Concepts of Programming Languages (3:3).

  • Pr. grade of at least C in 330.

Concepts of block-structured, object-oriented, functional, logic, and concurrent programming languages. Comparative study of syntactic and semantic features of these languages and writing programs using them. (SP)

340 Software Engineering (3:3).

  • Pr. grade of at least C in in 330.

Practical and theoretical concepts of software engineering. (SP)

Courses For Advanced Undergraduates and Graduate Students

521 Computer Graphics and Image Processing (3:3).

  • Pr. grades of at least C in 330 and in MAT 353, or permission of instructor.

Survey of graphics and image processing hardware, algorithms, data structures, and techniques. (Odd SP)

523 Numerical Analysis and Computing (3:3).

  • Pr. grades of at least C in 130, and in MAT 353 and MAT 293.

Number systems and errors, solutions of non-linear and linear systems, eigenvalue problems, interpolation and approximation, numerical differentiation and integration, solution of differential equations. (Odd FA)

524 Numerical Analysis and Computing (3:3).

  • Pr. grade of at least C in 523.

Continuation of 523 with special topics in numerical analysis, emphasis on applied mathematics. (Even SP)

529 Artificial Intelligence (3:3).

  • Pr. grade of at least C in 330.

Knowledge representations. Resolution refutation systems. Best-first search algorithms. Heuristic, minimax, alpha-beta pruning techniques. Selected topics from machine learning, natural language processing, expert systems, neural networks. Functional or logic programming language. (Odd SP)

539 Introduction to Compiler Design (3:3).

  • Pr. grades of at least C in 261 and 330 or permission of instructor. Successful completion of 553 helpful.

Basic techniques of compiler design and implementation: lexical analysis, parsing, code generation. Sizable programming project implementing a compiler for a block-structured language with strong typing. (Even SP)

553 Theory of Computation (3:3).

  • Pr. grade of at least C in MAT 353 and programming experience .

Finite state automata and regular expressions, context-free grammars, push-down automata and their use in parsing, overview of language translation systems, models for programming language semantics, computability and undecidability. (FA)

555 Algorithm Analysis and Design (3:3).

  • Pr. grade of at least C in 330.

Sequential algorithm design and complexity analysis. Dynamic programming. Greedy algorithms. Graph algorithms. Selected advanced topics from NP-completeness; approximation, randomized, parallel, number-theoretic algorithms; Fast Fourier Transform; computational geometry; string matching. (FA)

561 Principles of Computer Architecture (3:3).

  • Pr. grades of at least C in 261, MAT 253 or permission of instructor.

Hardware and software components of computer systems, their organization and operations. Topics: comparative instruction set architectures, microprogramming, memory management, processor management, I/O, interrupts, and emulation of processors. (FA)

562 Principles of Operating Systems (3:3).

  • Pr. grades of at least C in 261 and 330 or permission of instructor. Successful completion of 561 helpful.

Techniques and strategies used in operating system design and implementation: managing processes, input/output, memory, scheduling, file systems, and protection. (SP)

567 Principles of Computer Networks (3:3).

  • Pr. grades of at least C in CSC 261 and 330 or equivalent courses.

Hardware and software components of computer networks, their organization and operations. Topics: open system interconnection; local area networks; TCP/IP internetworking, routing, and packet switching; network programming. (FA)

570 Principles of Database and Knowledge-Base Systems (3:3).

  • Pr. grade of at least C in CSC 330, or consent of instructor.

Contemporary database and knowledge-base systems. Emphasis on relational, extended relational, deductive, and object-oriented models. Query processing, modeling and implementation of applications in these models. (FA)

593, 594 Directed Study in Computer Science (1 to 3), (1 to 3). (FA,SP)

 

 

Mathematics Courses (MAT)

Courses For Undergraduates

100 Intermediate Algebra (3:3).

  • Credit does not apply toward graduation nor count in the student's GPA.

Real numbers and their properties, linear equations, systems of equations, polynomials and functions, fractional expressions, exponents and roots, quadratic equations, graphing, inequalities. (FA,SP)

112 Contemporary Topics in Mathematics (3:3).

Selected topics from sets and logic, mathematical systems, statistics and probability, geometry and matrix algebra, consumer mathematics. Designed primarily for liberal arts student. [MT, CMT]. (FA,SP)

119 College Algebra (3:3).

  • Pr. an acceptable score on the mathematics placement test or a grade of at least C in 100.

Review of elementary algebra, equations, inequalities, relations, functions, transformations, graphing, complex numbers, polynomial and rational functions. [MT, CMT]. (FA,SP)

120 Calculus for Business and the Social Sciences (3:3).

  • Pr. an acceptable score on the mathematics placement test or a grade of at least C in 119.
  • Credit cannot be received for both this course and MAT 191.
  • NOTE: this course does not serve as a prerequisite for 292 (Calculus II).

Limits and introductory differential calculus of the algebraic functions of one variable. [MT, CMT]. (FA,SP)

121 Analytic Trigonometry (3:3).

  • Pr. an acceptable score on the mathematics placement test or a grade of at least C in 119.

Review of relations, trigonometric (circular) functions and identities, exponential and logarithmic functions, solutions of triangles, equations of second degree and their graphs. [MT, CMT]. (FA,SP)

191 Calculus I (3:3).

  • Pr. a grade of at least C in 121 or permission of the instructor.
  • Credit cannot be received for both this course and MAT 120 (formerly MAT 191B).

Limits and introductory differential calculus of the algebraic and transcendental functions of one variable. [MT, CMT]. (FA,SP)

220 Plane and Solid Analytic Geometry (3:3).

  • Pr. grade of at least C in 121 or equivalent.
  • Hours count toward teacher licensure but do not count toward degree requirements for a mathematics major.

Study of conic sections (including rotation of axes), graphing with polar coordinates, quadric surfaces, and vectors. (SP)

253 Discrete Mathematics I (3:3).

  • Pr. grade of at least C in 121, acceptable score on mathematics placement test, or consent of instructor.
  • Only one of MAT 253 or MAT 295 can count toward degree requirements for a mathematics major.

Mathematical reasoning techniques and concepts in computer science. Topics include sets, functions, sequences, relations, induction and recursion, boolean algebra, and elementary propositional and predicate logic, including proof techniques. (FA,SP)

292 Calculus II (3:3).

  • Pr. a grade of at least C in 191 or permission of the instructor.

A continuation of the study of differential calculus of the elementary transcendental functions, introductory integral calculus of the algebraic and transcendental functions of one variable, techniques of integration, indeterminate forms, improper integrals.. (FA,SP)

293 Calculus III (3:3).

  • Pr. grade of at least C in 292.

Infinite series, Taylor's formula, conic sections, parametric equations, integration using polar coordinates, vectors, surfaces, vector-valued functions. (FA,SP)

295 Proofs and Mathematical Structures (3:3).

  • Pr. grade of at least C in 292.
  • At most one of MAT 253 or MAT 295 can count toward degree requirements for a mathematics major.

An introduction to basic mathematical concepts needed for most upper level mathematics courses. The language and logic of proofs, basic set theory, relations, functions, numbers, counting, cardinalities, introduction to algebra.

303 Topics in Mathematics (3:3).

  • Hours count toward teacher licensure but do not count toward degree requirements for a mathematics major.

Primarily for students seeking grades 6-9 certification. Extensive study of rational, irrational and real numbers; selected topics from number theory; clock and modular arithmetic. Concrete models used to illustrate many of the mathematical concepts studied.

304 Introduction to the Foundations of Geometry (3:3).

  • Hours do not count toward degree requirements for Mathematics majors.

Introductory course primarily for students seeking grade 6-9 certification. Designed to develop an understanding of the fundamental ideas of geometry. Includes both an intuitive and deductive study of points, lines, planes, curves, surfaces, congruences, parallelism, similarity and linear, angular, area, and volume measures.

310 Matrix Theory (3:3).

  • Pr. grade of at least C in 292.

Matrices, equivalence relations for square matrices, determinants, finite dimensional vector spaces, linear transformations, eigen- vectors. (FA,SP)

311 Modern Algebra (3:3).

  • Pr. grade of at least C in 310.

Introduction to theory of groups, rings, integral domains and fields, including basic properties of polynomials. (FA,SP)

345 Vector and Tensor Analysis (3:3).

  • Pr. grade of at least C in 293 and 390.

Vectors, scalar fields, vector fields. Dot and cross product. Vector differentiation and integration. Gradient, divergence and curl. Green's theorem, divergence theorem, Stokes' theorem. Curvilinear coordinates. Tensor Analysis: Physical laws. Coordinate transformations. Contravariant and covariant vectors. Contravariant, covariant, and mixed tensors. Tensor fields. Symmetric and skew-symmetric tensors. Conjugate or reciprocal tensors. Associated tensors. Transformation laws of Christoffel's symbols. Tensor form of gradient, divergence, and curl.

353 Discrete Mathematics II (3:3).

  • Pr. grade of at least C in 253 or consent of instructor.

Problem-solving and modeling using techniques and concepts of Discrete Mathematics with applications to algorithms. Topics include elementary graph theory, combinatorics, difference equations, and linear algebra. (FA)

390 Ordinary Differential Equations (3:3).

  • Pr. 292.

First order differential equations and linear equations of finite order, Laplace transforms, undetermined coefficients, variation of parameters, power series solutions near ordinary or regular singular points, applications, numerical methods. (SP)

394 Calculus IV (3:3).

  • Pr. grade of at least C in 293.

Partial differentiation, multiple integrals, vector calculus. (FA,SP)

395 Introduction to Mathematical Analysis (3:3).

  • Pr. grade of at least C in 293, 310.

Introduction to fundamental concepts of single variable calculus, including properties of real numbers, notion of limit, continuity, differentiation, integration, and infinite series. (FA)

493 Honors Work (3-6).

  • See prerequisites under Honors Program, XXX 493.
  • May be repeated for credit if the topic of study changes.

Courses For Advanced Undergraduates and Graduate Students

503 Problem Solving in Mathematics ((3:3).

  • Pr. grade of at least C in 191 and 303 or consent of instructor.
  • Hours count toward teacher licensure but do not count toward degree requirements for a mathematics major.

Investigates the nature of problem solving, covers procedures involved in problem solving, develops individual problem solving skills, and collects a set of appropriate problems. Required for middle grades mathematics concentration.

504 Foundations of Geometry for Teachers (3:3).

  • Pr. grade of at least C in 292 or consent of instructor.
  • Hours count toward teacher licensure but do not count toward degree requirements for a mathematics major.

Primarily for students seeking teacher certification. Includes logic and axiom systems, history, plane and solid Euclidean geometry, proof strategies, introduction to non-Euclidean geometries, and transformational geometry. (FA)

505 Foundations of Mathematics for Teachers (3:3).

  • Pr. grade of at least C in 292 or 303 or consent of instructor.
  • Hours count toward teacher licensure but do not count toward degree requirements for a mathematics major.

Primarily for students seeking teacher certification. Includes properties and algebra of real numbers; analytic geometry; polynomial, rational, exponential, logarithmic, and trigometric functions; complex numbers; concept of limits of functions. (SP)

513 Historical Development of Mathematics (3:3).

  • Pr. grade of at least C in 292.

Study of the historical development of mathematics, not a history of persons involved in development. (FA)

514 Theory of Numbers (3:3).

  • Pr. grade of at least C in 311 or permission of instructor.

An introductory course to both multiplicative and additive number theory. Divisibility, prime numbers, congruences, linear and nonlinear Diphantine equations (including Pell's equation), quadratic residues, number-theoretic functions, and other topics.

515 Mathematical Logic (3:3).

  • Pr. grade of at least C in 253 or 311 or consent of instructor.

Formal languages, recursion, compactness, and effectiveness. First-order languages, truth, and models. Soundness and completeness theorems. Models of theories. (Odd SP)

516 Polynomial Rings (3:3).

  • Pr. grade of at least C in 311.
  • Rings, integral domains, fields, division algorithm, factorization theorems, zeros of polynomials, greatest common divisor, relations between the zeros and the coefficients of a polynomial, formal derivatives, prime polynomials, Euclidean rings, the fundamental theorem of algebra.

    517 Theory of Groups (3:3).

    • Pr. grade of at least C in 311.

    Elementary properties of groups and homomorphisms, quotients and products of groups, the Sylow theorems, structure theory for finitely generated Abelian groups.

    518 Set Theory and Transfinite Arithmetic (3:3).

    • Pr. grade of at least C in 311 or 395.

    The axioms of set theory, operations on sets, relations and function, ordinal and cardinal numbers.

    519 Intuitive Concepts in Topology (3:3).

    • Pr. grade of at least C in 311 or 395.

    Basic concepts, vector fields, the Jordan curve theorem, surfaces, homology of complexes, continuity.

    520 Non-Euclidean Geometry (3:3).

    • Pr. grade of at least C in 311 or 395.

    Fifth postulate, hyperbolic geometries, elliptic geometries, consistency of non-Euclidean geometries, models for geometries, elements of inversion.

    521 Projective Geometry (3:3).

    • Pr. consent of instructor.

    Transformation groups and projective, affine and metric geometries of the line, plane, and space. Homogeneous coordinates, principles of duality, involutions, cross-ratio, collineations, fixed points, conics, ideal and imaginary elements, models, and Euclidean specializations.

    522 Hilbert Spaces and Spectral Theory (3:3).

    • Pr. grade of at least C in 311 or 395.

    Vector-spaces: basis, dimension, Hilbert spaces; pre-Hilbert spaces, norms, metrics, orthogonality, infinite sums. Linear subspaces; annihilators, closed and complete subspaces, convex sets. Continuous linear mappings; normed spaces. Banach spaces, Banach algebras, dual spaces. Reisz-Frechet theorem. Completion. Bilinear and seaquilinear maps. Adjoints. Operators in Hilbert space: isometric, unitary, self-adjoint, projection, and normal operations. Invariant subspaces. Continuous operators. Special theorems for a normal co-operator.

    531 Combinatorial Analysis (3:3).

    • Pr. grade of at least C in 253 or 295 or 311 or 395, or consent of instructor.

    The pigeon-hole principle, permutations, combinations, generating functions, principle of inclusion and exclusion, distributions, partitions, recurrence relations.

    532 Introductory Graph Theory (3:3).

    • Pr. grade of at least C in 310 and any one of the courses 253, 295, 311, 395, 531.

    Basic concepts, graph coloring, trees, planar graphs, networks.

    540 Complex Functions with Applications (3:3).

    • Pr. grade of at least C in 293.

    The complex number system, holomorphic functions, power series, complex integration, representation theorems, the calculus of residues.

    541, 542 Stochastic Processes (3:3), (3:3).

    • Pr. grade of at least C in MAT 394 and either MAT 353 or STA 351, or equivalents.

    Markov processes, Markov reward processes, queuing, decision making, graphs and networks. Applications to performance, reliability, and availability modeling.

    545 Differential Equations and Orthogonal Systems (3:3).

    • Pr. grade of at least C in 293 and 390 or consent of instructor.

    An introduction to Fourier series and orthogonal sets of functions, with applications to boundary value problems.

    546 Partial Differential Equations with Applications (3:3).

    • Pr. grade of at least C in 545.

    Fourier integrals, Bessel functions, Legendre polynomials and their applications. Existence and uniqueness of solutions to boundary value problems.

    549 Topics in Applied Mathematics (3:3).

    • Pr. grade of at least C in 293 and 390 or consent of instructor.
    • May be repeated for credit with approval of the Department Head.

    Selected topics of current interest in applied mathematics.

    556 Advanced Discrete Mathematics (3:3).

    • Pr. grade of at least C in 253 or consent of instructor.

    Advanced topics in discrete mathematics and their uses in studying computer science. (Even SP)

    591 Advanced Modern Algebra (3:3).

    • Pr. grade of at least C in 311.

    Set theory: sets, mappings, integers. Group theory: normal subgroups, quotient groups, permutation groups, Sylow theorems. Ring theory: homomorphisms, ideals, quotient rings, integral domains, fields, Euclidean rings, polynomial rings.

    592 Abstract Algebra (3:3).

    • Pr. grade of at least C in 591 or 311 with consent of instructor.

    Fields: extensions, transcendental elements, roots of polynomials, Euclidean constructions. Galois theory, solvability by radicals.

    593, 594 Directed Study in Mathematics (1 to 3), (1 to 3). (FA,SP)

    595, 596 Mathematical Analysis (3:3), (3:3).

    • Pr. 395 or permission of instructor.

    Real number axioms, metric spaces, sequences, series, continuity, differentiation, the Reimann-Stieltjes integral. (FA,SP)

     

    Statistics Courses (STA)

    Courses For Undergraduates

    108 Elementary Introduction to Probability and Statistics (3:3).

    • Pr. an acceptable score on the mathematics placement test or a grade of at least C in MAT 100.
    • May not be taken for credit by students who have received credit for ECO 250 or 350 or are concurrently enrolled in ECO 250.

    Finite sample spaces, discrete probability, random variables, expected value, binomial distribution, independent trials, random samples, point estimation, hypothesis testing, and confidence intervals. [MT, CMT] (FA,SP)

    271 Fundamental Concepts of Statistics (3:3).

    • Pr. grade of at least C in MAT 119 or STA 108 or consent of department.

    Survey of basic descriptive and inferential statistics for undergraduates from any discipline. Graphical and descriptive techniques. Measures of central tendency, variability, correlation. Estimation. Normal tests, t-tests, analysis of variance. Emphasis on statistical literacy and interpretation.

    351 Probability (3:3).

    • Pr. grade of at least C in MAT 292.

    Basic probability theory; combinatorial probability, conditional probability and independent events; univariate and multivariate probability distribution functions and their properties. (FA)

    352 Statistical Inference (3:3).

    • Pr. grade of at least C in 351 or consent of instructor.

    Descriptive and inferential statistics. Emphasis on sampling distributions; theory of estimation and tests of hypotheses, linear hypothesis theory, regression, correlation and analysis of variance. (SP)

    For Advanced Undergraduates and Graduate Students

    551, 552 Introduction to Probability and Mathematical Statistics (3:3), (3:3).

    • Pr. grade of at least C in 351 and MAT 293 or consent of instructor.

    Events and probabilities (sample spaces), dependent and independent events, random variables and probability distribution, discrete and continuous distributions, expectation, moment generating functions, point estimation, multivariate normal distribution, testing hypotheses, confidence intervals, correlation and regression, small sample distributions.

    571 Statistical Methods for Research I (3:3).

    • Coreq. enrollment in 571L.
    • Hours do not count toward degree requirements for a mathematics major.

    Introduction to statistical concepts. Basic probability, random variables, the binomial, normal and Student's t distributions, hypothesis tests, confidence intervals, chi-square tests, introduction to regression, and analysis of variance. (FA)

    571L Statistical Methods Laboratory I (1:0:2).

    • Coreq. enrollment in 571.
    • Hours do not count toward degree requirements for a mathematics major.

    Using statistical software packages for data analysis. Problems parallel assignments in 571. (FA)

    572 Statistical Methods for Research II (3:3).

    • Pr. 571 and 571L or permission of instructor; coreq. enrollment in 572L.

    Statistical methodology in research and use of statistical software. Regression, confidence intervals, hypothesis testing, design and analysis of experiments, one and two-factor analysis of variance, multiple comparisons, hypothesis tests. (SP)

    572L Statistical Methods Laboratory II (1:0:2).

    • Pr. 571 and 571L or permission of instructor; coreq. enrollment in 572.

    Using statistical software packages for data analysis. Problems parallel assignments in 572. (SP)

    573 Theory of Linear Regression (3:3).

    • Pr. grade of at least C in 352 and MAT 310, or 662, or consent of instructor.

    Linear regression, least squares, inference, hypothesis testing, matrix approach to multiple regression. Estimation, Gauss-Markov Theorem, confidence bounds, model testing, analysis of residuals, polynomial regression, indicator variables.

    574 Theory of the Analysis of Variance (3:3).

    • Pr. grade of at least C in 573 or consent of instructor.

    Multivariate normal distribution, one-way analysis of variance, balanced and unbalanced two-way analysis of variance, empty cells, multiple comparisons, special designs, selected topics from random effects models.

    575 Nonparametric Statistics (3:3).

    • Pr. grade of at least C in 352 or 572 or 662, or consent of instructor.

    Introduction to nonparametric statistical methods for the analysis of qualitative and rank data. Binomial test, sign test, tests based on ranks, nonparametric analysis of variance, nonparametric correlation and measures of association. (Even FA)

    593, 594 Directed Study in Statistics (1 to 3), (1 to 3). (FA,SP)

    593, 594 Directed Study in Statistics (1 to 3), (1 to 3). (FA,SP)

    Please refer to The Graduate School Bulletin for additional graduate level courses.


     
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