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Department of Mathematical Sciences
383 Bryan Building

Major / Minor Information

Courses


Paul F. Duvall, Professor and Head of Department

Professors Hildebrandt (Emeritus), Posey (Emeritus), Sher (Emeritus), J.Vaughan; Associate Professors Church (Emeritus), Gentry, Herr, Kissling, Landman, Lea, Long, Ludwig, Sadri, T. Vaughan; Assistant Professors Blanchet-Sadri, Byrd, Cooper, Love, Sivalingam, Wang; Instructors Griffin, Kilgariff; Lecturers 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 mathematics, computer science, or statistics) and the Certificate of Advanced Study (sixth-year program).

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", Chapter 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 pp. 70-73 for a complete description of the College requirements and pp. 65-66 and 71-72 for a listing of 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 and 212; or PHY 291 and 292; or CHE 103 and 104 (with required CHE 110 lab); or BIO 111 and 112

Requirements for the Bachelor of Science

Students must meet all of the requirements for the Bachelor of Arts and take two additional courses from list C above.

Computer Science Concentration

Students majoring in mathematics may elect to concentrate in computer science. Students seeking this concentration must satisfy the requirements for the B.S. degree and must include in their program: MAT 253; CSC 130, 230, 330; one of CSC 261, 339, 340; and two 500-level CSC electives.

Statistics Concentration

Students majoring in mathematics may elect to concentrate in statistics. Students seeking this concentration must satisfy the requirements for the B.S. degree and must include in their program: STA 351 (or 551), 352 (or 552), 573, 574, an approved course in analysis, and two additional statistics courses at the 200 level or above, excluding STA 571 and 572, and chosen with the advice and consent of the Department of Mathematical Sciences.

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," Chapter 7.

Mathematics as a Second Major

Requirements for a Second Major in Mathematics are the same as 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 on pp. 20-21 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. 174-175. 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 Catalog.

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 pp. 70-73 for a complete description of the College requirements and pp. 65-66 and 71-72 for a listing of courses meeting AULER/CLER requirements.

Major Requirements

1. CSC 130, 230, 261, 312, 330, 339, 340, 553, 561, 562
2. CSC Electives: 12 hours; select one option below:
Option 1-3 courses from Group A, and 1 course from any group
Option 2-2 courses from Group A, CSC 521, and 1 course from any group
Option 3-1 course from Group A, ISM sequence or CSC 570 from Group B, and 2 courses from any group
Option 4-ISM sequence or CSC 570 from Group B, CSC 521, 555, and either 539 or 1 course from Group C
Group A: CSC 322, 523, 524, 529, 593, 594
Group B: ISM sequence of 1 hour courses; all three courses must be taken: ISM 315, 316, and 317; CSC 521, 539, 555, 570, 593, 594
Group C: CSC 467, 593, 594, PHY 512*, PHY 513*
* May be used either here or in Science Requirement 2 below

Supporting Discipline Requirements

1. MAT 191, 253, 292, 293, 310, 353
2. One of MAT 515, 531, 532, 541, 542, 556, STA 551, STA 552

Science Requirements

1. PHY 291 and 292, or CHE 111, 112, 114, 115 (these courses also fulfill the College physical science, laboratory science, and unrestricted science requirements).
2. At least 6 hours of science courses selected from ATY 253 or any course carrying credit toward a biology, chemistry, or physics major. (Only BIO 111, 112 or ATY 253 fulfills the College life science requirement as well as one course in 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

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

COMPUTER SCIENCE COURSES (CSC)

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.

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.

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.

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.

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.

312 Ethics in Computer Science (1:1). Pr. grades of at least C in 230 and 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.

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.

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.

340 Software Engineering (3:3). Pr. grade of at least C in in 330.

Practical and theoretical concepts of software engineering.

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 310, or permission of instructor.

Survey of graphics and image processing hardware, algorithms, data structures, and techniques.

523 Numerical Analysis and Computing (3:3). Pr. grades of at least C in 130, and in MAT 310 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.

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.

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.

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.

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.

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.

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.

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.

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. (Formerly CSC 467)

570 Principles of Database and Knowledge-Base Systems (3:3). Pr. grade of at least C in CSC 330 or ISM 317, 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.

589 Experimental Course: Introduction to Parallel Computing (3:3). Pr. CSC 561.

Parallel and distributed computing. Introduction to PVM software. Course will be taught as a telecourse from UNC-Charlotte. (Offered FA 96)

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

For Graduate Students Only

621 Advanced Computer Graphics and Image Processing (3:3)

623, 624 Numerical Mathematics (3:3), (3:3).

670 Database System Architecture (3:3).

693 Advanced Topics in Computer Science (3 to 6).

695 Current Problems in Computer Science (3:3).

699 Thesis (3-6).

MATHEMATICS COURSES (MAT)

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.

112 Contemporary Topics in Mathematics (3:3).

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

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].

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].

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].

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].

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.

253 Discrete Mathematics I (3:3). Pr. grade of at least C in 121, acceptable score on mathematics placement test, or consent of instructor. At most 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, recurrence relations, boolean algebra, and elementary propositional and predicate logic, including proof techniques.

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.

293 Calculus III (3:3). Pr. grade of at least C in 292.

Indeterminate forms, Taylor's formula, infinite series, partial derivatives, multiple integrals.

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.

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.

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, discrete probability and random numbers.

390 Ordinary Differential Equations (3:3). Pr. 292.

First order differential equations and linear equations of finite order, inverse differential operators, undetermined coefficients, variation of parameters, power series solutions near ordinary or regular singular points, applications, numerical methods.

394 Calculus IV (3:3). Pr. grade of at least C in 293.

Application of partial derivative, infinite series, multiple integrals, line and surface integrals, integral theorems.

493 Honors Work (3-6). See prerequisites under Honors Program, XXX 493 (p. 379).

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.

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.

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.

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 295 or 311.

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

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.

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.

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.

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.

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 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, 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.

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).

595, 596 Mathematical Analysis (3:3), (3:3). Pr. consent of instructor.

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

For Graduate Students Only

606 Calculus for Middle Grade Teachers (3:3).

607 Abstract Algebra for Middle Grade Teachers (3:3).

613 Development of Mathematics and Logic (3:3).

614 Advanced Number Theory (3:3).

615 Symbolic Logic (3:3).

616 Polynomials over General Rings (3:3).

617 Algebraic Theory of Semigroups (3:3).

618 Transfinite Ordinal and Cardinal Numbers (3:3).

619 Conceptual Topology (3:3).

620 A Survey of Geometry (3:3).

621 Advanced Linear Geometry (3:3).

631 Combinatorics (3;3).

632 Graph Theory (3:3).

645, 646 Approximation Theory (3:3), (3:3).

647, 648 Linear Algebra and Matrix Theory (3:3), (3:3).

649 Topics in Operations Research (3:3).

650 Management Decision-Making under Uncertainty (3:3).

688, 689 Mathematical Logic and Axiomatic Set Theory (3:3), (3:3).

690 Mathematics Seminar (2:2).

691, 692 Modern Abstract Algebra (3:3), (3:3).

693, 694 Complex Analysis (3:3), (3:3).

695, 696 Real Analysis (3:3), (3:3).

697, 698 General Topology (3:3), (3:3).

699 Thesis (4 to 6).

800 Graduate Registration.

STATISTICS COURSES (STA)

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].

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.

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.

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.

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.

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

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

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

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.

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

For Graduate Students Only

651, 652 Mathematical Statistics (3:3), (3:3).

661 Advanced Statistics in the Behavioral and Biological Sciences I (3:3).

661L Advanced Statistics Laboratory (1:1)).

662 Advanced Statistics in the Behavioral and Biological Sciences II (3:3).

662L Advanced Statistical Laboratory (1:1)).

667 Statistical Consulting (1:1).

671 Multivariate Analysis (3:3).

672 Applied Statistical Computing. (3:3).

673 Statistical Linear Models I (3:3).

674 Statistical Linear Models II (3:3).

675 Experimental Design (3:3).

676 Sample Survey Methods (3:3).

677 Advanced Topics in Data Analysis (3:3).

699 Thesis (4-6).


 
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