# Department of Mathematics, Statistics, and Computer Science

## Introduction

Mathematics is the language of the sciences and of all fields where patterns and systematic processes need to be analyzed. The study of the various mathematical sciences involves learning ideas and techniques essential for the natural and social sciences and is increasingly important in all areas of a technological society.

Occupational fields open to students who have completed one of the curricula or majors in the department include mathematical analysis in industry or government, teaching, research, actuarial (insurance) work, computer programming and other statistical work, and mathematical aspects of business and finance.

The Department of Mathematics, Statistics, and Computer Science offers programs leading to the Bachelor of Science with a Major in Mathematics, the Bachelor of Science in the Teaching of Mathematics, the Bachelor of Science in Mathematics and Computer Science, and the Bachelor of Science with a Major in Statistics. A Minor in Mathematics and a Minor in Mathematics and Computer Science are also offered. Each major is assigned a department advisor who approves the student’s choice of courses.

## Transfer Students

A transfer student majoring in one of these programs must successfully complete at least half of the mathematics courses in residence at UIC. For the BS with a Major in Mathematics, at least 12 semester hours must be at the advanced level; for the BS in Mathematics and Computer Science, 14 semester hours must be upper division. No transfer course below calculus may be counted toward the BS with a Major in Mathematics, the BS in the Teaching of Mathematics, the BS in Mathematics and Computer Science, or the BS with a Major in Statistics. Only grades of A, B, or C in calculus and above from other colleges and universities will be accepted for transfer credit.

## Admission Requirements

Students must have concurrent registration in MATH 180, or equivalent standing, as a requirement for declaration of a major in any departmental program.

## Distinction

For consideration, the student must have a minimum of a 3.50/4.00 GPA in upper-division courses in the department. The department may award High and Highest Distinction in recognition of outstanding academic achievement.

## Degree Programs

- BS with a Major in Mathematics
- BS with a Major in Statistics
- BS in the Teaching of Mathematics
- BS with a Major in Mathematics and Computer Science

## Minors

Mathematical Computer Science

Math

Statistics

## Mathematical Computer Science

**MCS 260. Introduction to Computer Science. 4 hours.**

Computer literacy, number systems, concepts of operation systems, storage, files, databases, logic gates, circuits, networks, internet. Introduction to programming in Python, variables, assignments, functions, objects. Course Information: Prerequisite(s): Credit or concurrent registration in MATH 180. Class Schedule Information: To be properly registered, students must enroll in one Laboratory-Discussion and one Lecture.* Natural World - No Lab course*.

**MCS 275. Programming Tools and File Management. 4 hours.**

Theory, techniques, and tools of the Python programming language, with applications to data structures, algorithms, web programming, and selected topics. Course Information: Prerequisite(s): Grade of C or better in MATH 180, and grade of C or better in MCS 260 or grade of C or better in CS 102. Class Schedule Information: To be properly registered, students must enroll in one Laboratory and one Lecture.

**MCS 294. Special Topics in Computer Science. 1-4 hours.**

Course content is announced prior to each term in which it is given. Course Information: May be repeated. Prerequisite(s): Approval of the department.

**MCS 320. Introduction to Symbolic Computation. 3 hours.**

Introduction to computer algebra systems (MAPLE), symbolic computation, and the mathematical algorithms employed in such computation, with examples and applications to topics in undergraduate mathematics. Course Information: Prerequisite(s): Grade of C or better in MATH 210; and Grade of C or better in MCS 260 or Grade of C or better in CS 102 or Grade of C or better in CS 108.

**MCS 360. Introduction to Data Structures. 4 hours.**

Pointers and dynamic memory allocation in C/C++, recursion, stacks, queues, heaps, binary and multiway trees, graphs, hash tables. Sorting and searching algorithms. Course Information: Prerequisite(s): Grade of C or better in MCS 260 and Grade of C or better in MCS 275. Class Schedule Information: To be properly registered, students must enroll in one Discussion/Recitation and one Lecture.

**MCS 361. Discrete Mathematics. 3 hours.**

Discrete mathematical structures used in computer science: sets, functions and relations; induction, recursive definitions and relations, methods of proof, quantifiers; counting; graphs and trees; algorithms. Course Information: Previously listed as MCS 261. Prerequisite(s): Grade of C or better in MATH 215 and Grade of C or better in CS 102.

**MCS 394. Special Topics in Computer Science. 2-4 hours.**

Course content is announced prior to each term in which it is given. Course Information: May be repeated. Students may register in more than one section per term. Prerequisite(s): Approval of the department.

**MCS 401. Computer Algorithms I. 3 or 4 hours.**

Design and analysis of computer algorithms. Divide-and-conquer, dynamic programming, greedy method, backtracking. Algorithms for sorting, searching, graph computations, pattern matching, NP-complete problems. Course Information: Same as CS 401. 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MCS 360; or Grade of C or better in CS 202.

**MCS 411. Compiler Design. 3 or 4 hours.**

Language translation: lexical analysis, parsing schemes, symbol table management, syntax and semantic error detection, and code generation. Development of fully-functional compiler. Course Information: Same as CS 473. 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in CS 301 or Grade of C or better in MCS 441; and Grade of C or better in CS 251 or Grade of C or better in MCS 360; and Grade of C or better in CS 261.

**MCS 415. Programming Language Design. 3 or 4 hours.**

Definition, design, and implementation of programming languages. Syntactic and semantic description; variable bindings, control and data structures, parsing, code generation, optimization; exception handling; data abstraction. Course Information: Same as CS 476. 3 undergraduate hours. 4 graduate hours. Prerequisite(s): MCS 360; or CS 341.

**MCS 421. Combinatorics. 3 or 4 hours.**

The pigeonhole principle, permutations and combinations, binomial coefficients, inclusionexclusion principle, recurrence relations and generating functions, special counting sequences, Polya theory of counting. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 215; and Grade of C or better in MATH 310 or Grade of C or better in MATH 320; or consent of the instructor.

**MCS 423. Graph Theory. 3 or 4 hours.**

Basic concepts of graph theory including Eulerian and hamiltonian cycles, trees, colorings, connectivity, shortest paths, minimum spanning trees, network flows, bipartite matching, planar graphs. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 215; and Grade of C or better in MATH 310 or Grade of C or better in MATH 320; or consent of the instructor.

**MCS 425. Codes and Cryptography. 3 or 4 hours.**

Mathematics of communications theory, basic information theory necessary to understand both coding theory and cryptography, basic ideas and highlights for both coding theory and cryptography, including public-key cryptosystems. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 215; and Grade of C or better in MATH 310 or Grade of C or better in MATH 320; or consent of the instructor.

**MCS 441. Theory of Computation I. 3 or 4 hours.**

Introduction to formal languages; relations between grammars and automata; elements of the theory of computable functions. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): MATH 215.

**MCS 451. Object-Oriented Programming in C++. 3 or 4 hours.**

C++ as an object-oriented language, classes and member functions, access control, class scope, constructors, destructors, overloading, conversions, streams, derived classes, polymorphism through virtual functions, templates, class libraries. Course Information: 3 undergraduate hours. 4 graduate hours. Credit is not given for MCS 451 if the student has credit for CS 474. Extensive computer use required. Prerequisite(s): Grade of C or better in MCS 360 or the equivalent or consent of the instructor.

**MCS 471. Numerical Analysis. 3 or 4 hours.**

Introduction to numerical analysis; floating point arithmetic, computational linear algebra, iterative solution to nonlinear equations, interpolation, numerical integration, numerical solution of ODEs, computer subroutine packages. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MCS 275 or grade of C or better in CS 102 or grade of C or better in CS 108; or consent of instructor.

**MCS 472. Introduction to Industrial Math and Computation. 3 or 4 hours.**

Technical writing and oral presentations in preparation for industrial projects. Topics include quality control, operations research, cost-benefit analysis, differential equations, using scientific software. Course Information: Extensive computer use required. Prerequisite(s): Grade of C or better in MCS 471 or consent of the instructor. Recommended background: Designed for students with a desire to explore mathematics via practical field work.

**MCS 481. Computational Geometry. 3 or 4 hours.**

Algorithmic problems on sets of points, rectangles, intervals, arcs, chords, polygons. Counting, reporting, location, intersection, pairing; static and dynamic data structures. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MCS 401 or consent of the instructor.

**MCS 494. Special Topics in Computer Science. 3 or 4 hours.**

Topics in mathematical computer science, such as symbolic compution, automated reasoning, cryptography or geometric algorithms. Course Information: 3 undergraduate hours. 4 graduate hours. May be repeated to a maximum of 12 hours. Students may register in more than one section per term. Prerequisite(s): Approval of the department.

**MCS 496. Independent Study. 1-4 hours.**

Reading course supervised by a faculty member. Course Information: May be repeated. Students may register in more than one section per term. Prerequisite(s): Approval of the instructor and the department. Class Schedule Information: This course counts toward the limted number of independent study hours accepted toward the degree and the major.

**MCS 501. Computer Algorithms II. 4 hours.**

Continuation of MCS 401 (same as CS 401). Advanced topics in algorithms. Lower bounds. Union-find problems. Fast Fourier transform. Complexity of arithmetic, polynomial, and matrix calculations. Approximation algorithms. Parallel algorithms. Course Information: Same as CS 501. Prerequisite(s): MCS 401 or CS 401.

**MCS 507. Mathematical, Statistical and Scientific Software. 4 hours.**

The design, analysis, and use of mathematical, statistical, and scientific software. Course Information: Prerequisite(s): Grade of B or better in MCS 360 or the equivalent or consent of instructor.

**MCS 521. Combinatorial Optimization. 4 hours.**

Combinatorial optimization: network flows, bipartite matching, Edmonds algorithm for non-bipartite matching, the matching polytope, matroids, greedy algorithm, matroid union and intersection algorithms, matroid polyhedra, polymatroids. Course Information: Prerequisite(s): MCS 423 and STAT 471.

**MCS 541. Computational Complexity. 4 hours.**

Time and space complexity of computations, classification of mathproblems according to their computational complexity, P not equal NP problem. Course Information: Prerequisite(s): Consent of the instructor.

**MCS 548. Mathematical Theory of Artificial Intelligence. 4 hours.**

Valiant's learning model, positive and negative results in learnability, automation inference, perceptrons, Rosenblatt's theorem, convergence theorem, threshold circuits, inductive inference of programs, grammars and automata. Course Information: Prerequisite(s): MCS 541.

**MCS 549. Mathematical Foundations of Data Science. 4 hours.**

Topics will include random graphs, small world phenomena, random walks, Markov chains, streaming algorithms, clustering, graphical models, singular value decomposition, and random projections. Course Information: Prerequisite(s): MCS 401 and MCS 441; or consent of the instructor.

**MCS 563. Analytic Symbolic Computation. 4 hours.**

Analytic computation, including integration algorithms, differential equations, perturbation theory, mixed symbolic-numeric algorithms, and other related topics. Course Information: Prerequisite(s): Grade of C or better in MCS 460 or the equivalent, and MATH 480 or consent of the instructor.

**MCS 565. Mathematical Theory of Databases. 4 hours.**

Abstract systems for databases, sysntax and semantics of operational languages, dependencies and normal forms, axiomizations, queries and query optimization, null values, algebraic interpretations.

**MCS 571. Numerical Analysis of Partial Differential Equations. 4 hours.**

Numerical analysis of Finite Difference methods for PDE of mathematical physics: Wave, heat, and Laplace equations. Introduction to numerical analysis of the Finite Element method. Course Information: Prerequisite(s): MATH 481 and MCS 471 or consent of the instructor.

**MCS 572. Introduction to Supercomputing. 4 hours.**

Introduction to supercomputing on vector and parallel processors; architectural comparisons, parallel algorithms, vectorization techniques, parallelization techniques, actual implementation on real machines. Course Information: Prerequisite(s): MCS 471 or MCS 571 or consent of the instructor.

**MCS 573. Topics in Numerical Analysis of Partial Differential Equations. 4 hours.**

Topics in numerical analysis of partial differential equations which may include: High-order Finite Element methods, Discontinuous Glerkin methods, Spectral methods, or Integral Equation methods. Course Information: May be repeated if topics vary. Prerequisite(s): MATH 481 and MCS 471; and consent of the instructor.

**MCS 582. The Probabilistic Method. 4 hours.**

Introduction to the probabilistic method, which includes a range of applications to address various problems that arise in combinatorics. Prerequisite(s): MCS 421 and 423, or consent of the instructor.

**MCS 583. Extremal Combinatorics. 4 hours.**

Extremal combinatorics, including extremal graph and set theory, Ramsey theory, the linear algebra method, and applications to computer science. Prerequisite(s): MCS 421 and MCS 423, or consent of the instructor.

**MCS 584. Enumerative Combinatorics. 4 hours.**

Enumerative methods in combinatorics, including inclusion/exclusion, recursion, partitions, Latin squares and other combinatorial structures. Prerequisite(s): MCS 421 and MCS 423, or consent of the instructor.

**MCS 590. Advanced Topics in Computer Science. 4 hours.**

Topics in areas such as: mathematical aspects of artificial intelligence, symbolic methods in mathematics, mathematical cryptography, automated reasoning. Topics may vary from term to term. Course Information: May be repeated. Students may register in more than one section per term. Prerequisite(s): Approval of the department.

**MCS 591. Advanced Topics in Combinatorial Theory. 4 hours.**

Some of the following topics: combinatorial enumeration, designs, graph theory, matroid theory, combinatorial matrix theory, Ramsey theory. Contents vary from year to year. Course Information: May be repeated. Prerequisite(s): MCS 423.

**MCS 593. Graduate Student Seminar. 1 hour.**

For graduate students who wish to receive credit for participating in a learning seminar whose weekly time commitment is not sufficient for a reading course. This seminar must be sponsored by a faculty member. Course Information: Satisfactory/Unsatisfactory grading only. May be repeated. Students may register in more than one section per term. Prerequisite(s): Approval of the department.

**MCS 595. Graduate Seminar. 1 hour.**

Current developments in research with presentations by faculty, students, and visitors. Course Information: Satisfactory/Unsatisfactory grading only. May be repeated. Students may register in more than one section per term. Prerequisite(s): Approval of the department.

**MCS 596. Independent Study. 1-4 hours.**

Reading course supervised by a faculty member. Course Information: May be repeated. Students may register in more than one section per term. Prerequisite(s): Approval of the instructor and the department.

**MCS 598. Master's Thesis. 0-16 hours.**

Research work under the supervision of a faculty member leading to the completion of a master's thesis. Course Information: Satisfactory/Unsatisfactory grading only. Prerequisite(s): Approval of the department.

**MCS 599. Thesis Research. 0-16 hours.**

Research work under the supervision of a faculty member leading to the completion of a doctoral thesis. Course Information: Satisfactory/Unsatisfactory grading only. May be repeated. Students may register in more than one section per term. Prerequisite(s): Approval of the department.

## Math

**MATH 077. Mathematical Reasoning Workshop. 1 hour.**

A refresher of the algebra used in MATH 118. A more detailed reminder of algebraic techniques will be given in a student-centered environment with personalized homework and worksheets to address individual needs. Course Information: Satisfactory/Unsatisfactory grading only. No graduation credit. Extensive computer use required. Requires concurrent registration in MATH 118.

**MATH 088. Intermediate Algebra Workshop. 1 hour.**

Individualized lesson plans including: order of operations, properties of real numbers, linear equations, problem solving, graphing linear equations. Course Information: Satisfactory/Unsatisfactory grading only. No graduation credit. Extensive computer use required. Corequisites: Requires concurrent registration in MATH 090.

**MATH 090. Intermediate Algebra. 3 hours.**

Linear equations and inequalities, absolute values, linear graphs and modeling, systems of equations, functions, quadratic equations, exponents and polynomials, factoring, radicals and rational exponents. Course Information: Satisfactory/Unsatisfactory grading only. Not open to students with credit in a mathematics course at or above the 100 level. No graduation credit. Extensive computer use required. Prerequisite(s): Credit or concurrent registration in MATH 088; or appropriate score on the department placement test. Class Schedule Information: During the fall and spring terms, combined section final exam will be held on Wednesday of finals week from 6 to 8 p.m.

**MATH 109. College Algebra Workshop. 1 hour.**

A refresher of material prerequisite for and used in MATH 110, including: functions, polynomial and rational equations, graphs and transformations, exponentials and logarithms, trigonometry. Course Information: Satisfactory/Unsatisfactory grading only. Prerequisite(s): Appropriate ALEKS placement score. Corequisite(s):
Requires concurrent registration in MATH 110.

**MATH 110. College Algebra. 4 hours.**

Functions, composition and inverses; graphs and transformations, polynomial and rational functions, exponential functions, logarithms and applications; circles and introduction to trigonometry. Course Information: Credit is not given for MATH 110 if the student has credit in MATH 121 or MATH 165 or MATH 170 or MATH 180. Extensive computer use required. Prerequisite(s): MATH 090; credit or concurrent registration in MATH 109; or an appropriate score on the department placement test. To be properly registered, students must enroll in one Lecture and one Laboratory-Discussion.

**MATH 118. Mathematical Reasoning. 4 hours.**

Mathematical problem solving with a hands-on and learn-by-doing approach, using topics from linear equations, personal finance, geometry, probability, and statistics. Course Information: Credit is not given for MATH 118 if the student has credit in MATH 121 or MATH 160 or MATH 165 or MATH 170 or MATH 180 or the equivalent. No graduation credit for architecture, business administration, or engineering students. It may serve as a prerequisite for statistics courses in the social sciences. It does not replace MATH 090 as a prerequisite for any other mathematics department course. Prerequisite(s): Credit or concurrent registration in MATH 077; or appropriate score on the department placement test. Class Schedule Information: To be properly registered, students must enroll in one Lecture and one Laboratory-Discussion.

**MATH 121. Precalculus Mathematics. 5 hours.**

Functions, graphs, exponentials and logarithms, radicals, complex numbers, trigonometry (circle and triangle approaches), trigonometric graphs and inverses, introduction to polar coordinates and vectors Course Information: No credit will be given for MATH 121 if students have credit in MATH 165 or MATH 170 or MATH 180. Extensive computer use required. Prerequisite(s): Grade of C or better in MATH 110; or appropriate score on the department placement test. Class Schedule Information: During the fall and spring terms, combined section final exam will be held on Thursday of finals week from 6 to 8 p.m. To be properly registered, students must enroll in one Laboratory-Discussion and one Lecture.

**MATH 122. Emerging Scholars Workshop for Precalculus Mathematics. 1 hour.**

Intensive math workshop for students enrolled in MATH 121. Students work together in groups to solve challenging problems. Course Information: Satisfactory/Unsatisfactory grading only. Prerequisite(s): Admission to the Emerging Scholars Program. Must enroll concurrently in MATH 121.

**MATH 125. Elementary Linear Algebra. 5 hours.**

Introduction to systems of linear equations, matrices and vector spaces, with emphasis on business applications. Course Information: Prerequisite(s): Grade S in MATH 090 or appropriate score on the department placement test. Class Schedule Information: To be properly registered, students must enroll in one Lecture and one Discussion. During the fall and spring terms, combined section final exam will be held on Thursday of finals week from 6 to 8 p.m. To be properly registered, students must enroll in one Discussion/Recitation and one Lecture.* Natural World - No Lab course*.

**MATH 140. Arithmetic and Algebraic Structures. 4 hours.**

Problem solving; algebraic thinking; number systems; numeration; number theory; mathematical operations over natural, integer, and rational numbers; and proportional reasoning. Course Information: Prerequisite(s): Grade of S in MATH 090 or appropriate score on the department placement test. Class Schedule Information: During the fall and spring terms, combined section final exam will be held on Monday of finals week from 6 to 8 p.m.

**MATH 141. Algebraic and Geometric Structures. 4 hours.**

Area, perimeter, volume, surface area of plane and solid figures; integers, real and rational numbers; trigonometry and extended solution of general polygons; probability. Full purpose calculators used. Course Information: Designed for students in the B.A. in Elementary Education program. Prerequisite(s): Grade of C or better in MATH 140. Class Schedule Information: During the fall and spring terms, combined section final exam will be held on Tuesday of finals week from 6 to 8 p.m.

**MATH 160. Finite Mathematics for Business. 5 hours.**

Introduction to probability, statistics, and matrices, with emphasis on business applications. Course Information: Prerequisite(s): MATH 090; or Grade of C or better in MATH 110; or appropriate score on the department placement test. Class Schedule Information: During the fall and spring terms, combined section final exam will be held on Thursday of finals week from 6 to 8 p.m. To be properly registered, students must enroll in one Discussion/Recitation and one Lecture.* Natural World - No Lab course*.

**MATH 165. Calculus for Business. 5 hours.**

Introduction to differential and integral calculus of algebraic, exponential and logarithmic functions and techniques of partial derivatives and optimization. Emphasis on business applications. Course Information: Prior credit for MATH 170 or MATH 180 will be lost with subsequent completion of
MATH 165. Prerequisite(s): Grade of C or better in MATH 110; or appropriate score on the department placement test. Class Schedule Information: During the fall and spring terms, combined section final exam will be held on Wednesday of finals week from 6 to 8 p.m. To be properly registered, students must enroll in one Discussion/Recitation and one Lecture.* Natural World - No Lab course*.

**MATH 170. Calculus for the Life Sciences. 4 hours.**

Introduction to calculus with applications to the life sciences, mathematical modeling, differentiation, integration and applications. Course Information: Prior credit in MATH 165 or MATH 180 will be lost with subsequent completion of MATH 170. Prerequisite(s): Grade of C or better in MATH 110 or appropriate score on the department placement test. Class Schedule Information: To be properly registered, students must enroll in one Lecture and one Discussion.* Natural World - No Lab course*.

**MATH 179. Emerging Scholars Workshop for Calculus I. 1 hour.**

Intensive math workshop for students enrolled in MATH 180. Students work together in groups to solve challenging problems. Course Information: Satisfactory/Unsatisfactory grading only. Prerequisite(s): Admission to the Emerging Scholars Program. Must enroll concurrently in MATH 180.

**MATH 180. Calculus I. 4 hours.**

Differentiation, curve sketching, maximum-minimum problems, related rates, mean-value theorem, antiderivative, Riemann integral, logarithm, and exponential functions. Course Information: Prior credit in MATH 165 or MATH 170 will be lost with subsequent completion of MATH 180. Prerequisite(s): Grade of C or better in MATH 121 or appropriate performance on the department placement test. Class Schedule Information: During the fall and spring terms, combined section final exam will be held on Thursday of finals week from 1 to 3 p.m. To be properly registered, students must enroll in one Discussion/Recitation and one Lecture.* Natural World - No Lab course*.

**MATH 181. Calculus II. 4 hours.**

Techniques of integration, arc length, solids of revolution, applications, polar coordinates, parametric equations, infinite sequences and series, power series. Course Information: Prerequisite(s): Grade of C or better in MATH 180. Class Schedule Information: During the fall and spring terms, combined section final exam will be held on Thursday of finals week from 3:30 to 5:30 p.m. To be properly registered, students must enroll in one Discussion/Recitation and one Lecture.* Natural World - No Lab course*.

**MATH 182. Emerging Scholars Workshop for Calculus II. 1 hour.**

Intensive math workshop for students enrolled in MATH 181. Students work together in groups to solve challenging problems. Course Information: Satisfactory/Unsatisfactory grading only. Prerequisite(s): Admission to the Emerging Scholars Program. Must enroll concurrently in MATH 181.

**MATH 194. Special Topics in Mathematics. 1-4 hours.**

Course content is announced prior to each term in which it is given. Course Information: May be repeated. Prerequisite(s): Approval of the department.

**MATH 210. Calculus III. 3 hours.**

Vectors in space, functions of several variables, partial differential and optimization, multiple integrals, vector fields, Green?s Theorem, Stokes Theorem. Course Information: Prerequisite(s): Grade of C or better in MATH 181. Class Schedule Information: During the fall and spring terms, combined section final exam will be held on Thursday of finals week from 1 to 3 p.m. To be properly registered, students must enroll in one Discussion and one Lecture.* Natural World - No Lab course*.

**MATH 211. Emerging Scholars Workshop for Calculus III. 1 hour.**

Intensive math workshop for students enrolled in MATH 210. Students work together in groups to solve challenging problems. Course Information: Satisfactory/Unsatisfactory grading only. Prerequisite(s): Admission to the Emerging Scholars Program. Must enroll concurrently in MATH 210.

**MATH 215. Introduction to Advanced Mathematics. 3 hours.**

Introduction to methods of proofs used in different fields in mathematics. Course Information: Prerequisite(s): Grade of C or better in MATH 181 and approval of the department.

**MATH 220. Introduction to Differential Equations. 3 hours.**

Techniques and applications of differential equations, first and second order equations, Laplace transforms, series solutions, graphical and numerical methods, and partial differential equations. Course Information: Prerequisite(s): Grade of C or better in MATH 210. Class Schedule Information: During the fall and spring terms, combined section final exam will be held on Thursday of finals week from 6 to 8 p.m. To be properly registered, students must enroll in one Laboratory-Discussion and one Lecture.

**MATH 294. Special Topics in Mathematics. 1-4 hours.**

Course content is announced prior to each term in which it is given. Course Information: May be repeated. Prerequisite(s): Approval of the department.

**MATH 300. Writing for Mathematics. 1 hour.**

Fulfills Writing-in-the-Discipline requirement. Course Information: Prerequisite(s): ENGL 161 or the equivalent, and a grade of C or better in MATH 210. Students must have declared a major in the Mathematics, Statistics, and Computer Science Department.

**MATH 310. Applied Linear Algebra. 3 hours.**

Matrices, row reduction algorithm, vector spaces, LU-decomposition, orthogonality, Gram-Schmidt process, determinants, inner products, eigenvalue problems, applications to differential equations and Markov processes. Course Information: MATH 310 cannot be used as an elective for the Major in Mathematics. Prerequisite(s): Grade of C or better in MATH 181.

**MATH 313. Analysis I. 3 hours.**

The real number system, limits, continuous functions, differentiability, the Riemann integral. Course Information: Prerequisite(s): Grade of C or better in MATH 215 or consent of the instructor.

**MATH 320. Linear Algebra I. 3 hours.**

Linear equations, Gaussian elimination, matrices, vector spaces, linear transformations, determinants, eigenvalues and eigenvectors. Course Information: Prerequisite(s): A grade of C or better in MATH 215.

**MATH 330. Abstract Algebra I. 3 hours.**

Sets, properties of integers, groups, rings, fields. Course Information: Prerequisite(s): Grade of C or better in MATH 215.

**MATH 394. Special Topics in Mathematics. 2-4 hours.**

Course content is announced prior to each term in which it is given. Course Information: May be repeated. Students may register in more than one section per term. Prerequisite(s): Approval of the department.

**MATH 410. Advanced Calculus I. 3 or 4 hours.**

Functions of several variables, differentials, theorems of partial differentiation. Calculus of vector fields, line and surface integrals, conservative fields, Stokes's and divergence theorems. Cartesian tensors. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 210.

**MATH 411. Advanced Calculus II. 3 or 4 hours.**

Implicit and inverse function theorems, transformations, Jacobians. Point-set theory. Sequences, infinite series, convergence tests, uniform convergence. Improper integrals, gamma and beta functions, Laplace transform. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 410.

**MATH 414. Analysis II. 3 or 4 hours.**

Riemann-Stieltjes integration. Topology of metric spaces with emphasis on R^n. (Uniform) Continuity of functions on metric spaces. Multi-dimensional differentiation theory. Implicit and Inverse Function Theorem and applications. Introduction to Lebes. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade C or better in MATH 313 and MATH 310, or MATH 320.

**MATH 417. Complex Analysis with Applications. 3 or 4 hours.**

Complex numbers, analytic functions, complex integration, Taylor and Laurent series, residue calculus, branch cuts, conformal mapping, argument principle, Rouche's theorem, Poisson integral formula, analytic continuation. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade C or better in MATH 210.

**MATH 419. Models in Applied Mathematics. 3 or 4 hours.**

Introduction to mathematical modeling; scaling, graphical methods, optimization, computer simulation, stability, differential equation models, elementary numerical methods, applications in biology, chemistry, engineering and physics. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 220 and grade of C or better in MCS 260.

**MATH 425. Linear Algebra II. 3 or 4 hours.**

Canonical forms of a linear transformation, inner product spaces, spectral theorem, principal axis theorem, quadratic forms, special topics such as linear programming. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 320.

**MATH 430. Formal Logic I. 3 or 4 hours.**

First order logic, syntax and semantics, completeness-incompleteness. Course Information: 3 undergraduate hours. 4 graduate hours. Credit is not given for MATH 430 if the student has credit for PHIL 416. Prerequisite(s): Grade of C or better in CS 202 or grade of C or better in MCS 261 or grade of C or better in MATH 215.

**MATH 431. Abstract Algebra II. 3 or 4 hours.**

Further topics in abstract algebra: Sylow Theorems, Galois Theory, finitely generated modules over a principal ideal domain. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 320 and grade of C or better in MATH 330.

**MATH 435. Foundations of Number Theory. 3 or 4 hours.**

Primes, divisibility, congruences, Chinese remainder theorem, primitive roots, quadratic residues, quadratic reciprocity, and Jacobi symbols. The Euclidean algorithm and strategies of computer programming. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 215.

**MATH 436. Number Theory for Applications. 3 or 4 hours.**

Primality testing methods of Lehmer, Rumely, Cohen-Lenstra, Atkin. Factorization methods of Gauss, Pollard, Shanks, Lenstra, and quadratic sieve. Computer algorithms involving libraries and nested subroutines. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 435.

**MATH 442. Differential Geometry of Curves and Surfaces. 3 or 4 hours.**

Frenet formulas, isoperimetric inequality, local theory of surfaces, Gaussian and mean curvature, geodesics, parallelism, and the Guass-Bonnet theorem. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 320.

**MATH 445. Introduction to Topology I. 3 or 4 hours.**

Elements of metric spaces and topological spaces including product and quotient spaces, compactness, connectedness, and completeness. Examples from Euclidean space and function spaces. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 313.

**MATH 446. Introduction to Topology II. 3 or 4 hours.**

Topics in topology chosen from the following: advanced point set topology, piecewise linear topology, fundamental group and knots, differential topology, applications to physics and biology. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 445.

**MATH 480. Applied Differential Equations. 3 or 4 hours.**

Linear first-order systems. Numerical methods. Nonlinear differential equations and stability. Introduction to partial differential equations. Sturm-Liouville theory. Boundary value problems and Green's functions. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 220.

**MATH 481. Applied Partial Differential Equations. 3 or 4 hours.**

Initial value and boundary value problems for second order linear equations. Eiqenfunction expansions and Sturm-Liouville theory. Green's functions. Fourier transform. Characteristics. Laplace transform. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 220.

**MATH 494. Special Topics in Mathematics. 3 or 4 hours.**

Course content is announced prior to each term in which it is given. Course Information: 3 undergraduate hours. 4 graduate hours. May be repeated. Students may register in more than one section per term. Prerequisite(s): Approval of the department.

**MATH 496. Independent Study. 1-4 hours.**

Reading course supervised by a faculty member. Course Information: May be repeated. Students may register in more than one section per term. Prerequisite(s): Approval of the instructor and the department. Class Schedule Information: This course counts toward the limited number of independent study hours accepted toward the degree and the major.

## Statistics

**STAT 101. Introduction to Statistics. 4 hours.**

Applications of statistics in the real world, displaying and describing data, normal curve, regression, probability, statistical inference, confidence intervals and hypothesis tests. Course Information: Credit is not given for STAT 101 if the student has credit for STAT 130. Credit is not given for STAT 101 for majors in Mathematics and Computer Science. Extensive computer use required. This course is offered in both a blended and traditional format. If the section is marked "Blended-Online and Classroom," use of a computer and internet access is required. Blended sections require students to do some of their coursework online. A high-speed connection, while not required, is strongly suggested. Prerequisite(s): Grade S in MATH 090 or appropriate score on the department placement test. Class Schedule Information: To be properly registered, students must enroll in one Laboratory-Discussion and one Lecture.

**STAT 130. Introduction to Statistics for the Life Sciences. 4 hours.**

Basic concepts and methods of statistics with illustrations from different areas of the life sciences; graphical and summary representations, probability, random variables, normal distribution, estimation and tests of hypotheses, t, F and chi-square. Course Information: Credit is not given for STAT 130 if the student has credit for STAT 101. Extensive computer use required. Prerequisite(s): Grade of C or better in MATH 110; or appropriate score on the department placement test. Class Schedule Information: To be properly registered, students must enroll in one Lecture and one Laboratory-Discussion.

**STAT 361. Elements of Statistical Methods. 2 hours.**

Graphical and numerical summaries of data, statistical software package use; introduction to probability, random variables, and sampling distributions; point estimation, confidence intervals, and test of hypotheses. Course Information: Prerequisite(s): Grade of C or better in MATH 181.

**STAT 362. Elements of Statistical Computing. 2 hours.**

Statistical computation with the SAS and R software packages; data structure, entry, and manipulation; numerical and graphical summaries; basic statistical methods. Course Information: Prerequisite(s): Grade of C or better in STAT 361; or Grade of C or better in IE 342; or Grade of C or better in STAT 381.

**STAT 381. Applied Statistical Methods I. 3 hours.**

Graphical and tabular representation of data; Introduction to probability, random variables, sampling distributions, estimation, confidence intervals, and tests of hypotheses. Includes SAS and SPSSX applications. Course Information: Prerequisite(s): Grade of C or better in MATH 181.

**STAT 382. Statistical Methods and Computing. 3 hours.**

Statistical computation with the SAS and R software packages: data structure, entry, and manipulation; numerical and graphical summaries; basic statistical methods; select advanced methods. Course Information: Prerequisite(s): STAT 381.

**STAT 385. Elementary Statistical Techniques for Machine Learning and Big Data. 3 hours.**

Sampling algorithms; nonparametric tests; data mining: classification, clustering, LASSO, cross-validation, Principle Component Regression; and big data analysis focus on R-package. Course Information: Extensive computer use required. Prerequisite(s): STAT 382 or consent of the instructor.

**STAT 401. Introduction to Probability. 3 or 4 hours.**

Probability spaces, random variables and their distributions, conditional distribution and stochastic independence, special distributions, sampling distributions, limit theorems. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 210; or approval of the department.

**STAT 411. Statistical Theory. 3 or 4 hours.**

Estimation, tests of statistical hypotheses, best tests, sufficient statistics, Rao-Cramer inequality, sequential probability ratio tests, the multivariate normal distribution, nonparametric methods. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in STAT 401.

**STAT 416. Nonparametric Statistical Methods. 3 or 4 hours.**

Distribution free tests for location and dispersion problems, one-way and two-way layouts, the independence problem, regression problems involving slopes, detecting broad alternatives, resampling methods. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in STAT 381 or STAT 411.

**STAT 431. Introduction to Survey Sampling. 3 or 4 hours.**

Simple random sampling; sampling proportions; estimation of sample size; stratified random sampling; ratio estimators; regression estimators; systematic and cluster sampling. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in STAT 411 or STAT 481.

**STAT 451. Computational Statistics. 3 or 4 hours.**

Modern computationally-intensive statistical methods including Monte Carlo integration and simulation, optimization and maximum likelihood estimation, EM algorithm, MCMC, sampling and resampling methods, non-parametric density estimation. Course Information: 3 undergraduate hours. 4 graduate hours. Extensive computer use required. Prerequisite(s): STAT 411.

**STAT 461. Applied Probability Models I. 3 or 4 hours.**

Computing probabilities and expectations by conditioning, Markov chains, Chapman-Kolmogorov equations, branching processes, Poisson processes and exponential distribution, continuous-time Markov chains, reversibility, uniformization. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in STAT 401.

**STAT 471. Linear and Non-Linear Programming. 3 or 4 hours.**

Linear programming, simplex algorithm, degeneracy, duality theorem sensitivity analysis, convexity, network simplex methods, assignment problems. Constrained and unconstrained minima. Quasi-Newton methods. Ellipsoidal methods of Kachian. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 310.

**STAT 473. Game Theory. 3 or 4 hours.**

Introduction to the basic ideas of game theory. Static and dynamic games; mixed strategies, imperfect information; economic, political and biological applications. Course Information: Same as ECON 473. 3 undergraduate hours. 4 graduate hours. Prerequisite(s): STAT 381; or ECON 270; or equivalents.

**STAT 475. Mathematics and Statistics for Actuarial Sciences I. 3 or 4 hours.**

Financial mathematics as it pertains to the valuation of deterministic cash flows. Basic concepts and techniques regarding the theory of interest. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): MATH 210.

**STAT 481. Applied Statistical Methods II. 3 or 4 hours.**

Linear regression, introduction to model building, analysis of variance, analysis of enumerative data, nonparametric statistics, product and system reliability, quality control. SAS and SPSSX applications. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in STAT 381.

**STAT 486. Statistical Consulting. 3 or 4 hours.**

Introduction to statistical consulting methods and techniques. Handling and transformation of raw data sets in CMS. Statistical analysis of data sets with SAS and SPSSX. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in STAT 411 or STAT 481.

**STAT 494. Special Topics in Statistics, Probability and Operations Research. 3 or 4 hours.**

Course content announced prior to each semester in which it is given. Topics drawn from areas such as distribution theory; Bayesian inference; discrete optimization; applied probability models; resampling techniques; biostatistics; environmental sampling. Course Information: 3 undergraduate hours. 4 graduate hours. May be repeated. Students may register in more than one section per term. Prerequisite(s): Approval of the department.

**STAT 496. Independent Study. 1-4 hours.**

Reading course supervised by a faculty member. Course Information: May be repeated. Students may register in more than one section per term. Prerequisite(s): Approval of the instructor and approval of the department.