2017-18 Catalog

Mathematics

Mathematics is a subject of great intrinsic power and beauty. It is the universal language of science, and is essential for a clear and complete understanding of virtually all phenomena. Mathematical training prepares a student to express and analyze problems and relationships in a logical manner in a wide variety of disciplines including the physical, engineering, social, biological, and medical sciences, business, and pure mathematics itself. This is a principal reason behind the perpetual need and demand for mathematicians in education, research centers, government, and industry.

The department offers three major programs leading to the degrees of bachelor of arts in mathematics, bachelor of science in mathematics (with a general mathematics and an applied mathematics option), and bachelor of science in statistics. It also offers several minor programs for undergraduates.

At the graduate level, it offers programs leading to the degrees of master of science in mathematics, master of science in applied mathematics, master of science in statistics, doctor of philosophy in mathematics, and doctor of philosophy in applied mathematics.

The Division of Applied Mathematics and Statistics is a part of the Department of Mathematics.

Calculus Sequences

Many degree programs throughout the university include a mathematics requirement consisting of a sequence in calculus. The Department of Mathematics offers three calculus sequences:

MATH 021
MATH 022
MATH 023
Calculus I
and Calculus II
and Calculus III
12
MATH 031
MATH 032
MATH 033
Honors Calculus I
and Honors Calculus II
and Honors Calculus III
12
MATH 051
MATH 052
Survey of Calculus I
and Survey of Calculus II
7

The MATH 021, MATH 022, MATH 023 sequence is a systematic development of calculus. Most students of mathematics, science, engineering, and business will take some or all of this sequence.

As an honors sequence, the MATH 031, MATH 032, MATH 033 sequence covers essentially the same material but in greater depth and with more attention to rigor and proof. This sequence should be considered by students who have demonstrated exceptional ability in mathematics. Students who are contemplating a major in mathematics are strongly encouraged to consider this sequence.

The MATH 051, MATH 052 sequence is a survey of calculus. MATH 081 is a survey course with business applications. This sequence is not sufficient preparation for most subsequent mathematics courses. Students contemplating further study in mathematics should consider MATH 021, MATH 022 instead.

MATH 075, MATH 076 is a two-semester sequence that substitutes for MATH 021, covering the same material but at a slower pace.

The MATH 031, MATH 032, MATH 033 sequence will be accepted in place of the other two sequences. MATH 021, MATH 022 will be accepted in place of MATH 051, MATH 052. Credit will be awarded for only one course in each of the following groups:

Group 1
MATH 021Calculus I4
MATH 075/076Calculus I, Part A2
MATH 031Honors Calculus I4
MATH 051Survey of Calculus I4
MATH 081Calculus with Business Applications4
Group 2
MATH 022Calculus II4
MATH 032Honors Calculus II4
MATH 052Survey of Calculus II3
Group 3
MATH 023Calculus III4
MATH 033Honors Calculus III4

If two courses in the same group are taken, credit will be awarded for the more advanced course; 3x is the most advanced, while 5x is the least advanced.

Undergraduate Degree Programs

The Department of Mathematics offers degree programs in Mathematics and Statistics. These programs have the flexibility and versatility needed to prepare students for a wide variety of careers in government, industry, research and education.

Students in the degree programs in mathematics must satisfy three types of requirements beyond those required by the college: Core Mathematics Requirements, Major Requirements and General Electives. The Core Mathematics Requirement ensures a common core of knowledge appropriate for students in each program. The Major Program Electives consist of courses with specific mathematical or statistical content chosen by the student in consultation with the major advisor to complement the student's interest and career aspirations. With these further breadth and greater depth of knowledge are achieved. The General Electives consist of additional courses chosen from among those offered by the university faculty. Students can use these electives to pursue interests beyond the major, or may use these to expand upon the basic requirements of the degree program. Students are strongly encouraged to use some of these electives to earn a minor in another discipline.

Students in the degree program in statistics must satisfy four types of requirements beyond those required by the college: Required Major Courses, Major Electives, Professional Electives and Free Electives.

Each student is provided a faculty advisor to guide an individual program and supervise the selection of electives.

B.A. with a major in Mathematics

The B.A. program in mathematics emphasizes fundamental principles as well as the mastery of techniques required for the effective use of mathematics. The program provides a solid foundation for those who want to pursue a mathematically oriented career or advanced study in any mathematically oriented field.

Requirements

College Distribution Requirements excluding mathematics
31-34 credits31-34
Core Mathematics Requirements
Select one of the following:12
Calculus I
and Calculus II
and Calculus III
Honors Calculus I
and Honors Calculus II
and Honors Calculus III
MATH 163Introductory Seminar3
MATH 231Probability and Statistics3
or MATH 012
MATH 309
Basic Statistics
and Theory of Probability
MATH 242Linear Algebra3-4
MATH 205Linear Methods3
or MATH 320 Ordinary Differential Equations
MATH 301Principles of Analysis I3-4
MATH 208Complex Variables3
or MATH 316 Complex Analysis
Major Requirements
MATH 243Algebra3-4
Select at least 6 credits in electives at or above the 200-level chosen in consulation with the major advisor. At most one course may be taken outside the department6
General Electives
Select electives in consultation with faculty advisor41-47
Total Credits111-123

This program requires a total of 120 credit hours.

A student must achieve an average of 2.0 or higher in major courses.

B.S. in Mathematics

The BS in Mathematics program provides a more extensive and intensive study of mathematics and its applications. Students can pursue the General Mathematics Option or the Applied Mathematics Option. These programs are especially recommended for students intending to pursue advanced study in mathematics or applied mathematics. The General Mathematics Option is recommended for students who wish to pursue mathematics either by itself or in combination with a related field (e.g., physics, computer science or economics). The Applied Mathematics Option provides a broad background in the major areas of applicable mathematics.

General Mathematics Option

Requirements

College Distribution Requirements excluding mathematics
31-34 credits31-34
Core Mathematics Requirements
Select one of the following:12
Calculus I
and Calculus II
and Calculus III
Honors Calculus I
and Honors Calculus II
and Honors Calculus III
MATH 163Introductory Seminar3
MATH 231Probability and Statistics3
or MATH 309 Theory of Probability
MATH 242Linear Algebra3-4
MATH 205Linear Methods3
or MATH 320 Ordinary Differential Equations
MATH 301Principles of Analysis I3-4
MATH 208Complex Variables3
or MATH 316 Complex Analysis
Major Requirements
MATH 243Algebra3-4
Select four elective courses (at least 14 credits) at or above the 200 level. At most two courses may be taken outside the department14
Two approved CSE courses. (CSE 1 and CSE 2 are NOT sufficient to satisfy this requirement.)5-7
General Electives
Select electives in consultation with faculty advisor27-33
Total Credits110-124

This program requires a total of 120 credit hours.

A student must achieve an average of 2.0 or higher in major courses.

Applied Mathematics Option

Requirements

College Distribution Requirements excluding mathematics
31-34 credits
Core Mathematics Requirements
Select one of the following:
Calculus I
and Calculus II
and Calculus III
Honors Calculus I
and Honors Calculus II
and Honors Calculus III
MATH 163Introductory Seminar3
MATH 231Probability and Statistics3
or MATH 309 Theory of Probability
MATH 242Linear Algebra3-4
MATH 205Linear Methods3
or MATH 320 Ordinary Differential Equations
MATH 301Principles of Analysis I3-4
MATH 208Complex Variables3
or MATH 316 Complex Analysis
Major Requirements
Select five elective courses (at least 17 credits) at or above the 200 level chosen in consultation with the major adivsor to establish a concentration as described below. At most two courses may be taken outside the department.17
Two approved CSE courses. (CSE 1 and CSE 2 are NOT sufficient to satisfy this requirement.)5-7
General Electives
Select electives in consultation with faculty advisor28-33
Total Credits68-77

In consultation with the major advisor, a student must establish a concentration in a particular area of applied mathematics. The courses chosen must have specific mathematical or statistical content and together constitute a coherent program. At most two courses may be taken outside the Department of Mathematics. Students, in consultation with the major advisor, can design a concentration which reflects a particular area of interest or choose to pursue one of the following:

Concentration in Applied Analysis

Electives must include:

MATH 230Numerical Methods3
MATH 322Methods of Applied Analysis I3
MATH 341Mathematical Models and Their Formulation3
Total Credits9

Concentration in Discrete Mathematics and Theoretical Computer Science

Electives must include:

Select at least three of the following:9-10
Enumerative Combinatorics
Graph Theory
Computability Theory
Design and Analysis of Algorithms
Total Credits9-10

Concentration in Probability and Statistics

Electives must include:

Select at least three of the following:9-11
Theory of Probability
Random Processes and Applications
Statistical Computing and Applications
Mathematical Statistics
Linear Models in Statistics with Applications
Total Credits9-11

 This program requires a total of 120 credit hours.

A student must achieve an average of 2.0 or higher in major courses.

B.S. in Statistics

Statistics provides a body of principles for designing the process of data collection, for summarizing and interpreting data, and for drawing valid conclusions from data. It thus forms a fundamental tool in the natural and social sciences as well as business, medicine, and other areas of research. Mathematical principles, especially probability theory, underlie all statistical analyses.

College Distribution Requirements excluding mathematics
31-34 credits31-34
Required Major courses
Select one of the following:12
Calculus I
and Calculus II
and Calculus III
Honors Calculus I
and Honors Calculus II
and Honors Calculus III
MATH 012Basic Statistics4
or MATH 231 Probability and Statistics
Select one of the following:3-4
Survey of Linear Algebra
Linear Methods
Linear Algebra
MATH 309Theory of Probability3
MATH 310Random Processes and Applications3-4
MATH 312Statistical Computing and Applications3-4
MATH 334Mathematical Statistics3-4
MATH 338Linear Models in Statistics with Applications3-4
MATH 374Statistical Project3
Two approved CSE courses. (CSE 1 and CSE 2 are NOT sufficient to satisfy this requirement.)5-7
Major Electives
At least three courses with specific mathematical or statistical content chosen with the approval of the faculty advisor12
Professional Electives
Courses selected from two or three fields of application of statistics and probability21
Free Electives
Select 6-11 credits in free electives6-11
Total Credits112-127

CONCENTRATION IN ACTUARIAL SCIENCE

Major Electives must include:

MATH 202Actuarial Exam I1
MATH 203Actuarial Exam II - Financial Mathematics1

Professional Electives (21 credit hours) must include:

ACCT 151Introduction to Financial Accounting3
ECO 029Money, Banking, and Financial Markets3
ECO 119Intermediate Macroeconomic Analysis3
FIN 125Introduction to Finance3

Departmental Honors

Students may earn departmental honors by writing a thesis during their senior year. Students are accepted into the program during their junior year by the department chairperson. This acceptance is based upon the student's grades and a thesis proposal, which the student must prepare in conjunction with a thesis advisor selected by the student. An oral presentation as well as a written thesis are required for completion of the program.

Minor Programs

The department offers minor programs in different branches of the mathematical sciences. The requirement consists of MATH 023 or MATH 033 and four additional courses shown below for each of the programs. At most one of these five courses in the minor program may also be required in the major program. For substitutions, the student should consult the chairperson.

Minor in Pure Mathematics

MATH 242Linear Algebra3-4
MATH 243Algebra3-4
MATH 301Principles of Analysis I3-4
Select one of the following:3-4
Principles of Analysis II
Mathematical Logic
General Topology I
Complex Analysis
Number Theory
Total Credits12-16

Minor in Applied Mathematics

Select three of the following:9-10
Linear Methods
Complex Variables
Numerical Methods
Probability and Statistics
Linear Algebra
Ordinary Differential Equations
Methods of Applied Analysis I
Methods of Applied Analysis II
MATH 341Mathematical Models and Their Formulation3
Total Credits12-13

Minor in Probability and Statistics 

MATH 012Basic Statistics4
or MATH 231 Probability and Statistics
MATH 309Theory of Probability3
Select two of the following:6-8
Random Processes and Applications
Statistical Computing and Applications
Mathematical Statistics
Linear Models in Statistics with Applications
Total Credits13-15

Minor in Actuarial Science

MATH 309Theory of Probability3
MATH 310Random Processes and Applications3-4
MATH 202Actuarial Exam I1
MATH 203Actuarial Exam II - Financial Mathematics2
ACCT 108Fundamentals of Accounting3
or ACCT 151 Introduction to Financial Accounting
ECO 105Intermediate Microeconomic Analysis3
or ECO 119 Intermediate Macroeconomic Analysis
Total Credits15-16

For information on examinations of actuarial societies, students may consult their minor advisor.

Graduate Programs in Mathematics

The department offers graduate programs leading to the degrees of master of science in mathematics, applied mathematics, or statistics, and the doctor of philosophy in mathematics or applied mathematics.

The Department does not offer a doctorate in statistics. However, students may choose statistics or mathematical statistics as a concentration in the doctor of philosophy programs in mathematics and applied mathematics. The Department is a part of the interdisciplinary program in Analytical Finance. For details on the Master of Science in Analytical Finance see the Interdisciplinary Graduate Study and Research, Analytical Finance section.

To begin graduate work in mathematics a student must present evidence of adequate undergraduate preparation. The undergraduate program should have included a year of advanced calculus, a semester of linear algebra, and a semester of abstract algebra.

M.S. in Mathematics or Applied Mathematics

The master's program requires 30 credit hours of graduate courses with at least 18 hours at the 400 level. With the permission of the chairperson, up to six hours of these courses can be replaced by a thesis. All students in the master's program must also pass a comprehensive examination. The M.S. degree can serve both as a final degree in mathematics or as an appropriate background for the Ph.D. degree.

M.S. in Statistics

This program requires 30 credit hours of graduate courses with at least 18 hours of 400-level STAT or MATH courses. The choice of courses must be approved by the graduate advisor, and up to six hours of coursework may be replaced with a thesis. All students in the program must also pass a comprehensive examination.

The M.S. program in statistics has two tracks:

statistics track

The statistics track has recommended courses:

MATH 309Theory of Probability3
STAT 412Statistical Computing and Applications3
STAT 434Mathematical Statistics3
MATH 462Modern Nonparametric Methods in Statistics3
Electives
STAT 410Random Processes and Applications3
STAT 438Linear Models In Statistics with Applications3
STAT 461Topics In Mathematical Statistics3
Select three other possible electives:9
Seminar in Statistics and Probability
Seminar in Statistics and Probability
Multivariate Statistical Models
Product Quality
Time Series Analysis
Design of Experiments
Time Series Analysis
Topics in Game Theory
Advanced Programming Techniques
Nondeterministic Models in Engineering
Total Credits30

stochastic modeling track

MATH 309Theory of Probability3
MATH 401Real Analysis I3
STAT 410Random Processes and Applications3
STAT 463Advanced Probability3
Electives
MATH 341Mathematical Models and Their Formulation3
STAT 434Mathematical Statistics3
STAT 438Linear Models In Statistics with Applications3
STAT 464Advanced Stochastic Processes3
Select two other possible electives:6
Seminar in Statistics and Probability
Seminar in Statistics and Probability
Real Analysis II
Numerical Analysis
Financial Calculus I
Financial Calculus II
Topics in Game Theory
Advanced Programming Techniques
Nondeterministic Models in Engineering
Optimization Models and Applications
Stochastic Models and Applications
Time Series Analysis
Dynamic Programming
Queueing Systems
Total Credits30

Ph.D. in Mathematics

The plan of work toward the doctor of philosophy degree will include a comprehensive examination, a qualifying examination, and an advanced topic examination. A language exam may be required at the discretion of the thesis committee. The qualifying examination tests the student’s command of algebra and real analysis. The content of the advanced topic examination is determined by a department committee. A general examination, the doctoral dissertation and its defense complete the work for the Ph.D. degree.

Each candidate's plan of work must be approved by a special committee of the department. A Ph.D. student is required to have 18 credits of approved graduate level course work beyond the master's level. Successful completion of MATH 316 and MATH 307 is required of all students. After completion of 18 credits a student is required to take at least one course per academic year other than MATH 409, MATH 410, and MATH 499.


 

Ph.D. in Applied Mathematics

The plan of work toward the doctor of philosophy degree will include a comprehensive examination, a qualifying examination, and an advanced topic examination. A language examination may be required at the discretion of the thesis committee. The Ph.D. in Applied Mathematics qualifying examination tests the student's command of Statistics and Applied Probability or of Real Analysis and Differential Equations. The content of the advanced topic examination is determined by a department committee. A general examination, the doctoral dissertation and its defense complete the work for the Ph.D. degree.

Each candidate's plan of work must be approved by a special committee of the department. A Ph.D. student is required to have 18 credits of approved graduate level course work beyond the master's level. After completion of 18 credits a student is required to take at least one course per academic year other than MATH 409, MATH 410, and MATH 499.

Mathematics Courses

MATH 000 Preparation for Calculus 2 Credits

Intensive review of fundamental concepts in mathematics utilized in calculus, including functions and graphs, exponentials and logarithms, and trigonometry. This course is for students who need to take MATH 51 or 21, but who require remediation in precalculus. In particular, students who fail the MATH 51 Readiness Exam must pass MATH 0 before being admitted to MATH 51. The credits for this course do not count toward graduation, but do count toward GPA and current credit count. Consent of department required.
Attribute/Distribution: MA

MATH 005 Introduction to Mathematical Thought 3 Credits

Meaning, content, and methods of mathematical thought illustrated by topics that may be chosen from number theory, abstract algebra, combinatorics, finite or nonEuclidean geometries, game theory, mathematical logic, set theory, topology.
Attribute/Distribution: MA

MATH 009 Introduction to Finite Mathematics 4 Credits

Systems of linear equations, matrices, introduction to linear programming. Sets, counting methods, probability, random variables, introduction to Markov chains.
Attribute/Distribution: MA

MATH 012 Basic Statistics 4 Credits

A first course in the basic concepts and methods of statistics with illustrations from the social, behavioral, and biological sciences. Descriptive statistics; frequency distributions, mean and standard deviation, two-way tables, correlation and regression; random sampling, rules of probability, probability distributions and parameters, parameter estimation, confidence intervals, hypothesis testing, statistical significance. Note: Mathematics and Statistics majors may not receive credit for both MATH 012 & ECO 045.
Attribute/Distribution: MA

MATH 021 Calculus I 4 Credits

Functions and graphs; limits and continuity; derivative, differential, and applications; indefinite and definite integrals; trigonometric, logarithmic, exponential, and hyperbolic functions.
Attribute/Distribution: MA

MATH 022 Calculus II 4 Credits

Applications of integration; techniques of integration; separable differential equations; infinite sequences and series; Taylor's Theorem and other approximations; curves and vectors in the plane.
Prerequisites: MATH 021 or MATH 076 or MATH 031 or MATH 097
Attribute/Distribution: MA

MATH 023 Calculus III 4 Credits

Vectors in space; partial derivatives; Lagrange multipliers; multiple integrals; vector analysis; line integrals; Green's Theorem, Gauss's Theorem.
Prerequisites: MATH 022 or MATH 096 or MATH 032
Attribute/Distribution: MA

MATH 031 Honors Calculus I 4 Credits

Same topics as in MATH 021, but taught from a more thorough and rigorous point of view.
Attribute/Distribution: MA

MATH 032 Honors Calculus II 4 Credits

Same topics as in MATH 022, but taught from a more thorough and rigorous point of view.
Prerequisites: (MATH 031)
Attribute/Distribution: MA

MATH 033 Honors Calculus III 4 Credits

Same topics as in MATH 023, but taught from a more thorough and rigorous point of view.
Attribute/Distribution: MA

MATH 043 Survey of Linear Algebra 3 Credits

Matrices, vectors, vector spaces and mathematical systems, special kinds of matrices, elementary matrix transformations, systems of linear equations, convex sets, introduction to linear programming.
Attribute/Distribution: MA

MATH 051 Survey of Calculus I 4 Credits

Limits. The derivative and applications to extrema, approximation, and related rates. Exponential and logarithm functions, growth and decay. Integration. Trigonometric functions and related derivatives and integrals.
Attribute/Distribution: MA

MATH 052 Survey of Calculus II 3 Credits

Techniques of integration. Differential equations. Probability and calculus. Partial derivatives and extrema. Multiple integrals and applications.
Prerequisites: MATH 051 or MATH 021 or MATH 031 or MATH 076 or MATH 097 or MATH 081
Attribute/Distribution: MA

MATH 075 Calculus I, Part A 2 Credits

Covers the same material as the first half of MATH 021. Meets three hours per week, allowing more class time for each topic than does MATH 021.
Attribute/Distribution: MA

MATH 076 Calculus I, Part B 2 Credits

Continuation of MATH 075, covering the second half of MATH 021. Meets three hours per week. Final exam for this course is similar to the MATH 021 final.
Prerequisites: MATH 075
Attribute/Distribution: MA

MATH 081 Calculus with Business Applications 4 Credits

Limits and continuity; exponential, logarithmic and trigonometric functions; derivatives; extrema; approximations; indefinite and definite integrals. Applications with emphasis on business and economics.
Attribute/Distribution: MA

MATH 114 (PHIL 114) Symbolic Logic 4 Credits

A first course in logical theory, introducing the notions of logical consequence and proof, as well as related concepts such as consistency and contigency. Formal systems taught may include: term, sentence logic, and predicate logic.
Attribute/Distribution: MA

MATH 130 (BIOS 130) Biostatistics 4 Credits

Elements of statistics and probability with emphasis on biological applications. Statistical analysis of experimental and observational data.
Prerequisites: MATH 052 or MATH 022

MATH 163 Introductory Seminar 3 Credits

An introduction to the discipline of mathematics designed for students considering a major in mathematics. The course will provide an introduction to rigorous mathematical reasoning and will survey some area of mathematics. Topics covered will vary.
Attribute/Distribution: MA

MATH 171 Readings 1-3 Credits

Study of a topic in mathematics under individual supervision. Intended for students with specific interests in areas not covered in the listed courses. Consent of department chair required.
Attribute/Distribution: MA

MATH 201 Problem Solving 1 Credit

Practice in solving problems from mathematical contests using a variety of techniques. Permission of instructor required.
Repeat Status: Course may be repeated.
Attribute/Distribution: MA

MATH 202 Actuarial Exam I 1 Credit

Preparation for the first actuarial exam – probability. Problems in calculus and probability with insurance applications.
Prerequisites: (MATH 023 or MATH 033) and (MATH 231)
Attribute/Distribution: MA

MATH 203 Actuarial Exam II - Financial Mathematics 2 Credits

Preparation for the second actuarial exam - financial mathematics. Mathematics of interest and investments, interest rate measurement, present value, annuities, loan repayment schemes, bond valuation, introduction to derivative securities. Practice in solving problems from past exams.
Prerequisites: MATH 022
Attribute/Distribution: MA

MATH 205 Linear Methods 3 Credits

Linear differential equations and applications; matrices and systems of linear equations; vector spaces; eigenvalues and application to linear systems of differential equations.
Prerequisites: MATH 022 or MATH 096 or MATH 032
Attribute/Distribution: MA

MATH 208 Complex Variables 3 Credits

Functions of a complex variable; calculus of residues; contour integration; applications to conformal mapping and Laplace transforms.
Prerequisites: MATH 023 or MATH 033
Attribute/Distribution: MA

MATH 214 (PHIL 214) Topics in Philosophical Logic 4 Credits

Topics may include the many systems of non-classical logic, truth theory, the impact of incompleteness and undecidability results on philosophy, the foundational projects of various philosopher/mathematicians, or the work of an important figure in the history of philosophical logic. Consent of instructor required.
Repeat Status: Course may be repeated.
Attribute/Distribution: MA

MATH 229 Geometry 3-4 Credits

Discussion of geometry as an axiomatic system. Euclid's postulates. History of and equivalent versions of Euclid's fifth postulate. Finite projective geometries. NonEuclidean geometries based upon negation of the fifth postulate: Geometry on the sphere; Hyperbolic and elliptic geometries. Examination of the concepts of “straight”, angle, parallel, symmetry and duality in each of these geometries. Applications of the different geometries will be considered.
Attribute/Distribution: MA

MATH 230 Numerical Methods 3 Credits

Representation of numbers and rounding error; polynomial and spline interpolation; numerical differentiation and integration; numerical solution of nonlinear systems; Fast Fourier Transformation; numerical solution of initial and boundary value problems; Monte Carlo methods. Knowledge of MATLAB or PYTHON or C required.
Prerequisites: MATH 205
Attribute/Distribution: MA

MATH 231 Probability and Statistics 3 Credits

Probability and distribution of random variables; populations and random sampling; chisquare and t distributions; estimation and tests of hypotheses; correlation and regression theory of two variables.
Prerequisites: MATH 022 or MATH 096 or MATH 032 or MATH 052
Attribute/Distribution: MA

MATH 234 Fractal Geometry 3 Credits

Metric spaces and iterated function systems; various types of fractal dimension; Julia and Mandelbrot sets. Other topics such as chaos may be included. Small amount of computer use.
Prerequisites: MATH 023 or MATH 033
Attribute/Distribution: MA

MATH 242 Linear Algebra 3-4 Credits

Solution of systems of linear equations, matrices, vector spaces, bases, linear transformations, eigenvalues, eigenvectors, additional topics as time permits.
Prerequisites: MATH 022 or MATH 096 or MATH 032
Attribute/Distribution: MA

MATH 243 Algebra 3,4 Credits

Introduction to basic concepts of modern algebra: groups, rings, and fields.
Prerequisites: (MATH 163 or MATH 261 or CSE 261) and (MATH 242 or MATH 205)
Attribute/Distribution: MA

MATH 261 (CSE 261) Discrete Structures 3 Credits

Topics in discrete mathematical structures chosen for their applicability to computer science and engineering. Sets, propositions, induction, recursion; combinatorics; binary relations and functions; ordering, lattices and Boolean algebra; graphs and trees; groups and homomorphisms.
Prerequisites: (MATH 021 or MATH 031 or MATH 076)
Attribute/Distribution: MA

MATH 271 Readings 1-3 Credits

Study of a topic in mathematics under individual supervision. Intended for students with specific interests in areas not covered in the listed courses. Consent of department chair required.
Repeat Status: Course may be repeated.
Attribute/Distribution: MA

MATH 291 Undergraduate Research 1-4 Credits

Research in mathematics or statistics under the direction of a faculty member. Department permission required.
Repeat Status: Course may be repeated.
Attribute/Distribution: ND

MATH 301 Principles of Analysis I 3-4 Credits

Existence of limits, continuity and uniform continuity; HeineBorel Theorem; existence of extreme values; mean value theorem and applications; conditions for the existence of the Riemann integral; absolute and uniform convergence; emphasis on theoretical material from the calculus of one variable.
Prerequisites: MATH 023 or MATH 033
Attribute/Distribution: MA

MATH 302 Principles of Analysis II 3-4 Credits

Continuation of MATH 301. Functions of several variables; the implicit function theorem, and further topics with applications to analysis and geometry.
Prerequisites: MATH 301
Attribute/Distribution: MA

MATH 303 (PHIL 303) Mathematical Logic 3-4 Credits

Detailed proofs are given for the basic mathematical results relating the syntax and semantics of firstorder logic (predicate logic): the Soundness and Completeness (and Compactness) Theorems, followed by a brief exposition of the celebrated limitative results of Gödel, Turing, and Church on incompleteness and undecidability. The material is conceptually rigorous and mathematically mature; the necessary background is a certain degree of mathematical sophistication or a basic knowledge of symbolic logic. Consent of instructor required.
Attribute/Distribution: MA

MATH 304 Axiomatic Set Theory 3-4 Credits

A development of set theory from axioms; relations and functions; ordinal and cardinal arithmetic; recursion theorem; axiom of choice; independence questions. Consent of instructor required.
Attribute/Distribution: MA

MATH 305 Enumerative Combinatorics 3 Credits

An introduction to basic theoretical results and techniques of enumerative combinatorics such as combinatorial identities, generating functions, inclusion/exclusion, recurrence relations, bijective proofs and permutations. Additional topics will be covered as time permits.
Prerequisites: MATH 242 and (MATH 163 or MATH 261 or CSE 261)
Attribute/Distribution: MA

MATH 306 Introduction to Biomedical Engineering and Mathematical Biology 3 Credits

Study of human physiology, including the cardiovascular, nervous and respiratory systems, and renal physiology. Mathematical analysis of physiological processes, including transport phenomena. Mathematical models of excitation and propagation in nerve. Biomechanics of the skeletal muscle system. Mathematical models in population dynamics and epidemiology. Independent study projects.
Prerequisites: MATH 205
Attribute/Distribution: MA

MATH 307 General Topology I 3-4 Credits

An introductory study of topological spaces, including metric spaces, separation and countability axioms, connectedness, compactness, product spaces, quotient spaces, function spaces.
Prerequisites: MATH 301
Attribute/Distribution: MA

MATH 309 Theory of Probability 3 Credits

Probabilities of events on discrete and continuous sample spaces; random variables and probability distributions; expectations; transformations; simplest kind of law of large numbers and central limit theorem. The theory is applied to problems in physical and biological sciences.
Prerequisites: MATH 023 or MATH 033 or MATH 052
Attribute/Distribution: MA

MATH 310 Random Processes and Applications 3-4 Credits

Theory and applications of stochastic processes. Limit theorems, introduction to random walks, Markov chains, Poisson processes, birth and death processes, and Brownian motion. Applications to financial mathematics, biology, business and engineering.
Prerequisites: MATH 309 or MATH 231
Attribute/Distribution: MA

MATH 311 Graph Theory 3 Credits

An introduction to basic theoretical results and techniques of graph theory such as trees, connectivity, matchings, coloring, planar graphs and Hamiltonicity. Additional topics will be covered as time permits.
Prerequisites: MATH 163 or MATH 261
Attribute/Distribution: MA

MATH 312 Statistical Computing and Applications 3-4 Credits

Use of statistical computing packages; exploratory data analysis; Monte Carlo methods; randomization and resampling, application and interpretation of a variety of statistical methods in real world problems.
Prerequisites: MATH 012 or MATH 231
Attribute/Distribution: MA

MATH 316 Complex Analysis 3-4 Credits

Concept of analytic function from the points of view of the CauchyRiemann equations, power series, complex integration, and conformal mapping.
Prerequisites: MATH 301
Attribute/Distribution: MA

MATH 320 Ordinary Differential Equations 3-4 Credits

The analytical and geometric theory of ordinary differential equations, including such topics as linear systems, systems in the complex plane, oscillation theory, stability theory, geometric theory of nonlinear systems, finite difference methods, general dynamical systems.
Prerequisites: MATH 205 or (MATH 242 and (MATH 023 or MATH 033), )
Attribute/Distribution: MA

MATH 321 Topics in Discrete Mathematics 3 Credits

Selected topics in areas of discrete mathematics. Consent of department chair required.
Repeat Status: Course may be repeated.
Attribute/Distribution: MA

MATH 322 Methods of Applied Analysis I 3 Credits

Fourier series, eigenfunction expansions, SturmLiouville problems, Fourier integrals and their application to partial differential equations; special functions. Emphasis is on a wide variety of formal applications rather than logical development.
Prerequisites: MATH 205
Attribute/Distribution: MA

MATH 323 Methods of Applied Analysis II 3 Credits

Green's functions; integral equations; variational methods; asymptotic expansions, method of saddle points; calculus of vector fields, exterior differential calculus.
Prerequisites: MATH 322
Attribute/Distribution: MA

MATH 327 Groups and Rings 3-4 Credits

An intensive study of the concepts of group theory including the Sylow theorems, and of ring theory including unique factorization domains and polynomial rings.
Prerequisites: MATH 242 and MATH 243
Attribute/Distribution: MA

MATH 329 Computability Theory 3-4 Credits

Core development of classical computability theory: enumeration, index and recursion theorems, various models of computation and Church's Thesis, uncomputability results, introduction to reducibilities and their degrees (in particular, Turing degrees, or degrees of uncomputability), computable operators and their fixed points.
Attribute/Distribution: MA

MATH 331 Differential Geometry of Curves and Surfaces 3 Credits

Local and global differential geometry of curves and surfaces in Euclidean 3space. Frenet formulas for curves, isoperimetric inequality, 4vertex theorem; regular surfaces, first fundamental form, Gauss map, second fundamental form; curvatures for curves and surfaces and their relations; The GaussBonnet theorem.
Prerequisites: MATH 023 or MATH 033
Attribute/Distribution: MA

MATH 334 Mathematical Statistics 3-4 Credits

Populations and random sampling; sampling distributions; theory of statistical estimation; criteria and methods of point and interval estimation; theory of testing statistical hypotheses.
Prerequisites: MATH 309
Attribute/Distribution: MA

MATH 338 Linear Models in Statistics with Applications 3-4 Credits

Least square principles in multiple regression and their interpretations; estimation, hypotheses testing, confidence and prediction intervals, modeling, regression diagnostic, multicollinearity, model selection, analysis of variance and covariance; logistic regression. Introduction to topics in time series analysis such as ARMA, ARCH, and GARCH models. Applications to natural sciences, finance and economics. Use of computer packages.
Prerequisites: (MATH 012 or MATH 231) and (MATH 043 or MATH 205 or MATH 242)
Attribute/Distribution: MA

MATH 340 (CSE 340) Design and Analysis of Algorithms 3 Credits

Algorithms for searching, sorting, manipulating graphs and trees, finding shortest paths and minimum spanning trees, scheduling tasks, etc.: proofs of their correctness and analysis of their asymptotic runtime and memory demands. Designing algorithms: recursion, divide-andconquer, greediness, dynamic programming. Limits on algorithm efficiency using elementary NP-completeness theory. Credit will not be given for both MATH 340 (CSE 340) and MATH 441 (CSE 441).
Prerequisites: (MATH 022 or MATH 096 or MATH 032) and (CSE 261 or MATH 261)

MATH 341 Mathematical Models and Their Formulation 3 Credits

Mathematical modeling of engineering and physical systems with examples drawn from diverse disciplines. Emphasis is on building models of real world problems rather than learning mathematical techniques.
Prerequisites: MATH 205
Attribute/Distribution: MA

MATH 342 Number Theory 3-4 Credits

Basic concepts and results in number theory, including such topics as primes, the Euclidean algorithm, Diophantine equations, congruences, quadratic residues, quadratic reciprocity, primitive roots, number-theoretic functions, distribution of primes, Pell’s equation, Fermat’s theorem, partitions. Consent of instructor required.
Attribute/Distribution: MA

MATH 343 Introduction To Cryptography 3,4 Credits

Classical elementary cryptography: Caesar cipher, other substitution ciphers, block ciphers, general linear ciphers. Fast random encryption (DES and AES: Advanced Encryption Standard). Public key systems (RSA and discrete logs). Congruences, modular arithmetic, fast exponentiation, polynomials, matrices. Distinction between polynomial time (primality), Subexponential time (factoring) and fully Exponential computation (elliptic curves). Introduction to sieving and distributed computation. Consent of instructor required.
Attribute/Distribution: MA

MATH 350 Special Topics 3 Credits

A course covering special topics not sufficiently covered in listed courses. Consent of department chair required.
Repeat Status: Course may be repeated.
Attribute/Distribution: MA

MATH 371 Readings 1-3 Credits

The study of a topic in mathematics under appropriate supervision, designed for the individual student who has studied extensively and whose interests lie in areas not covered in the listed courses. Consent of department chair required.
Repeat Status: Course may be repeated.
Attribute/Distribution: MA

MATH 374 Statistical Project 3 Credits

Supervised field project or independent reading in statistics or probability. Consent of department chair required.
Attribute/Distribution: MA

MATH 391 Senior Honors Thesis 3 Credits

Independent research under faculty supervision, culminating in a thesis presented for departmental honor. Consent of department chair required.
Repeat Status: Course may be repeated.
Attribute/Distribution: MA

MATH 401 Real Analysis I 3 Credits

Set theory, real numbers; introduction to measures, Lebesgue measure; integration, general convergence theorems; differentiation, functions of bounded variation, absolute continuity; Lp spaces.
Prerequisites: MATH 301

MATH 402 Real Analysis II 3 Credits

Metric spaces; introduction to Banach and Hilbert space theory; Fourier series and Fejer operators; general measure and integration theory, RadonNikodym and Riesz representation and theorems; LebesgueStieljtes integral.
Prerequisites: MATH 307 or MATH 401

MATH 403 Topics in Real Analysis 3 Credits

Intensive study of topics in analysis with emphasis on recent developments. Requires permission of the department chair.
Repeat Status: Course may be repeated.

MATH 404 Topics in Mathematical Logic 3 Credits

Intensive study of topics in mathematical logic. Consent of instructor required.
Repeat Status: Course may be repeated.

MATH 405 Partial Differential Equations I 3 Credits

Classification of partial differential equations; methods of characteristics for first order equations; methods for representing solutions of the potential, heat, and wave equations, and properties of the solutions of these equations; maximum principles.
Prerequisites: MATH 301

MATH 406 Partial Differential Equations II 3 Credits

Continuation of MATH 405. Emphasis on second order equations with variable coefficients and systems of first order partial differential equations.
Prerequisites: MATH 405

MATH 408 Algebraic Topology I 3 Credits

Polyhedra; fundamental groups; simplicial and singular homology.

MATH 409 Mathematics Seminar 1-6 Credits

An intensive study of some field of mathematics not offered in another course. Consent of department chair required.

MATH 410 Mathematics Seminar 1-6 Credits

Continuation of the field of study in MATH 409 or the intensive study of a different field. Consent of department chair required.

MATH 416 Complex Function Theory 3 Credits

Continuation of MATH 316.
Prerequisites: MATH 316

MATH 421 Introduction To Wavelets 3 Credits

Continuous and discrete signals; review of Fourier analysis; discrete wavelets; time frequency spaces; Haar and Walsh systems; multiresolution analysis; Hilbert spaces; quadratic mirror filters; fast wavelet transforms; computer code; applications to filtering, compression, and imaging.
Prerequisites: ECE 108 or MATH 205

MATH 423 Differential Geometry I 3 Credits

Differential manifolds, tangent vectors and differentials, submanifolds and the implicit function theorem. Lie groups and Lie algebras, homogeneous spaces. Tensor and exterior algebras, tensor fields and differential forms, de Rham cohomology, Stokes' theorem, the Hodge theorem. Must have completed MATH 301, or MATH 243 or MATH 205 with permission of instructor.

MATH 424 Differential Geometry II 3 Credits

Curves and surfaces in Euclidean space; mean and Gaussian curvatures, covariant differentiation, parallelism, geodesics, GaussBonnet formula. Riemannian metrics, connections, sectional curvature, generalized GaussBonnet theorem. Further topics.
Prerequisites: MATH 423

MATH 428 Fields And Modules 3 Credits

Field theory, including an introduction to Galois theory; the theory of modules, including tensor products and classical algebras.
Prerequisites: MATH 327

MATH 430 Numerical Analysis 3 Credits

Multistep methods for ordinary differential equations; finite difference methods for partial differential equations; numerical approximation of functions. Use of computer required.
Prerequisites: MATH 230

MATH 435 Functional Analysis I 3 Credits

Banach spaces and linear operators; separation and extension theorems; open mapping and uniform boundedness principles; weak topologies; local convexity and duality; Banach algebras; spectral theory of operators; and compact operators.
Prerequisites: MATH 307 and MATH 401

MATH 441 (CSE 441) Advanced Algorithms 3 Credits

Algorithms for searching, sorting, manipulating graphs and trees, scheduling tasks, finding shortest path, matching patterns in strings, cryptography, matroid theory, linear programming, max-flow, etc., and their correctness proofs and analysis of their time and space complexity. Strategies for designing algorithms, e.g. recursion, divide-and-conquer, greediness, dynamic programming. Limits on algorithm efficiency are explored through NP completeness theory. Quantum computing is briefly introduced. Credit will not be given for both CSE 340 (MATH 340) and CSE 441 (MATH 441).

MATH 444 Algebraic Topology II 3 Credits

Continuation of MATH 408. Cohomology theory, products, duality.
Prerequisites: MATH 408

MATH 445 Topcs in Algebraic Topology 3 Credits

Selected topics reflecting the interests of the professor and the students.
Prerequisites: MATH 444

MATH 449 Topics In Algebra 3 Credits

Intensive study of topics in algebra with emphasis on recent developments. Consent of department chair required.
Repeat Status: Course may be repeated.

MATH 450 Special Topics 3 Credits

Intensive study of some field of the mathematical sciences not covered in listed courses. Consent of department chair required.
Repeat Status: Course may be repeated.

MATH 455 Topics In Number Theory 3 Credits

Selected topics in algebraic and/or analytic number theory. Consent of instructor required.
Repeat Status: Course may be repeated.

MATH 461 Topics In Mathematical Statistcs 3 Credits

An intensive study of one or more topics such as theory of statistical tests, statistical estimation, regression, analysis of variance, nonparametric methods, stochastic approximation, and decision theory.
Repeat Status: Course may be repeated.
Prerequisites: MATH 334 and MATH 401

MATH 462 Modern Nonparametric Methods in Statistics 3 Credits

Classical and modern methods of nonparametric statistics; order and rank statistics; tests based on runs, signs, ranks, and order statistics; distribution free statistical procedures for means, variances, correlations, and trends; relative efficiency; KolmogorovSmirnov statistics; statistical applications of Brownian process; modern techniques such as robust methods, nonparametric smoothing, and bootstrapping; additional topics such as nonparametric regression and dimension reduction.
Prerequisites: (MATH 334 or STAT 334) and (MATH 338 or STAT 338)

MATH 463 (STAT 463) Advanced Probability 3 Credits

Measure theoretic foundations; random variables, integration in a measure space, expectations; convergence of random variables and probability measures; conditional expectations; characteristic functions; sums of random variables, limit theorems.
Prerequisites: MATH 309 and MATH 401

MATH 464 Advanced Stochastic Process 3 Credits

Theory of stochastic processes; stopping times; martingales; Markov processes; Brownian motion; stochastic calculus; Brownian bridge, laws of suprema; Gaussian processes.
Prerequisites: MATH 309 and MATH 401

MATH 465 Topics in Probability 3 Credits

Selected topics in probability. Consent of department chair required.
Repeat Status: Course may be repeated.

MATH 467 Financial Calculus I 3 Credits

Basic mathematical concepts behind derivative pricing and portfolio management of derivative securities. Development of hedging and pricing by arbitrage in the discrete time setting of binary trees and BlackScholes model. Introduction to the theory of Stochastic Calculus, Martingale representation theorem, and change of measure. Applications of the developed theory to a variety of actual financial instruments.
Prerequisites: MATH 231 or MATH 309

MATH 468 Financial Calculus II 3 Credits

Models and mathematical concepts behind the interest rates markets. HeathJarrowMorton model for random evolution of the term structure of interest rates and short rate models. Applications of the theory to a variety of interest rates contracts including swaps, caps, floors, swapoptions. Development of multidimensional stochastic calculus and applications to multiple stock models, quantos, and foreign currency interestrate models.
Prerequisites: MATH 467

MATH 470 Proseminar 3 Credits

Preparation for entering the mathematics profession. Seminar will concentrate on methods of teaching mathematics, and will include other topics such as duties of a professor and searching for a job. Consent of department chair required.

MATH 471 Homological Algebra 3 Credits

Modules, tensor products, categories and functors, homology functors, projective and injective modules.
Prerequisites: MATH 428

MATH 472 Group Representations 3 Credits

Linear representations and character theory with emphasis on the finite and compact cases.
Prerequisites: MATH 428

MATH 475 Topics in Geometry 3 Credits

Selected topics in geometry, such as geometric analysis, algebraic geometry, complex geometry, characteristic classes, geometric flows or geometric measure theory, with emphasis on recent developments. Consent of department chair required.
Repeat Status: Course may be repeated.

MATH 485 Topics in Financial Mathematics 3 Credits

Selected topics in financial mathematics. Consent of department chair required.
Repeat Status: Course may be repeated.

MATH 490 Thesis 1-6 Credits

MATH 499 Dissertation 1-15 Credits

Repeat Status: Course may be repeated.

Statistics Courses

STAT 342 Linear Algebra 3 Credits

Solution of systems of linear equations, matrices, vector spaces, bases, linear transformations, eigenvalues, eigenvectors, additional topics as time permits. Restricted to graduate students in the MS in Statistics program. Prerequisites as noted below or consent of instructor. Credit may not be received for both MATH 242 and STAT 342,.

STAT 408 Seminar in Statistics and Probability 1-6 Credits

Intensive study of some field of statistics or probability not offered in another course. Consent of department required.

STAT 409 Seminar in Statistics and Probability 1-6 Credits

Intensive study of some field of statistics or probability not offered in another course. Consent of department required.

STAT 410 Random Processes and Applications 3 Credits

See MATH 310.

STAT 412 Statistical Computing and Applications 3 Credits

See MATH 312.

STAT 434 Mathematical Statistics 3 Credits

See MATH 334.

STAT 438 Linear Models In Statistics with Applications 3 Credits

See MATH 338.
Prerequisites: (MATH 012 or MATH 231) and (MATH 043 or MATH 205 or MATH 242)

STAT 461 Topics In Mathematical Statistics 3 Credits

See MATH 461.

STAT 462 Modern Nonparametric Methods in Statistics 3 Credits

See MATH 462.

STAT 463 (MATH 463) Advanced Probability 3 Credits

See MATH 463.
Prerequisites: MATH 309 and MATH 401

STAT 464 Advanced Stochastic Processes 3 Credits

See MATH 464.

STAT 471 Topics in Statistical Learning and Computing 3 Credits

Selected advanced topics in statistical learning and computing. Possible topics include linear and nonlinear regression, applied spatial statistics, applied multivariate and longitudinal data analysis, functional data analysis, survival analysis, data analytics, statistical methods that use intensive-computing or simulations, data mining techniques, with application and interpretation of a variety of statistical methods in real world problems. Topics could vary from one semester to another depending on the interests of the faculty member and the students.
Repeat Status: Course may be repeated.

Professors. Huai-Dong Cao, PhD (Princeton University); Donald M Davis, PhD (Stanford University); Bennett Eisenberg, PhD (Massachusetts Institute of Technology); Wei-Min Huang, PhD (University of Rochester); Garth Isaak, PhD (Rutgers University); David L. Johnson, PhD (Massachusetts Institute of Technology); Terrence J. Napier, PhD (University of Chicago); Lee J. Stanley, PhD (University of California Berkeley); Steven H. Weintraub, PhD (Princeton University); Joseph E. Yukich, PhD (Massachusetts Institute of Technology)

Associate Professors. Soutir Bandyopadhyay, PhD (Texas A&M University); Daniel Conus, PhD (Swiss Federal Institute of Technology); Bruce A. Dodson, PhD (Stony Brook University); Robert W. Neel, PhD (Harvard University); Mark Skandera, PhD (Massachusetts Institute of Technology); Xiaofeng Sun, PhD (Stanford University); Susan Szczepanski, PhD (Rutgers University New Brunswick); Ping-Shi Wu, PhD (University of California Davis); Linghai Zhang, PhD (University of Minnesota)

Assistant Professors. Angela Hicks, PhD (University of California San Diego); Yue Yu, DA (Brown University)

Professors Of Practice. Vincent E Coll, PhD (University of Pennsylvania); Miranda Ijang Teboh Ewungkem, PhD (Lehigh University)

Emeriti. Samir A. Khabbaz, PhD (University of Kansas); Jerry P. King, PhD (University of Kentucky Fort Knox); Clifford S. Queen, PhD (Ohio State University); Eric P. Salathe, PhD (Brown University); Andrew K Snyder, PhD (Lehigh University); Ramamirtham Venkataraman, PhD (Brown University)