Mathematical Sciences Department
Emily Stone, Chair
Mathematics is studied both as a tool and for its own sake. Its usefulness in the sciences  physical, biological, social, behavioral, and environmental  and in decisionmaking processes is so established that it is an indispensable part of many curricula.
Mathematics is chosen as a major area of study by individuals who find it challenging, fascinating, and beautiful. It is also appreciated by many who seek primarily to use mathematics as a tool.
A career in mathematics, except for teaching at the secondary level, generally requires a graduate degree as preparation. Careers include teaching, research, and the application of mathematics to diverse problems in institutions of higher learning, business, industry, and government.
The Bachelor of Arts, Master of Arts, and Doctor of Philosophy degrees are offered as well as a Bachelor of Science in Mathematical Sciences–Computer Science.
High School Preparation: For studying mathematics at the University level, it is recommended that the high school course work consist of four years of collegepreparatory mathematics, including geometry, trigonometry, and college algebra or precalculus. A course in calculus or statistics is helpful, but not necessary. It is unusual to complete an undergraduate degree in mathematics in four years without the necessary background to take Calculus I (M 171) during the freshman year (preferably during the first semester at the university).
Undergraduate Degrees Available
Subject  Type  Option  Track 

Mathematical SciComputer Sci  Bachelor of Science  
Mathematics  Bachelor of Arts  
Mathematics  Bachelor of Arts  Applied Mathematics  
Mathematics  Bachelor of Arts  Combinatorics & Optimization  
Mathematics  Bachelor of Arts  Mathematics Education  
Mathematics  Bachelor of Arts  Pure Mathematics  
Mathematics  Bachelor of Arts  Statistics  
Mathematics  Minor  
Mathematics  Minor  Teaching Math 
Department Faculty
Professors
 Johnathan Bardsley, Professor
 Jonathan Graham, Professor
 Leonid Kalachev, Professor
 Mark Kayll, Professor
 Jenny McNulty, Associate Dean / Professor
 George McRae, Professor Emeritus
 David Patterson, Professor
 Bharath Sriraman, Professor
 Brian Steele, Professor
 Emily Stone, Department Chair, Professor
 Karel Stroethoff, Professor
 Nikolaus Vonessen, Professor, and Associate Chair  Undergraduate Program
Associate Professors
 Jennifer Brooks, Associate Professor
 Eric Chesebro, Associate Professor
 Kelly McKinnie, Associate Professor
 Gregory St. George, Associate Professor
 Ke Wu, Associate Professor
Assistant Professors
 Cory Palmer, Assistant Professor and Associate Chair  Graduate Program
 Frederick Peck, Assistant Professor
 Matthew Roscoe, Assistant Professor
Adjunct Faculty
 John Duffield, Adjunct Research Professor
 Solomon Harrar, Adjunct Research Professor
 Daniel Johnston, Visiting Assistant Professor
 Richard Lane, Adjunct Instructor
 N'Djekornom Dara Laobeul, Adjunct Instructor
 Louis Lutz, Adjunct Instructor
 Justin Lynd, Visiting Assistant Professor
 Michael Olear, Adjunct Instructor
 Joyce Schlieter, Adjunct Instructor
 Mickey Smith, Lecturer
 Grant Swicegood, Postdoctoral Lecturer
Lecturers
 Lauren Fern, Lecturer
 Cindy Leary, Lecturer
 Regina Souza, Lecturer
Emeritus Professors
 Richard Billstein, Emeritus
 James Hirstein, Professor Emeritus
Course Descriptions
Mathematics

M 104  Numbers as News
Credits: 3. Offered spring. Prereq., M 090 with a grade of B or better, or M 095, or ALEKS placement >= 3. An exploration of mathematics and statistics as used in the popular media. For students in the School of Journalism only. 
M 105  Contemporary Mathematics
Credits: 3. Offered every term. Prereq., M 090 with a grade of B or better, or M 095, or ALEKS placement >= 3. An introduction to mathematical ideas and their impact on society. Intended for students wishing to satisfy the general education mathematics requirement. 
M 115  Probability and Linear Mathematics
Credits: 3. Offered every term. Prereq., M 090 with a grade of B or better, or M 095, or ALEKS placement >= 3. Systems of linear equations and matrix algebra. Introduction to probability with emphasis on models and probabilistic reasoning. Examples of applications of the material in many fields.Course Attributes:
 Practical Nursing Prog Rqrmnt
 Registered Nursing Prog Rqrmnt

M 118  118 Mathematics for Music Enthusiasts
Credits: 3. Offered autumn and/or spring. Prereq. M 090 with a grade of B or better, or M 095, or ALEKS placement >= 3; and elementary music background. An introduction to the interplay between mathematics and music. Course intended for Music majors/minors, and others with musical backgrounds/interests, who wish to satisfy the general education mathematics requirement. 
M 121  College Algebra
Credits: 3. Offered autumn and spring. Prereq., M 095 or ALEKS placement >= 4. Intended to strengthen algebra skills. The study of functions and their inverses; polynomial, rational, exponential, and logarithmic functions. Credit not allowed for both M 121, and M 151.Course Attributes:
 Practical Nursing Prog Rqrmnt
 Registered Nursing Prog Rqrmnt

M 122  College Trigonometry
Credits: 3. Offered autumn and spring. Prereq., M 121 or ALEKS placement >= 4. Preparation for calculus based on college algebra. Review of functions and their inverses. Trigonometric functions and identities, polar coordinates and an optional topic such as complex numbers, vectors or parametric equations. Credit not allowed for both M 122 and M 151. 
M 132  Numbers and Operations for Elementary School Teachers
Credits: 3. Offered autumn and spring. Prereq., M 095 or M 115, or ALEKS placement >= 4. The study of number and operations for prospective elementary and middle school teachers, including whole numbers, decimals, fractions, percent, integers, operations, numeration systems, and problem solving. 
M 133  Geometry and Measurement for Elementary School Teachers
Credits: 3. Offered autumn and spring. Prereq., M 132. The study of geometry and geometric measurement for prospective elementary and middle school teachers, including synthetic, transformational, and coordinate geometry, constructions, congruence and similarity, 2dimensional and 3dimensional measurement, and problem solving. 
M 135  Mathematics for K8 Teachers I
Credits: 5. Offered autumn and spring. Prereq., M 095, M 115, or ALEKS placement >= 4. Open only to elementary education majors. Topics include problemsolving, sets and logic, functions, whole numbers, integers, rational numbers, real numbers, number theory, probability and statistics. 
M 136  Mathematics for K8 Teachers II
Credits: 4. Offered autumn and spring. Prereq., M 135. Topics include introductory geometry, geometric constructions, congruence, similarity, measurement, coordinate geometry and an introduction to computer geometry. 
M 151  Precalculus
Credits: 4. Offered autumn and spring. Prereq., ALEKS placement >= 4. A one semester preparation for calculus (as an alternative to M 121122. Functions of one real variable are introduced in general and then applied to the usual elementary functions, namely polynomial and rational functions, exponential and logarithmic functions, trigonometric functions, and miscellaneous others. Inverse functions, polar coordinates and trigonometric identities are included. Credit not allowed for both M 151 and M 121 or 122.Course Attributes:
 Practical Nursing Prog Rqrmnt
 Registered Nursing Prog Rqrmnt

M 162  Applied Calculus
Credits: 4. Offered autumn and spring. Prereq., ALEKS placement >= 5 or one of M 121, 122 or 151. Introductory course surveying the principal ideas of differential and integral calculus with emphasis on applications and computer software. Mathematical modeling in discrete and continuous settings. Intended primarily for students who do not plan to take higher calculus. 
M 171  Calculus I
Credits: 4. Offered autumn and spring. Prereq., M 122 or 151 or ALEKS placement >= 5. Differential calculus, including limits, continuous functions, Intermediate Value Theorem, tangents, linear approximation, inverse functions, implicit differentiation, extreme values and the Mean Value Theorem. Integral Calculus including antiderivatives, definite integrals, and the Fundamental Theorem of Calculus.Course Attributes:
 Practical Nursing Prog Rqrmnt
 Registered Nursing Prog Rqrmnt

M 172  Calculus II
Credits: 4. Offered autumn and spring. Prereq., M 171 or 181. Techniques of Integration. Area computations. Improper integrals. Infinite series and various convergence tests. Power series. Taylor's Formula. Polar coordinates. Parametric curves. 
M 181  Honors Calculus I
Credits: 4. Offered autumn. Prereq., consent of instr. Coreq., Honors Calculus Seminar, a section of M 294. Honors version of M 171.Course Attributes:
 Honors Course

M 182  Honors Calculus II
Credits: 4. Offered spring. Prereq., M 181 or consent of instr. Coreq., Honors Calculus Seminar, a section of M 294. Honors version of M 172.Course Attributes:
 Honors Course

M 191  Special Topics
Credits: 1 TO 6. (R6) Offered autumn and spring. Prereq., consent of instr. Experimental offerings of visiting professors, experimental offerings of new courses, or one time offerings of current topics. 
M 192  Independent Study
Credits: 1 TO 6. (R6) Offered intermittently. Course material appropriate to the needs and objectives of the individual student. 
M 210  Introduction to Mathematical Software
Credits: 3. Offered spring. Prereq., one of M 162, 171, or 181, or consent of instr. Software packages useful for doing and writing mathematics. Introduction to a computer algebra system (such as Maple or Mathematica), a numerical package (such as MATLAB or R), and elementary programming. Writing and communicating mathematics using the mathematical typesetting system LaTeX. 
M 221  Introduction to Linear Algebra
Credits: 4. Offered autumn and spring. Prereq., M 172 or 182. Vectors in the plane and space, systems of linear equations and Gauss–Jordan elimination, matrices, determinants, eigenvalues and eigenvectors, vector spaces, linear transformations. Calculators and/or computers used where appropriate. 
M 225  Introduction to Discrete Mathematics
Credits: 3. Offered autumn. Prereq., one of M 162, 171, or 181 or consent of instr. Mathematical concepts used in computer science with an emphasis on mathematical reasoning and proof techniques. Elementary logic, sets, functions and relations, combinatorics, mathematical induction, recursion and algorithms. Mathematics majors should take M 307 instead of 225. 
M 231  Topics in Geometry
Credits: 3. Offered intermittently. Prereq., M 136 or consent of instr. Geometry topics for teaching grades 6–12 mathematics. Intended primarily for students in elementary education who plan to teach middle school mathematics. 
M 234  Higher Mathematics for Elementary School Teachers
Credits: 3. Offered autumn and spring. Prereq., M 132. The study of algebra, number theory, probability and statistics for prospective elementary and middle school teachers, including proportional reasoning, functions, elementary number theory, statistical modeling and inference, and elementary probability theory. 
M 273  Multivariable Calculus
Credits: 4. Offered autumn and spring. Prereq., M 172 or 182. Calculus of functions of several variables; differentiation and elementary integration. Vectors in the plane and space. 
M 274  Introduction to Differential Equations
Credits: 3. Offered spring. Prereq., one of M 162, 171 or 181 and knowledge of basic trigonometry. Solution of ordinary differential equations and systems with emphasis on applications, numerical methods and computer software. 
M 291  Special Topics
Credits: 1 TO 3. (R9) Offered autumn and spring. Prereq., consent of instr. Experimental offerings of visiting professors, experimental offerings of new courses, or onetime offerings of current topics. 
M 292  Independent Study
Credits: 1 TO 9. (R9) Offered autumn and spring. Prereq., consent of instr. Guidance of an individual student in doing independent study on material not offered in a regular course. 
M 294  Seminar
Credits: 1 TO 9. (R–9) Offered autumn and spring. Prereq., consent of instr. 
M 300  Undergraduate Mathematics Seminar
Credits: 1. (R–6) Offered every semester. Prereq., M 171 or 181. Discussion seminar focused on topics and issues of interest to students in the mathematical sciences. 
M 301  Mathematics Technology for Teachers
Credits: 3. Offered autumn. Prereq., M 221. Discrete and continuous mathematical models from a variety of disciplines using appropriate technology. 
M 307  Introduction to Abstract Mathematics
Credits: 3. Offered autumn and spring. Prereq., M 172 or 182. Designed to prepare students for upper–division proof–based mathematics courses. Topics include proof techniques, logic, sets, relations, functions and axiomatic methods. Students planning to take both M 221 and 307 are encouraged to take M 221 first. 
M 311  Ordinary Differential Equations and Systems
Credits: 3. Offered autumn. Prereq., M 273. Ordinary differential equations. Systems of linear differential equations from a matrix viewpoint. Series solutions. Existence and uniqueness for initial value problems. Numerical methods. Stability and selected topics. M 317 computer lab recommended. 
M 317  Ordinary Differential Equations Computer Lab
Credits: 1. Offered autumn. Coreq., M 311 or consent of instr. Intended primarily for student in M 311. 
M 325  Discrete Mathematics
Credits: 3. Offered spring. Prereq., M 171 and 225 or 307. Continuation of 225 and topics from graph theory, Boolean algebras, automata theory, coding theory, computability and formal languages. 
M 326  Number Theory
Credits: 3. Offered spring. Prereq., M 225 or 307. Congruences, Diophantine equations, properties of primes, quadratic residues, continued fractions, algebraic numbers. 
M 361  Discrete Optimization
Credits: 3. Offered spring. Prereq., one of M 162, 172 or 182 (221 or 225 recommended). Intended for non–mathematics majors as well as mathematics majors. Introduction to discrete optimization and modeling techniques with applications. Topics from combinatorics and graph theory, including enumeration, graph algorithms, matching problems and networks. 
M 362  Linear Optimization
Credits: 3. Offered autumn. Prereq., one of M 162, 172 or 182 (221 recommended). Coreq., M 363 recommended. Intended for non–mathematics majors as well as majors. Introduction to linear programming and modeling techniques with applications. Topics include the simplex method, duality, sensitivity analysis and network models. 
M 363  Linear Optimization Laboratory
Credits: 1. Offered autumn. Coreq., M 362. Introduction to linear optimization software. 
M 381  Advanced Calculus I
Credits: 3. Offered autumn . Prereq., M 307. Rigorous development of singlevariable calculus with formal proof. Functions, sequences, limits, continuity, differentiation, and integration. 
M 391  Special Topics
Credits: 1 TO 9. (R9) Offered autumn and spring. Prereq., consent of instr. Experimental offerings of visiting professors, experimental offerings of new courses, or onetime offerings of current topics. 
M 392  Independent Study
Credits: 1 TO 9. (R9) Offered autumn and spring. Prereq., consent of instr. Guidance of an individual student in doing independent study on material not offered in a regular course. 
M 394  Seminar
Credits: 1 TO 9. (R–9) Offered autumn and spring. Prereq., consent of instr. 
M 398  Internship
Credits: 1 TO 6. Offered autumn and spring. Prereq., consent of instructor. Extended classroom experience which provides practical application of classroom learning during placements off campus. Prior approval must be obtained from the faculty supervisor and the Internship Services office. A maximum of 6 credits of Internship (198, 298, 398, 498) may count toward graduation.Course Attributes:
 Internships/Practicums
 Internship graduation limit 6

M 412  Partial Differential Equations
Credits: 3. Offered spring. Prereq., M 311. Fourier series, Sturm–Liouville and boundary value problems. Partial differential equations: Cauchy problems and the method of characteristics, separation of variables and Laplace transform methods. Numerical methods and selected topics. M 418 computer lab recommended. 
M 414  Deterministic Models
Credits: 3. Offered autumn or spring. Prereq., M 274 or 311 or consent of instr. Linear and nonlinear difference and differential equations: stability, phase–plane analysis, oscillatory behavior, limit cycles, and chaos. Eigenvalues and eigenfunctions. Emphasis on models in biology. 
M 418  Partial Differential Equations Computer Lab
Credits: 1. Offered spring. Coreq., M 412 or consent of instr. Intended primarily for students in M 412. 
M 429  History of Mathematics
Credits: 3. Offered spring. Prereq., M307. Historical study of the development of mathematics from the Egyptian and Babylonian eras to the 20th century.Course Attributes:
 Writing CourseUpperDivision
 Writing CourseAdvanced

M 431  Abstract Algebra I
Credits: 4. Offered autumn. Prereq., M 221 and 307 or consent of instr. An introduction to modern ideas of algebra through the study of groups, rings, and fields. 
M 432  Abstract Algebra II
Credits: 4. Offered spring. Prereq., M 431. Continues the investigation of groups, rings, and fields begun in M 431. Further topics include vector spaces and field extensions. 
M 439  Euclidean and Non–Euclidean Geometry
Credits: 3. Offered autumn. Prereq., M 307; M 231 recommended. Euclidean geometry from a rigorous, axiomatic viewpoint and Non–Euclidean geometries chosen from Lobachevskian, projective, finite and Riemannian. 
M 440  Numerical Analysis
Credits: 4. Offered intermittently. Prereq., M 307, 311, one computer language. Error analysis; approximation and interpolation, numerical solution of linear and nonlinear equations, numerical integration of ordinary and partial differential equations. 
M 445  Statistical, Dynamical, and Computational Modeling
Credits: 4. Offered autumn oddnumbered years. Prereq., consent of instr. An interdisciplinary course on the integration of statistical and dynamical models with applications to biological problems. Linear and nonlinear models, estimation, systems of ordinary differential equations, numerical integration, bootstrapping, MCMC methods. Intended both for students in mathematics and the natural sciences. 
M 461  Practical Big Data Analytics
Credits: 3. Offered autumn. Prereq., STAT 341, and one of M 221 or M 273, or consent of instructor. This is a methods course supporting the Big Data Certificate Program. The course provides the students with the essential tools for the analysis of big data. The content consists of map reduce and canonical information methods for analyzing massively large data sets, windowing methods for the analysis of streaming data, an introduction to predictive analytics, and an introduction to data visualization methods. 
M 462  Theoretical Basics of Big Data Analytics and Real Time Computation Algorithms
Credits: 3. Offered spring. Prereq., M 221 and two other Mathematics / Statistics classes at the 200level or above, or consent of instr. The main goal of this course is to provide students with a unique opportunity to acquire conceptual knowledge and theoretical background behind mathematical tools applicable to Big Data Analytics and Real Time Computations. Specific challenges of Big Data Analytics, e.g., problems of extracting, unifying, updating, and merging information, and processing of highly parallel and distributed data, will be reviewed. The tools for Big Data Analytics, such as regression analysis, linear estimation, calibration problems, real time processing of incoming (potentially infinite) data, will be studied in more detail. It will be shown how these approaches can be transformed to conform to the Big Data demands. 
M 467  Big Data Analytic Projects
Credits: 3. Offered spring. Prereq., two courses chosen from STAT 341, M 221 and M 273, and one of M 461 or M 462, or consent of instructor. This course is a practicum course aimed at developing skills needed to solve big data problems facing industry and academics. Problems are brought to the class by local technologyoriented businesses and university researchers. Lecture topics include project management, interacting with clients, and written and oral presentation of results. Additional lecture topics will be selected to address the specific problems brought to the class and may cover data reduction methods, algorithm design and predictive analytics. 
M 472  Introduction to Complex Analysis
Credits: 4. Offered spring. Prereq., M 273, M 307. Analytic functions, complex integration, singularities and application to contour integration, harmonic functions, spaces of analytic functions. 
M 473  Introduction to Real Analysis
Credits: 4. Offered autumn oddnumbered years. Prereq., M 273, M 307. Theory of metric spaces and point set topology, RiemannStieltjes integral, sequences and series of functions. StoneWeierstrass theorem, theorem of ArzelaAscoli, introduction to Lebesgue integration. 
M 485  Graph Theory
Credits: 3. Offered autumn. Prereq., M 325, or M 307 and M 361, or consent of instr. Theory and applications of graphs. Topics chosen from trees, matchings, connectivity, coloring, planarity, Ramsey theory, random graphs, combinatorial designs and matroid theory. 
M 490  Undergraduate Research
Credits: 1 TO 4. (R12) Offered every term. Prereq., consent of instr. Undergraduate research in the mathematical sciences under the direction of a faculty member. Graded credit/no credit. 
M 491  Special Topics
Credits: 1 TO 9. (R–9) Offered autumn and spring. Prereq., consent of instr. Experimental offerings of visiting professors, experimental offerings of new courses, or one–time offerings of current topics. 
M 492  Independent Study
Credits: 1 TO 9. (R–9) Offered autumn and spring. Prereq., consent of instr. Guidance of an individual student in doing independent study on material not offered in a regular course 
M 494  Seminar
Credits: 1 TO 9. (R9) Offered autumn and spring. Prereq., consent of instr. 
M 498  Internship
Credits: 1 TO 6. Offered autumn and spring. Prereq., consent of instr. Extended classroom experience which provides practical application of classroom learning during placements off campus. Prior approval must be obtained from the faculty supervisor and the Internship Services office. A maximum of 6 credits of Internship (198, 298, 398, 498) may count toward graduation.Course Attributes:
 Internships/Practicums
 Internship graduation limit 6

M 499  Senior Thesis
Credits: 1 TO 12. (R–12) Offered autumn and spring. Prereq., consent of instr. Senior thesis for mathematics majors and/or Watkins Scholars.Course Attributes:
 Writing CourseUpperDivision
 Writing CourseAdvanced

M 500  Current Mathematical Curricula
Credits: 3. Offered intermittently. Prereq., teacher certification or consent of instructor. Analysis of contemporary materials for secondary school mathematics: the goals, the mathematical content, alternative methodologies, and curriculum evaluation. Level: Graduate 
M 501  Technology in Mathematics for Teachers
Credits: 3. Offered intermittently. Prereq., teacher certification or consent of instructor. Technology usage when it is appropriate and when it is not. Experience is provided with scientific calculators, graphing utilities, computers, and identification of exemplary software. Level: Graduate 
M 504  Topics in Math Education
Credits: 1 TO 12. (R–12) Offered intermittently. Prereq., teacher certification. Topics of current interest which may include calculus, number theory, probability and statistics, geometry, or algebra, at a level suitable for teachers. Level: Graduate 
M 510  Problem Solving for Teachers
Credits: 3. Offered intermittently. Prereq., teacher certification or consent of instructor. Strategies for problem solving, problem posing in a variety of situations, modeling and applications. Problems are selected from various areas of mathematics. Level: Graduate 
M 511  Advanced Mathematical Methods I
Credits: 3. Offered autumn odd–numbered years. Prereq., M 311, and 412 or 414. Methods in applied mathematics related to the qualitative and quantitative solution of nonlinear and differential integral equations, dynamical systems, and perturbation methods. Applications of these methods to other sciences. Level: Graduate 
M 512  Advanced Mathematical Methods II
Credits: 3. Offered spring even–numbered years. Prereq., M 511. Continuation of M 511. Level: Graduate 
M 514  Topics in Applied Mathematics
Credits: 1 TO 12. (R–12) Offered autumn even–numbered years. Prereq., consent of instr. or M 511512. Topics of current interest in applied mathematics, mathematical modeling, dynamic modeling, and optimal management in stochastic or deterministic environments. Level: Graduate 
M 521  Advanced Algebra I
Credits: 3. Offered alternate years. Prereq., M 432 or consent of instr. Topics covered include group theory, field theory and Galois theory. Level: Graduate 
M 522  Advanced Algebra II
Credits: 3. Offered alternate years. Prereq., M 521 or consent of instr. Continuation of 521; rings, modules, commutative algebra, and further topics. Level: Graduate 
M 524  Topics in Algebra
Credits: 3. (R12) Offered alternate years in fall and spring. Prereq., consent of instr. Topics chosen from algebra and related areas, for example from commutative algebra, algebraic geometry, linear algebra, group theory, ring theory, or number theory. Level: Graduate 
M 530  Geometries for Teachers
Credits: 3. Offered intermittently in summer. Prereq., M 439 or equiv. Comparison of synthetic, analytic, vector, and transformational approaches to geometry. Includes classification of geometries, geometric representations, axiomatics, and the applications of modern geometries. Level: Graduate 
M 531  Topology
Credits: 3. Offered autumn even–numbered years. Prereq., M 473 or consent of instr. Set theory, topological spaces, metrizability, continuous mappings and selected topics. Level: Graduate 
M 532  Algebraic Topology
Credits: 3. Offered spring alternate years. Prereq., M 431 and M 531 or consent of instr.Introduction to algebraic topology through one or more topics chosen from the fundamental group and higher homotopy groups, singular homology, and simplicial homology. Level: Graduate 
M 551  Real Analysis
Credits: 3. Offered spring even–numbered years. Prereq., M 473 or 472 or consent of instr. Measure theory, abstract integration theory, theory of Lp–spaces. Level: Graduate 
M 555  Functional Analysis
Credits: 3. Offered spring odd–numbered years. Prereq., M 473 or 472 or consent of instr. Normed linear spaces, linear functionals, separation theorems, topological linear spaces, weak topologies, dualities. Level: Graduate 
M 564  Topics in Analysis
Credits: 3. (R–12) Offered autumn odd–numbered years. Prereq., consent of instr. Research projects or topics in analysis. May include but not restricted to Banach algebras, Fourier analysis, Harmonic analysis, Hilbert space theory, integral equations, or operator theory. Level: Graduate 
M 570  Calculus for Middle School Teachers
Credits: 3. Offered online in fullyear format. Prereq., teacher certification or consent of instr. A first course in differential and integral calculus. Concepts, definitions, properties, and elementary applications of the calculus of singlevalued real variables. Level: Graduate 
M 572  Algebra for Middle School Teachers
Credits: 3. Offered intermittently in summer. Prereq., teacher certification or consent of instr. Topics include algebraic number fields, linear algebra topics, polynomials, and applications appropriate for teachers of middle school mathematics. Level: Graduate 
M 573  Geometry for Middle School Teachers
Credits: 3. Offered intermittently in summer. Prereq., teacher certification or consent of instr. Introduction to synthetic, analytic, vector, and transformational approaches to geometry. Includes topics in 2 and 3dimensional geometry and measurement appropriate for teachers of middle school mathematics. Level: Graduate 
M 574  Probability and Statistics for Middle School Teachers
Credits: 3. Offered intermittently in summer. Prereq., teacher certification or consent of instr. A survey of topics in probability and statistics appropriate for teachers of middle school mathematics. Level: Graduate 
M 578  Discrete Mathematics for Middle School Teachers
Credits: 3. Offered intermittently. Prereq., teacher certification or consent of instr. Elements and operations of finite structures, combinatorics, recursion, graphs, matrices, and finite models appropriate for teachers of middle school mathematics. Level: Graduate 
M 581  Combinatorics
Credits: 3. Offered autumn odd–numbered years. Prereq., consent of instr. Theory and applications of discrete mathematics. Topics chosen from enumeration, combinatorial analysis, and graph theory. Level: Graduate 
M 582  Optimization
Credits: 3. Offered autumn even–numbered years. Prereq., consent of instr. Theory and applications of optimization. Topics chosen from linear, non–linear, and discrete optimization, including duality theory, convexity and networks. Level: Graduate 
M 584  Topics in Combinatorics and Optimization
Credits: 3. (R–12) Offered spring odd–numbered years. Prereq., consent of instr. Topics chosen from the areas of combinatorics and optimization. May include classical problems, current trends, research interests or other topics chosen by the instructor. Level: Graduate 
M 593  Professional Project
Credits: 1 TO 6. (R–6) Offered autumn and spring. Prereq., consent of advisor. Preparation of a professional paper appropriate to the needs and objectives of the individual student. Level: GraduateCourse Attributes:
 FacultyLed Study Abroad

M 595  Special Topics
Credits: 1 TO 12. (R–12) Offered autumn and spring. Prereq., consent of instr. Experimental offerings of visiting professors, experimental offerings of new courses, or one–time offerings of current topics. Level: GraduateCourse Attributes:
 Internships/Practicums

M 596  Independent Study
Credits: 1 TO 12. (R–12) Offered autumn and spring. Prereq., consent of instr. Course material appropriate to the needs and objectives of the individual student. Level: GraduateCourse Attributes:
 Service Learning/Volunteer

M 597  Research
Credits: 1 TO 12. (R–12) Offered autumn and spring. Prereq., consent of instr. Directed individual research and study appropriate to the back ground and objectives of the student. Level: Graduate 
M 598  Internship
Credits: 1 TO 12. (R–12) Offered autumn and spring. Prereq., consent of department. Extended classroom experience which provides practical application of classroom learning during placements off campus. Prior approval must be obtained from the faculty supervisor and the Internship Services office. Level: GraduateCourse Attributes:
 Internships/Practicums

M 599  Thesis
Credits: 1 TO 6. (R–6) Offered autumn and spring. Prereq., consent of instr. Preparation of a thesis or manuscript based on research for presentation and/or publication. Level: Graduate 
M 600  Mathematics Colloquium
Credits: 1 TO 3. (R–3) Offered autumn and spring. Prereq., consent of advisor. Presentations of research topics in mathematics and related fields. Level: Graduate 
M 602  Teaching College Mathematics
Credits: 3. Prereq., second year standing in graduate school. Topics include publishing, grant writing, writing in mathematics classes, media use in mathematics, evaluation and assessment of curricular materials and programs, instructional methods in university mathematics courses, and other selected topics. Level: Graduate 
M 605  Learning Theories in Mathematics
Credits: 3. Prereq., graduate status. How children learn mathematical content and processes. Models of mental development, concept formation, problem solving, reasoning, and creative thinking. Level: Graduate 
M 606  Current Topics in the History of Mathematics
Credits: 3. Examination of mathematical history topics from the latter part of the 20th century. Discussions may focus on the impact of Hilbert’s Problems. Research on current mathematics. Level: Graduate 
M 609  Research Methods in Mathematics Education
Credits: 3. Prereq., Consent of instr. Resources for learning of reported research, critical reviews of research, quantitative and qualitative processes. Level: Graduate 
M 610  Graduate Seminar in Applied Mathematics
Credits: 1 TO 12. (R–12) Offered autumn and spring. Prereq., consent of instr. A review and discussion of current research. Level: Graduate 
M 620  Graduate Seminar in Algebra
Credits: 1 TO 12. (R–12) Offered autumn and spring. Prereq., consent of instr. Level: Graduate 
M 630  Graduate Seminar in Geometry/Topology
Credits: 1 TO 12. (R–12) Offered autumn and spring. Prereq., consent of instr. A review and discussion of current research. Level: Graduate 
M 650  Graduate Seminar in Analysis
Credits: 1 TO 12. (R–12) Offered autumn and spring. Prereq., consent of instr. A review and discussion of current research. Level: Graduate 
M 680  Graduate Seminar in Combinatorics and Optimization
Credits: 1 TO 12. (R–12) Offered autumn and spring. Prereq., consent of instr. A review and discussion of current research. Level: Graduate 
M 690  Supervised Internship
Credits: 1 TO 12. (R–6) Offered autumn and spring. Prereq., consent of department. Supervised Teaching Internship. Level: GraduateCourse Attributes:
 Research & Creative Schlrshp

M 691  Practicum
Credits: 3. Prereq., consent of instr. Resources for learning of reported research, critical reviews of research, quantitative and qualitative processes. Level: Graduate 
M 694  Seminar
Credits: 1 TO 12. (R–12) Offered autumn and spring. Prereq., consent of instr. A review and discussion of current research. Topics vary. Level: Graduate 
M 699  Dissertation
Credits: 1 TO 9. (R–9) Offered autumn and spring. Level: Graduate
MathematicsStatistics

STAT 216  Introduction to Statistics
Credits: 4. Offered autumn and spring. Prereq., M 115 (preferred), or one of M 121, 135, 151, 162 or 171, or ALEKS placement >= 4. Introduction to major ideas of statistical inference. Emphasis is on statistical reasoning and uses of statistics. 
STAT 341  Introduction to Probability and Statistics
Credits: 3. Offered autumn and spring. Prereq., one of M 162, 172 or 182. Probability, probability models and simulation, random variables, density functions, special distributions, and a brief survey of estimation and hypothesis testing. Computer use integrated throughout. 
STAT 421  Probability Theory
Credits: 3. Offered autumn. Prereq., M 273 and STAT 341 or consent of instr. An introduction to probability, random variables and their probability distributions, estimation and hypothesis testing. This course is the foundation on which more advanced statistics courses build. 
STAT 422  Mathematical Statistics
Credits: 3. Offered spring. Prereq., STAT 421. Continuation of 421. 
STAT 451  Statistical Methods I
Credits: 3. Offered autumn. Prereq., one year of college mathematics including M 115 or equiv. course in probability or consent of instr. May not be counted toward a major in mathematics. Intended primarily for nonmathematics majors who will be analyzing data. Graphical and numerical summaries of data, elementary sampling, designing experiments, probability as a model for random phenomena and as a tool for making statistical inferences, random variables, basic ideas of inference and hypothesis testing. 
STAT 452  Statistical Methods II
Credits: 3. Offered spring. Prereq., STAT 451. Continuation of STAT 451. May not be counted toward a major in mathematics. Multiple regression, experimental design, analysis of variance, other statistical models. 
STAT 457  Computer Data Analysis I
Credits: 1. Offered autumn. Coreq., STAT 451 or consent of instr. An introduction to software for doing statistical analyses. Intended primarily for students in STAT 451. 
STAT 458  Computer Data Analysis II
Credits: 1. Offered spring. Coreq., STAT 452 or consent of instr. Continuation of STAT 457. Intended primarily for students in STAT 452. 
STAT 491  Special Topics
Credits: 1 TO 9. (R 9) Offered autumn and spring. Prereq., consent of instr. Experimental offerings of visiting professors, experimental offerings of new courses, or one time offerings of current topics. 
STAT 540  Probability and Statistics for Teachers
Credits: 3. Offered intermittently in summer. Prereq., STAT 341 or equiv. A survey of modern topics in probability and statistics. Emphasis will be on applications of statistics in real situations. Level: Graduate 
STAT 541  Advanced Mathematical Statistics
Credits: 3. Offered intermittently. Prereq., STAT 422. Advanced theory of estimation and hypothesis testing including large sample theory. Level: Graduate 
STAT 542  Applied Linear Models
Credits: 3. Offered autumn evennumbered years. Prereq., STAT 422 or consent of instr. Numerical and graphical data summaries, simple linear and multiple regression and analysis of variance, including estimation, hypothesis testing, residual analysis, diagnostics, and modelbuilding strategies. Use of the computer and real data sets integrated throughout. Level: Graduate 
STAT 543  Applied Multivariate Statistical Analysis
Credits: 4. Offered spring evennumbered years. Prereq., STAT 452 or 422, or consent of instr. Introduction to multivariate statistical methods and applications. Includes appropriate linear algebra, random vectors, multivariate normal distribution, multivariate ANOVA, principal components, clustering, discriminant analysis, and related topics. Use of the computer and real data sets integrated throughout. Intended for students in mathematics and in other fields. Level: Graduate 
STAT 544  Topics in Probability and Statistics
Credits: 3. (R12) Offered intermittently. Prereq., STAT 422 and consent of instr. May include theory of nonparametric statistics, generalized linear models, stochastic processes or other topics chosen by the instructor. Level: Graduate 
STAT 545  Theory of Linear Models
Credits: 3. Offered autumn oddnumbered years. Prereq., STAT 422. Multivariate normal distribution, distribution of quadratic forms, estimation and hypothesis testing in the full rank and less than full rank general linear models. Level: Graduate 
STAT 547  Applied Nonparametric Statistics
Credits: 3. Offered autumn oddnumbered years. Prereq., STAT 421 or 452 or consent of instr. Statistical estimation and inference based on ranks and elementary counting methods. Applications to a variety of situations including one and twosample, correlation, regression, analysis of variance, and goodnessoffit problems. Use of the computer and real data sets integrated throughout. Intended for students in mathematics and in other fields. Level: Graduate 
STAT 549  Applied Sampling
Credits: 3. Offered autumn evennumbered years. Theory and application of methods for selecting samples from populations in order to efficiently estimate parameters of interest. Includes simple random, systematic, cluster, stratified, multistage, line transect, distance and adaptive sampling. Use of the computer and real data sets integrated throughout. Intended for students in mathematics and in other fields. Level: Graduate 
STAT 640  Graduate Seminar in Probability and Statistics
Credits: 1 TO 12. (R12) Offered autumn and spring. Prereq., consent of instr. A review and discussion of current research. Level: Graduate