Mathematics Courses (MATH) College of Arts and Sciences
Subject Area  Course #  Course Title  Semester  Credit Hours  Expand 

MATH  1002  Functions and Differential Calculus  Fall/Spring  3  
Course Description
This course is intended for students who are required to take Calculus I (either MATH1100 or MATH1102) but whose backgrounds necessitate additional preparation. Topics include the real line and coordinate plane; linear and quadratic functions; higher degree polynomials and rational functions; trigonometry, emphasizing the trigonometric functions; and exponential and logarithmic functions. Note: This course does not satisfy the University Core Requirement in Mathematics. Department permission is required: see the Assistant Chair for Undergraduates. Instructor(s): Prerequisites: None


MATH  1003  Functions and Differential Calculus II  Spring  3  
Course Description
This course is a continuation of MATH1002 Instructor(s): Prerequisites: None


MATH  1004  Finite Probability and Applications  Fall/Spring  3  
Course Description
This course, for students in the humanities, the social sciences, School of Education, and School of Nursing, is an introduction to finite combinatorics and probability, emphasizing applications. Topics include finite sets and partitions, enumeration, probability, expectation, and random variables. Instructor(s): Prerequisites: None
Comments: Not open to students who have completed their Mathematics Core Curriculum Requirement without permission of the Department Chairperson (except for Psychology majors completing their second mathematics corequisite). 

MATH  1007  Ideas in Mathematics  Spring  3  
Course Description
This course is designed to introduce the student to the spirit, beauty, and vitality of mathematics. The emphasis is on development of ideas rather than problem solving skills. Topics vary, but are typically chosen from diverse areas such as geometry, number theory, computation, and graph theory. Schedule: Periodically Instructor(s): Prerequisites: None
Comments: Not open to students who have completed their Mathematics Core Curriculum Requirement without permission of the Department Chairperson (except for Psychology majors completing their second mathematics corequisite). 

MATH  1034  PreCalculus for OTE  Fall  3  
Course Description
TBD Instructor(s): Prerequisites: None


MATH  1035  Intro to Probability and Statistics for OTE  Fall/Summer  3  
Course Description
TBD Instructor(s): Prerequisites: None


MATH  1036  Intro to Calculus for OTE  Fall  3  
Course Description
TBD Instructor(s): Prerequisites: None


MATH  1100  Calculus I  Fall/Spring  4  
Course Description
MATH1100 is a first course in the calculus of one variable intended for biology, computer science, economics, management, and premedical students. It is open to others who are qualified and desire a more rigorous mathematics course at the core level. Topics include a brief review of polynomials and trigonometric, exponential, and logarithmic functions, followed by discussion of limits, derivatives, and applications of differential calculus to realworld problem areas. The course concludes with an introduction to integration. Instructor(s): Prerequisites: Trigonometry.
Comments: MATH1100 is not open to students who have completed a calculus course at the college level. Students contemplating majors in Chemistry, Computer Science/B.S., Environmental Geosciences, Geological Sciences, Mathematics, or Physics should enroll in MATH1102. 

MATH  1101  Calculus II  Fall/Spring  4  
Course Description
MATH1101 is a second course in the calculus of one variable intended for biology, computer science, economics, management, and premedical students. It is open to others who are qualified and desire a more rigorous mathematics course at the core level. Topics include an overview of integration, basic techniques for integration, a variety of applications of integration, and an introduction to (systems of) differential equations. Instructor(s): Prerequisites: MATH1100. MATH1100.
Comments: MATH1101 is not open to students who have completed MATH1103 or MATH1105. Students contemplating majors in Chemistry, Computer Science/B.S., Environmental Geosciences, Geological Sciences, Mathematics, or Physics should enroll in either MATH1103 (Spring) or MATH1105 (Fall). 

MATH  1102  Calculus I (Mathematics/Science Majors)  Fall  4  
Course Description
MATH1102 is a first course in the calculus of one variable intended for Chemistry, Computer Science/B.S., Geology, Geophysics, Mathematics, and Physics majors. It is open to others who are qualified and desire a more rigorous calculus course than MATH1100. Topics covered include the algebraic and analytic properties of the real number system, functions, limits, derivatives, and an introduction to integration. Instructor(s): Prerequisites: Trigonometry.
Comments: Not open to students who have completed a calculus course at the college level. 

MATH  1103  Calculus II (Mathematics/Science Majors)  Spring  4  
Course Description
MATH1103 is a continuation of MATH1102. Topics covered in the course include several algebraic techniques of integration, many applications of integration, and infinite sequences and series. Schedule: Periodically Instructor(s): Prerequisites: MATH1102.
Comments: Not open to students who has completed MATH1105. 

MATH  1105  Calculus IIAP (Mathematics/Science Majors)  Fall  3  
Course Description
MATH1105 is a second course in the calculus of one variable intended for Chemistry, Computer Science/B.S.,Environmental Geosciences, Geological Sciences, Mathematics, and Physics majors. It is designed for students who have completed either MATH1101 or a year of Calculus in high school at either the AB or BC curriculum level, but who are not yet prepared to advance to MATH2202 Multivariable Calculus. The course first reviews the primary techniques and interesting applications of integration. The remainder of the course provides an introduction to the topics of infinite sequences and series. Other topics may be introduced as time permits. Instructor(s): Prerequisites: None
Comments: Not open to students who have completed MATH1103. 

MATH  1121  Discussion/MATH1100  Fall/Spring  0  
Course Description
Recitation section, corequisite to MATH1100. Discussion of problemsolving techniques, examples, and homework in a smallclass setting. One hour per week. Each section of MATH1100 has a specific corequisite recitation, numbered MATH1121MATH1135; students should sign up for the recitation that matches the corequisite listed in the section of MATH1100 they select. Instructor(s): Prerequisites: None


MATH  1122  Discussion/MATH1100  Fall/Spring  0  
Course Description
Recitation section, corequisite to MATH1100. Discussion of problemsolving techniques, examples, and homework in a smallclass setting. One hour per week. Instructor(s): Prerequisites: None


MATH  1123  Discussion/MATH1100  Fall/Spring  0  
Course Description
Recitation section, corequisite to MATH1100. Discussion of problemsolving techniques, examples, and homework in a smallclass setting. One hour per week. Instructor(s): Prerequisites: None


MATH  1124  Discussion/MATH1100  Fall/Spring  0  
Course Description
Recitation section, corequisite to MATH1100. Discussion of problemsolving techniques, examples, and homework in a smallclass setting. One hour per week. Instructor(s): Prerequisites: None


MATH  1125  Discussion/MATH1100  Fall/Spring  0  
Course Description
Recitation section, corequisite to MATH1100. Discussion of problemsolving techniques, examples, and homework in a smallclass setting. One hour per week. Instructor(s): Prerequisites: None


MATH  1126  Discussion/MT 10006  Fall/Spring  0  
Course Description
Recitation section, corequisite to MATH1100. Discussion of problemsolving techniques, examples, and homework in a smallclass setting. One hour per week. Instructor(s): Prerequisites: None


MATH  1127  Discussion/MT 10007  Fall/Spring  0  
Course Description
Recitation section, corequisite to MATH1100. Discussion of problemsolving techniques, examples, and homework in a smallclass setting. One hour per week. Instructor(s): Prerequisites: None


MATH  1129  Discussion/MT 10009  Fall/Spring  0  
Course Description
Recitation section, corequisite to MATH1100. Discussion of problemsolving techniques, examples, and homework in a smallclass setting. One hour per week. Instructor(s): Prerequisites: None


MATH  1141  Discussion/MATH1101  Fall/Spring  0  
Course Description
Recitation section, corequisite to MATH1101. Discussion of problemsolving techniques, examples, and homework in a smallclass setting. One hour per week. Each section of MATH1101 has a specific corequisite recitation, numbered MATH1141MATH1145; students should sign up for the recitation that matches the corequisite listed in the section of MATH1101 they select. Instructor(s): Prerequisites: None


MATH  1142  Discussion/MT 10102  Fall/Spring  0  
Course Description
Recitation section, corequisite to MATH1101. Discussion of problemsolving techniques, examples, and homework in a smallclass setting. One hour per week. Instructor(s): Prerequisites: None


MATH  1143  Discussion/MT 10103  Fall/Spring  0  
Course Description
Recitation section, corequisite to MATH1101. Discussion of problemsolving techniques, examples, and homework in a smallclass setting. One hour per week. Instructor(s): Prerequisites: None


MATH  1146  Discussion/MATH1102  Fall  0  
Course Description
TBD Instructor(s): Prerequisites: None


MATH  1147  Discussion/MATH1102  Fall/Spring  0  
Course Description
Recitation section, corequisite to MATH1102. Discussion of problemsolving techniques, examples, and homework in a smallclass setting. One hour per week. Instructor(s): Prerequisites: None


MATH  1148  Discussion/MT 10301  Spring  0  
Course Description
TBD Instructor(s): Prerequisites: None


MATH  1149  Discussion/MATH1103  Spring  0  
Course Description
TBD Instructor(s): Prerequisites: None


MATH  1180  Principles of Statistics for the Health Sciences  Spring  3  
Course Description
This course introduces statistics as a liberal arts discipline and applies the principles of statistics to problems of interest to health sciences professionals. Students will gain an understanding of statistical ideas and methods, acquire the ability to deal critically with numerical arguments, and gain an understanding of the impact of statistical ideas on the health sciences, public policy, and other areas of application. Schedule: Periodically Instructor(s): Prerequisites: Connell School of Nursing students only.


MATH  1190  Fundamentals of Mathematics I  Fall/Spring  3  
Course Description
MATH11901191 is a course sequence designed for those who plan to teach mathematics in grades K8. The emphasis is on building conceptual understanding of the mathematics present in the emerging K8 curriculum and on deepening content knowledge. Number and number systems through the real number system will be studied; functions and the structure of algebra will be developed. Problem solving and reasoning, applications, and making connections will be featured. Schedule: Periodically Instructor(s): Prerequisites: None
Comments: Restricted to Lynch School of Education students. 

MATH  1191  Fundamentals of Mathematics II  Spring  3  
Course Description
As in MATH1190, the course emphasizes building conceptual understanding of the mathematics present in the emerging K8 curriculum and on deepening the content knowledge. Topics drawn from geometry and measurement, data analysis, statistics, and probability will be developed. Problem solving and reasoning, applications, and making connections will be featured. Schedule: Periodically Instructor(s): Prerequisites: MATH1190.
Comments: Restricted to Lynch School of Education students. 

MATH  2202  Multivariable Calculus  Fall/Spring  4  
Course Description
Topics in this course include vectors in two and three dimensions, analytic geometry of three dimensions, parametric curves, partial derivatives, the gradient, optimization in several variables, multiple integration with change of variables across different coordinate systems, line integrals, and Green's Theorem. Schedule: Periodically Instructor(s): Prerequisites: MATH1101 AND MATH1103 AND MATH1105. Or with permission of the Instructor.
Comments: This course is for students majoring in Chemistry, Computer Science/B.S., Geology, Geophysics, Mathematics, and Physics, as well as other students who have completed integral Calculus. 

MATH  2203  Multivariable Calculus (Honors)  Fall  4  
Course Description
TBD Instructor(s): Prerequisites: None


MATH  2210  Linear Algebra  Fall/Spring  3  
Course Description
This course is an introduction to the techniques of linear algebra in Euclidean space. Topics covered include matrices, determinants, systems of linear equations, vectors in ndimensional space, complex numbers, and eigenvalues. The course is required of mathematics majors but is also suitable for students in the social sciences, natural sciences, and management. Instructor(s): Prerequisites: None


MATH  2211  Linear Algebra (Honors)  Fall  3  
Course Description
This honors course in Linear Algebra is intended for students with strong preparation and high motivation. Topics covered include matrices, linear equations, determinants, eigenvectors and eigenvalues, vector spaces and linear transformations, inner products, and canonical forms. The course will include significant work with proofs. Instructor(s): Prerequisites: MATH2203.


MATH  2216  Introduction to Abstract Mathematics  Fall/Spring  3  
Course Description
This course is designed to develop the student's ability to do abstract mathematics through the presentation and development of the basic notions of logic and proof. Topics include elementary set theory, mappings, integers, rings, complex numbers, and polynomials. Instructor(s): Prerequisites: None


MATH  2251  Discussion Group/MATH2202  Fall  0  
Course Description
TBD Instructor(s): Prerequisites: None


MATH  2252  Discussion/MATH2202  Fall  0  
Course Description
TBD Instructor(s): Prerequisites: None


MATH  2253  Discussion Group/MATH2202  Fall/Spring  0  
Course Description
TBD Schedule: Periodically Instructor(s): Prerequisites: None


MATH  2290  Number Theory for Teachers  Spring  3  
Course Description
This course is intended to focus on the wealth of topics that relate specifically to the natural numbers. These will be treated as motivational problems to be used in an activityoriented approach to mathematics in grades K9. The course will demonstrate effective ways to use the calculator and computer in mathematics education. Topics include prime number facts and conjectures, magic squares, Pascal's triangle, Fibonacci numbers, modular arithmetic, and mathematical art. Schedule: Biennially Instructor(s): 

MATH  2291  Geometry for Teachers  Spring  3  
Course Description
This course is intended to fill a basic need of all teachers of grades K9. Geometry now occupies a significant role in the elementary mathematics curriculum. The course will treat content, but ideas for presenting geometry as an activitybased program will also be stressed. Topics to be covered include the geoboard and other key manipulatives, elements of motion and Euclidean geometry, and suggestions for using Logo as a tool to enhance teaching geometry. Instructor(s): 

MATH  3305  Advanced Calculus (Science Majors)  Spring  4  
Course Description
MATH3305 is required for GeologyGeophysics, Geophysics, and Physics majors. It is also recommended for Chemistry majors. Topics include linear second order differential equations, series solutions of differential equations including Bessel functions and Legendre polynomials, and solutions of the diffusion and wave equations in several dimensions. Instructor(s): Prerequisites: MATH2202.
Comments: Cannot be used for major credit. 

MATH  3310  Introduction to Abstract Algebra  Fall/Spring  3  
Course Description
This course studies four fundamental algebraic structures: groups, including subgroups, cyclic groups, permutation groups, symmetry groups and Lagrange's Theorem; rings, including subrings, integral domains, and unique factorization domains; polynomials, including a discussion of unique factorization and methods for finding roots; and fields, introducing the basic ideas of field extensions and ruler and compass constructions. Instructor(s): Prerequisites: MATH2210 AND MATH2216.
Comments: Students may not take both MATH3310 and MATH3311. 

MATH  3311  Algebra I  Fall  3  
Course Description
This course, with MATH3312, studies the basic structures of abstract algebra. Topics include groups, subgroups, factor groups, Lagrange's Theorem, the Sylow Theorems, rings, ideal theory, integral domains, field extensions, and Galois theory. Instructor(s): Prerequisites: MATH2210 AND MATH2216.
Comments: Students may not take both MATH3310 and MATH3311. 

MATH  3312  Algebra II  Spring  3  
Course Description
This course, with MATH3311, studies the basic structures of abstract algebra. Topics include groups, subgroups, factor groups, Lagrange's Theorem, the Sylow Theorems, rings, ideal theory, integral domains, field extensions, and Galois theory. Instructor(s): Prerequisites: MATH3311. With the permission of the Assistant Chair for Undergraduates, students who have taken MATH3310 may be allowed to take MATH3312. However, they may need to do additional work on their own in order to make that transition.


MATH  3320  Introduction to Analysis  Fall/Spring  3  
Course Description
The purpose of this course is to give students the theoretical foundations for the topics taught in MATH11021103. It will cover algebraic and order properties of the real numbers, the least upper bound axiom, limits, continuity, differentiation, the Riemann integral, sequences, and series. Definitions and proofs will be stressed throughout the course. Instructor(s): Prerequisites: MATH2202 AND MATH2216.
Comments: Students may not take both MATH3320 and MATH3321. 

MATH  3321  Analysis I  Fall  3  
Course Description
This course, with MATH3322, studies the basic structure of the real numbers. Topics include the least upper bound principle, compactness of closed intervals (the HeineBorel theorem), sequences, convergence, the BolzanoWeierstrass theorem, continuous functions, boundedness and intermediate value theorems, uniform continuity, differentiable functions, the mean value theorem, construction of the Riemann integral, the fundamental theorem of calculus, sequences and series of functions, uniform convergence, the Weierstrass approximation theorem, special functions (exponential and trig), and Fourier series. Instructor(s): Prerequisites: MATH2216 AND MATH2202.
Comments: Students may not take both MATH3320 and MATH3321. 

MATH  3322  Analysis II  Spring  3  
Course Description
This course, with MATH3321, studies the basic structure of the real numbers. Topics include the least upper bound principle, compactness of closed intervals (the HeineBorel theorem), sequences, convergence, the BolzanoWeierstrass theorem, continuous functions, boundedness and intermediate value theorems, uniform continuity, differentiable functions, the mean value theorem, construction of the Riemann integral, the fundamental theorem of calculus, sequences and series of functions, uniform convergence, the Weierstrass approximation theorem, special functions (exponential and trig), and Fourier series. Instructor(s): Prerequisites: MATH3321. With the permission of the Assistant Chair for Undergraduate Programs, students who have taken MATH3320 may be allowed to take MATH3322. However, they may need to do additional work on their own in order to make that transition.


MATH  3353  Statistics  Fall  4  
Course Description
TBD Instructor(s): Prerequisites: None


MATH  3370  Applications of Abstract Algebra  Fall  1  
Course Description
This course is open to all majors who have had MATH3310. The immediate goal is to present some topics that extend and apply the subject matter of 3310. At the same time students may gain a deeper understanding of groups and rings that they only imperfectly understood the first time around. A secondary goal is for students to appreciate that the abstract concepts learned in 310 can have relevance to the outside world; for example, cryptography as applied to modern communications, or concepts from algebra and number theory that may be taught in the high school classroom. Schedule: Periodically Instructor(s): Prerequisites: MATH3310.


MATH  3371  Proof and Truth in Mathematics  Fall  1  
Course Description
Can mathematical truths be deduced from a set of first principles or axioms? The wide use of axioms in mathematics shows that many can, but what can be proven falls short of all mathematical truths and even of all truths in the theory of numbers. This course will explore what is known about the limitations of the axiomatic method and computation as they relate to the discovery of mathematical truth, and will include Godel's incompleteness theorems. Schedule: Periodically Instructor(s): Prerequisites: MATH2216.


MATH  3372  Intro to Mathematical Problem Solving/Mathematica  Fall  1  
Course Description
The purpose of this course is to give a directed introduction to Mathematica (Wolfram Research Inc.), to allow students to apply this powerful tool in such courses as mathematical modeling, ordinary and partial differential equations, dynamical systems, probability theory, and mathematical statistics. Topics include computer algebra, 2D/3D graphics, and the calculus and simulation capabilities of Mathematica. Schedule: Periodically Instructor(s): Prerequisites: MATH2210 AND MATH3305. May be taken concurrently.


MATH  3373  Numbers, Notations, and Recreations  Spring  1  
Course Description
This 1credit course applies the introductory abstract mathematics of MATH2216 to parts of the secondary mathematics curriculum, in particular topics related to numbers systems and notations, and recreational math problems in these areas. Many examples which are directly useful in secondary mathematics will be included, and we will use ideas from MATH2216 to explain and generalize them. Specific topics include applications of modular arithmetic; decimal notation (and other bases) for integers, rationals, and reals; complex numbers; Fibonacci numbers and similar sequences; binomial coefficients and their applications. Schedule: Periodically Instructor(s): Prerequisites: MATH2216.


MATH  3374  Pedagogical Lab for Intro to Analysis (Mt320)  Spring  1  
Course Description
This 1credit course is designed for our current or previous MATH3320 (Introduction to Analysis) students that are interested in teaching high school mathematics. The pedagogical lab will emphasize how to apply those abstract theories from MATH3320 to the teaching of high school precalculus and calculus. We will also discuss various issues involved in the teaching of these courses, such as reformed curriculums, common misconceptions, and mistakes in the learning of this material. Schedule: Periodically Instructor(s): Prerequisites: MATH3320. May be taken concurrently.


MATH  4410  Differential Equations  Fall/Spring  3  
Course Description
This course is a juniorsenior elective intended primarily for the general student who is interested in seeing applications of mathematics. Among the topics covered will be the following: first order linear equations, higher order linear equations with constant coefficients, linear systems, qualitative analysis of nonlinear systems, and an introduction to stability and bifurcations. Instructor(s): Prerequisites: MATH2202 AND MATH2210.


MATH  4412  Partial Differential Equations  Spring  3  
Course Description
This course investigates the classical partial differential equations of applied mathematics (diffusion, Laplace/Poisson, and wave) and their methods of solution (separation of variables, Fourier series, transforms, Green's functions, and eigenvalue applications). Additional topics will be included as time permits. Instructor(s): Prerequisites: MATH4410.


MATH  4414  Numerical Analysis  Spring  3  
Course Description
Topics include the solution of linear and nonlinear algebraic equations, interpolation, numerical differentiation and integration, numerical solution of ordinary differential equations, and approximation theory. Instructor(s): Prerequisites: MATH2202 AND MATH2210.


MATH  4426  Probability  Fall/Spring  3  
Course Description
This course provides a general introduction to modern probability theory. Topics include probability spaces, discrete and continuous random variables, joint and conditional distributions, mathematical expectation, the central limit theorem, and the weak law of large numbers. Applications to real data will be stressed, and we will use the computer to explore many concepts. Instructor(s): Prerequisites: MATH2202.


MATH  4427  Mathematical Statistics  Fall/Spring  3  
Course Description
Topics studied include the following: sampling distributions, parametric point and interval estimation, hypothesis testing, goodnessoffit, and parametric and nonparametric twosample analysis. Applications to real data will be stressed, and the computer will be used to explore concepts and analyze data. Instructor(s): Prerequisites: MATH4426.


MATH  4430  Introduction to Number Theory  Fall  3  
Course Description
Topics covered include divisibility, unique factorization, congruences, numbertheoretic functions, primitive roots, diophantine equations, continued fractions, quadratic residues, and the distribution of primes. An attempt will be made to provide historical background for various problems and to provide examples useful in the secondary school curriculum. Instructor(s): Prerequisites: MATH2216.


MATH  4435  Mathematical Programming  Fall  3  
Course Description
This course demonstrates how mathematical theory can be developed and applied to solve problems from management, economics, and the social sciences. Topics studied from linear programming include a general discussion of linear optimization models, the theory and development of the simplex algorithm, degeneracy, duality, sensitivity analysis, and the dual simplex algorithm. Integer programming problems and the transportation and assignment problems are considered, and algorithms are developed for their resolution. Other topics are drawn from game theory, dynamic programming, Markov decision processes (with finite and infinite horizons), network analysis, and nonlinear programming. Instructor(s): Prerequisites: MATH2210.


MATH  4440  Dynamical Systems  Spring  3  
Course Description
This course is an introduction to nonlinear dynamics and their applications, emphasizing qualitative methods for differential equations. Topics include fixed and periodic points, stability, linearization, parameterized families and bifurcations, and existence and nonexistence theorems for closed orbits in the plane. The final part of the course is an introduction to chaotic systems and fractals, including the Lorenz system and the quadratic map. Instructor(s): Prerequisites: MATH4410 AND MATH2202. Or permission of the instructor.


MATH  4445  Combinatorics  Spring  3  
Course Description
This course is an introduction to graph theory and combinatorics, with a strong emphasis on creative problemsolving techniques and connections with other branches of mathematics. Topics will center around the following: enumeration, Hamiltonian and Eulerian cycles, extremal graph theory, planarity, matching, colorability, Ramsey theory, hypergraphs, combinatorial geometry, and applications of linear algebra, probability, polynomials, and topology to combinatorics. Schedule: Periodically Instructor(s): Greene Prerequisites: MATH2216.
Comments: Not open to students who have completed MATH2245 or MATH2248 or CSCI2245 

MATH  4451  Euclidean and NonEuclidean Geometry  Fall  3  
Course Description
This course surveys the history and foundations of geometry from ancient to modern times. Topics will be selected from among the following: Mesopotamian and Egyptian mathematics, Greek geometry, the axiomatic method, history of the parallel postulate, the Lobachevskian plane, Hilbert's axioms for Euclidean geometry, elliptic and projective geometry, the trigonometric formulas, models, and geometry and the study of physical space. Instructor(s): Prerequisites: MATH2216.


MATH  4453  Euclid's Elements  Spring  3  
Course Description
This course is a close reading of Euclid's Elements in seminar style, with careful attention to axiomatic reasoning and mathematical constructions that build on one another in a sequence of logical arguments. We will also emphasize clear and creative communication on mathematical ideas, with some attention to the cultural background of the Elements and its place in a modern education. Instructor(s): Mark Reeder Prerequisites: None


MATH  4455  Mathematical Problem Solving  Fall  3  
Course Description
This course is designed to deepen students' mathematical knowledge through solving, explaining, and extending challenging and interesting problems. Students will work both individually and in groups on problems chosen from polynomials, trigonometry, analytic geometry, precalculus, onevariable calculus, probability, and numerical algorithms. The course will emphasize explanations and generalizations rather than formal proofs and abstract properties. Some pedagogical issues, such as composing good problems and expected points of confusion in explaining various topics, will come up, but the primary goal is mathematical insight. The course will be of particular use to future secondary math teachers. Schedule: Periodically Instructor(s): Prerequisites: MATH2202 AND MATH2210 AND MATH2216. Permission of the instructor required for students outside the Lynch School of Education.


MATH  4460  Complex Variables  Spring  3  
Course Description
This course gives an introduction to the theory of functions of a complex variable, a fundamental and central area of mathematics. It is intended for mathematics majors and wellprepared science majors. Topics covered include: complex numbers and their properties, analytic functions and the CauchyRiemann equations, the logarithm and other elementary functions of a complex variable, integration of complex functions, the Cauchy integral theorem and its consequences, power series representation of analytic functions, and the residue theorem and applications to definite integrals. Instructor(s): Prerequisites: MATH2202 AND MATH2210.


MATH  4461  Stochastic Processes  Fall/Spring  3  
Course Description
A stochastic process describes the evolution of a system that changes over time in a random manner. This course introduces and studies various properties of some fundamental stochastic processes, including Markov chains in discrete and continuous time, renewal processes, and Brownian motion. Instructor(s): Prerequisites: MATH2216 AND MATH4426.


MATH  4462  Topology  Fall  3  
Course Description
This course is an introduction to pointset topology. Topics include topological spaces, continuous functions, connectedness, compactness, metric spaces, the Urysohn Metrization Theorem, manifolds, the fundamental group, and the classification of surfaces. We will also discuss applications of these concepts to problems in science and engineering. Instructor(s): Prerequisites: None


MATH  4470  Mathematical Modeling  Spring  3  
Course Description
This course introduces students to methods of mathematical modeling. The emphasis is on ways to analytically represent and study today’s complex modeling problems, with cases from the natural and social sciences. Topics include the model building process, mathematical models of systems, and modeling data to discover properties and hidden characteristics. The calculus of finite differences and solutions to classes of difference equations will serve as the core mathematical theory taught in this course. The dynamics of certain linear and nonlinear models will be explored from various domains (e.g., population models, economic models, Markov models). The course will conclude with an introduction to mathematical graph theory and its application to modeling interacting and interdependent systems and networks. Schedule: Periodically Instructor(s): Prerequisites: MATH2202 AND MATH2210.


MATH  4474  Pedagogy for Lab Analysis  Fall  1  
Course Description
TBD Instructor(s): Prerequisites: None


MATH  4475  History of Mathematics  Fall  3  
Course Description
This course studies the development of mathematical thought, from ancient times to the twentieth century. Naturally, the subject is much too large for a single semester, so we will concentrate on the major themes and on the contributions of the greatest mathematicians. The emphasis in the course will be on the mathematics. Students will follow the historical arguments and work with the tools and techniques of the period being studied. Schedule: Biennially Instructor(s): Prerequisites: MATH3320 AND MATH3310. One of which may be taken concurrently.


MATH  4480  Topics in Mathematics  Spring  3  
Course Description
Topics for this onesemester course vary from year to year according to the interests of faculty and students. With department permission it may be repeated. Schedule: Periodically Instructor(s): Prerequisites: MATH4427.


MATH  4901  Readings and Research  Fall/Spring  3  
Course Description
This is an independent study course, taken under the supervision of a Mathematics Department faculty member. Interested students should see the Assistant Chair for Undergraduates. Instructor(s): Prerequisites: With permission of the Department.


MATH  4961  Honors Thesis  Fall/Spring  3  
Course Description
This course may be taken to complete the requirements for Departmental Honors in Mathematics. Students must make arrangements with an individual faculty member, and receive permission from the Assistant Chair for Undergraduates. Instructor(s): Prerequisites: None


MATH  5500  Advanced Independent Research I  Fall  3  
Course Description
TBD Instructor(s): Prerequisites: None


MATH  5501  Advanced Independent Research II  Fall  3  
Course Description
TBD Instructor(s): Prerequisites: None


MATH  8801  Thesis Seminar  Spring  3  
Course Description
Problems of research and thesis guidance, supplemented by individual conferences. Instructor(s): Prerequisites: None


MATH  8804  Analysis I  Fall  3  
Course Description
The MATH88048805 sequence is intended to emphasize the basic ideas and results of calculus and to provide an introduction to abstract analysis. The course begins with an axiomatic introduction to the real number system. Metric spaces are then introduced. Theoretical aspects of convergence, continuity, differentiation, and integration are treated carefully and are studied in the context of a metric space. The course includes an introduction to the Lebesgue integral. Instructor(s): Prerequisites: MATH3320. Or equivalent.


MATH  8805  Analysis II  Spring  3  
Course Description
This course is a continuation of MATH8804. Instructor(s): Prerequisites: MATH8804.


MATH  8806  Algebra I  Fall  3  
Course Description
This course, with MATH8807, will cover the following topics: Group Theory (Group actions, Sylow, Nilpotent/Solvable, simple groups, JordanHolder series, presentations); commutative algebra (uniqueness of factorization, Jordan decomposition, Dedekind rings, class groups, local rings, Spec); finite fields; algebraic numbers; Galois theory; Homological algebra; and Semisimple algebra. Instructor(s): Prerequisites: None


MATH  8807  Algebra II  Spring  3  
Course Description
This course, with MATH8806, will cover the following topics: Group Theory (group actions, Sylow, Nilpotent/Solvable, simple groups, JordanHolder series, presentations); commutative algebra (uniqueness of factorization, Jordan decomposition, Dedekind rings, class groups, local rings, Spec); finite fields; algebraic numbers; Galois theory; Homological algebra; and Semisimple algebra. Instructor(s): Prerequisites: None


MATH  8808  Geometry/Topology I  Fall  3  
Course Description
This course, with MATH8809, will cover the following topics: pointset topology, fundamental group and covering spaces, smooth manifolds, smooth maps, partitions of unity, tangent and general vector bundles, (co)homology, tensors, differential forms, integration and Stokes' theorem, and de Rham cohomology. Instructor(s): Prerequisites: None


MATH  8809  Geometry/Topology II  Spring  3  
Course Description
This course, with MATH8808, will cover the following topics: Pointset topology, fundamental group and covering spaces, smooth manifolds, smooth maps, partitions of unity, tangent and general vector bundles, (co)homology, tensors, differential forms, integration and Stokes' theorem, and de Rham cohomology. Instructor(s): Prerequisites: None


MATH  8810  Real Analysis  Fall  3  
Course Description
Measure Theory, Hilbert Space, and Fourier Theory. Possible topics from: Lebesgue measure starting on R, convergence and Fubini theorems, and generalizing to locally compact spaces and groups. Instructor(s): Prerequisites: None


MATH  8811  Complex Analysis  Spring  3  
Course Description
Local and global theory of analytic functions of one variable. Instructor(s): Prerequisites: None


MATH  8814  Theory of Functions of a Complex Variable I  Fall  3  
Course Description
Topics for the MATH88148815 sequence include: differentiation and integration of a function of a complex variable, series expansion, residue theory, entire and meromorphic functions, multiplevalued functions, Riemann surfaces, and conformal mapping problems. Instructor(s): Prerequisites: MATH3320. Or equivalent.


MATH  8815  Theory of Functions of a Complex Variable II  Spring  3  
Course Description
This course is a continuation of MATH8814. Instructor(s): Prerequisites: MATH8814.


MATH  8816  Modern Algebra I  Fall  3  
Course Description
The MATH88168817 course sequence will study the basic structures of abstract algebra. Topics will include groups, rings, ideal theory, unique factorization, homomorphisms, field extensions, and Galois theory. Instructor(s): Prerequisites: MATH3310. Or permission of instructor.


MATH  8817  Modern Algebra II  Spring  3  
Course Description
This course is a continuation of MATH8816. Instructor(s): Prerequisites: MATH8816.


MATH  8820  Introduction to Representation Theory  Fall  3  
Course Description
Introduction of a broad range of representation theory, including representations of finite and compact Lie groups, and finite dimensional representations of complex semisimple Lie groups and Lie algebras, and quantum groups. Instructor(s): Mark Reeder Prerequisites: None


MATH  8821  Number Theory I  Fall  3  
Course Description
Along with MATH8822, possible topics include factorization of ideals, local fields, local versus global Galois theory, Brauer group, adèles and idèles, class field theory, Dirichlet Lfunctions, Chebotarev density theorem, class number formula, and Tate's thesis. Instructor(s): Prerequisites: None


MATH  8822  Number Theory II  Spring  3  
Course Description
Along with MATH8821, possible topics include factorization of ideals, local fields, localversusglobal Galois theory, Brauer group, adles and idles, class field theory, Dirichlet Lfunctions, Chebotarev density theorem, class number formula, and Tate's thesis. Instructor(s): Prerequisites: None


MATH  8831  Geometry/Topology III  Fall  3  
Course Description
This course, along with MATH8832, will cover topics from this list of possibilities: differential geometry, hyperbolic geometry, threedimensional manifolds, and knot theory. Instructor(s): Prerequisites: None


MATH  8832  Geometry/Topology IV  Spring  3  
Course Description
This course, along with MATH8831, will cover topics from this list of possibilities: differential geometry, hyperbolic geometry, threedimensional manifolds, and knot theory. Instructor(s): Prerequisites: None


MATH  8844  Riemann Surfaces  Fall  3  
Course Description
This course will present some of the basic theorems about Riemann Surfaces from a modern point of view. Time permitting, topics will include the definition of a Riemann Surface (RS), branched coverings and topological properties of RS's, cohomology, the RiemannRoch Theorem, the relationship between RSs and algebraic curves over the complex numbers, and uniformization. Schedule: Periodically Instructor(s): Prerequisites: None


MATH  8845  Topics in Algebra and Number Theory  Fall  3  
Course Description
Selected topics in Algebra and Number Theory. Schedule: Periodically Instructor(s): Prerequisites: None


MATH  8854  Fuchsian Groups  Spring  3  
Course Description
Selected topics in the theory of Fuchsian Groups with emphasis on connections to the study of manifolds and orbifolds. Schedule: Periodically Instructor(s): Prerequisites: None


MATH  8855  Topics in Geometry and Topology  Spring  3  
Course Description
Selected topics in Geometry and Topology. Schedule: Periodically Instructor(s): Prerequisites: None


MATH  8865  Topics in Algebraic Geometry  Fall/Spring  3  
Course Description
Selected topics in Algebraic Geometry Instructor(s): Prerequisites: None


MATH  8880  Dissertation Research  Fall  3  
Course Description
TBD Instructor(s): Prerequisites: None


MATH  8890  Graduate Teaching Seminar I  Fall  1  
Course Description
This course is designed to assist graduate students in making the transition to the duties of a teaching assistant. Instructor(s): Prerequisites: None


MATH  8891  Graduate Teaching Seminar II  Fall  1  
Course Description
This course is intended to assist graduate students as they make the transition to teaching fellows. Instructor(s): Prerequisites: None


MATH  8892  Graduate Research Seminar  Spring  1  
Course Description
The research seminar is an opportunity for students to present their own research or give lectures on advanced topics. Participation in the research seminar is encouraged by the department. A student may be required by their advisor to participate and/or speak in the research seminar. Instructor(s): Prerequisites: None


MATH  8899  Readings and Research  Fall/Spring  3  
Course Description
This is an independent study course, taken under the supervision of a Mathematics Department faculty member. Interested students should see the Director of the Graduate Program. Instructor(s): Prerequisites: With permission of the Department.


MATH  9903  Seminar  Spring  3  
Course Description
This seminar is required of all candidates for the M.A. degree who do not take MATH8801. It is limited to secondyear graduate students. Instructor(s): Prerequisites: None


MATH  9911  DOCTORAL CONTINUATION  Fall/Spring/Summer  1  
Course Description
All students who have been admitted to candidacy for the Ph.D. degree are required to register and pay the fee (tuition credits can be used for this) for doctoral continuation during each semester of their candidacy when they are taking no other courses. Doctoral Continuation requires a commitment of at least 20 hours per week working on the dissertation Instructor(s): Prerequisites: None
