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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

Cross listed with:

Comments:

MATH 1003 Functions and Differential Calculus II Spring 3
Course Description

This course is a continuation of MATH1002


Instructor(s):

Prerequisites: None

Cross listed with:

Comments:

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

Cross listed with:

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

Cross listed with:

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 Pre-Calculus for OTE Fall 3
Course Description

TBD


Instructor(s):

Prerequisites: None

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Comments:

MATH 1035 Intro to Probability and Statistics for OTE Fall/Summer 3
Course Description

TBD


Instructor(s):

Prerequisites: None

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Comments:

MATH 1036 Intro to Calculus for OTE Fall 3
Course Description

TBD


Instructor(s):

Prerequisites: None

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Comments:

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 real-world problem areas. The course concludes with an introduction to integration.


Instructor(s):

Prerequisites: Trigonometry

Cross listed with:

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

Cross listed with:

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

Cross listed with:

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

Cross listed with:

Comments: Not open to students who has completed MATH1105.

MATH 1105 Calculus II-AP (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

Cross listed with:

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 problem-solving techniques, examples, and homework in a small-class setting. One hour per week. Each section of MATH1100 has a specific corequisite recitation, numbered MATH1121-MATH1135; students should sign up for the recitation that matches the corequisite listed in the section of MATH1100 they select.


Instructor(s):

Prerequisites: None

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Comments:

MATH 1122 Discussion/MATH1100 Fall/Spring 0
Course Description

Recitation section, corequisite to MATH1100. Discussion of problem-solving techniques, examples, and homework in a small-class setting. One hour per week.


Instructor(s):

Prerequisites: None

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Comments:

MATH 1123 Discussion/MATH1100 Fall/Spring 0
Course Description

Recitation section, corequisite to MATH1100. Discussion of problem-solving techniques, examples, and homework in a small-class setting. One hour per week.


Instructor(s):

Prerequisites: None

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Comments:

MATH 1124 Discussion/MATH1100 Fall/Spring 0
Course Description

Recitation section, corequisite to MATH1100. Discussion of problem-solving techniques, examples, and homework in a small-class setting. One hour per week.


Instructor(s):

Prerequisites: None

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Comments:

MATH 1125 Discussion/MATH1100 Fall/Spring 0
Course Description

Recitation section, corequisite to MATH1100. Discussion of problem-solving techniques, examples, and homework in a small-class setting. One hour per week.


Instructor(s):

Prerequisites: None

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Comments:

MATH 1126 Discussion/MT 10006 Fall/Spring 0
Course Description

Recitation section, corequisite to MATH1100. Discussion of problem-solving techniques, examples, and homework in a small-class setting. One hour per week.


Instructor(s):

Prerequisites: None

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Comments:

MATH 1127 Discussion/MT 10007 Fall/Spring 0
Course Description

Recitation section, corequisite to MATH1100. Discussion of problem-solving techniques, examples, and homework in a small-class setting. One hour per week.


Instructor(s):

Prerequisites: None

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Comments:

MATH 1129 Discussion/MT 10009 Fall/Spring 0
Course Description

Recitation section, corequisite to MATH1100. Discussion of problem-solving techniques, examples, and homework in a small-class setting. One hour per week.


Instructor(s):

Prerequisites: None

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Comments:

MATH 1141 Discussion/MATH1101 Fall/Spring 0
Course Description

Recitation section, corequisite to MATH1101. Discussion of problem-solving techniques, examples, and homework in a small-class setting. One hour per week. Each section of MATH1101 has a specific corequisite recitation, numbered MATH1141-MATH1145; students should sign up for the recitation that matches the corequisite listed in the section of MATH1101 they select.


Instructor(s):

Prerequisites: None

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Comments:

MATH 1142 Discussion/MT 10102 Fall/Spring 0
Course Description

Recitation section, corequisite to MATH1101. Discussion of problem-solving techniques, examples, and homework in a small-class setting. One hour per week.


Instructor(s):

Prerequisites: None

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Comments:

MATH 1143 Discussion/MT 10103 Fall/Spring 0
Course Description

Recitation section, corequisite to MATH1101. Discussion of problem-solving techniques, examples, and homework in a small-class setting. One hour per week.


Instructor(s):

Prerequisites: None

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Comments:

MATH 1146 Discussion/MATH1102 Fall 0
Course Description

TBD


Instructor(s):

Prerequisites: None

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Comments:

MATH 1147 Discussion/MATH1102 Fall/Spring 0
Course Description

Recitation section, corequisite to MATH1102. Discussion of problem-solving techniques, examples, and homework in a small-class setting. One hour per week.


Instructor(s):

Prerequisites: None

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Comments:

MATH 1148 Discussion/MT 10301 Spring 0
Course Description

TBD


Instructor(s):

Prerequisites: None

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MATH 1149 Discussion/MATH1103 Spring 0
Course Description

TBD


Instructor(s):

Prerequisites: None

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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.

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Comments:

MATH 1190 Fundamentals of Mathematics I Fall/Spring 3
Course Description

MATH1190-1191 is a course sequence designed for those who plan to teach mathematics in grades K-8. The emphasis is on building conceptual understanding of the mathematics present in the emerging K-8 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

Cross listed with:

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 K-8 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

Cross listed with:

Comments: Restricted to Lynch School of Education students.

MATH 1701 Understanding Mathematics: Its Philosophical Origins, Evolution, and Humanity Fall 3
Course Description

The dynamic and constantly evolving field of mathematics is central to the advancement of human knowledge. Yet who decides what mathematics is? How has the discipline changed and why? This course follows the development of mathematics from the ancient to the contemporary, tracing the paths of some of its “big ideas” from their “elementary” roots to their modern-day forms. Students will examine the philosophical origins of familiar concepts and experience what it means to invent mathematics through studying the field’s pioneers. By the end of the semester, students will decide for themselves what mathematics is. Non-math majors are encouraged to enroll.


Schedule: Biennially

Instructor(s): Ellen Julia Goldstein

Prerequisites: None

Cross listed with:

Comments: Core Renewal Course: Enduring Questions

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.


Instructor(s):

Prerequisites: MATH1101, MATH1103, MATH1105, or permission of instructor.

Cross listed with:

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

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Comments:

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 n-dimensional 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

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Comments:

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: Prerequisite: MATH2203 Multivariable Calculus (Honors)

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Comments:

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

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Comments:

MATH 2251 Discussion Group/MATH2202 Fall 0
Course Description

TBD


Instructor(s):

Prerequisites: None

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Comments:

MATH 2252 Discussion/MATH2202 Fall 0
Course Description

TBD


Instructor(s):

Prerequisites: None

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Comments:

MATH 2253 Discussion Group/MATH2202 Fall/Spring 0
Course Description

TBD


Instructor(s):

Prerequisites: None

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Comments: COREQUISITE OF MATH2202

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 activity-oriented approach to mathematics in grades K-9. 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):

Prerequisites: MATH1190-1191

Cross listed with: EDUC2290

Comments:

MATH 2291 Geometry for Teachers Spring 3
Course Description

This course is intended to fill a basic need of all teachers of grades K-9. Geometry now occupies a significant role in the elementary mathematics curriculum. The course will treat content, but ideas for presenting geometry as an activity-based 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.


Schedule: Biennially

Instructor(s):

Prerequisites: MATH1190-1191

Cross listed with: EDUC2291

Comments:

MATH 3305 Advanced Calculus (Science Majors) Spring 4
Course Description

MATH3305 is required for Geology-Geophysics, 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

Cross listed with:

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 sub-rings, 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

Cross listed with:

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.

Cross listed with:

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.

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Comments:

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 MATH1102-1103. 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

Cross listed with:

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 Heine-Borel theorem), sequences, convergence, the Bolzano-Weierstrass 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: MATH2202 and MATH2216.

Cross listed with:

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 Heine-Borel theorem), sequences, convergence, the Bolzano-Weierstrass 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.

Cross listed with:

Comments:

MATH 3353 Statistics Fall 4
Course Description

TBD


Instructor(s):

Prerequisites: None

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Comments:

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

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Comments:

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

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Comments:

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 or MATH3305. May be taken concurrently.

Cross listed with:

Comments:

MATH 3373 Numbers, Notations, and Recreations Spring 1
Course Description

This 1-credit 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

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Comments:

MATH 3374 Pedagogical Lab for Intro to Analysis (Mt320) Spring 1
Course Description

This 1-credit 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 pre-calculus 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 (or concurrent)

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Comments:

MATH 4410 Differential Equations Fall/Spring 3
Course Description

This course is a junior-senior 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 non-linear systems, and an introduction to stability and bifurcations.


Instructor(s):

Prerequisites: MATH2202 and MATH2210

Cross listed with:

Comments:

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

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Comments:

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, MATH2210, and familiarity with using a computer.

Cross listed with:

Comments:

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, familiarity with using a computer

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Comments:

MATH 4427 Mathematical Statistics Fall/Spring 3
Course Description

Topics studied include the following: sampling distributions, parametric point and interval estimation, hypothesis testing, goodness-of-fit, and parametric and nonparametric two-sample analysis. Applications to real data will be stressed, and the computer will be used to explore concepts and analyze data.


Instructor(s):

Prerequisites: MT 426 and familiarity with using a computer.

Cross listed with:

Comments:

MATH 4430 Introduction to Number Theory Fall 3
Course Description

Topics covered include divisibility, unique factorization, congruences, number-theoretic 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

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Comments:

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 non-linear programming.


Instructor(s):

Prerequisites: MATH2210

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Comments:

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: MATH2202 and MATH4410 or permission of the instructor

Cross listed with:

Comments:

MATH 4445 Combinatorics Spring 3
Course Description

This course is an introduction to graph theory and combinatorics, with a strong emphasis on creative problem-solving 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. Prerequisite: MT216 Pre/corequisite MATH2210


Schedule: Periodically

Instructor(s): Greene

Prerequisites: MATH2216

Cross listed with:

Comments: Not open to students who have completed MATH2245 or MATH2248 or CSCI2245

MATH 4451 Euclidean and Non-Euclidean 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

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Comments:

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

Cross listed with:

Comments:

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, pre-calculus, one-variable 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, MATH2210, MATH2216 (or equivalent mathematical background). Permission of the instructor required for students outside the Lynch School of Education.

Cross listed with:

Comments:

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 well-prepared science majors. Topics covered include: complex numbers and their properties, analytic functions and the Cauchy-Riemann 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

Cross listed with:

Comments:

MATH 4462 Topology Fall 3
Course Description

This course is an introduction to point-set 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

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Comments:

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, MATH2210, and familiarity with using a computer

Cross listed with:

Comments:

MATH 4474 Pedagogy for Lab Analysis Fall 1
Course Description

TBD


Instructor(s):

Prerequisites: None

Cross listed with:

Comments:

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: MATH3310 and MATH3320, one of which may be taken concurrently.

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MATH 4480 Topics in Mathematics Spring 3
Course Description

Topics for this one-semester 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 Mathematical Statistics and familiarity with using a computer to solve mathematics problems.

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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: Department permission is required.

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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

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MATH 5500 Advanced Independent Research I Fall 3
Course Description

TBD


Instructor(s):

Prerequisites: None

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MATH 5501 Advanced Independent Research II Fall 3
Course Description

TBD


Instructor(s):

Prerequisites: None

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MATH 8801 Thesis Seminar Spring 3
Course Description

Problems of research and thesis guidance, supplemented by individual conferences.


Instructor(s):

Prerequisites: None

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MATH 8804 Analysis I Fall 3
Course Description

The MATH8804-8805 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

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MATH 8805 Analysis II Spring 3
Course Description

This course is a continuation of MATH8804.


Instructor(s):

Prerequisites: MATH8804

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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, Jordan-Holder 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.


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Prerequisites: None

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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, Jordan-Holder 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.


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Prerequisites: None

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MATH 8808 Geometry/Topology I Fall 3
Course Description

This course, with MATH8809, will cover the following topics: point-set 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

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MATH 8809 Geometry/Topology II Spring 3
Course Description

This course, with MATH8808, will cover the following topics: Point-set 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.


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Prerequisites: None

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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

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MATH 8811 Complex Analysis Spring 3
Course Description

Local and global theory of analytic functions of one variable.


Instructor(s):

Prerequisites: None

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MATH 8814 Theory of Functions of a Complex Variable I Fall 3
Course Description

Topics for the MATH8814-8815 sequence include: differentiation and integration of a function of a complex variable, series expansion, residue theory, entire and meromorphic functions, multiple-valued functions, Riemann surfaces, and conformal mapping problems.


Instructor(s):

Prerequisites: MATH3320 or equivalent

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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

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MATH 8816 Modern Algebra I Fall 3
Course Description

The MATH8816-8817 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

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MATH 8817 Modern Algebra II Spring 3
Course Description

This course is a continuation of MATH8816.


Instructor(s):

Prerequisites: MATH8816

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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

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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 L-functions, Chebotarev density theorem, class number formula, and Tate's thesis.


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Prerequisites: None

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MATH 8822 Number Theory II Spring 3
Course Description

Along with MATH8821, possible topics include factorization of ideals, local fields, local-versus-global Galois theory, Brauer group, adles and idles, class field theory, Dirichlet L-functions, Chebotarev density theorem, class number formula, and Tate's thesis.


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Prerequisites: None

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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, three-dimensional manifolds, and knot theory.


Instructor(s):

Prerequisites: None

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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, three-dimensional manifolds, and knot theory.


Instructor(s):

Prerequisites: None

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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 Riemann-Roch Theorem, the relationship between RSs and algebraic curves over the complex numbers, and uniformization.


Schedule: Periodically

Instructor(s):

Prerequisites: None

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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

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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

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MATH 8855 Topics in Geometry and Topology Spring 3
Course Description

Selected topics in Geometry and Topology.


Schedule: Periodically

Instructor(s):

Prerequisites: None

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MATH 8880 Dissertation Research Fall 3
Course Description

TBD


Instructor(s):

Prerequisites: None

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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

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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

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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.


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Prerequisites: None

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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: Department permission is required.

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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 second-year graduate students.


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Prerequisites: None

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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

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