# Mathematics (MAT)

**MAT 097 Logic (0 credits)**

**MAT 098 Algebra Review (0 credits)**

**MAT 099 Logic & Problem Solving (0 credits)**

**MAT 101 Mathematical Explorations I (3 credits)**

For humanities majors, the course covers set theory and a number of its applications, topics from logic including propositions, truth tables, number systems, and elementary geometry. Other topics may be covered at instructor’s discretion. Satisfies GEP requirement for PLS students only. Open to PLS students only.

*Restrictions:* Enrollment is limited to PLS/HDC level students.

*Attributes:* Undergraduate

**MAT 102 Mathematical Explorations II (3 credits)**

This is a second course for humanities majors. The course covers elementary probability, including independent and dependent events, conditional probability, binomial probability, and certain applications in a wide variety of situations. MAT 1015 is not required for MAT 102. Other topics may be covered at instructor's discretion. Satisfies GEP requirement for PLS students only. Open to PLS students only.

*Restrictions:* Enrollment is limited to PLS/HDC level students.

*Attributes:* Undergraduate

**MAT 103 Quantitative Appl in Business (3 credits)**

Topics in finite mathematics: matrices, solving linear systems, optimization using linear programming, simplex algorithm. Pre-calculus topics: linear, quadratic, exponential, and logarithmic functions and their graphs, mathematical models, and certain applications. Prerequisite: 2 years of high school algebra. Satisfies GEP requirement for PLS and HDC students only. Open to PLS and HDC students only.

*Restrictions:* Enrollment is limited to PLS/HDC level students.

*Attributes:* Undergraduate

**MAT 104 Calculus Appl in Business (3 credits)**

Introduction to Calculus: mathematical models using polynomial, rational, exponential, and logarithmic functions, rates of change and the derivative, optimization using the derivative, and integration. Prerequisite: MAT 103 or Pre-Calculus Math. Satisfies GEP requirement for PLS students and HDC only. Open to PLS and HDC students only.

*Restrictions:* Enrollment is limited to PLS/HDC level students.

*Attributes:* Undergraduate

**MAT 107 Contemporary Topics in Math (3 credits)**

This course is designed to enable the student to recognize, understand and apply various mathematical concepts and principles that are the foundation for many things that we take for granted in our everyday lives, such as Voting, Traveling, Finances, Government and the wonders of Nature. Satisfies GEP requirement for PLS students only. Open to PLS students only.

*Attributes:* Undergraduate

**MAT 108 Exploration of Statistics (3 credits)**

Descriptive statistics: histograms, mean and standard deviation, introduction to probability, the normal distribution, introduction to sampling and statistical inference, the central limit theorem, hypothesis testing.

*Restrictions:* Enrollment is limited to PLS/HDC level students.

*Attributes:* Undergraduate

**MAT 110 Fundamental Math for Educators (3 credits)**

**MAT 111 The Mathematics of Patterns (3 credits)**

**MAT 112 Math Model Middle Sch Teachers (3 credits)**

**MAT 118 Introduction to Statistics (3 credits)**

Introduction to statistics and probability: measures of central tendency, variability, correlation, regression, chance and randomness, random variables, probability distributions, law of large numbers, central limit theorem. Students will be required to use a computer software package to solve various statistical problems. Designed for Social Science majors. This course does not fulfill the GEP Mathematics requirement. Students may NOT receive credit for this course and for MAT 128.

*Attributes:* Undergraduate

**MAT 119 Applied Business Calculus (4 credits)**

Review of mathematical models using polynomial, rational, exponential and logarithmic functions with business applications. Introduction to calculus including limits, rates of change and the derivative, optimization using the derivative, integration. This course does not fulfill the GEP Mathematics requirement. Students may NOT receive credit for both this course and for any of the following courses: MAT 104 (formerly MAT 106), MAT 123, MAT 155, or MAT 161.

*Attributes:* Undergraduate

**MAT 120 The Mathematics of Modeling (3 credits)**

Algebra: factoring, simultaneous equations, polynomial, rational, and exponential functions, binomial theorem, word problems. Trigonometry: basic functions, formulae, graphs. Analytic Geometry: straight line, circle, conic sections. This course does not fulfill the GEP Mathematics requirement.

*Prerequisites:* Math Placement with a score of MA120

*Attributes:* Undergraduate

**MAT 121 Math Modeling for MS Teachers (3 credits)**

Designed for students who will become middle school teachers, this course will explore mathematical topics in the context of building of building models to solve problems. The emphasis will be on using multiple representations to develop mathematical models that describe some phenomena and learning the mathematical techniques necessary for working with the model in order to use effectively to answer questions about the situation being modeled. Students will interpret results given the context of the model and develop their communication skills for explaining mathematics. This course does not fulfill the GEP Mathematics requirement.

**MAT 123 Differential Calculus (3 credits)**

Review of mathematical models using polynomial, rational, exponential and logarithmic functions with business applications Introduction to differential calculus including limits, rates of change and the derivative, optimization using the derivative. This course does not fulfill the GEP Mathematics requirement. Students may NOT receive credit for both this course and for any of the following courses: MAT 104 (formerly MAT 106), MAT 119, MAT 155 or MAT 161.

**MAT 128 Applied Statistics (3 credits)**

Introduction to statistics and probability: design of a study, measures of central tendency, variability, correlation, regression; probability, random variables, probability distributions, central limit theorem; inferential statistics, hypothesis testing, etc. Students will be required to use a computer software package to solve various statistical problems. Data analysis projects will be assigned. This course does not fulfill the GEP Mathematics requirement. Students may NOT receive credit for both this course and for MAT 118.

*Attributes:* Undergraduate

**MAT 130 Whole Truth about Whole Number (3 credits)**

This course involves studying properties of natural numbers and integers. Topics include divisibility, prime numbers, the Euclidean Algorithm and the RSA Encryption system for putting messages into code. This course fulfills the GEP Mathematics Requirement.

*Prerequisites:* Math Placement with a score of BEAUT

*Restrictions:* Students cannot enroll who have a major in Actuarial Science, Biology, Chemistry, Chemical Biology, Environmental Science, Information Technology, Mathematics or Physics.

*Attributes:* Math Beauty (New GEP), Undergraduate

**MAT 131 Linear Methods (3 credits)**

This course studies basic properties and applications of matrices and vectors. Then, matrices and vectors will be used in a variety of applications, including vector geometry, elementary graph theory, solving word problems involving systems of linear equations, least-squares functions, and geometric transformations. The course also covers some topics in basic logic, including logical operators, the conditional, truth tables, quantifiers, and syllogisms. Students in this course will be required to have a graphing calculator that can perform standard matrix operations. This course fulfills the GEP Mathematics Requirement.

*Prerequisites:* Math Placement with a score of BEAUT

*Restrictions:* Students cannot enroll who have a major in Actuarial Science, Biology, Chemistry, Chemical Biology, Environmental Science, Information Technology, Mathematics or Physics.

*Attributes:* Math Beauty (New GEP), Undergraduate

**MAT 132 Math of Games & Politics (3 credits)**

This course will focus on both computational and theoretical aspects of probability theory, game theory and social choice theory. Topics include expected value, counting methods and conditional probability, dominant strategies, combinatorial games, Nash equilibria, social dilemmas and, for zero sum games, saddle points and the Minimax theorem. Social choice theory topics include voting methods, weighted voting, fairness criteria and impossibility theorems. This course fulfills the GEP Mathematics Requirement.

*Prerequisites:* Math Placement with a score of BEAUT

*Restrictions:* Students cannot enroll who have a major in Actuarial Science, Biology, Chemistry, Chemical Biology, Environmental Science, Information Technology, Mathematics or Physics.

*Attributes:* Math Beauty (New GEP), Undergraduate

**MAT 134 Math of Uncertainty:Rules/Prob (3 credits)**

This course provides students with an in-depth introduction to probability and its many real-life applications. Students will study counting techniques including permutations, combinations, binomial coefficients, occupancy problems and runs within random orderings and will prove combinatorial identities. Students will study topics in probability including sample spaces, DeMorgan’s Laws, conditional probability, independent events, Bayes Theorem, random variables and expected value. Students will examine many of the classical problems in probability theory including Prisoner’s Dilema, Gambler’s Ruin and the Birthday Problem as well as lotteries, card games and random walks. This course fulfills the GEP Mathematics Requirement.

*Prerequisites:* Math Placement with a score of BEAUT

*Restrictions:* Students cannot enroll who have a major in Actuarial Science, Biology, Chemistry, Chemical Biology, Environmental Science, Information Technology, Mathematics or Physics.

*Attributes:* Math Beauty (New GEP), Undergraduate

**MAT 135 Sounding Number: Music & Math (3 credits)**

Music has many connections to mathematics. The ancient Greeks discovered that chords with pleasing sounds are related to simple ratios of integers. Other connections include equations describing the sounds of musical instruments, the mathematics of digital recording, the use of symmetry in composition, and the systematic exploration of patterns by African and Indian drummers. This course introduces basic concepts in trigonometry, set and group theory, and combinatorics and investigates their applications in the analysis, recording, and composition of music. Along the way, we consider the role of creativity in mathematics and the ways in which mathematics has inspired musicians. The course will involve hands-on laboratory work in audio engineering and music composition. This course fulfills the GEP Mathematics Requirement.

*Prerequisites:* Math Placement with a score of BEAUT

*Restrictions:* Students cannot enroll who have a major in Actuarial Science, Biology, Chemistry, Chemical Biology, Environmental Science, Information Technology, Mathematics or Physics.

*Attributes:* Math Beauty (New GEP), Undergraduate

**MAT 136 Mathematics & Visual Arts (3 credits)**

This course will explore connections between mathematics and the arts. Mathematics - itself an aesthetic endeavor - has made fundamental contributions to art history and continues to be a source of inspiration to many contemporary artists. We will begin with the study of mathematical perspective, and of optical devices, such as the camera obscura, which assisted artists and illustrators in depicting the world around them. At the beginning of the twentieth century, artists turned to non-Euclidean geometries and higher dimensional spaces for inspiration and to break free from the constraints of linear perspective. We will take some time to understand these geometries as well. The remaining topics will be chosen according to the interests and talents of the students in the course. Possibilities include fractals, math and music, math and architecture, and advanced perspective topics. This course fulfills the GEP Mathematics Requirement.

*Prerequisites:* Math Placement with a score of BEAUT

*Restrictions:* Students cannot enroll who have a major in Actuarial Science, Biology, Chemistry, Chemical Biology, Environmental Science, Information Technology, Mathematics or Physics.

*Attributes:* Math Beauty (New GEP), Undergraduate

**MAT 137 Ethnomathematics (3 credits)**

This course aims to strengthen and expand students’ understanding of fundamental mathematics – number systems, arithmetic, geometry, combinatorics, and mathematical reasoning – through study of the mathematics of world cultures. In addition, the course is designed to explore the connections between mathematics and the arts, to engage students’ imagination and creativity, and to increase the diversity of offerings in the mathematics classroom. This course fulfills the GEP Mathematics Requirement.

*Prerequisites:* Math Placement with a score of BEAUT

*Restrictions:* Students cannot enroll who have a major in Actuarial Science, Biology, Chemistry, Chemical Biology, Environmental Science, Information Technology, Mathematics or Physics.

*Attributes:* Math Beauty (New GEP), Undergraduate

**MAT 138 Symmetry (3 credits)**

"Symmetry" is a ubiquitous concept in modern mathematics and science. Certain shapes and images seem more symmetric than others, yet is not immediately obvious how to best measure and understand an object’s symmetry. In fact, the quest to more precisely quantify the concept of symmetry has been a driving force in science and mathematics, and will form the central theme of this course. This course fulfills the GEP Mathematics Requirement.

*Prerequisites:* Math Placement with a score of BEAUT

*Restrictions:* Students cannot enroll who have a major in Actuarial Science, Biology, Chemistry, Chemical Biology, Environmental Science, Information Technology, Mathematics or Physics.

*Attributes:* Math Beauty (New GEP), Undergraduate

**MAT 139 Mathematics, Culture & Society (3 credits)**

The course considers the relationship of mathematics to other areas of human thought and culture and to the society in which it develops. Several periods in the history of mathematics will be considered, from the beginnings of mathematics to modern times. This course fulfills the GEP Mathematics Requirement. Students may NOT receive credit for both this course and for MAT 150 – Art, Poetry, Mathematics and Society (First Year Seminar).

*Prerequisites:* Math Placement with a score of BEAUT

*Restrictions:* Students cannot enroll who have a major in Actuarial Science, Biology, Chemistry, Chemical Biology, Environmental Science, Information Technology, Mathematics or Physics.

*Attributes:* Math Beauty (New GEP), Undergraduate

**MAT 150 First Year Seminar (3 credits)**

**MAT 155 Fundamentals of Calculus (3 credits)**

This course covers the fundamentals of differential calculus (limit, continuity, and the derivative) and introduces the definite integral and its connection to the antiderivative. In addition, we discuss the historical roots of calculus and the challenges faced in establishing a rigorous logical foundation for its concepts. This course fulfills the GEP Mathematics Requirement. Prerequisite: MAT 120 or adequate performance on calculus readiness test. Students may NOT receive credit for both this course and for any of the following courses: MAT 104 (formerly MAT 106), MAT 119, MAT 123 or MAT 161

*Prerequisites:* MAT 120 or Math 155 Placement with a score of 1 or Math 161 Placement with a score of 1 or Math Placement with a score of MA155

*Attributes:* Math Beauty (New GEP), Undergraduate

**MAT 156 Applied Calculus II (3 credits)**

This course covers the definite integral, techniques of integration, solving differential equations and the calculus of several variables. The emphasis is on applications to the Business and Social Sciences. Prerequisite: MAT 155 or MAT 161. This course does not fulfill the GEP Mathematics requirement. Students may NOT receive credit for both this course and for MAT 162.

*Prerequisites:* (MAT 1251 or MAT 1255 or MAT 155 or MAT 161 or MAT 1351)

*Attributes:* Undergraduate

**MAT 161 Calculus I (4 credits)**

Limits; slopes, rates of change and the derivative; techniques of differentiation; implicit differentiation; derivatives of transcendental functions; related rates; linear approximation; L’Hosptial’s Rule; the Mean Value Theorem; applications of differentiation (including curve sketching and optimization); introduction to integration; the Fundamental Theorem of Calculus. This course fulfills the GEP Mathematics Requirement. Prerequisite: MAT 120 or adequate performance on calculus readiness test. Students may NOT receive credit for both this course and for any of the following courses: MAT 104 (formerly MAT 106), MAT 119, MAT 123 or MAT 155.

*Prerequisites:* MAT 120 or Math 161 Placement with a score of 1 or Math Placement with a score of MA161

*Attributes:* Math Beauty (New GEP), Undergraduate

**MAT 162 Calculus II (4 credits)**

Techniques of integration; applications of integration; improper integrals; exponential growth; infinite sequences and series; power series and Taylor series. Prerequisite: a grade of C or better in MAT 161 or permission of department. This course fulfills the GEP Mathematics Requirement. Students may NOT receive credit for both this course and for MAT 156.

*Prerequisites:* MAT 161 or Math 162 Placement with a score of 1 or Math Placement with a score of MA162

*Attributes:* Math Beauty (New GEP), Undergraduate

**MAT 180 Theory of Numbers (3 credits)**

Division Algorithm; Mathematical induction; Euclidean algorithm; fundamental theorem of arithmetic; linear Diophantine equations; modular arithmetic; number theoretic functions; prime numbers; Fermat’s last theorem; quadratic residues, primitive roots, Chinese Remainder theorem. This course fulfills the GEP Mathematics requirement but is at a more advanced level that courses in the MAT 130 - MAT 139 range.

*Attributes:* Math Beauty (New GEP), Undergraduate

**MAT 213 Calculus III (4 credits)**

Vector geometry in R2 and R3; polar coordinates; introduction to the calculus of vector-valued functions (velocity, speed, acceleration, curvature, parametric equations); differentiation of functions of several variables (partial derivatives, the differential, chain rules, directional derivatives); applications of differentiation (linear approximation, optimization, the method of Lagrange multipliers); integrals of functions of several variables; applications of integration. Also, if time permits, cylindrical and spherical coordinates; some surface integrals; the Change of Variable theorem. This course fulfills the GEP Mathematics Requirement. Prerequisite: a grade of C or better in MAT 162 or permission of department chairperson.

*Prerequisites:* MAT 1361 or MAT 162

*Attributes:* Math Beauty (New GEP), Undergraduate

**MAT 225 Fundamental Ideas of Math (3 credits)**

An introduction to: (i) the basic ideas used throughout Mathematics—logic, sets, functions, relations, counting principles — and (ii) the fundamental activity of mathematics—proving theorems. Topics include: basic set theory and logic, functions and relations, permutations and combinations, combinatorial proofs, discrete probability, and the Principle of Inclusion-Exclusion. Corequisite: MAT 161. Students may NOT receive credit both for this course and for either of CSC 240 /MED 553.

*Prerequisites:* MAT 162 or MAT 1361

*Attributes:* Undergraduate

**MAT 226 Introduction to Linear Algebra (4 credits)**

Linear systems, vector spaces, dimension, linear transformations, matrices, inner product, orthogonality, characteristic polynomials, diagonalization, eigenvalues, and eigenvectors. Prerequisite: MAT 225 or permission of the chair of Mathematics.

*Prerequisites:* (MAT 1371 or MAT 1375) or MAT 213

*Attributes:* Math Beauty (New GEP), Undergraduate

**MAT 231 The Mathematics of Music (3 credits)**

Music has many connections to mathematics. The ancient Greeks discovered that chords with a pleasing sound are related to simple ratios of integers. The mathematics of rhythm has also been studied for centuries—in fact, ancient Indian writers discovered the celebrated Fibonacci sequence in the rhythms of Sanskrit poetry. Other connections between math and music investigated in this course include the equations describing the sounds of musical instruments, the mathematics behind digital recording, the use of symmetry and group theory in composition, the exploration of patterns by African and Indian drummers, the application of chaos theory to modeling the behavior of melodies, and the representation of chords by exotic geometric objects called orbifolds. Along the way, we discuss the role of creativity in mathematics and the ways in which mathematics has inspired musicians. Prerequisite: MAT 162 and some musical training (ART 1511 or equivalent). Students with exceptional performance in Calculus I (or AP) and musical training will be admitted on a case-by-case basis as determined by the chair of Mathematics.

*Prerequisites:* (MAT 162 or MAT 1361) and (ART 151 or ART 1511)

*Attributes:* Math Beauty (New GEP), Undergraduate

**MAT 232 Chaos, Fractals & Dynamic Syst (3 credits)**

Introduction to dynamical systems: one dimensional dynamics; attracting, repelling, periodic and chaotic orbits; bifurcation; dynamics in the complex plane, Julia sets, the Mandelbrot set; two dimensional dynamics. Introduction to fractals: self-similarity, iterated function systems, fractal dimension. Prerequisite: MAT 162.

*Prerequisites:* (MAT 1261 or MAT 156 or MAT 162 or MAT 1361)

*Attributes:* Math Beauty (New GEP), Undergraduate

**MAT 233 History of Mathematics (3 credits)**

Development of mathematical ideas over 2500 years, beginning with Greek geometry and including Euclid, Archimedes, Newton, Euler, Gauss, and Poincare. Prerequisite: MAT 213 or permission of the chair of Mathematics.

*Prerequisites:* MAT 162 or MAT 1361

*Attributes:* Math Beauty (New GEP), Undergraduate

**MAT 238 Differential Equations (3 credits)**

Solution of ordinary differential equations using analytic, numerical, and qualitative techniques. Modeling via differential equations, systems of differential equations. Laplace transforms; discrete dynamical systems. Use of a computer software package is required. Prerequisite: MAT 213 or equivalent.

*Prerequisites:* MAT 1371 or MAT 213

*Attributes:* Math Beauty (New GEP), Undergraduate

**MAT 239 Problem Solving (3 credits)**

The course is designed to involve students in an active way in the mathematical process by having them participate in the major activity of both pure and applied mathematics: the solving of problems. Problems will be chosen from many areas of mathematics, and an attempt will be made to develop general approaches to and general paradigms for problem solving. Prerequisite: MAT 225.

*Prerequisites:* MAT 1431 or MAT 180

*Attributes:* Math Beauty (New GEP), Undergraduate

**MAT 240 Advanced Calculus (4 credits)**

This course covers three main groups of topics. I) Calculus of functions from Rn to Rk: Differentials, Inverse Function Theorem, Implicit Function Theorem, Jacobian, change of variables. II) Vector calculus. Vector fields, line and surface integrals, Green’s Theorem, Stokes’s Theorem, the Divergence Theorem. III) Sequences and series of functions. Pointwise and uniform convergence; continuity, differentiation and integration of sequences and series; Fourier series; Taylor series for functions of several variables. Prerequisite: MAT 213 or equivalent.

*Prerequisites:* MAT 213 or MAT 1371

*Attributes:* Math Beauty (New GEP), Undergraduate

**MAT 293 Mathematical Symmetry (3 credits)**

**MAT 311 Numerical Analy & Comp Tech (3 credits)**

An introduction to numerical methods for solving a variety of problems. Included will be rootfinding, numerical integration and differentiation, polynomial approximation, systems of equations, ordinary differential equations, and discussion of convergence issues, error analysis and machine arithmetic. Prerequisite: MAT 213. Concurrent enrollment in or prior completion of MAT 226 would be beneficial.

*Prerequisites:* (MAT 1371 or MAT 1391) or MAT 213

*Attributes:* Math Beauty (New GEP), Undergraduate

**MAT 313 Mathematical Optimization (3 credits)**

The course covers basic ideas in optimization beginning with linear programming, the simplex method and duality and finishes with non-linear optimization and algorithms and conditions leading to a solution of non- linear problems. Prerequisite: MAT 226 or permission of the chair of Mathematics.

*Prerequisites:* MAT 1391 or MAT 226 or MAT 1461

*Attributes:* Math Beauty (New GEP), Undergraduate

**MAT 316 Operations Research (3 credits)**

The course will cover some of the basic models and techniques used in operations research. Topics include: linear programming, the simplex method, duality, network problems, transportation problems, and time permitting, game theory. Prerequisite: MAT 226 or permission of the chair of Mathematics.

*Prerequisites:* MAT 1461 or MAT 226 or MAT 1391

*Attributes:* Math Beauty (New GEP), Undergraduate

**MAT 321 Probability (3 credits)**

The first part of a two-semester sequence, this course includes discrete probability and counting methods, conditional probability and independence , Bayes’ Theorem, discrete and continuous random variables, expectation, variance, moment-generating functions, special probability distributions, joint distributions, marginal and conditional distributions , independent random variables , covariance and correlation, conditional expectations , and distributions of functions of random variables. Co-requisite: MAT 213.

*Prerequisites:* (MAT 1371 or MAT 1391) or MAT 213

*Attributes:* Math Beauty (New GEP), Undergraduate

**MAT 322 Mathematical Statistics (3 credits)**

Random samples, statistics and sampling distributions, the Central Limit Theorem, point and interval estimation, hypothesis testing (one-sample and two-sample tests), analysis of variance, correlation, regression analysis and Chi Square goodness of fit and other nonparametric methods. Applications. Data analysis projects will be assigned. Prerequisite: MAT 321

*Prerequisites:* MAT 2211 or MAT 321

*Attributes:* Undergraduate

**MAT 332 Geometry (3 credits)**

An axiomatic treatment of the foundations of geometry. Axioms of incidence, order, congruence, Bolyai- Lobachevsky parallel axiom, angle of parallelism. A rigorous development of selected topics in non-Euclidean geometry. Prerequisite: MAT 225.

*Prerequisites:* MAT 225 or MAT 1591

*Attributes:* Math Beauty (New GEP), Undergraduate

**MAT 334 Combinatorics & Graph Theory (3 credits)**

Introduction to combinatorics and graph theory and to methods by which each theory is applied to the other. Topics include basic counting formulas; generating functions; the principle of inclusion-exclusion; counting labeled trees (Cayley’s Theorem, Kirchhoff’s Theorem, Prüfer’s Theorem); directed Euler circuits; Pólya-deBrujin theory; Möbius inversion. Prerequisite: MAT 162.

*Prerequisites:* MAT 162 or MAT 1361

*Attributes:* Math Beauty (New GEP), Undergraduate

**MAT 336 Logic & Foundations (3 credits)**

Cantorian set theory and the crisis in foundations (Cantor’s paradox, Russell’s paradox); the intuitionist challenge and the formalist response; formal logic and meta mathematics (Propositional Calculus, Predicate Calculus, formal number theory); Goedel’s incompleteness theorems of 1931. Prerequisite: MAT 162.

*Prerequisites:* MAT 162 or MAT 1361

*Attributes:* Math Beauty (New GEP), Undergraduate

**MAT 403 Abstract Algebra (3 credits)**

Group theory, including finite groups, subgroups, cyclic groups, permutation groups, group isomorphisms, and cosets; introduction to rings and fields, including integral domains, polynomial rings, unique factorization domains and Euclidean domains. Prerequisite: MAT 225.

*Prerequisites:* (MAT 1431 or MAT 1571) or MAT 180

*Attributes:* Undergraduate

**MAT 404 Abstract Algebra II (3 credits)**

A more in-depth treatment of rings and fields including integral domains, fields, field extensions, homomorphisms, and the insolvability of the quintic by radicals. Galois theory. Prerequisite: MAT 403.

*Prerequisites:* MAT 2031 or MAT 403

*Attributes:* Math Beauty (New GEP), Undergraduate

**MAT 409 Real Analysis (3 credits)**

Elementary topology of Euclidean spaces, including open, closed and compact sets; convergence of sequences and series; least upper bound axiom and its equivalents; sequences of functions, pointwise and uniform convergence, continuity, differentiation and integration of sequences. Topics which overlap MAT 240 will be covered in more depth in this course. Prerequisite: MAT 213 and 225.

*Prerequisites:* MAT 1371 or MAT 213

*Attributes:* Math Beauty (New GEP), Undergraduate

**MAT 410 Complex Analysis (3 credits)**

Analytic functions; complex integration; singularities. Prerequisite: MAT 240, MAT 409, or permission of the chair of Mathematics.

*Prerequisites:* MAT 2091 or MAT 409

*Attributes:* Math Beauty (New GEP), Undergraduate

**MAT 415 Differential Geometry (3 credits)**

Tangent vectors and directional derivatives; mappings and differential forms on E3; Frenet fields; covariant derivatives; frame fields; Cartan structural equations; orientation; Euclidean geometry; surfaces in R3; calculus on surfaces; integration of forms; shape operators; normal and Gaussian curvature; geometry of surfaces. Prerequisite: MAT 409.

*Prerequisites:* (MAT 1371 or MAT 1391) or MAT 213

*Attributes:* Math Beauty (New GEP), Undergraduate

**MAT 418 Topology of Point Sets (3 credits)**

Open and closed sets, closure and interior, continuity, metric spaces, connectivity, compactness; the Heine- Borel and Bolzano-Weierstrass Theorems. The Classification of Surfaces may also be covered. Prerequisite: MAT 409 or equivalent.

*Prerequisites:* MAT 409 or MAT 2091 or MAT 2093

*Attributes:* Undergraduate

**MAT 423 Applied Statistical Methods (3 credits)**

Statistical models, design and analysis of experiments, regression, Monte Carlo methods, and other advanced topics in statistics.

*Prerequisites:* MAT 1261 or MAT 156 or MAT 162 or MAT 1361

*Attributes:* Math Beauty (New GEP), Undergraduate

**MAT 491 Mathematics Internship (3 credits)**

The course goals are: to gain first-hand experience of the daily activities of professionals in mathematics and related fields, to verify an interest in a particular area of mathematics, to develop and hone skills required for mathematical professions, to establish contacts outside the academic community who will facilitate a career in mathematics. An internship journal and an academic paper are also required.

**MAT 492 Mathematics Internship II (3 credits)**

The course goals are: to gain first-hand experience of the daily activities of professionals in mathematics and related fields, to verify an interest in a particular area of mathematics, to develop and hone skills required for mathematical professions, to establish contacts outside the academic community who will facilitate a career in mathematics. An internship journal and an academic paper are also required.

**MAT 493 Independent Research (3 credits)**

Students need to complete the application form for independent study (available in the Dean’s Office) and have the approval of the department chair and Associate Dean in order to register. Honors Research (6 credits) Must be elected in junior year to allow adequate research time. Students need to complete the application form for independent study (available in the Dean’s Office) and have the approval of the department chair, Associate Dean and the Honors Program Director in order to register. Honors Students must complete this sequence.

*Attributes:* Math Beauty (New GEP), Undergraduate

**MAT 494 Independent Research (3 credits)**

Students need to complete the application form for independent study (available in the Dean’s Office) and have the approval of the department chair and Associate Dean in order to register. Honors Research (6 credits) Must be elected in junior year to allow adequate research time. Students need to complete the application form for independent study (available in the Dean’s Office) and have the approval of the department chair, Associate Dean and the Honors Program Director in order to register. Honors Students must complete this sequence.

*Attributes:* Math Beauty (New GEP), Undergraduate