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MATH 1340 AND FOR (5 MATHEMATICS (MATH) credits) A combined algebra and trigonometry course for science and engineering MATH 1120 INTRODUCTION TO MATHEMATICAL AND students planning to enroll in MATH 1950. Topics include: systems of COMPUTATIONAL THINKING (3 credits) equations, and rational functions, exponential and logarithmic This course embraces the visual arts to introduce students to the functions, trigonometric functions and their inverses, trigonometric foundational elements of mathematical and computational thinking. identities and applications, conic sections, and complex . Credit Visual patterns form the basis for explorations in and geometric for both MATH 1320/MATH 1324 and MATH 1340, or both MATH 1330 and sequences, from which algebraic functions and corresponding functions in MATH 1340 will not be given. computer programs are reasoned. Prerequisite(s)/Corequisite(s): One of the following within the last two Distribution: Math years: ALEKS score of at least 4, ACT Math at least 23, Math SAT at least 540, Math SAT2016 at least 570, Accuplacer at least 5, MATH 1310 or MATH 1130 QUANTITATIVE LITERACY (3 credits) MATH 1220 C- or better, or MATH 1340 Designed to equip students with the mathematical, statistical, and computational skills necessary to explore real-life situations. Students will MATH 1370 APPLIED ALGEBRA AND OPTIMIZATION WITH learn and practice critical-thinking and problem-solving skills needed to use (4 credits) quantitative information to make responsible decisions in a variety of areas This is an applied algebra course with optimization, teaching the following such as finance, health, and the environment. topics with an emphasis on data analysis and application: algebraic, Distribution: Math exponential, and logarithmic functions; and applications thereof; and . The course will emphasize data analysis and applications MATH 1210 INTERMEDIATE ALGEBRA (3 credits) of covered topics in order to demonstrate the relevance of mathematics to This course is designed to prepare students to be successful in MATH 1220. solving real-world problems. Topics include simplifying mathematical expressions, the properties of Prerequisite(s)/Corequisite(s): One of the following within the last two equality, solving linear equations in one , using linear equations years: ALEKS score of at least 4, ACT Math sub score at least 23, SAT Math to solve problems, , ratios and proportions, graphing and the at least 540, SAT2016 Math at least 570, Accuplacer at least 4, MATH 1310 rectangular coordinate system, relations and functions, systems of linear or MATH 1220 with C- or better, or MATH 1370 equations and inequalities in two variables, expressions and functions, factoring and solving polynomial equations. Credit earned in MATH 1930 CALCULUS FOR THE MANAGERIAL, LIFE, AND SOCIAL MATH 1210 will not count toward degree requirements. SCIENCES (3 credits) Prerequisite(s)/Corequisite(s): One of the following within the last two Topics covered include functions, limits, derivatives, , and years: ALEKS score of 1 or 2, ACT Math sub score of 18 or less, Math SAT applications. Trigonometry is not required. May not be used as a sub score at least 220, Math SAT2016 sub score at least 230, Accuplacer prerequisite for MATH 1960. Credit will not be granted for both MATH 1930 score of 1 or 2, or MATH 1210. and 1950. Prerequisite(s)/Corequisite(s): One of the following within the last two MATH 1220 COLLEGE ALGEBRA (3 credits) years: ALEKS score of at least 5, ACT Math sub score at least 25, Math SAT This course presents properties of real numbers, linear equations and at least 570, or Math SAT2016 at least 590, Accuplacer score at least 6, graphing, systems of equations, linear inequalities, polynomials, algebraic MATH 1320 with C- or better, or MATH 1930 fractions, exponents, logarithms, and an Introduction to Statistics. This course is designed to prepare students to be successful in MATH 1320 or MATH 1940 CALCULUS FOR BIOMEDICINE (5 credits) MATH 1370. Students who have passed MATH 1310 with a C- or better Introductory calculus with an emphasis on dynamical systems analysis should not take this course. applied to biological systems. Topics include differential and Prerequisite(s)/Corequisite(s): Within the last two years: ALEKS score at calculus, elementary chaos theory, discrete modeling, neural networks, and least 3, ACT Math at least 19, SAT Math at least 460, SAT2016 Math at least elementary differential equations, population dynamics, and biochemical 500, Accuplacer at least 3, MATH 1210 C- or better or MATH 1220. Students signal transduction. who passed MATH 1310 (C- or better) should not take MATH 1220. Prerequisite(s)/Corequisite(s): One of the following within the last two Distribution: Math years: ALEKS score of at least 5, ACT Math sub score at least 25, Math SAT at least 570, Math SAT2016 at least 590, Accuplacer score at least 6, MATH 1320 PRE-CALCULUS ALGEBRA (3 credits) MATH 1320 with C- or better; or permission of instructor An advanced algebra course that teaches the following topics: algebraic operations, functions, graphs, linear and quadratic equations and MATH 1950 CALCULUS I (5 credits) inequalities, polynomial and rational functions, systems of equations, This is a course in plane analytic emphasizing the study of binomial theorem, complex numbers, exponentials, logarithms, sequences, functions, limits, derivatives and applications, and an introduction to series, and . integration. Prerequisite(s)/Corequisite(s): One of the following within the last two Prerequisite(s)/Corequisite(s): One of the following within the last two years: ALEKS score of at least 4, ACT Math at least 23, Math SAT at least years: ALEKS score of at least 6, ACT Math at least 26, Math SAT at least 540, Math SAT2016 at least 570, Accuplacer score at least 4, MATH 1220 or 590, Math SAT2016 at least 610, Accuplacer score of 7, MATH 1320 and MATH 1310 each with C- or better, or MATH 1320 MATH 1330 or MATH 1340 with C- or better; or permission of instructor MATH 1330 TRIGONOMETRY (3 credits) MATH 1960 CALCULUS II (5 credits) This course introduces elements of plane trigonometry, including This course introduces applications of integration, techniques of integration, trigonometric and circular functions, inverse trigonometric functions, infinite sequences and series, vectors in the plane, and polar functions. A solutions of triangles, identities and conditional equations, vectors, and mathematical software package is introduced, with required assignments. conic sections. Prerequisite(s)/Corequisite(s): MATH 1950 with a grade of C- or better Prerequisite(s)/Corequisite(s): One of the following within the last two or permission of instructor. years: ALEKS score of at least 5, ACT Math at least 25, Math SAT at least 570, Math SAT2016 at least 590, Accuplacer at least 5, MATH 1320 with C- or better, or MATH 1330 2 Mathematics (MATH)

MATH 1970 CALCULUS III (4 credits) MATH 3230 INTRODUCTION TO ANALYSIS (3 credits) This course presents vector functions, parametric equations, analytic This course provides a theoretical foundation for the concepts of elementary geometry, partial differentiation, multiple integration, and an introduction calculus. Topics include real system, of the real , limits, to vector calculus. A mathematical software package is introduced with functions of one variable, continuity, differentiation. (Cross-listed with required assignments. MATH 8235). Prerequisite(s)/Corequisite(s): MATH 1960 with a grade of C- or better, Prerequisite(s)/Corequisite(s): MATH 1960 and MATH 2230 each with a or MATH 1970 with a grade of F or better, or permission of instructor. grade of C- or better. MATH 2030 (3 credits) MATH 3300 NUMERICAL METHODS (3 credits) A foundations course in discrete mathematics for applied disciplines, This course involves solving nonlinear algebraic equations and systems including and computer engineering. Topics include: of equations, interpolation and polynomial approximation, numerical logic, sets, relations, functions, complexity functions and big congruences, differentiation and integration, numerical solutions to ordinary differential induction and recursive definitions, elementary combinatorics, discrete equations, analysis of and errors, and computational efficiency. , graphs and trees. (Cross-listed with MATH 8305, CSCI 3300, CSCI 8305). Prerequisite(s)/Corequisite(s): MATH 1950 or MATH 1930. Prerequisite(s)/Corequisite(s): MATH 1960 with a C- or better or permission of instructor MATH 2050 APPLIED (3 credits) This course presents Matrix algebra, simultaneous equations, vector spaces, MATH 3400 THEORY OF INTEREST (3 credits) with applications of linear algebra and computational considerations. A study of the measurement of interest, annuities, amortization schedules Mathematical software is utilized, with required assignments. and other financial mathematics topics. Prerequisite(s)/Corequisite(s): MATH 1940 or MATH 1950 with a grade Prerequisite(s)/Corequisite(s): MATH 1970 of C- or better MATH 3640 MODERN GEOMETRY (3 credits) MATH 2200 MATHEMATICAL COMPUTING I (3 credits) This course will study the modern foundations of Euclidean and Non- This is a first course in mathematical computing. It covers the basic Euclidian Geometry. Included will be a study of the principles of axiomatic elements of scientific programming in both a system and systems. will be investigated using Hilbert's a high-level programming language. Explored are implementation issues, for Euclidean geometry (or another equivalent Euclidean geometry problem description, model building, method development, and solution ). Hyperbolic geometry will be encountered through the models of Klein assessment. and Poincare. Neutral geometry with Lambert and Saccheri quadrilaterals Prerequisite(s)/Corequisite(s): MATH 1950 will be studied. Finite and projective geometries will also be explored. (Cross-listed with MATH 8645). MATH 2230 INTRODUCTION TO ABSTRACT MATH (3 credits) Prerequisite(s)/Corequisite(s): MATH 2230 with a grade of C- or better. This course provides a transition from the calculus to more abstract mathematics. Topics include logic, sets and functions, an introduction MATH 3850 (3 credits) to mathematical proof, mathematical induction, relations. Important An overview of the history of mathematics and famous mathematicians prerequisite material for a number of more advanced mathematics courses via studying and solving famous mathematical problems, exploring is studied. Credit will not be given for both MATH 2030 (or MATH 2040) and famous mathematical theorems, and studying the biographies of famous MATH 2230. mathematicians. (Cross-listed with MATH 8855). Prerequisite(s)/Corequisite(s): MATH 1960 or permission Prerequisite(s)/Corequisite(s): Students who enroll in this course should have completed MATH 1970 and MATH 2230 in order to have the MATH 2350 DIFFERENTIAL EQUATIONS (3 credits) minimum amount of mathematical background needed to appreciate the Topics include solutions of linear and first-order nonlinear differential mathematical content of the course. equations with applications, higher-order linear differential equations with applications, power series solutions, and Laplace transform methods. MATH 4010 INTRODUCTION TO THE THEORY OF RECURSIVE Prerequisite(s)/Corequisite(s): MATH 1960 with a grade of C- or better FUNCTIONS (3 credits) or permission of instructor. This is a proof-oriented course presenting the foundations of Recursion Theory. We present the definition and properties of the class of primitive MATH 3100 APPLIED COMBINATORICS (3 credits) recursive functions, study the formal models of computation, and Basic counting methods, generating functions, recurrence relations, investigate partially computable functions, universal programs. We principle of inclusion-exclusion. Polya's formula. Elements of , prove Rice's Theorem, the Recursion Theorem, develop the arithmetic trees and searching network algorithms. (Cross-listed with MATH 8105, hierarchy, demonstrate Post's theorem. Introduction to the formal theories CSCI 3100, CSCI 8105). of computability and complexity is also given. (Cross-listed with CSCI 4010, Prerequisite(s)/Corequisite(s): MATH 2030, MATH 2040, MATH 2230, or CSCI 8016, MATH 8016). CSCI 2030 all with a C- or better. ; ; Relations; Prerequisite(s)/Corequisite(s): MATH 2230 or MATH 2030 with a C- or Functions; Congruences; Inductive and recursive definitions; Discrete better or CSCI 3660 with a C- or better or instructor's permission. probability; sets, graphs, trees, & matrices MATH 4030 MODERN ALGEBRA (3 credits) MATH 3200 MATHEMATICAL COMPUTING II (3 credits) Algebra is the study of mathematical manipulations that preserve This course is a second course in mathematical computing. It covers the something (like equality - when solving equations). The areas in which design and development of algorithms and more advanced elements of Algebra finds application are quite diverse, from Ancient Greek Geometry programming in a mathematical context. The programming language through to Modern Information Protection and Security (error correcting Python will be used. The programming assignments are primarily based codes, data compression, and ). This course begins with on data science and calculus concepts and are designed to reinforce and topics that should be familiar (such as ruler-and-compass constructions, deepen the understanding of these concepts. and modular arithmetic) and builds upon this foundation through Prerequisite(s)/Corequisite(s): CIST 1400 or MATH 2200, and polynomial rings up to finite fields and basic . (Cross-listed with MATH 1970 (the latter may be taked concurrently) MATH 8036). Prerequisite(s)/Corequisite(s): MATH 2230 with a C- or better or MATH 2030 with a C- or better Mathematics (MATH) 3

MATH 4050 LINEAR ALGEBRA (3 credits) MATH 4240 II (3 credits) Linear algebra is extensively utilized in the mathematical modeling of many Provides a theoretical foundation for the concepts of classical Calculus natural phenomena. Many scientific and engineering disciplines, such as (vector calculus included). Topics include sequences and series of functions, data science, chemical engineering and , make extensive use of uniform convergence, power series, Fourier series, multivariable real the theory and techniques commonly present in basic to advanced linear differential and integral calculus, the Implicit Function Theorem, integration algebra courses. The goal of this course is to help students to grasp a of different forms, and the important formulas, connecting those integrals, solid theoretical understanding of vectors, vector spaces, inner product due to: Green, Gauss, Riemann, and Ostrogradski. (Cross-listed with spaces, linear transformations, eigenvalues, canonical forms, complex MATH 8246). vectors, matrices, and orthogonality. By going through the materials in Prerequisite(s)/Corequisite(s): MATH 4230/MATH 8236 a mathematically rigorous way, students will develop deeper and more MATH 4270 (3 credits) accurate intuitions of the basic concepts in linear algebra. Consequently, This course is an introduction to the theory of functions of a complex the applications of linear algebra will become much more transparent. variable, a fundamental area of mathematics with multiple applications (Cross-listed with MATH 8056). to science and engineering. Topics include the of complex numbers, Prerequisite(s)/Corequisite(s): MATH 2050 with a grade of C- or better; complex differentiation, the complex contour integral and Cauchy's integral MATH 2030 or MATH 2230 or equivalent with a grade of C- or better; or formula, Taylor expansions and analytic functions, conformal mapping and permission Riemann's conformal equivalence theorem, residue theory and Laurent MATH 4110 I (3 credits) series, harmonic functions, and applications. (Cross-listed with MATH 8276). An introduction to group theory. Various classes of group are studied: Prerequisite(s)/Corequisite(s): MATH 3230/MATH 8235 or permission symmetric groups, abelian, cyclic, and permutation groups. Basic tools are of the instructor. developed and used: subgroups, normal subgroups, cosets, the Lagrange MATH 4300 DETERMINISTIC MODELS (3 theorem, group homomorphisms, quotient groups, direct products, and credits) group actions on a set. The course culminates with the Sylow theorems in This is a survey course of deterministic operations research models and finite group theory. The theory is illustrated with examples from geometry, algorithms. Topics include linear programming, network programming, linear algebra, , crystallography, and combinatorics. (Cross- and programming. (Cross-listed with CSCI 4300, CSCI 8306, listed with MATH 8116). MATH 8306). Prerequisite(s)/Corequisite(s): MATH 4050/MATH 8056 with a C- or Prerequisite(s)/Corequisite(s): MATH 2050 with a C- or better or better or MATH 4560/MATH 8566 with a C- or better or permission of permission of instructor. instructor MATH 4310 PROBABILISTIC OPERATIONS RESEARCH MODELS (3 MATH 4120 ABSTRACT ALGEBRA II (3 credits) credits) An introduction to and field theory. Various classes of commutative This is a survey course of probabilistic operations, research models and rings are considered including polynomial rings, and the Gaussian . algorithms. Topics include Markov chains, queueing theory, inventory Examples of fields include finite fields and various extensions of the models, forecasting, and simulation. (Cross-listed with CSCI 4310, rational numbers. Concepts such as that of an , integral domain, CSCI 8316, MATH 8316). characteristic and extension field are studied. The course culminates with Prerequisite(s)/Corequisite(s): MATH 2050 and either MATH 4740 or an introduction to . Applications include the resolution of two MATH 8746 or STAT 3800 or STAT 8805 all with a C- or better or permission classical problems: the impossibility of angle-trisection and the general of instructor. insolvability of polynomial equations of degree 5 or higher. (Cross-listed with MATH 8126). MATH 4320 COMPUTATIONAL OPERATIONS RESEARCH (3 credits) Prerequisite(s)/Corequisite(s): MATH 4110/MATH 8116 with a C- or Survey of computational methods used in the solution of operations better or permission of instructor research problems. Topics include scripting to guide optimization software, metaheuristics for optimization, and basic machine learning algorithms. MATH 4150 GRAPH THEORY & APPLICATIONS (3 credits) (Cross-listed with MATH 8326). Introduction to graph theory. Representations of graphs and graph Prerequisite(s)/Corequisite(s): MATH 3200 and MATH 4300 each with a isomorphism. Trees as a special case of graphs. Connectivity, covering, grade of C- or better or permission of instructor. matching and coloring in graphs. Directed graphs and planar graphs. Applications of graph theory in several fields such as networks, social MATH 4330 INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS sciences, VLSI, and parallel processing. (Cross-listed with (3 credits) MATH 8156, CSCI 4150, CSCI 8156). This course introduces the basic methods of PDEs guided by applications in Prerequisite(s)/Corequisite(s): CSCI 2030 with a C- or better, or and engineering. The main topics to be covered include The Linear MATH 2030 with a C- or better, or MATH 2230 with a C- or better, or First order PDEs, Transport equations, Characteristics, Classification of permission of instructor. PDEs, Separation of variables, Heat conduction, vibrating membranes, boundary value problems, Maximum principle, Sturm-Liouville problems, MATH 4230 MATHEMATICAL ANALYSIS I (3 credits) Fourier series, Fourier integrals, Harmonic functions, Legendre polynomials, Provides a theoretical foundation for the concepts of elementary calculus. Distributions, Green's functions. (Cross-listed with MATH 8336). Topics include ordered fields and the system, basic properties Prerequisite(s)/Corequisite(s): MATH 1970 with a C- or better and of complex numbers, topology, sequences and series in Rk, MATH 2350 with a C- or better, or permission of instructor; MATH 2050 limits and continuity in a metric space, monotonic functions. (Cross-listed recommended, not required. with MATH 8236). Prerequisite(s)/Corequisite(s): MATH 3230/MATH 8235 MATH 4350 ORDINARY DIFFERENTIAL EQUATIONS (3 credits) This course covers the theory of initial-, boundary-, and eigenvalue problems, existence theorems, real and complex linear systems of differential equations, and stability theory. There will be a strong emphasis on methods for finding solutions of initial and boundary value problems and analyzing properties of these solutions for various ordinary differential equations. (Cross-listed with MATH 8356). Prerequisite(s)/Corequisite(s): MATH 1970 with a C- or better, MATH 2050 with a C- or better, and MATH 2350 with a C-, or better or instructor's permission. 4 Mathematics (MATH)

MATH 4400 THE (3 credits) MATH 4660 AUTOMATA, COMPUTABILITY, AND FORMAL Introduction to finite elements methods for solving ordinary and partial LANGUAGES (3 credits) differential equations. Theoretical foundations of finite element methods This course presents a sampling of several important areas of theoretical for boundary value problems, approximation by piecewise polynomial computer science. Definition of formal models of computation and functions, variation formulation of partial differential equations, basic important properties of such models, including finite automata and Turing error estimates. The Rayleigh-Ritz-Galerkin method, convergence of machines. Definition and important properties of formal grammars and approximations, time-dependent problems, error analysis, discretization their languages. Introduction to the formal theories of computability and and computer implementation, applications to problems in , heat complexity. (Cross-listed with CSCI 4660, CSCI 8666, MATH 8666) transfer, and . (Cross-listed with MATH 8406). Prerequisite(s)/Corequisite(s): MATH 2030. Recommended: CSCI 3320/ Prerequisite(s)/Corequisite(s): MATH 1970, MATH 2050 and CSCI 8325. MATH 2350 all with a C- or better or instructor permission. MATH 3300/ MATH 4740 INTRODUCTION TO PROBABILITY AND STATISTICS I (3 MATH 8305 and MATH 4330/MATH 8336 recommended. Students credits) should be able to use a programming language (ie MATLAB) to complete A mathematical introduction to including the properties computational assignments of probability; probability distributions; expected values and moments; MATH 4450 INTRODUCTION TO MACHINE LEARNING AND DATA specific discrete and continuous distributions; and transformations of MINING (3 credits) random variables. (Cross-listed with MATH 8746). This is an introduction to machine learning and data mining which covers Prerequisite(s)/Corequisite(s): MATH 1970 and either MATH 2230 or the following topics with an emphasis on mathematical and statistical MATH 2030 or permission of instructor. analysis: linear and nonlinear regression models, model selection and MATH 4750 INTRODUCTION TO PROBABILITY AND STATISTICS II (3 regularization methods, resampling methods, classification models, tree- credits) based models, and unsupervised learning topics. If time allows, text mining Theory and methods of statistical inference including sampling and deep learning will also be introduced in the course. Statistical software distributions, estimators, estimation, and statistical hypotheses. (Cross- will be used. (Cross-listed with MATH 8456, STAT 4450, STAT 8456) listed with MATH 8756). Prerequisite(s)/Corequisite(s): MATH 4740/8746 with a C- or better or Prerequisite(s)/Corequisite(s): MATH 4740/MATH 8746 STAT 3800/8805 with a C- or better or permission of instructor. MATH 4760 TOPICS IN (3 credits) MATH 4560 NUMBER THEORY & CRYPTOGRAPHY (3 credits) Selection of such topics such as dynamical systems and chaos, Boolean An overview of one of the many beautiful areas of mathematics and its networks, modeling of discrete or continuous systems, matrix theory, modern application to secure communication. The course is ideal for difference equations, , discrete events simulation any student who wants a taste of mathematics outside of, or in and other approved by Upper Curriculum Committee. (Cross-listed with to, the calculus sequence. Topics to be covered include: prime numbers, MATH 8766). congruences, perfect numbers, primitive roots, quadratic reciprocity, Prerequisite(s)/Corequisite(s): MATH 3100/CSCI 3100 sums of squares, and Diophantine equations. Applications include error- correcting codes, symmetric and public key cryptography, secret sharing, MATH 4900 INDEPENDENT STUDIES (1-3 credits) and zero knowledge proofs. (Cross-listed with MATH 8566, CSCI 4560, A variable credit course for the junior or senior who will benefit from CSCI 8566). independent reading assignments and research-type problems. Independent Prerequisite(s)/Corequisite(s): MATH 2230 with a C- or better or study makes available courses of study not available in scheduled course MATH 2030 with a C- or better or CSCI 2030 with a C- or better or offerings. The student wishing to take an independent study course should permission of instructor find a faculty member willing to supervise the course and then submit, for approval, a written proposal (including amount of credit) to the MATH/ MATH 4610 INTRODUCTION TO TOPOLOGY (3 credits) STAT Undergraduate Curriculum Committee at least one week prior to This is a proof-oriented course presenting the foundations of topology. registration. Metric spaces and general topological spaces are introduced. The course Prerequisite(s)/Corequisite(s): Junior and permission of the chair explores the properties of connectedness, compactness and completeness, and operations of Tychonoff product and hyperspace. (Cross-listed with MATH 4970 SEMINAR IN APPLIED MATHEMATICS (3 credits) MATH 8616). A seminar in Applied Mathematics, where the students would read and Prerequisite(s)/Corequisite(s): MATH 3230 with a C- or better or present research in applied math and write their exposition of those topics. permission of instructor. Prerequisite(s)/Corequisite(s): MATH 3100/CSCI 3100 MATH 4620 ITERATED FUNCTION SYSTEMS AND FRACTALS (3 MATH 4980 SEMINAR (1-3 credits) credits) A seminar in mathematics. This course introduces students to an This is a proof-oriented course presenting the foundations of fractal important form of mathematical activity and culture, where a specialized geometry. It introduces students to the beauty, magic, and applications of mathematical subject matter (not covered in typical courses) is studied fractals and iterated function systems, with emphasis on the mathematics and discussed in a collaborative setting. The course may be repeated for behind it all. Topics range from contractions on hyperspaces and their fixed different topics up to a maximum of six credit hours. The specific topics will points to fractal to Julia and Mandelbrot sets. (Cross-listed with vary, depending upon when the course is offered. One example of a seminar MATH 8626). topic is Current Trends in Set Theory of the Reals. Prerequisite(s)/Corequisite(s): MATH 4610 with a C- or better or Prerequisite(s)/Corequisite(s): Permission of instructor. permission of instructor.