# Mathematics (MATH)

**MATH0900** BASIC ALGEBRA

Algebraic operations and equations, exponents and radicals, polynomials and factoring, and introduction to the geometry of angles and triangles. **Prerequisite:** Placement through the College of Professional and Continuing Education (4 credits)

**MATH1000** COLLEGE MATHEMATICS

Algebra and trigonometry, including algebraic fractions, systems of linear equations, quadratic equations, literal equations, word problems and their solutions, right triangles, and vectors. Applications will be stressed. (4 credits) fall, spring

**MATH1005** COLLEGE MATHEMATICS A

Topics in college algebra including exponents, radicals, complex numbers, polynomials, factoring, algebraic fractions, equation solving techniques, an introduction to functions and their graphs, and linear functions. (3 credits)

**MATH1007** APPLICATIONS IN COLLEGE MATHEMATICS

This class provides additional enrichment applications for students enrolled in MATH1000, College Mathematics. Students will take a leadership role in this class to work on advanced application problems and look at how College Mathematics fits in with the rest of their major's curriculum. **Corequisite:** MATH1000

**MATH1020** PLANE & SOLID GEOMETRY

A survey of elementary Euclidean geometry including lines and angles, measurement and units, properties of triangles, parallelograms, trapezoids, regular polygons, circles, conic sections, spheres, cylinders, pyramids, polyhedra, areas, and volumes. (4 credits) spring

**MATH1030** STATISTICS & APPLICATIONS

This course is designed to introduce students to statistical concepts relating to engineering design, inspection, and quality assurance. Topics covered include probability, normality, sampling, regression, correlation, and confidence intervals in reliability. (4 credits) fall, spring

**MATH1035** COLLEGE MATHEMATICS B

Topics in college algebra including functions and their graphs, composite and inverse functions, applied functions and variation, quadratic functions, exponential functions, logarithmic functions, systems of equations, and applications. **Prerequisite:** MATH1005 (3 credits)

**MATH1040** APPLIED MATHEMATICS FOR BUSINESS

The purpose of this course is to provide students with the basic math skills useful in solving real-life business problems. Linear and quadratic equations will be studied and applied to finance and social sciences. Functions and graphs will be studied and applied to the basic data analysis. Systems of linear equations and linear programming will be applied to maximizing profit. An introduction to probability and statistics and basic financial mathematics are provided. (4 credits) fall

**MATH1065** COLLEGE MATHEMATICS C

Topics in college algebra and trigonometry including the trigonometric functions, inverse trigonometric functions, trigonometric identities, trigonometric equations, and applications. **Prerequisite:** MATH1035 (3 credits)

**MATH1500** PRECALCULUS

Topics include: polynomial and rational functions, exponential and logarithmic functions, trigonometric functions, parametric equations, analytic trigonometry, multivariable systems, and applications and modeling. **Prerequisite:** MATH1000 (4 credits) fall, spring, summer

**MATH1550** FOUNDATIONS OF APPLIED MATHEMATICS

Problems, methods, and recent developments in applied mathematics will be discussed. Topics include, but are not limited to, the following: difference equations, fitting models to data and choosing a best model, probabilistic models, sequential decisions and conditional probability and game theory. Students will gain familiarity with technical word processors such as LaTeX, spreadsheet software and also with high level programming packages such as python, R, and MATLAB. Students will also hear guest speakers describe the role that mathematics plays in their respective careers. (4 credits) fall

**MATH1600** INTRODUCTION TO CALCULUS

The first part of the course reviews algebra and precalculus skills, as they appear in calculus. The second part of the course introduces students to the main concepts of calculus including limits, rates of change, and accumulation. This course does not satisfy any degree requirements. (2 credits)

**MATH1700** CALCULUS I

**MATH1750** ENGINEERING CALCULUS I

Limits, continuity, differentiability, the limit definition of the derivative, differentiation, linearization and some integration of algebraic and transcendental functions, implicit differentiation. Intended for engineering majors or advanced technology students. (4 credits) fall, spring, summer

**MATH1775** INTEGRATED ENGINEERING CALCULUS I

Limits (including L'Hopital's Rule), continuity, differentiability, the limit definition of the derivative, differentiation of algebraic and transcendental functions. Integrates symbolic tools, graphical concepts, data and numerical calculations. Students will model engineering and scientific problems in lecture and lab. (4 credits)

**MATH1776** CALCULUS 1A

This course builds on the understanding of functions and a basic concept of limit as developed in a precalculus course. This course covers the fundamental calculus concepts of instantaneous rate of change and accumulation, with an emphasis on conceptual relationships and on numerical approximations of derivatives and integrals. This is a seven week course. (2 credits) fall, spring

**MATH1777** CALCULUS 1B

This course builds on knowledge of basic derivatives and continues to develop rules for derivatives of combinations, such as the product and chain rules. It also covers applications of derivatives, including related rates and optimization. This is a seven week course. **Prerequisite:** MATH1776 (2 credits) fall, spring

**MATH1800** CALCULUS II

Techniques of integration, the fundamental theorem of calculus, area, L'Hopital's Rule, improper integrals, and applications of definite integrals. **Prerequisite:** MATH1700 (4 credits)

**MATH1850** ENGINEERING CALCULUS II

Define integrals as a limit of Riemann sums, computation of definite and indefinite integrals using the techniques of integration, improper integrals, convergence of sequences and series, and approximating functions and estimating the error using Taylor and Maclaurin series. **Prerequisite:** MATH1750 or MATH1775 (4 credits) fall, spring, summer

**MATH1875** INTEGRATED ENGINEERING CALCULUS II

Define integrals as a limit of Reimann sums, computation of definite and indefinite integrals using the techniques of integration, improper integrals, convergence of sequences and series, including Taylor series. Integrates symbolic tools, graphical concepts, data and numerical calculations. Students will model engineering and scientific problems in lecture and lab. **Prerequisite:** MATH1775 (4 credits)

**MATH1876** CALCULUS 2A

This course builds on a basic knowledge of accumulation and the relationship of Riemann sums to definite integrals. Building on that foundation, the course covers methods of integration including substitution, integration by parts, integration by partial fractions, and the use of tools such as tables or integral calculators. The course also considers geometric applications of integrals of a single variable and the application of integration to solving real world problems. This is a seven week course. **Prerequisite:** MATH1776 or MATH1750 (2 credits) fall, spring

**MATH1877** CALCULUS 2B

This course solidifies the basic calculus competencies from integral and differential calculus while building on the relations between them, including discussion of initial value problems and Taylor series. This is a seven week course. **Prerequisites:** MATH1777 or MATH1750 and MATH1876 (2 credits) fall, spring

**MATH1900** INTRODUCTION TO OPERATIONS RESEARCH

This course serves as an introduction to the field of operations research (OR). The course will cover basic deterministic (non-probabilistic) methods of operations research (linear programming, network flows, and integer programming) and their applications to resource allocation problems in business and networking. **Prerequisite:** MATH1500 or MATH2800 (4 credits) summer

**MATH1950** FINANCIAL MATHEMATICS

This course is designed to prepare students for the Society of Actuaries Exam FM ( Financial Mathematics) This course will develop knowledge of the fundamental concepts of financial mathematics and how these concepts are applied in the time of value of money, loans, bonds and general cash flows and portfolios. General theories of interest such as annuities, yield rates, and amortization will be covered. Bonds and other securities and additional topics in financial analysis such as determining interest rates and interest rate swaps will be covered. **Prerequisites:** MATH1800, MATH1850 or MATH1875 (4 credits)

**MATH2000** CALCULUS III

Three dimensional Cartesian coordinate system, vectors, lines in three dimensions, planes and other surfaces, partial derivatives, directional derivatives, local extrema, polar coordinates, and multiple integrals in Cartesian and polar coordinates. **Prerequisite:** MATH1800 (4 credits)

**MATH2025** MULTIVARIABLE CALCULUS

Three dimensional Cartesian coordinate system, vectors, lines in three dimensions, planes and other surfaces, partial derivatives, directional derivatives, local extrema, polar coordinates, and multiple integrals in Cartesian and polar coordinates, vector fields, line integrals, and Green's Theorem. **Prerequisite:** MATH1850 or MATH1875 (4 credits) fall, spring, summer

**MATH2100** PROBABILITY & STATISTICS FOR ENGINEERS

**MATH2200** ADVANCED STATISTICS

Topics include: design of experiments, correlation and regression, analysis of variance, t-tests, nonparametric methods, failure, mode, and effects analysis. **Prerequisite:** MATH2100 (4 credits) spring

**MATH2250** TIME SERIES

The course will provide a basic instruction to time series. Topics include time series regression and exploratory data analysis, ETS, MA, ARMA/ARIMA models, parameter estimate, model diagnostics, seasonal models and forecasting. **Prerequisite:** MATH2100 (4 credits) fall

**MATH2300** DISCRETE MATHEMATICS

Topics of this course to be chosen from: elementary logic, sets, permutations and combinations, induction, relations, digraphs, functions, trees, Warshall's Algorithm, and Boolean algebra. **Prerequisite:** MATH1500 or MATH1065or MATH1800 or MATH1700 or MATH1750 or MATH1850 (4 credits) fall, spring, summer

**MATH2425** CRYPTOLOGY

This course will introduce the mathematics of historical and modern cryptology. There will be emphasis on both cryptography, the making of codes, and cryptanalysis, the deciphering of coded messages without a key. Topics include, but are not limited to: enumerative combinatorics, probability, statistics, linear algebra, finite groups and number theory. (4 credits) fall. **Prerequisite:** MATH2300

**MATH2500** DIFFERENTIAL EQUATIONS

Introduction to the solution of ordinary differential equations (ODEs). Topics will include solving first and higher order ODEs with constant coefficients, simple matrix equations and systems of ODEs, applications, and Euler’s and Laplace transform solution methods. **Prerequisite:** MATH1850 or MATH1875 (4 credits) fall, spring, summer

**MATH2550** TRANSITION TO ADVANCED MATH

Students will review elementary logic and earn standard proof techniques: direct proof, proof by contradiction, contraposition, cases and induction. Students will write proofs of statements related to sets, relations, functions. Quantifiers, set operations, equivalent forms of mathematical induction, equivalence relations, partitions, graphs of relations, surjections, injections and cardinality will be discussed. **Prerequisite:** MATH2300 (4 credits) spring

**MATH2650** QUANTITATIVE METHODS

Set theory and logic, basic matrix notation and manipulation, linear programming, and simplex method are studied. An introduction to probability and statistics is provided. Applications of these concepts are then applied to management problems with a survey of inventory problems, forecasting, and decision-making. **Prerequisites:** MATH1065 (3 credits)

**MATH2750** DIFFERENTIAL EQUATIONS & SYSTEMS MODELING

**MATH2800** FINITE MATH

Set theory and logic, matrix notation and manipulation, linear programming and simplex method are studied. An introduction to probability and statistics is provided. Problem-solving by computer. **Prerequisite:** MATH1000 (4 credits) spring

**MATH2850** LINEAR AND VECTOR ALGEBRA

This course is an introduction to linear and vector algebra with computer science applications. Topics include: vector and matrix operations, linear transformations, curves and surfaces. **Prerequisite:** MATH1500 Precalculus.

**MATH2860** LINEAR ALGEBRA & MATRIX THEORY

Topics include the basic operations of n-tuples and matrices, geometric vectors, equations of lines and planes, systems of linear equations, row reduction of matrices, linear independence, determinants, and an introduction to basis, dimension, eigenvalues, eigenvectors, and vector spaces. **Prerequisite:** MATH1850 (4 credits) fall, spring

**MATH3100** MEDICAL IMAGING: A MATHEMATICAL APPROACH

This course will provide basic mathematical foundations for medical imaging. There will be emphasis on both theoretical background and numerical methods to implement inversion algorithms. Topics include, but are not limited to: Radon and Fourier transforms, convolution, sampling, filters, and image reconstructions. **Prerequisite:** MATH2025 (4 credits)

**MATH3150** STOCHASTIC PROCESSES

This is an introduction to stochastic processes and their application to a large variety of probabilistic problems. The material will be taught without the need to measure theory. Topics include: Markov chains with both finite and infinite state spaces, random walks, transience and recurrence, branching processes, continuous time Markov chains such as the Poisson process and birth-death processes. We will also discuss martingales and Brownian motion. Other topics may be included as time permits and depending on student interest. Computer visualization will be employed, along with simulation. There is a project component to the course as well, and topics will be chosen according to student interest that relates to specific stochastic processes. **Prerequisite:** MATH2100 (4 credits)

**MATH3200** DIFFERENTIAL GEOMETRY

This course covers basic differential geometry curves and surfaces, with generalization to abstract differentiable manifolds. Topics include arc length, curvature and Frenet frame of space curves, and Gaussian and normal curvature of surfaces. For embedded curves and surfaces as well as for abstract manifolds, geometry is defined in terms of tangent and cotangent spaces, with diffeomorphisms giving rise to mappings between geometries via pullback and pushforward maps. The course includes treatment of the Gauss-Bonnet Theorem and its importance in relating geometric and topological aspects of surfaces. **Prerequisites:** MATH2025 and MATH2860 (4 credits)

**MATH3225** FUNCTIONAL ANALYSIS

This course covers analytic properties of normed linear spaces, in particular functional spaces important to the theory of differential equations and probability. Topics include metric spaces and the notion of completeness; normed and Banach spaces; bounded linear operations; dual spaces; inner product spaces and Hilbert spaces. **Prerequisites:** MATH2500 and MATH2860 (4 credits)

**MATH3250** HAZARD & CATASTROPHE MODELING

This course is designed to introduce student to the development of catastrophe models in the context of determining insurance policy premiums. We will discuss model development, parallel computing used to generate a catalogue of data, parameter estimation for models and statistical analysis to test quality assurance. Students will work in small groups to work on either earthquake, flood or wildfire models, and present their progress and final results throughout the semester in a professional manner. **Prerequisites:** MATH2850 and MATH2500 or MATH2750; and MATH2100 or BMED4600; and MATH2025 (4 credits)

**MATH3500** CALCULUS IV

Topics include the analytic geometry of two- and three-dimensional coordinate systems including polar, cylindrical and spherical coordinates; a review of the fundamental theorem of line integrals and Green's theorem; orientation and parametrization of lines and surfaces; surface integrals; the divergence theorem; Stokes' theorem; the Jacobian; the general substitution rule for integration; constrained optimization and curvature. Other topics may be included as time permits. Computer visualization will be emphasized. **Prerequisite:** MATH2025 (4 credits)

**MATH3700** OPERATIONS RESEARCH

An introduction to operations research, with topics chosen from linear programming (covering formulation of a number of different types of linear models, the simplex algorithm, duality and sensitivity analysis, the transportation and assignment problems, and integer linear programming).Network models, constrained optimization, modeling and simulation, and game theory are also discussed. **Prerequisite:** MATH2860 (4 credits) fall

**MATH3800** SPECIAL TOPICS IN APPLIED MATHEMATICS

Presents topics that are not covered by existing courses and are likely to change from semester to semester. Refer to the Class Schedule for a specific semester for details of offerings for the semester. (1 - 4 credits)

**MATH3900** NUMERICAL ANALYSIS I

Analysis of algorithms frequently used in mathematics, the sciences, engineering and industry. Topics include: root-finding, interpolation, linear systems, numerical differentiation and integration, solution of initial value problems. Numerical experiments will be conducted with C, Matlab, Java, Python or another appropriate high-level language. **Prerequisites:** COMP1000 and MATH1850 (4 credits) fall

**MATH3950** NUMERICAL ANALYSIS II

This course will discuss the theoretical basis of convergence and numerical linear algebra. Topics include: proofs, Cauchy sequences, absolute convergence, orthogonal polynomials, matrix factorization, and error bounds. Numerical experiments will be conducted with C, Matlab, Java, Python or other appropriate high-level language. **Prerequisite:** MATH3900; **Corequisite:** MATH2860 (4 credits) spring

**MATH4050** MACHINE LEARNING

Introduction to the field of machine learning. This course focuses on algorithms to help identify patterns in data and predict or generalize rules from these patterns. Topics include supervised learning (parametric/non-parametric algorithms, kernels, support vector machines), model selection, and applications (such as speech and handwriting recognition, medical imaging, and drug discovery). Students who have basic programming skills and who have taken a course in probability are encouraged to take this course. Cross-list with COMP4050 **Prerequisite:** COMP1000 and MATH2100 (4 credits)

**MATH4100** INDUSTRIAL PROBLEMS IN APPLIED MATHEMATICS

This is an applied problems course in mathematics. Students will work in small teams to solve problems arising in industry under the guidance of the course professor and an industrial liaison. Every term will be different. (4 credits)

**MATH4400** INTRODUCTION TO ABSTRACT ALGEBRA

Topics include groups, subgroups, and factor groups, homomorphisms, rings and fields, and applications that may include symmetry groups, frieze groups, and crystallographic groups and/or introductions to algebraic coding theory. This course is recommended for students intending to go to graduate school for mathematics or a mathematics-related discipline. **Prerequisite:** MATH2300 (4 credits)

**MATH4475** ACTUARIAL MATHEMATICS

This course is designed to prepare students for the Society of Actuaries' exam P/CAS Exam 1. We will develop knowledge of the fundamental probability tools for quantitatively assessing risk with an emphasis on problems encountered in actuarial science. **Prerequisite:** MATH2100 completed with a grade of B or better (4 credits)

**MATH4575** COMPLEX VARIABLES

Topics in this course include complex algebra and functions; analyticity; contour integration, Cauchy's theorem; signatures. Taylor and Laurent series; residues, evaluation on integrals; multivalued functions, potential theory in two dimensions. **Prerequisites:** MATH2025 (4 credits)

**MATH4875** REAL ANALYSIS I

Introduction to real analysis. Topics include introductory proof writing, the real number system, limits, continuity, properties of real-valued functions, differentiation and elementary theory of integration. **Prerequisite:** MATH2025 (4 credits)

**MATH4900** PARTIAL DIFFERENTIAL EQUATIONS

An introductory course in partial differential equations which covers the methods of characteristics, separation of variables, Fourier Series, finite differences, Fourier Transforms and Green's Functions. **Prerequisite:** MATH2500 (4 credits) fall

**MATH4950** DYNAMICAL SYSTEMS AND CHAOS

Introduction to dynamical systems and chaos with emphasis on applications in science and engineering. Topics include one-dimensional flows (fixed points, stability and bifurcations), two-dimensional flows (phase planes, limit cycles, and bifurcations), and chaos (lorenz equations, maps, fractals and strange attractors). This course counts as a technical elective for applied mathematics majors and minors. **Prerequisite:** MATH2500 (4 credits)

**MATH4975** REAL ANALYSIS II

Continued introduction to real analysis. Topics include sequences, series, Fourier series, functions defined by integrals, improper integrals, Riemann-Stieltjes integrals, functions of bounded variation, fixed-point theorems, implicit function theorems, Lagrange multipliers, functions on metric spaces, approximation, Green's Theorem and Stokes' Theorem for real vector fields. **Prerequisite:** MATH4875 (4 credits)

**MATH5000** APPLIED MATHEMATICS FINAL YEAR DESIGN I

Student will work alone and in small group projects to study, analyze, design, and sometimes build and test concepts in an applied mathematics subfield of their choosing. The study will be performed under the direction of one or more faculty advisors. Projects from industry be encouraged to increase the interaction and cooperation with firms. Course requirements include regular oral and written progress reports throughout the semester. The final technical report by students may include a plan for the following Applied Mathematics Final Year Design II course. **Prerequisite:** Final year standing in BSAM program (4 credits) fall

**MATH5200** METHODS OF CALCULUS

This course is a gateway course into the MSACS program. Topics include limits, integrals, derivatives, numerical derivatives, numerical integrals, Sequences, Series, Taylor series, Newton’s method, Lagrange polynomials, Hermite polynomials, steepest ascent/descent, vectors, matrices, eigenvalues, and eigenvectors. (4 credits) fall

**MATH5500** APPLIED MATHEMATICS FINAL YEAR DESIGN II

This course is a continuation of Applied Math Final Year Design I. Students will continue with their design and analysis (or with new designs and analysis) with emphasis on improvements and applications. Other faculty and local industry professionals will review the student work and make recommendations. (4 credits) summer

**MATH5700** MATHEMATICS FOR MACHINE LEARNING

This course prepares students with additional mathematics needed to succeed in a variety of computational disciplines. Topics include linear algebra, matrix decompositions, multivariable calculus, and optimization. (3 credits) fall

**MATH5750** APPLIED STATISTICS

This course introduces students to the tools used for statistical and probabilistic analysis. The focus is on the basics of probability, regressions models, hypothesis testing, and understanding the use and interpretation of output data with attention to applications in artificial intelligence. **Prerequisites:** MATH5200 (4 credits) spring

**MATH5800** MATHEMATICAL METHODS

This course provides the necessary analytical and numerical background for graduate students in engineering and sciences. Topics include error-bound, truncation method, least square regression for linear and polynomial models, linear algebra and matrix theory, ordinary differential equations (ODE), partial differential equations (PDE), Fourier transform, and discrete Fourier Transform. The expected background of students is knowledge of ordinary differential equations. (3 credits)

**MATH7800** GRADUATE SPECIAL TOPICS IN APPLIED MATHEMATICS

Presents topics that are not covered by existing courses and are likely to change from semester to semester. Refer to the Class Schedule for a specific semester for details of special topics course offerings. (4 credits)