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# 2017-2018 Academic Catalog: Course Descriptions - Mathematics

**MATH 0900 BASIC ALGEBRA**

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

**MATH 1000 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*

**MATH 1005 COLLEGE MATH 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)

**MATH 1020 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*

**MATH 1030 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*

**MATH 1035 COLLEGE MATH 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. *(3 credits)***Prerequisite:** MATH1005

**MATH 1065 COLLEGE MATH C**

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

**MATH 1500 PRECALCULUS**

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

**MATH 1550 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*

**MATH 1700 CALCULUS I**

Topics include: introduction to limits, definition of the derivative, differentiation of algebraic and transcendental functions, implicit differentiation, applications of the derivative and introduction to integration. *(4 credits) ***Prerequisite:** MATH1065 or MATH1500.

**MATH 1750 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*

**MATH 1775 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)*

**MATH 1800 CALCULUS II**

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

**MATH 1850 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. *(4 credits) fall, spring, summer***Prerequisite:** MATH1750 or MATH1775

**MATH 1875 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. *(4 credits)***Prerequisite:** MATH1775

**MATH 1900 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. *(4 credits) summer***Prerequisite:** MATH1500 or MATH2800

**MATH 2000 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. *(4 credits) ***Prerequisite:** MATH1800

**MATH 2025 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. *(4 credits) fall, spring, summer***Prerequisite:** MATH1850 or MATH1875

**MATH 2100 PROBABILITY & STATISTICS FOR ENGINEERS**

Topics studied are basic probability and a variety of probability distributions used in engineering modeling and reliability (expected life of products); linear regression and correlation; and hypothesis testing. *(4 credits) **fall, spring, summer***Prerequisite:** MATH1800 or MATH1850 or MATH1875

**MATH 2200 ADVANCED STATISTICS**

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

**MATH 2300 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. *(4 credits) fall, spring, summer***Prerequisite:** MATH1500 or MATH1065

**MATH 2500 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. *(4 credits) **fall, spring, summer***Prerequisite:** MATH1850 or MATH1875

**MATH 2550 TRANSITION TO ADVANCED MATHEMATICS**

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. (*4 credits) spring***Prerequisite**: MATH2300

**MATH 2650 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. *(3 credits)***Prerequisites:** MATH1065

**MATH 2750 DIFFERENTIAL EQUATIONS & SYSTEMS MODELING**

Linear systems, matrix algebra, eigenvalues and eigenvectors, solutions of first and second order ordinary differential equations, stability and equilibrium solutions, Laplace transforms, state space models and simulation. *(4 credits) fall***Prerequisite:** MATH1800 or MATH1850 or MATH1875

**MATH 2800 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. *(4 credits) spring***Prerequisite:** MATH1000

**MATH 2860 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. *(4 credits) fall, spring***Prerequisite:** MATH1850

**MATH 2990 INDEPENDENT STUDY IN APPLIED MATHEMATICS**

This course investigates a topic of special interest to faculty and students that is outside existing course offerings. *(1 – 4 credits) ***Prerequisite:** Consent of department head and instructor.

**MATH 3150 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. *(4 credits)***Prerequisite:** MATH2100

**MATH 3200 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. *(4 credits)***Prerequisites:** MATH2025 and MATH2860.

**MATH 3225 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. *(4 credits) fall***Prerequisite: **MATH2500 and MATH2860

**MATH 3250 HAZARD & CATASTROPHE MODELING**

This course is designed to introduce students 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 catalog 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. (*4 credits)***Prerequisite: ** MATH2850 and MATH2500 or MATH2750; and MATH2100 or BMED4600 or COMP3673; and MATH2025

**MATH 3500 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. *(4 credits)***Prerequisite:** MATH2025

**MATH 3700 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. *(4 credits) fall***Prerequisite:** MATH2860

**MATH 3800 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)*

**MATH 3900 NUMERICAL ANALYSIS I**

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

**MATH 3950 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. (*4 credits) spring***Prerequisite**: MATH3900; **Corequisite**: MATH2860

**MATH 4050 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 *(4 credits)***Prerequisite:** COMP1000 or COMP1099 and MATH2100

**MATH 4100 INDUSTRIAL PROBLEMS IN APPLIED MATH**

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) *

**MATH 4150 MATHEMATICAL METHODS IN SCIENCE & ENGINEERING**

Students study various mathematical concepts and their application to physical systems. Topics include vector calculus, tensor calculus, applications of transformations, vector spaces, Hilbert spaces and group theory. *(4 credits) ***Prerequisite:** MATH1800 or MATH1850 or MATH1875**Corequisite****:** MATH2025

**MATH 4400 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. *(4 credits)***Prerequisite****:** MATH2300

**MATH 4475 ACTUARIAL MATH**

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. *(4 credits)***Prerequisite:** MATH2100 completed with a grade of B or better

**MATH 4575 COMPLEX VARIABLES**

Complex algebra and functions; analyticity; contour integration, Cauchy's theorem; singularities, power series; residues, evaluation of integrals; multivalued functions, potential theory in two dimensions, conformal mapping. *(4 credits) ***Prerequisites:** MATH2025 and MATH2500

**MATH 4675 TOPOLOGY**

This course covers some basic notions of point-set topology, such as topological spaces, connectedness and compactness, Heine-Borel Theorem, quotient spaces, topological groups, groups acting on spaces, homotopy equivalences, separation axioms, Euler characteristic and classification of surfaces. *(4 credits) ***Prerequisite:** MATH1850 or MATH1875

**MATH 4875 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. *(4 credits) ***Prerequisite:** MATH2025

**MATH 4900 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. *(4 credits) fall***Prerequisite:** MATH2500

**MATH 4950 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. *(4 credits) ***Prerequisite:** MATH2400 or MATH2500

**MATH 4975 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. *(4 credits) ***Prerequisite:** MATH4875

**MATH 5000 APPLIED MATH 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. *(4 credits) fall***Prerequisite:** Final year standing in BSAM program.

**MATH 5500 APPLIED MATH 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*