**MAT 090 Preparation for College Mathematics (0)**

A mathematics skills course designed for the student who needs to develop basic arithmetic, geometry and pre-algebra skills. Only S/U grades are assigned for this course.

**MAT 110 College Algebra (4)**

Techniques of algebra manipulation needed for success in the Calculus courses will be introduced and developed. Topics will include: sets, polynomials, factoring, rational expressions, exponents, radicals, coordinate geometry, inequalities, simultaneous equations, quadratic equations, and partial fractions. Applications with word problems will be included.

**MAT 111 College Mathematics (4)**

The course provides a basic background in critical thinking and problem solving through the language and methods of mathematics. Topics include a review and extension of algebra, geometry, quantitative reasoning and data analysis. An emphasis is placed upon logic and reasoning in a mathematical context. Students who have previously completed MAT 112 or higher may not enroll in this course for degree credit. Prerequisite: High school algebra and geometry. A terminal college course in mathematics for students who will not take other mathematics courses (such as Precalculus, Elements of Calculus, etc.). Meets 2023 General Education Mathematics (and Quantitative Reasoning).

**MAT 112 Elements of Calculus (4)**

This is a terminal introductory course in calculus suitable for business, computer science, and telecommunications majors. Topics in both the differential and the integral calculus are covered. These include: functions and graphs, the derivative, differentiation rules, optimization problems, rates of change, exponential and logarithmic functions, the antiderivative, the definite integral, and integration by substitution and by parts. Applications will be drawn from diverse areas such as business, economics, and the life sciences. Students who have previously completed MAT 121 or higher may not enroll in this course for degree credit. Prerequisite: MAT 110 College Algebra or equivalent. Meets 2023 General Education Mathematics (and Quantitative Reasoning).

**MAT 115 Finite Mathematics (4)**

A rigorous introduction to discrete mathematics as it is used in computer science. Topics include functions, relations, sets, propositional and predicate logic, simple circuit logic, proof techniques, elementary combinatorics, and discrete probability. Meets 2023 General Education Mathematics (and Quantitative Reasoning). Prerequisite: CS 108.

**MAT 120 Precalculus (4)**

Introduces the student to some of the fundamental concepts needed to be able to study calculus. Topics include: algebra review, functions, graphing, exponential, logarithmic, and circular functions, trigonometry, complex numbers, and vectors. Students who have previously completed MAT 121 or higher may not enroll in this course for degree credit. Prerequisite: MAT 110 or equivalent. Meets 2023 General Education Mathematics (and Quantitative Reasoning).

**MAT 121 Calculus for Engineering Technology I (4)**

Introduces the student to the differential calculus. Topics include: analytic geometry in a plane, functions, limits, the derivative and differentiation rules, partial derivatives, related rates, extrema, curve sketching, mean value theorem, linear approximations and parametric equations. Prerequisite: MAT 120 or equivalent. Meets 2023 General Education Mathematics (and Quantitative Reasoning).

**MAT 122 Calculus for Engineering Technology II (4)**

Introduces the student to the integral calculus. Topics include: the indefinite and definite integrals, areas, volumes, work, the exponential, logarithmic, inverse trigonometric, and hyperbolic functions, integration techniques, improper integrals, L’Hopital’s rule, Taylor polynomials and polar co‑ordinates. Prerequisite: MAT 121 or equivalent.

**MAT 151 Calculus I (4)**

More advanced than MAT 121, this course is required for mathematics and engineering majors, and is recommended for mathematics minors. Covers the concept of the derivative and begins the study of integration. Topics include: functions, limits, continuity, the derivative, differentiation rules, mean value theorem, related rates, extrema, curve sketching, Newton’s method, linear approximations, definite and indefinite integrals, the fundamental theorem of calculus and parametric equations. Meets 2023 General Education Mathematics (and Quantitative Reasoning). Prerequisite: MAT 120 or equivalent with a grade C or better, or permission of instructor. MAT 121 and MAT 151 cannot both be taken for credit.

**MAT 152 Calculus II (4)**

More advanced than MAT 122, this course is required for mathematics and engineering majors, and is recommended for mathematics minors. Continues the study of integration and also includes infinite series. Topics include: integration techniques, transcendental functions, applications of integration, conic sections, L’Hopital’s rule, improper integrals, sequences and series, and polar co-ordinates Prerequisite: MAT 151 with a grade C or better or equivalent or MAT 121 with permission of instructor. MAT 152 and MAT 122 cannot both be taken for credit.

**MAT 225 Applied Statistical Analysis (4) (Cross Listed with STA 225)**

Deals in depth with statistical methods used to analyze data. Applications are drawn from many diverse areas. Topics include: measures of location and scale for frequency distributions, addition and multiplication laws for probability, the binomial, Poisson, and normal distributions, inferences about proportions and location parameters in one‑sample and two‑sample problems, analysis of completely randomized and randomized blocks designs, simple linear regression and correlation, sign test, median test, rank sum test, and signed rank test. Prerequisites: MAT 112, MAT 122 or MAT 152.

**MAT 230 Differential Equations (4)**

An introduction to the theory of ordinary differential equations and matrices. The emphasis is on the development of methods important in engineering and the physical sciences. Topics include: theory and applications of first order and second order differential equations, Laplace transform method, matrix algebra, determinants, Cramer’s rule, eigenvalues, and systems of linear differential equations. Applied Mathematics majors must take MAT 260 and can’t receive credit for this course. Prerequisite: MAT 122 or equivalent.

**MAT 253 Calculus III (4)**

Many properties of systems studied in applied science are functions of several variables or vector valued functions. This course develops the calculus of such functions. Topics include: vectors and vector valued functions, analytic geometry in space, functions of several variables, partial differentiation, the gradient, maxima and minima, Lagrange multipliers, and multiple integrals, line and surface integrals, Stokes and Divergence theorems. Prerequisite: MAT 122 or equivalent.

**MAT 260 Ordinary Differential Equations and Series Solutions (4)**

The course will allow students to become familiar with the subject of differential equations. It covers methods of solutions such as: separation of variables, integrating factor, reduction of order. Differential equations with constant and variable (Cauchy-Euler) coefficients are treated as well as series solutions of differential equations are introduced (method of Frobenius, Bessel and Legendre equations). Laplace transform and system of Linear first order equations are covered. Examples of applications of differential equations in physics, engineering are given. Prerequisite: MAT 152 with a grade C or better, or permission of instructor.

**MAT 280 Linear Algebra (3)**

Many systems studied in science, engineering, and computer science involve a linear relationship among many variables. Linear algebra is the mathematical description of such problems. Topics include: systems of linear equations, Gaussian elimination, matrices, determinants, Cramer’s rule, vector spaces, linear transformations, eigenvalues and eigenvectors. Prerequisite: MAT 121 or MAT 151 or permission of instructor.

**MAT 290 Topics in Mathematics (1-4)**

An introductory course in selected topics in Mathematics not currently covered in any of the listed classes. Topics are chosen to illustrate different fields and applications which are all part of mathematics.

**MAT 335 Mathematical Modeling (4)**

Designed to teach the student some of the skills necessary to construct and critique mathematical models of physical and industrial processes. The student will apply skills acquired in MAT 230 to the models presented. Topics include: applications of first and second order ordinary differential equations, systems of nonlinear ordinary differential equations, stability, phase plane analysis, optimization, conservation laws and finite differences. Prerequisite: MAT 230 and familiarity with a computer language, or permission of instructor.

**MAT 345 Introduction to Graph Theory (4)**

Provides students with an introduction to graphs and their properties. Topics include graphs and digraphs, eulerian and hamiltonian graphs, connectivity, planarity, shortest path problems, trees, and coloring. Attention will be paid to theorems and their proofs. Applications will be given throughout the course. Prerequisite: MAT 122 or MAT 413.

**MAT 370 Applied Probability (4)**

An introduction to the theory of probability and its applications. Topics include: basic set theory, elementary probability, counting arguments, conditional probability and independence, random variables and their properties, functions of random variables, distribution functions, probability models and applications such as stochastic processes. Prerequisite: MAT 122.

**MAT 380 Abstract Mathematics: An Introduction (4)**

An introduction to rigorous mathematics. Students will be exposed to the building blocks of mathematical theory – axioms, definitions, theorems, and proofs. The emphasis will be on constructing proofs and writing clear mathematics. The language and methods of mathematics will be explored while introducing students to the basics of set theory, number theory, topology on the real line, and functions. Prerequisite: MAT 122.

**MAT 381 Modern Algebra (4)**

An introductory course in Abstract/Modern Algebra. Topics will include elementary theory of groups, rings and fields: Groups, Subgroups, Quotient Groups, Symmetry, Rings, Fields, and Extension Fields. We will explore connections between Modern Algebra, Number Theory and Linear Algebra. SUNY Polytechnic Institute mathematics course at 200 level or higher excluding MAT 225 or, permission of the instructor.

**MAT 401 Series and Boundary Value Problems (4)**

Introduces advanced mathematical methods used to solve certain problems in engineering and the physical sciences. Topics include: sequences and series, Fourier series and transforms, series solutions of ordinary differential equations, partial differential equations, and solution of some boundary value problems. Prerequisite: MAT 230 or equivalent.

**MAT 405 Financial Mathematics I (3)**

Mathematical foundation and a practical understanding of interest theory in finite and continuous time will be developed. Topics include measuring of interest rates, valuation of annuities, loans, amortization schedules. Interest rate swaps, forward rate agreements and options are introduced. Prerequisites: MAT 370 and FIN 302.

**MAT 406 Financial Mathematics II (3)**

An overview of the derivatives and their uses in difference financial situations. Equity, fixed income and foreign exchange derivative products, including forwards, futures, options and swaps are considered. Valuation of options using binomial and Black-Scholes models will be described. Prerequisites: MAT 405 Financial Mathematics I.

**MAT 413 Discrete Mathematics for Computer Science (4)**

Background to understanding computer science as the science of clear and concise descriptions of computable, discrete sets. Provides conceptual tools useful for any advanced study in computer science. Topics include: review of set theory, logic and relational calculus, algebraic structures (lattices, Boolean algebra, semi‑groups, groups, rings, etc.) and morphisms and their application in computer science (automata theory, coding, switching theory, etc.), formal languages and their acceptors, and elements of information theory and of the theory of computability. Prerequisite: CS 108.

**MAT 420 Complex Variables and their Applications (4)**

An introductory study of functions involving complex numbers. Subjects are selected based upon their importance in physical and engineering applications. Included are complex numbers, complex functions, analytic functions, complex integration, infinite series, residue theorem, contour integration, conformal mapping and application of harmonic functions. Prerequisite: MAT 122 or equivalent.

**MAT 423 Vector and Tensor Calculus (4)**

Vector and tensor calculus is a fundamental area of mathematics, and is used extensively in science, engineering, and technology. The methods developed in this course include: the gradient, curl, and divergence, the del operator in general curvilinear coordinates, covariant differentiation, line integrals, surface integrals, Gauss’s theorem, Stoke’s theorem, Green’s theorem, and the divergence theorem. Selected applications will be included from fluid and continuum mechanics, and from electromagnetism. Prerequisite: MAT 253 or equivalent.

**MAT 425 Real Analysis (4)**

Introduces the student to a rigorous development of the real number system and the theory of Calculus on the real number line. Topics include: basic set theory, the real number system, sequences and series, limits and continuity, the derivative, the Riemann Integral, the Fundamental Theorem of Calculus, and sequences and series of functions. Prerequisite: MAT 381.

**MAT 430 Number Theory and Its Applications (4)**

Introductory course in Number Theory that will introduce students to the basic concepts as well as some modern applications. Topics include: prime numbers, Greatest Common Divisors, The Euclidean Algorithm, congruences, Fermat’s Little Theorem, primality testing, etc. Applications of Number Theory: cryptography, pseudorandom numbers, etc. Prerequisite: MAT 380 or MAT 381 or MAT 413 or permission of the instructor. Cross listed with 530.

**MAT 450 Partial Differential Equations (4)**

A study of Partial Differential Equations, or Pde’s, and their applications in science and engineering. The basic development of physical models leading to partial differential equations is discussed. Solution methods and basic theory are presented. Topics include: first order Pde’s, method of characteristics, the canonical second order Pde’s, separation of variables, Hilbert space methods, finite difference methods. Prerequisites: MAT 260 and MAT 253.

**MAT 453 Differential Geometry (4)**

Provides a detailed introduction to mathematical principles and computational techniques of vector calculus to study geometric shapes of curves and surfaces in three-dimensional Euclidean space. Emphasizes modern approaches to differential geometry, including differential forms, moving frames, and techniques of Riemannian geometry. Topics include: curvature and torsion of a smooth curve in three-dimensional Euclidean space; Fundamental theorem of curve theory; The first and second forms of a surface and Fundamental theorem of surface theory; Exterior differential form formulation and Cartan’s moving frame approach to surface theory; Definition and coordinate atlas of a differentiable manifold and integration on a differential manifold. Prerequisite: MAT 253.

**MAT 460 Numerical Differential Equations (4)**

Fundamental mathematical methods associated with the numerical solution of ordinary and partial differential equations are investigated. Algorithms emphasizing both standard and newly developed methodologies are developed in the context of theoretical and practical considerations. Mathematical questions such as convergence, accuracy, and appropriateness of method are developed in a systematic manner. A variety of mathematical models and problems of current interest are used to emphasize many of the core results. Students will learn to develop their own algorithms and to use algorithms from existing high quality numerical libraries. Many of the models studied in this course will come from both standard mathematical models and topics related to current faculty research interests. Topics include: Runge-Kutta methods, finite difference techniques, finite element techniques, approximation methods, error estimation, and accuracy. Prerequisites: MAT 253, MAT 260 and familiarity with a programming language.

**MAT 471 Time Series Analysis and its Applications (3)**

An introduction to the theory and applications of time series analysis and modeling. The students will acquire a working knowledge of stochastic processes, time series and forecasting methods as applied in economics, finance, engineering and the natural and social sciences. Topics covered include stationary stochastic processes, AR, MA, ARMA, ARIMA, SARIMA, ARCH and GARCH processes. A computational environment for simulation and data analysis is integrated throughout the course. Prerequisite: MAT 370 with a grade of C or better.

**MAT 480 Advanced Linear Algebra (3)**

This second course in linear algebra is a mixture of theory and applications. It is a mathematically rigorous course with some proofs, designed for Math majors and will also be useful for Computer Science, Physics, and Engineering majors. We will understand geometrically and verify algebraically finite-dimensional vector spaces over the real and complex numbers and linear operations which act on them. Topics include the definition of a vector space, obtaining new vector spaces from old ones, linear maps and duality, eigenvalues and invariant subspaces, inner product spaces and orthogonality, the spectral theorem for normal, Hermitian and unitary transformations, polar and singular decomposition, complex vector spaces and canonical forms. Applications from sciences and engineering, focusing on linear models and linear estimation will be covered.

**MAT 482 Symmetry Methods for Differential Equations- an Introduction (3)**

The objective of the course is to expand techniques for finding solutions of differential equations. One of those techniques is the introduction and use of Lie symmetries. We will introduce the concept of groups and Lie algebras, introduce the concept of symmetry of differential equation. Method for computing point symmetries will be presented. How to find invariants and perform symmetry reduction of ODEs will be discussed. Additional topics may include symmetries of Partial Differential Equations, symmetries of systems of ODEs, conditional and hidden symmetries. Maple software will be used. Prerequisites: MAT 253 with a grade of C or better or MAT 260 with a grade of C or better.

**MAT 490 Selected Topics in Mathematics (Variable 1-4)**

An in-depth treatment of a selected topic not normally treated extensively in other mathematics courses. Prerequisite: Permission of instructor.

**MAT 491 Independent Study (Variable 1‑4)**

Extensive study and research on a particular topic of student interest under the supervision of a faculty member. The student is required to submit a written proposal which includes a description of the project, its duration, educational goals, method of evaluation, and number of credits to be earned. Prerequisites: Matriculated students only, permission of instructor and dean of subject area.

**MAT 492 Applied Mathematics Internship (4)**

The internship is available to qualified Applied Mathematics majors. It is designed to provide students with an opportunity to integrate academic and practical experience in an industrial setting in a field related to mathematics. Before the internship is approved, the student, the employer, and a Mathematics faculty member develop a contract concerning the nature of the internship. Weekly reports and a final presentation are required for the internship. Prerequisites: 3.0 or better GPA in major and approval of Applied Mathematics faculty.