# Mathematics

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Name | Title | Credits | School |
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MATH 096 | Developmental Mathematics I | 4 | College of Arts & Sciences |

This course is for students who have not acquired the techniques of algebra. It can also serve as a refresher course and must be followed by MATH 100, as a prerequisite for MATH 120, 125, 140, or TMAT 135. Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 5-0-4 |
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MATH 101 | Developmental Mathematics I/II | 4 | College of Arts & Sciences |

Designed for the accelerated student who has had some skills in algebra and is more motivated to finish at a faster pace. Topics covered include basic operations of signed integers and fractions, factoring, basic operations of algebraic fractions, exponents and radicals, functions and graphs, and equations. This course or its equivalent is a prerequisite for MATH 120, 125, 140, or TMAT 135. Prerequisite Course(s): Prerequisite: Math Placement ExamClassroom Hours - Laboratory and/or Studio Hours – Course Credits: 5-0-4 |
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MATH 115 | Introductory Concepts of Mathematics | 3 | College of Arts & Sciences |

A course on selected topics in mathematics for students of the humanities, especially in communication arts. Topics include: graphs, matrices, elements of linear programming, finite probabilities, introduction to statistics. Applications to real-life situations are emphasized. The place of these topics in the history of mathematics is outlined. Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 3-0-3 |
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MATH 125 | Finite Mathematics | 3 | College of Arts & Sciences |

Review of elementary algebra and selected topics in statistics and probability. Sets, real numbers, graphing, linear and quadratic equations and inequalities, relations and functions, solving systems of linear equations, descriptive statistics, frequency distributions, graphical displays of data, measures of central tendency and dispersion, introduction to probability. Prerequisite Course(s): Prerequisite: MATH 101 or Math Placement Exam.Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 3-0-3 |
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MATH 135 | Fundamentals of Precalculus I | 4 | College of Arts & Sciences |

The first course in a two semester precalculus sequence. Review of algebra: exponents, factoring, fractions. Linear equations, ratio, proportions. Word problem application. Coordinate systems and graphs of functions: straight line, slope. Systems of linear equations and their applications. Complex numbers. Quadratic equations. Introduction to trigonometry. Classroom Hours- Laboratory and/or Studio Hours- Course Credits: 5-0-4 Prerequisite Course(s): Prerequisite: MATH 101 or Math Placement Exam.Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 5-0-4 |
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MATH 136 | Fundamentals of Precalculus II | 4 | College of Arts & Sciences |

The second course in a two semester precalculus sequence. Topics include trigonometric functions, identities and equations, the sine and cosine Jaws, graphs of the trigonometric functions; functions of a composite angle; DeMoivre's theorem; logarithms; binomial theorem; and Cramer's rule. Note: Successful completion of both MATH 135 (Fundamentals of Precalculus I) and MATH 136 (Fundamentals of Precalculus II) is equivalent to completion of MATH 141 (Precalculus). Classroom Hours- Laboratory and/or Studio Hours- Course Credits: 5-0-4 Prerequisite Course(s): Prerequisite: MATH 135 or MATH 161 or MATH 170.Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 5-0-4 |
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MATH 141 | Precalculus | 4 | College of Arts & Sciences |

A study of relations and functions; inequalities; complex numbers; quadratic equations; linear systems of equations; higher degree equations; trigonometric functions; identities; functions of composite angles; graphs of the trigonometric functions; exponential and logarithmic functions; and binomial theorem. Note: A graphing calculator is used throughout the course. Prerequisite Course(s): Prerequisite: MATH 101 or Math Placement Exam.Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 5-0-4 |
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MATH 151 | Fundamentals of Calculus | 3 | College of Arts & Sciences |

This course provides a comprehensive introduction to calculus and its applications in business and the applied sciences. Topics covered include functions, limits, continuity, derivatives, tangent lines, extrema, concavity, curve sketching, optimization, exponential and logarithmic functions, antiderivatives, definite integrals, and applications such as marginal analysis, business models, optimization of tax revenue, minimization of storage costs, finding areas, and concepts of probability extended to discrete and continuous sample spaces. Prerequisite Course(s): Prerequisite: MATH 125 or higher or Math Placement Exam.Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 3-0-3 |
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MATH 161 | Basic Applied Calculus | 3 | College of Arts & Sciences |

This course provides a comprehensive introduction to calculus and its applications in business and the applied sciences. Topics covered include functions, limits, continuity, derivatives, tangent lines, extrema, concavity, curve sketching, optimization, exponential and logarithmic functions, antiderivatives, definite integrals, and applications such as marginal analysis, business models, optimization of tax revenue, minimization of storage costs, finding areas, and concepts of probability extended to discrete and continuous sample spaces. Prerequisite Course(s): Prerequisite: MATH 136 or higher or Math Placement Exam.Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 3-0-3 |
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MATH 170 | Calculus I | 4 | College of Arts & Sciences |

Study of lines and circles. Functions, limits, derivatives of algebraic functions, introduction to derivatives of trigonometric functions. Application of derivatives to physics problems, related rates, maximum-minimum word problems and curve sketching. Introduction to indefinite integrals. The conic sections. Prerequisite Course(s): Prerequisite: MATH 141 or Math Placement Exam.Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 5-0-4 |
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MATH 180 | Calculus II | 4 | College of Arts & Sciences |

Riemann sums, the definite integral, the fundamental theorem of the calculus. Area, volumes of solids of revolution, arc length, work. Exponential and logarithmic functions. Inverse trigonometric functions. Formal integration techniques. L'Hopital's rule, improper integrals. Polar coordinates. Prerequisite Course(s): Prerequisite: MATH 170. Students in BS Electrical and Computer Engineering and BS Mechanical Engineering must earn a grade of C or better in MATH 170.Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 5-0-4 |
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MATH 200 | Scientific Presentation Skills | 1 | College of Arts & Sciences |

In this course, students will develop their scientific presentation skills. They will learn principles and best practices for clear, engaging science talks, and will put these into practice by giving presentations about scientific topics, including scientific work they have participated in. They will also workshop their own and other students' talks in a close-knit, collaborative atmosphere. The coursework will culminate in a presentation at SOURCE, open to the whole New York Tech community. Research experience in a technical or scientific field is a prerequisite for the course and will need to be confirmed by the student's research mentor. (Instructor permission required.) Prerequisite Course(s): Prerequisites: FCSP 105 or SPCH 105, scientific research experience to be confirmed by student's research mentorClassroom Hours - Laboratory and/or Studio Hours – Course Credits: 1-0-1Inst Cnst |
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MATH 220 | Probability Theory | 3 | College of Arts & Sciences |

An introduction to probability theory and its applications with emphasis on stochastic processes such as random walk phenomena and waiting time distributions. Computer graphics simulations will be used. Students use mathematical modeling/multiple representations to provide a means of presenting, interpreting communication, and connecting mathematical information and relationships. Topics include sets; events; sample spaces; mathematical models of random phenomena; basic probability laws; conditional probability; independent events; Bernoulli trials; binomial, hypergeometric, Poisson, normal and exponential distributions; random walk and Markov chains. Prerequisite Course(s): Prerequisite: MATH 180Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 3-0-3 |
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MATH 235 | Applied Statistics | 3 | College of Arts & Sciences |

An introduction to modern inferential statistics with appropriate applications to telecommunications and related fields. Major topics covered are descriptive statistics, introduction to probability, binomial distribution, normal distribution, sampling and the Central Limit Theorem, estimation, hypothesis testing, regression and correlation, chi-square analysis and analysis of variance. The primary focus in this course will be on application of these statistical ideas and methods. Students will be required to conduct individual statistical projects involving the collection, organization and analysis of data. Prerequisite Course(s): Prerequisite: MATH 150 or MATH 151 or MATH 170Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 3-0-3 |
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MATH 260 | Calculus III | 4 | College of Arts & Sciences |

Sequences and series, Taylor series. Vector analysis and analytic geometry in three dimensions. Functions of several variables, partial derivatives, total differential, the chain rule, directional derivatives and gradients. Multiple integrals and applications. Prerequisite Course(s): Prerequisite: MATH 180Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 4-0-4 |
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MATH 310 | Linear Algebra | 3 | College of Arts & Sciences |

Matrices and systems of linear equations, vector spaces, change of base matrices, linear transformations, determinants, eigen-values and eigen-vectors, canonical forms. Prerequisite Course(s): Prerequisite: MATH 180Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 3-0-3 |
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MATH 320 | Differential Equations | 3 | College of Arts & Sciences |

Solving first order ordinary differential equations: exact, separable, and linear. Application to rates and mechanics. Theory of higher order linear differential equations. Method of undetermined coefficients and variation of parameters. Application to vibrating mass and electric circuits. Power series solutions: ordinary and singular points, the method of Frobenius. Partial differential equations: the method of separation of variables. Prerequisite Course(s): Prerequisite: MATH 260Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 3-0-3 |
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MATH 330 | Computational Analysis | 4 | College of Arts & Sciences |

This course consists of a calculus-based introduction to the use of mathematical software in applied problems in science and engineering. Matlab: basic syntax and development environment; debugging; help interface; basic math objects; visualization and graphical output; vectorization; scripts and functions; file i/o; arrays, structures, and strings; Mathematica: basic syntax and the notebook interface, visualization, symbolic operations such as differentiation, integration, partial fractions, series expansions, solution of algebraic equations. Mathematica programming (rule-based, functional, and procedural) and debugging, plotting, and visualization. The course will emphasize good programming habits, choosing the appropriate language/software for a given scientific task and the use of numerical and symbolic math software to enhance learning and perform tests. Each of the concepts and programming tools covered should be illustrated through the application and integration of calculus tools to scientific problems. This will be reinforced via individual lab work during class as well as teamwork in homework and class projects. Prerequisite Course(s): Prerequisite: MATH 260Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 3-2-4 |
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MATH 350 | Advanced Calculus | 3 | College of Arts & Sciences |

Topics include: Vector functions of several variables, the Jacobian matrix, the generalized chain rule, inverse function theorem, curvilinear coordinates, the Laplacian in cylindrical and spherical co-ordinates, Lagrange multipliers, line integrals, vector differential and integral calculus including Green's, Stokes's and Gauss's theorem. The change of variable in multiple integrals, Leibnitz's rule, sequences and uniform convergence of series. Prerequisite Course(s): Prerequisite: MATH 260Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 3-0-3 |
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MATH 360 | Functions of a Complex Variable | 3 | College of Arts & Sciences |

The general theory of functions of a complex variable, analytic functions, the Cauchy-Riemann equations, the Cauchy integral theorem and formula, Taylor series, Laurent series, singularities and residues, conformal mappings with applications to problems in applied science. Prerequisite Course(s): Prerequisite: MATH 260Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 3-0-3 |
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MATH 370 | Real Analysis | 3 | College of Arts & Sciences |

This course focuses on rigorous treatment of the foundations of real analysis in one variable. Topics include: properties of the real number system, sequences, continuous functions, topology of the real line, compactness, derivatives, the Riemann integral, sequences of functions, uniform convergence, infinite series and Fourier series. Additional topics may include: Lebesgue measure and integral on the real line, metric spaces, and analysis on metric spaces. Prerequisite Course(s): Prerequisite: MATH 260Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 3-0-3 |
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MATH 410 | Numerical Linear Algebra | 3 | College of Arts & Sciences |

This course focuses on computational algebra methods and their applications, using basic programming with Matlab or Python. Topics should include: Direct methods (gauss elimination), Iterative methods (CG and GMRES), QR/ Gram Schmidt, Eigen decomposition, SYD and applications (matrix norms, condition number, low rank approximation, principal component analysis, linear regression). Extra time can be used for applications and projects, or discussion of sparse and structured matrix methods. Prerequisite Course(s): Prerequisites: MATH 310Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 3-0-3 |
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MATH 430 | Mathematics of X-ray Imaging | 3 | College of Arts & Sciences |

ln this course we introduce the mathematical techniques used to model measurements and reconstruct images. As a simple representative case we study transmission X-ray tomography (CT).I n this context we will cover the basic principles of mathematical analysis, the Fourier transform¿Interpolation and approximation of functions, sampling theory, digital filtering and noise analysis. Since imaging is done with computers, there will be a programming part to each homework assignment in Mathematica to complement theoretical ideas with numerical implementation. Prerequisite Course(s): Prerequisites: MATH 260, MATH 310, MATH 320Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 3-0-3 |
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MATH 440 | Numerical Optimization | 3 | College of Arts & Sciences |

Many problems in science, engineering, medicine and business involve optimization. in which we seek to optimize a mathematical measure of goodness subject to constraints. This course will cover the basics of smooth unconstrained and constrained optimization in one and more variables: first and second order conditions, Lagrange multipliers, KKT conditions, Gradient descent, Newton and Quasi-Newton methods. .Key concepts and methods in mathematical programming will then be covered: linear programming, quadratic and convex programming (simplex method, primal-dual methods, interior point methods) with applications to engineering, optimal control and machine learning. Prerequisite Course(s): Prerequisites: MATH 410Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 3-0-3 |
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MATH 450 | Partial Differential Equations | 3 | College of Arts & Sciences |

Generalities on linear partial differential equations and their applications to physics. Solution of initial boundary value problems for the heat equation in one dimension, eigen-function expansions. Definition and use of Fourier series and Fourier transform. Inhomogeneous problems. The wave equation in one dimension. Problems in two dimensions: vibrating rectangular membranes, Dirichlet and Neumann problems. Prerequisite Course(s): Prerequisite: MATH 320Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 3-0-3 |
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MATH 455 | Numerical Analysis | 3 | College of Arts & Sciences |

This is a survey of the basic numerical methods which are used to solve scientific problems. The emphasis is evenly divided between the analysis of the methods and their practical applications. After reviewing calculus and covering floating point arithmetic, it introduces students to numerical solution of nonlinear equations (bisection, fixed-point iteration, Newton's methods, etc.), interpolation and polynomial approximation (Lagrange polynomial, Divided differences, Hermite interpolation, Cubic Spline interpolation, etc.), numerical differentiation and integration (Newton-Cotes, Gaussian quadrature, etc.), and ODE methods (explicit and implicit methods). Some convergence theorems and error bounds are proved. The course also provides an introduction to MATLAB, an interactive program for numerical linear algebra, as well as practice in computer programming. Prerequisite Course(s): Prerequisites: MATH 320Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 3-0-3 |
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MATH 460 | Advanced Seminar | 3 | College of Arts & Sciences |

Advanced topics of current interest in mathematics. Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 3-0-3 |
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MATH 470 | Mathematical Fluid Dynamics | 3 | College of Arts & Sciences |

Introduction to the basic idea of fluid dynamics, with an emphasis on rigorous treatment of fundamentals and the mathematical developments and issues. The course focuses on the background and motivation for recent mathematical and numerical work on the Euler and Navier-Stokes equations, and presents a mathematically intensive investigation of various model equations of fluid dynamics Prerequisite Course(s): Prerequisites: MATH 450 or MATH 455Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 3-0-3 |
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MATH 490 | Mathematical Modeling | 5 | College of Arts & Sciences |

This is the capstone course and final requirement for the applied and computational mathematics (ACM) major. As such, it consists of a project-based introduction to the theory and practice of mathematical modeling and simulation. Thesis and interdisciplinary work in teams is strongly encouraged. Techniques include scaling and nondimensionalization, data -fitting, linear and exponential models, elementary dynamical systems, probability, optimization, Markov chain modeling. Models will be drawn from a wide range of application fields; synergy with double majors, graduate work and/or interests in industry / internships is encouraged wherever relevant. Students will also learn scientific presentation skills and do oral presentations throughout the semester. Prerequisite Course(s): Prerequisites: MATH 450 or MATH 455Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 5-0-5 |