# Mathematics Minor

Curriculum

### Minor Requirements

Required Courses |
Credits: | |

MATH 260 | Calculus III | 4 |

Prerequisite: Prerequisite: MATH 180Sequences 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. Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 4-0-4 |
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Total: 4 Credits | ||

Advanced Electives (select four**) |
Credits: | |

MATH 210 | Plane Geometry | 3 |

Please view all course descriptions: http://www.nyit.edu/courses | ||

MATH 215 | Introduction to Sets and Logic | 3 |

Please view all course descriptions: http://www.nyit.edu/courses | ||

MATH 220 | Probability Theory | 3 |

Prerequisite: Prerequisite: MATH 180An 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. Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 3-0-3 |
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MATH 235 | Applied Statistics | 3 |

Prerequisite: Prerequisite: MATH 150 or MATH 151 or MATH 170An 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. Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 3-0-3 |
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MATH 310 | Linear Algebra | 3 |

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

Prerequisite: Prerequisite: MATH 260Solving 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. Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 3-0-3 |
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MATH 330 | Computational Analysis | 4 |

Prerequisite: Prerequisite: MATH 260This 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. Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 3-2-4 |
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MATH 350 | Advanced Calculus | 3 |

Prerequisite: Prerequisite: MATH 260Topics 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. Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 3-0-3 |
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MATH 360 | Functions of a Complex Variable | 3 |

Prerequisite: Prerequisite: MATH 260The 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. Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 3-0-3 |
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MATH 370 | Real Analysis | 3 |

Prerequisite: Prerequisite: MATH 260This 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. Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 3-0-3 |
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MATH 410 | Numerical Linear Algebra | 3 |

Prerequisite: Prerequisites: MATH 310This 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. Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 3-0-3 |
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MATH 430 | Mathematics of X-ray Imaging | 3 |

Prerequisite: Prerequisites: MATH 260, MATH 310, MATH 320ln 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. Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 3-0-3 |
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MATH 440 | Numerical Optimization | 3 |

Prerequisite: Prerequisites: MATH 410Many 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. Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 3-0-3 |
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MATH 450 | Partial Differential Equations | 3 |

Prerequisite: Prerequisite: MATH 320Generalities 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. Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 3-0-3 |
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MATH 455 | Numerical Analysis | 3 |

Prerequisite: Prerequisites: MATH 320This 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. Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 3-0-3 |
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MATH 460 | Advanced Seminar | 3 |

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 |

Prerequisite: Prerequisites: MATH 450 or MATH 455Introduction 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 Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 3-0-3 |
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Total: 12–13 Credits | ||

** Two or more elective courses must be at or above the 300-level. At least one of these courses MUST NOT be required for the major. |
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Prerequisite Courses- MATH 141 Precalculus
- MATH 170 Calculus I
- MATH 180 Calculus II
Grade RequirementsThe grade received for each mathematics course counted toward the minor must be C or higher. The combined GPA for all mathematics courses used for the minor must be 2.7 or higher. At least six credits must be taken in residence at New York Tech IN EXCESS of the mathematics requirements of the major. |