# Applied and Computational Mathematics, B.S.

Curriculum

### Discovery Core

Foundations |
Credits: | |

FCWR 101 | Writing I: College Composition | 3 |

Prerequisite: Prerequisite: WRIT 100 or Writing Placement ExamA course introducing students to the fundamentals of college composition. Topics include writing process, rhetorical strategies, basics of critical reading and thinking, analytical writing, and argumentative writing. This course serves as a foundation to prepare students to succeed in other academic writing contexts. Coursework includes a computer lab component. Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 3-0-3 |
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FCWR 151 | Writing II: Research Writing | 3 |

Prerequisite: Prerequisite: FCWR 101 or WRIT 101Further development of the academic writing, critical thinking, and analytical reading skills taught in Writing I. An introduction to academic discourse in the four core seminar areas: literature, social sciences, behavioral sciences, and philosophy. Development of library skills leading to a documented research paper. Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 3-0-3 |
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FCSP 105 | Foundations of Speech Communication | 3 |

Study of the fundamentals of verbal communication including public speaking, interpersonal communication, and small group interaction. Training in methods of obtaining and organizing materials and ideas for effective verbal communication. Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 3-0-3 |
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FCIQ 101 | Foundations of Inquiry | 3 |

This course introduces you to the fundamentals of critical thinking. Topics include an overview of the research methods in various academic disciplines, reasoning, constructing an argument, and evaluating information. This course serves as a foundation for your continued development of critical thinking skills in other core classes, your major program coursework, and your personal and professional life. Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 3-0-3 |
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FCSC 101 | Foundations of Scientific Process | 3 |

This course is designed to provide students with an introduction to the big ideas of different scientific disciplines, and is grounded in the scientific process. The course focuses on interdisciplinary aspects, the scientific process, and it is writing intensive, interactive and relevant. Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 3-0-3 |
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FCWR 3XX | Foundation of Communication Choice | 3 |

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Total: 18 Credits | ||

Seminars |
Credits: | |

ICBS 3XX | Behavioral Science Choice | 3 |

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ICLT 3XX | Literature Choice | 3 |

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ICPH 3XX | Philosophy Choice | 3 |

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ICSS 3XX | Social Science/Economics Choice | 3 |

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Total: 12 Credits | ||

### Major Requirements

Computer Science |
Credits: | |

CSCI 125 | Computer Programming I | 3 |

Prerequisite: Prerequisite: MATH 141 or higherThis course provides basic skills in problem solving and object-oriented programming using a high level language such as Java or C++. Topics include algorithm development, simple data types, expressions and statements, program flow control structures, objects, methods and arrays. Knowledge of Algebra Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 3-1-3 |
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CSCI 185 | Computer Programming II | 3 |

Prerequisite: Prerequisite: CSCI 120 or CSCI 125This course provides advanced skills in object-oriented programming and problem solving techniques using a high level language such as Java C++. Topics include polymorphism, inheritance, exception handling, stream and file I/O, recursion, and dynamic data structures. Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 3-1-3 |
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Total: 6 Credits | ||

Physics |
Credits: | |

PHYS 170 | General Physics I | 4 |

Co-Requisite: Co-requisite: MATH 170A basic course covering vectors, Newton's laws of motion, particle kinematics and dynamics, work, energy, momentum, and rotational motion. Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 4-2-4 |
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PHYS 180 | General Physics II | 4 |

Prerequisite: Prerequisite: PHYS 170.Co-Requisite: Co-requisite: MATH 180. Students in BS Electrical and Computer Engineering and BS Mechanical Engineering must earn a grade of C or better in PHYS 170.A continuation of PHYS 170. Topics include fluids, wave motion, electric fields and electric potential, DC circuits, magnetic fields, capacitance and inductance, AC circuits, and electromagnetic waves. Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 4-2-4 |
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Total: 8 Credits | ||

General Electives |
Credits: | |

Consult with advisor on all liberal arts electives | 12 | |

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

Mathematics Electives |
Credits: | |

MATH 3XX | Math electives must be at 300-level and above. Consult with advisor on all elective choices. | 6 |

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

Mathematics Requirement (all concentrations) |
Credits: | |

MATH 170 | Calculus I | 4 |

Prerequisite: Prerequisite: MATH 140 or MATH 141 or TMAT 155 or Math Placement ExamStudy 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. Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 5-0-4 |
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MATH 180 | Calculus II | 4 |

Prerequisite: 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.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. Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 5-0-4 |
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MATH 220 | Probability and Statistics | 3 |

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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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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 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 490 | Mathematical Modeling Capstone Course | 5 |

Prerequisite: Prerequisites: MATH 450 or MATH 455This 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. The muscles of mathematics are connected to the bones of science by the tendons of mathematical modeling. This course focuses on developing the mathematical intuition needed for critical problem solving by focusing on the connections of mathematics to various academic disciplines. Many modeling techniques will be used in this course including scaling and dimension, fitting of data, linear and exponential models, elementary dynamical systems, probability, optimization, Markov chain modeling and asymptotic analysis. Models will be drawn from a wide range of application fields. For example, applying biomedical models to simulate drug effects in clinical trials or applying finite element analysis to predict stress in 3D printed materials. Synergy with double majors, graduate work and/or interests in industry / internships is strongly promoted in this course. Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 5-0-5 |
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Total: 36 Credits | ||

## Concentration Options:Students may choose between General Concentration, Mathematical Modeling, or Scientific Computation. |
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General Concentration |
Credits: | |

MATH 45X | Choose between MATH 450 Partial Differential Equations and MATH 455 Numerical Analysis | 3 |

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

MATH 3XX | Math elective must be at 300-level and above. Consult with advisor on all elective choices. | 3 |

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

Science Elective | 4 | |

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Computer Science Elective | 3 | |

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Computer Science or Science Elective Choice | 9 | |

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Mathematical Modeling Concentration |
Credits: | |

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 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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PHYS 220 | General Physics III | 4 |

Prerequisite: Prerequisite: PHYS 180The final basic course covering the laws of thermodynamics, reflection and refraction of light, interference and diffraction, radiation, atomic physics, waves and corpuscles, and nuclear physics. Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 4-2-4 |
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PHYS 225 | Intro to Modern Physics | 3 |

Prerequisite: Prerequisite: PHYS 180This course is designed to familiarize students with the following topics: thermodynamics, optics, relativity, atomic and nuclear physics, fundamental quantum theory of photons, and semiconductors. Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 3-0-3 |
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PHYS 450 | Mathematical Physics | 3 |

Prerequisite: Prerequisite: MATH 260 and PHYS 220A course designed to provide the student with the mathematics required for advanced undergraduate and beginning graduate study in the physical sciences. Topics covered are vector analysis, introduction to vector space and matrix algebra, infinite series, the partial differential equations of physics , an introduction to the special functions of Bessel, Legendre, Hermite, and Laguerre, and Fourier series. Physical applications are stressed. Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 3-0-3 |
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Computer Science Elective | 3 | |

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Computer Science or Science Elective Choice | 3 | |

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Scientific Computation Concentration |
Credits: | |

CSCI 235 | Elements of Discrete Structures | 3 |

Prerequisite: Prerequisite: Take CSCI 185 and one course in this group: MATH 161 or MATH 170This course provides students with an introduction to discrete structures with applications to computing problems. Topics include logic, sets, functions, relations, proof techniques, counting and algorithmic analysis in addition to graph theory and trees. Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 3-0-3 |
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CSCI 312 | Theory of Computations | 3 |

Prerequisite: Prerequisite: CSCI 235The basic concepts of the theory of computation are studied including set theory, finite automata, context free and context-sensitive languages, Turing machines, Church's thesis, and uncomputability. The classes of computation complexity and their practical limitations are studied. Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 3-0-3 |
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CSCI 335 | Design and Analysis of Algorithms | 3 |

Prerequisite: Prerequisite: CSCI 260The fundamentals of designing computer algorithms are introduced. An overview of advanced data structures such as balanced trees, heaps and hash tables is presented. A discussion of algorithm design techniques will include, but not be limited to sorting and ordering, divide and conquer, shortest path and dynamic programming. The complexity of algorithms to various applications is discussed. 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 455 | Numerical Analysis | 3 |

Prerequisite: Prerequisites: MATH 320, MATH 410This course is a broad introduction to numerical methods and their applications. After covering floating point arithmetic and reviewing Numerical Linear Algebra, it introduces students to Nonlinear equations I root-finding (bisection, Newton and Quasi-Newton methods), Interpolation methods (polynomial, splines), Integration (Newton-Cotes, adaptive, gaussian quadrature), ODE methods (explicit and implicit methods), PDE methods, and the Fast Fourier Transform. Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 3-0-3 |
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Science Elective | 4 | |

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

Computer Science or Science Elective Choice | 3 | |

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Total Program Requirement = 120 credits |