# Applied and Computational Mathematics, B.S.

Curriculum

### General Education

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 process, critical thinking, and analytical reading skills taught in FCWR 101. Focus on academic research planning, source evaluation skills, and audience awareness leading to a documented research paper. Specific attention to academic integrity in research writing. Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 3-0-3 |
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FCWR 3XX | Foundation of Communication Choice | 3 |

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

Total: 9 Credits | ||

Data Literacy |
Credits: | |

DATA 101 | Making Sense of a Data-Oriented Society | 3 |

This course introduces students to the power of data as applied to real-life problems in today's data-driven world. Students will learn basic statistical concepts, how to identify reliable data, and to think critically about how to extract meaning from data. The course will discuss various biases, including social biases, how they affect data gathering and analysis, and how to address these biases. The course will also address ethical and moral issues associated with statistics, data collection and visualization, and data analysis. Students will learn how to present a narrative supported by data. Classroom Hours - Laboratory and/or Studio Hours – Course Credits: 3-0-3 |
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Seminars (select courses from at least three of the four areas) |
Credits: | |

ICBS 3XX | Behavioral Science Choice | 3 |

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

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 |

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

Total: 12 Credits | ||

Students must take four seminar courses from at least three different areas of study.*Students may choose between ICSS 3XX or IENG 400 Technology and Global Issues. |
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### Major Requirements

Computer Science |
Credits: | |

CSCI 125 | Computer Programming I | 3 |

Prerequisite: Corequisite: 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 |

Prerequisite: 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: 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. | 18 | |

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 141 or Math Placement Exam.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. 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 |

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 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. 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. 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 | |

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

Computer Science Elective | 3 | |

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

Computer Science or Science Elective Choice | 9 | |

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

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 |

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

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 |

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

Computer Science Elective | 3 | |

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

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 | |

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

Total Program Requirement = 120 credits
Grades for all MATH courses must be a C or higher. The combined GPA for all mathematics courses must be a 2.7 or higher. |