# Bachelor of ScienceApplied Mathematics

The Applied Mathematics Bachelor of Science degree program consists of a strong core of courses in applied advanced mathematics, statistics and computational science.

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The structure of the program allows the student to choose between two broad areas of study that are, at their root, highly mathematical: data analytics and natural sciences. The purpose of the program is to provide foundational and hands-on experience in applied problems associated with the two disciplines.

## Program Goals

A graduate of the Applied Mathematics program is prepared to:

- Develop expertise in problem-formation, problem-solving, and modeling techniques and strategies central to a wide variety of applications;
- Establish the ability to communicate analytic arguments clearly and concisely in oral and written forms;
- Exhibit expertise in numerical problem-solving techniques using high-level programming languages and commercial computational software packages; and
- Demonstrate foundational knowledge and skills within an interdisciplinary-work environment.

## Program Concentrations

- Data Analytics
- Natural Sciences

## Program Courses

This program requires a total of 46-50 semester hours: 34 semester hours from core course listed below and 12 semester hours completed in the Data Analytics Concentration or 16 semester hours in the Natural Sciences Concentration. The semester hour value of each course appears in parentheses ( ).

CISC 120 –
Programming I
(4 credits)

This course introduces the concepts and techniques of computer programming. Emphasis is placed on developing the student’s ability to apply problem-solving strategies to design algorithms and to implement these algorithms in a modern, structured programming language. Topics include fundamental programming constructs, problem solving techniques, simple data structures, Object-Oriented Programming (OOP), program structure, data types and declarations, control statements, algorithm strategies and algorithm development.

CISC 140 –
Programming II
(3 credits)

This course builds upon fundamental concepts of programming and introduces several more advanced concepts. Emphasis is placed on the practical applications of the techniques and structures, as opposed to abstract theory, in the hopes of rendering the content accessible and useful in the context of using programming as a tool to solve problems. Topics covered include the basics of Object-Oriented Programming (OOP), sorting and searching algorithms, and basic data structures. Offered Fall and Spring Semester, annually.

MATH 220 –
Calculus I
(3 credits)

This course introduces techniques to evaluate limits and covers continuity, special trigonometric limits, absolute value limits and differentiation of algebraic, trigonometric, and logarithmic functions. The course explores intermediate value theorem, mean value theorem, and extreme value theorem. Other topics for exploration are application and formal definition of derivative average rate of change versus instantaneous rate of change, velocity, and the introduction of the definite integral and its applications. A graphing calculator is required for this course.

MATH 250 –
Introduction to Linear Algebra
(3 credits)

As science and engineering disciplines grow so does the use of mathematics; new mathematical problems are encountered, and new mathematical skills are required. In this respect, linear algebra has an essential role in various engineering and scientific disciplines. This course develops the fundamental algebraic tools involving matrices and vectors to study linear systems of equations and Gaussian elimination, linear transformations, orthogonal projection, least squares, determinants, eigenvalues and eigenvectors and their applications. This course develops concrete computational skills along with theoretical considerations.

MATH 260 –
Calculus II
(3 credits)

This course focuses on the exploration of differential calculus, the derivatives of all functions. An emphasis is placed on the rules of differentiation and their proofs. The course analyzes graphs of functions using the concept of derivative and its application and includes an introduction to integral calculus, integration properties, differential equations and notation. Problem solving is learned using elementary integration techniques, elementary trigonometric integration, and hyperbolic functions. A graphing calculator is required for this course.

MATH 261 –
Calculus III
(3 credits)

This course develops vector algebra, the calculus of more than one variable; partial derivative; volume; surface and line integrals; the polar, cylindrical and spherical coordinate systems; and the theory of vector fields. It develops the theory of vector calculus and conservative vector fields which lead to the conservation laws of nature. In addition, the course fully treats the mathematical framework of defining geometry in three dimensions.

MATH 300 –
Experiment Design and Analysis
(3 credits)

This course is an introduction to applied design of experiments and the statistical analysis of scientific data. It provides a detailed development of specific parametric and non-parametric statistical procedures and their application to various experimental designs. This course is well-suited for a student to apply sound data analysis technique to experimental data. Key course objectives are: designing experimental procedures to obtain the desired information, application of the statistical procedures consistent with the design, and to draw meaningful inferences from the results.

MATH 320 –
Ordinary Differential Equations
(3 credits)

This course serves as an introduction to Ordinary Differential Equations (ODEs) and their applications. Topics include: Existence, uniqueness and the stability of solutions; first and second order ODEs; applications; the Laplace transform; numerical methods; systems of ODEs and solutions of linear equations with constant coefficients. Developing applied models taken from a wide variety of fields and learning to communicate your understanding by writing effective arguments are key objectives of this course.

MATH 370 –
Numerical Methods
(3 credits)

This course covers the math methodologies that underlie the techniques of scientific computing and related numerical methods. Topics include: direct and iterative methods for linear systems, eigenvalue decompositions and factorizations, stability and accuracy of numerical algorithms, the IEEE floating-point standard, sparse and structured matrices, and linear algebra software. Other topics may include memory hierarchies and the impact of caches on algorithms, nonlinear optimization, numerical integration, FFTs, and sensitivity analysis. Problem sets will involve use of C++ programming language. The course is intensely practical with solved examples and graded exercises.

MATH 380 –
Mathematical Modeling
(3 credits)

This course involves applications of mathematics to real-world problems drawn from industry, research, laboratories, the physical sciences, engineering and scientific literature. Techniques used include parameter estimation, curve fitting, calculus, elementary probability, optimization, computer programming, and ordinary and partial differential equations. People routinely solve problems using estimation, probability, optimization, and simulation or modeling techniques without considering themselves mathematicians. This course broadensand strengthens the exposure of the interested student to applications of mathematics frequently seen in industry, science, and government. The student planning to pursue a career in industry, science, or government will synthesize mathematical skills appropriate to these fields from topics learned in a variety of more elementary mathematics courses.

MATH 420 –
Methods in Applied Mathematics
(3 credits)

Several topics in advanced calculus are developed in this course including functions of a complex variable, infinite series, Fourier series, Partial Differential Equations, Probability Theory and Mathematical Statistics. Applied problems arising from many fields of science and data analysis are treated using the mathematical topics covered. Computer Aided Software is used to supplement the material in each topic.

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