# Bachelor of ScienceEngineering and Mathematical Sciences

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

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This program consists of a strong core of courses central to general engineering and data analysis with principles in science, applied advanced mathematics, statistics, and computational science. Students in this program will gain strong problem solving and computation skills through project-based learning within a flexible program that is specific to the career aspirations of the individual student. The structure of the program allows the student to choose between two broad areas of study that are, at their root, highly mathematical: (1) data sciences, and (2) engineering sciences.

## Program Goals

A graduate of the Engineering and Mathematical Sciences 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 Sciences

This concentration is interdisciplinary in nature and was designed to allow students to gain strong problem-solving skills in computer science and statistics. Students in this concentration will learn how to develop computational programs and algorithms that would be useful in visualizing, analyzing and interpreting large data involved in solving real world problems. This concentration allows for the design and analysis of software through knowledge and project-based learning using various programming tools beneficial to Data Science. Students in this concentration have the flexibility to choose courses that are specific to their future career goals. The concentration allows students to pursue various tracks involving Big Data within Healthcare and Biological sciences, Actuarial Sciences and Business Analytics.

Engineering Sciences

The Engineering Sciences concentration was designed for students who have an interest in entering general engineering or technology fields. This area focuses on how mathematical concepts can be applied to science and engineering applications towards solving real world problems. Students in this concentration can enjoy a flexible curriculum by choosing concentration approved electives that meets their own career aspirations after completing the program and concentration core courses. This will give student’s the option to gain general knowledge and skills in various engineering and technology fields such as Mechanics, Electronics, as well as other scientific disciplines involved in the Environmental, Materials and Biological Sciences. Within this program students will focus on project-based learning in a series of Mathematics and Physics courses as well as gain hands-on skills in Computational Programming, 3D modeling, Electronics and Engineering Design.

## Program Courses

This program requires a total of 48 semester hours: 1) 24 semester hours from core course listed below and 2) 24 semester hours completed in the Data Sciences or Engineering Sciences Concentrations. 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.

CISC 233 –
Essential Algorithms
(3 credits)

This course covers the basic techniques used to analyze problems and algorithms, including asymptotic, upper/lower bounds, and best/average/worst case analysis. Amortized analysis, complexity, and basic techniques are used to design algorithms (including divide & conquer/greedy/dynamic programming/heuristics, choosing appropriate data structures) and important classical algorithms (including sorting, string, matrix, and graph algorithms). The goal for the student is to be able to apply all of the above to design solutions for real-world problems.

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 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.

PHYS 330 –
University Physics I
(4 credits)

This calculus-based physics course covers the classical physics founded upon Newton’s Laws, and the conservation of energy and momentum. Applications of these principles treat topics such as the rotational dynamics of rigid bodies, Newton’s theory of gravity, oscillations, fluids and elasticity. The course includes weekly laboratory exercises.

PHYS 350 –
University Physics II
(4 credits)

This course is a continuation of University Physics I. University Physics II develops the physical principles of electricity and magnetism, DC electric circuits, electromagnetic radiation, interference phenomena, quantification, and quantum theory of the atom. The course makes extensive use of vector calculus.

ANLY 405 –
Predictive Modeling
(3 credits)

The development and implementation of models to predict outcomes based on input data is becoming an essential skill in modern enterprises. The objective of this course is to teach this skill. The course covers the principles of qualitative as well as quantitative models that can be used for predicting outcome based on input data. The predictions may be definitive, based on the assumptions or estimates based on probabilities. The student explores how to prepare input data, build predictive models, and assess the models by examining the output produced. Topics include: exploratory data analysis, linear regression, multiple linear regression, regression diagnostics, logistics regression, analysis of variance (ANOVA), time series and forecasting, statistical methods for process improvement, classifiers, and non-linear models. General concepts behind how software packages roll up and how they screen data and produce risk scores on topics such as in-patient probability of readmissions.

ANLY 415 –
Advanced Analytics and Reporting
(3 credits)

This course focuses on risk management models and tools and the measurement of risk using statistical and stochastic methods, hedging, and diversification. Examples of this are insurance risk, financial risk, and operational risk. Topics covered include estimating rare events, extreme value analysis, time series estimation of external events, axioms of risk measures, hedging using financial options, credit risk modeling, and various insurance risk models.

ADMA 240 –
Computer Assisted Drawing
(3 credits)

Computer Assisted Drawing is a basic course in computer-aided drawing, which integrates with manufacturing and automation. Content stresses learning major CAD commands and using the graphic user interface. Conceptual drawings, 2D drawings, 3D drawings, and spatial relationships will be explored. Additional topics include file maintenance, printing formats, plotting and 3D printing are used to create two and three-dimensional design models.

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