Bachelor of ScienceEngineering and Mathematical Sciences

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

The Computer-Aided Design (CAD) course introduces three dimensional solid modeling design skills for manufacturing – skills critical in modern manufacturing environments. Using industry-leading software packages, content stresses foundational skills in 2D modeling, 3D solid object modeling, blueprint reading, and computer-aided drafting. The student will learn to create objects and assemblies in the digital realm; read and accurately create useful technical drawings that enable accurate communication of design concepts and requirements; and learn about various roles that CAD software and related software packages play in the manufacturing lifecycle.