Mathematics

Abstract Algebra

Introduction to group theory. Properties of the integers, functions, and equivalence relations. A concrete approach to cyclic groups and permutation groups; isomorphisms and the theorems of Lagrange and Cayley.

Triangular Peg Solitaire Project

Probability Theory

An introduction to the mathematical treatment of random phenomena occurring in the natural, physical, and social sciences. Axioms of mathematical probability, combinatorial analysis, random variables and probability distributions, expectation, binomial distribution, Poisson and normal approximation, generating functions and the Central Limit Theorem.

Real Analysis

Rigorous examination of the calculus of functions of one variable: convergence, continuity, differentiation, the mean-value theorem, and the Riemann integral.

Complex Analysis

Theory of functions of a complex variable including analytic functions and their properties, sequences and power series, Cauchy’s theorem on integration and its consequences, and evaluation of real integrals using residue theory.

Numerical Linear Algebra

Roundoff errors and computer arithmetic. Direct and iterative methods for solving linear systems; norms and condition numbers, iterative refinement. Linear least squares problems: the normal equations and QR approach for overdetermined systems. Numerical methods for eigenvalues: an introduction to the QR iteration.

Model Building in Applied Mathematics

An introduction to the formulation, analysis and interpretation of mathematical models in the study of selected problems in the natural sciences, the social sciences, and management science. Topics covered include discrete dynamical systems, proportion and geometric similarity, least squares and optimization, dimensional analysis, ordinary differential equations, and autonomous systems of differential equations.

Math Modeling Projects

Numerical Analysis

Polynomial interpolation, numerical solutions of nonlinear equations, least squares approximation by polynomials, orthogonal polynomials, economization of power series. Numerical integration including quadrature formulae, adaptive quadrature, composite quadrature formulae, and Romberg integration.

Economics

Private Valuation

How to get people to tell you what they really want, a study on how different types of auctions evoke different strategies from buyers and sellers and how to distinguish the properties of an effective survey & how to create one yourself.

Private Valuation Podcast

Students create a podcast for a topic related to auction theory: topic chosen was the market for retro video games.

Principles of Microeconomics

Introductory study of market and nonmarket mechanisms in the allocation of productive resources and in the distribution of income. Includes the study of monopolies, oligopolies, and labor unions as well as applications to selected current economic problems. Sophomore standing recommended unless student is majoring or minoring in economics.

Principles of Macroeconomics

Introductory study of factors determining aggregate income, employment, and general price level. Such factors include roles of government, the banking system, and international monetary relations. Sophomore standing recommended unless student is majoring or minoring in economics.

Game Theory

Analysis of decision makers who are aware that their actions and any assumptions made by others about their actions will affect the actions of those others. In the last 25 years, game theory has become the core of economic theory, both micro and macro. Introduction to the tools of game theory and the usefulness of this approach by analyzing several examples.

Game Theory Project

Students create and analyze a game from a selected group topic: crime in media.

Computer Science

Data Structures

This course covers the application of analysis and design techniques to nonnumeric algorithms acting on data structures, and the utilization of algorithmic analysis and design criteria in the selection of methods for data manipulation. Topics studied include sequential and associative containers, algorithms (including sorting and algorithm analysis), binary trees & balancing, heaps, B-Trees, hashes, graphs (including representation, traversals, and algorithms).

Introduction to Software Engineering

Phases of the systems development life cycle and the tools used by the analyst in planning, specifying, and implementing a complex computer-based system. Related topics include documentation standards, interaction with users, and design of interfaces.

Quote System Project

Databases

Software development in a representative current database and an online interactive teleprocessing system. Data normalization with relational databases and DDL & DML commands in SQL using MariaDB. Databases linked to online webpages using HTML & PHP.

Karaoke Project

UNIX & Network Programming

UNIX system usage and commands. Shell script programming. Network programming concepts and protocols. System call level and basic network programming in C++.

Programming in Assembler Language

An in-depth study of assembler language programming on a third-generation computer, including internal and external subroutines, conditional assembly, and the macro language. Students are required to write a number of substantial programs. Extensive laboratory work.

Theory of Computation

Introduction to automata theory, formal languages, and computability theory with an emphasis on how these topics relate to computers and computer programs.

Computer Graphics

This course will provide an examination of fundamental techniques used to create 3D models in computer graphics. Topics studied include basic modeling primitives (point, lines, and polygons), quadrics & super quadrics, basic modeling transformations, hierarchical modeling, Bezier curves & rational Bezier curves, B-splines, NURBS, subdivision surfaces, free-form deformation, noise functions, particle systems, and fractals.

Graphics Projects

Computer Architecture & System Organization

To understand the architecture and organization of computer systems and related software. Emphasis will be placed on how computers execute programs and other issues relevant to programming. Basic concepts and examples from microcomputers and networks, peripheral components, data communications, and the relationship between hardware components and the operating system.

Programming & Software Tools Summary

Languages: C++, Java, Python, SQL, PHP, HTML, Shell Scripting, Assembly

Frameworks/Tools: Android Studio, Git, Jira, Confluence, MariaDB, Julia

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