Curriculum for Applied Mathematics Degree

This is the second course in single-variable calculus. Students will learn techniques and applications of integration, be given further exposure to trigonometric, logarithmic, and exponential functions, and learn the basics of infinite sequences and series.

This course is designed to develop the topics of multivariate calculus. Emphasis is placed on multivariate functions, partial derivatives, multiple integration, solid analytical geometry, vector valued functions, and line and surface integrals. Upon completion, students should be able to select and use appropriate models and techniques for finding the solution to multivariate-related problems.

This course will introduce students with a background in Calculus to the fields of probability and statistics. Topics include discrete and continuous probability, key terms and theorems, and different statistical distributions and models. Students will work with concepts by-hand and with technology in order to develop a greater understanding of the structure and applications of probability and statistics as a whole.

Students will learn the concepts, techniques, and structures of discrete mathematics necessary for the software engineer, including logic, sets, functions, relations, Boolean algebra, and combinatorics. The course also introduces the concept of mathematical proof.

This is an introductory course in linear algebra. Topics include systems of linear equations, matrix algebra, determinants, eigenvalues & eigenvectors, and an introduction into the theory of vector spaces.

This course is an exploration of different types of geometries. Starting with compass and straightedge constructions, students identify and prove theorems in Euclidean geometry. By relaxing Euclid's Parallel Postulate, students explore neutral and non-Euclidean geometries. The course concludes with a survey of finite geometries.

Students will learn the history and basics of computing as well as the fundamentals of Python programming. General topics include: the history of computing, number systems, Boolean logic, algorithm design and implementation, and modern computer organization. Programming topics include: memory and variables, data types, mathematical operations, basic file I/O, decision-making, repetitions, functions, and list basics.

Students explore how computers process numbers and equations to solve problems. Such problems have various levels of error and limitations that different methods address differently. This course includes a variety of different methods to find roots of equations, solve systems of linear equations, and interpolate a polynomial. Additionally, students get an introduction to solutions of ordinary and partial differential equations, as well as applications of numerical methods to dynamical systems and chaos.

Matrices, Vectors, and 3D Math introduces students to applied Linear Algebra, including systems of linear equations, matrix and vector operations, change of basis, and transformations. Additionally, it presents a variety of topics from 3D mathematics including vector mathematics, lines and planes, vector-valued functions, velocity, acceleration, and surfaces. Students will write computer programs and use mathematical software to explore all aspects of the topic.

Students explore the mathematical foundation, attacks, and historical significance of various ciphers. Mathematical topics include modular arithmetic, elementary number theory, elementary combinatorics, and Boolean algebra. Cryptographic topics include shift ciphers, substitution ciphers, block ciphers, Hill Cipher, Vigenere Cipher, the Enigma machine, RSA, DES/3DES, Rijndael Cipher/AES, and TLS/SSL. The emphasis will be on understanding the underlying mathematics, so previous programming experience is not necessary.

Teaches the practical side of exploring, presenting, and analyzing data. Students will learn to effectively use a statistical software package to accomplish these tasks. After learning to graphically display data in meaningful ways, students will learn to analyze data, test claims, and make valid conclusions. These analyses will include hypothesis tests involving more than one sample, linear and multiple linear regressions, chi-squared tests of independence and goodness of fit, and ANOVA.

Students develop a deeper understanding and appreciation for mathematics by seeing how different ideas were developed in different locations over time. From ancient Egyptian geometry to Newton, Leibniz and calculus, this course allows students to see historical evidence of the different and perfectly valid ways to view mathematical concepts across cultures. In this course, students view mathematical theories in a historical context to recreate methods and connect old techniques to modern perspectives.

This special topics course will allow students to explore topics in mathematics based on faculty expertise and student interest. The topics selected will allow students to expand their mathematical knowledge to areas beyond the standard curriculum and focus on an area of mathematics that relates to current industry and research trends.