Mathematics

Learn to utilize principles of single and multivariable calculus to solve relevant problems from across STEM. Traditional calculus courses focus on the techniques needed to perform complex computations by hand, and evaluate students primarily on their ability to do so quickly. This course takes a different approach by shifting the focus to applying foundational calculus concepts to analyze and solve problems in practical contexts while building the facility to take full advantage of technologies such as Sage to perform complex computations. In addition to honing skills from critical and creative thinking, an emphasis is placed on effective collaborative problem-solving and communication of technical processes and results to appropriate audiences. Note: This course was previously CS111A.

This course develops the tools necessary for the analysis of linear systems. The emphases are both on abstract notions such as vectors spaces, linear maps between them and their matrix representations, and concrete applications such as Markov chains and graphical network analysis. Students apply their knowledge to explore a wide variety of problems such as Page Rank, least squares fitting, and traffic modeling. Note: This course was previously CS111B. In addition to the listed prerequisites, the following courses are recommended prior to taking this course: CS111

Students learn how to read, write, and evaluate rigorous mathematical arguments. These skills are practiced on foundational material that forms a bridge to topics in advanced mathematics—both applied and pure. Subtopics in modern algebra and real analysis are chosen to illustrate the fundamental concepts of careful bounding, counting, and the application of equivalence classes.

Methods are explored to interpolate data, solve linear and non-linear systems of equations, and model dynamical systems with the use of ordinary and partial differential equations. Additionally, Fourier Analysis is applied to model and process signals. Numerical implementations of the mathematical methods are developed using MATLAB or Octave. NOTE: Students may request to take CS113 in the same semester, as a corequisite.

Learn to use and analyze optimization techniques such as linear, quadratic, semidefinite and mixed-integer programming. Explore optimization algorithms such as Newton’s method, interior point methods and branch and bound methods.