Core courses
In their second year, Computational Sciences majors enroll in core courses that provide the foundation for the Computational Sciences concentrations. They also take electives from core courses offered in other majors.
Apply core concepts in design and analysis of algorithms, data structures, and computational problem-solving techniques to address complex problems. Hashing, searching, sorting, tree algorithms, dynamic programming, greedy algorithms, divide and conquer, backtracking, random number generation, and randomized algorithms are examples of algorithms you will learn to exploit to solve problems ranging from logistics to route optimization to DNA sequencing.
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
When can you find patterns in seemingly random noise? Or determine when an observed pattern is likely due to chance? This course focuses on the concepts from probability and statistics used to extract meaning from data. In addition to building a strong, theoretical foundation, students learn how to apply these tools to understand real-world scenarios. Formal topics include Sample spaces, conditional probability and independence, Bayes’ theorem, discrete and continuous random variables, joint distributions, the law of large numbers as well as the central limit theorem among others. These techniques are then used in applications such as statistical learning, linear regression, simulation, maximum likelihood and least squares.
Concentrations Courses
In their third year, Computational Sciences majors select a concentration, begin taking courses within it and begin work on their capstone courses. They also take electives chosen from other Minerva courses (other concentration courses in Computational Sciences, core and concentration courses in other colleges). Computational Sciences offers concentrations shown in the table below.
In the fourth year, Computational Sciences majors enroll in additional electives chosen from Minerva’s course offerings within or outside the major. Additionally, they take senior tutorials in the major, and finish their capstone courses.
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.