Computational Sciences Major
Computational sciences provide the scientific foundations for making sense of natural, human-mediated and social phenomena through analytics, computational methods and modeling.
In an age of ubiquitous — often overwhelming — data, the ability to harness that data to reflect, reach out and make better decisions is increasingly crucial. The Computational Sciences major prepares students to be analytics-driven and logical decision makers, innovators, and leaders.
In their first year, Computational Sciences majors complete their Cornerstone 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.
CS110 / Computation: Solving Problems with Algorithms
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.
CS111A / Continuous Mathematical Systems
In this course, students learn the principles of single and multivariable calculus needed to succeed in the concentration courses and beyond. While a traditional course in these topics focuses on the analytic techniques needed to do complex computations by hand, and evaluates students primarily on their ability to do so, this course takes a different approach. Students primarily learn to understand and apply concepts to solve problems in a variety of practical contexts. While the standard computational techniques are covered and practiced, students will take full advantage of technologies such as Sage to supplement their skills.
CS111B / Linear Mathematical Systems
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.
CS112 / Knowledge: Information Based Decisions
The course focuses on the application of predictive and causal statistical inference for decision making across a wide range of scenarios and contexts. The first part of the course focuses on parametric and non-parametric predictive modeling (regression, cross-validation, bootstrapping, random forests, etc.). The second part of the course focuses on causal inference in randomized control trials and observational studies (statistical matching, synthetic control methods, encouragement design/instrument variables, regression discontinuity design, etc.). Technical aspects of the course focus on computational approaches and real-world challenges, drawing cases from the life sciences, public policy and political science, education, and business. This course also emphasizes the importance of being able to articulate one’s findings effectively and tailor methodology and policy/decision-relevant recommendations for different audiences.
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.
|Computational Theory and Analysis||Contemporary Knowledge Discovery||Applied Problem Solving|
|Computer Science and Artificial Intelligence||CS142 / Computability and Complexity||CS152 / Harnessing Artificial Intelligence Algorithms||CS162 / Software Development: Building Powerful Applications|
|Mathematics and Operations Research||CS144 / Principles of Advanced Mathematics||CS154 / Contemporary Applied Mathematics||CS164 / Optimization Methods|
|Data Science and Statistics||CS146 / Modern Computational Statistics||CS156 / Machine Learning for Science and Profit||CS166 / Modeling, Simulation, and Decision Making|
Each row and each column of the matrix represent a different concentration, as noted above.
CS142 / Computability and Complexity
Students learn about models of computation that provide the theoretical basis for modern computer science. Topics include deterministic and nondeterministic finite state machines, Turing machines, formal language theory, computational complexity and the classification of algorithms. Students practice building a variety of automata and Turing machines using Python. What are the language grammars? and what role does a grammar plays in the way we analyze problems, solve problems, communicate with the computer, and even analyze natural languages? What makes a problem difficult to solve? Are some problems intrinsically harder than others, or is it that just because we have not yet discovered more efficient solutions? What, if any, are the limits of what can be solved with a computer? The techniques presented in this course shed light on why some computational problems are hard or even tractable. Students also gain experience communicating mathematical ideas in a rigorous fashion.
CS144 / Principles of Advanced Mathematics
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.
CS146 / Modern Computational Statistics
Learn to apply Bayesian inference which is the mathematical framework for using observed data to update the information we have about a system. The course proceeds from the fundamentals of probability theory and Bayesian inference to the data modeling process, covering various real-world scenarios from sports, medicine, vehicle tracking, social sciences, and more. The second half of the course covers approximate methods for automating inference in the form of variational inference (approximations using functions) and Monte Carlo methods (approximations using random samples). These methods allow us to work with large models containing many unknown variables and large data sets.
CS152 / Harnessing Artificial Intelligence Algorithms
Apply methods and algorithms from artificial intelligence -- such as propositional logic, logic programming, predicate calculus, and computational reasoning -- to practical problems of information retrieval, robot navigation, logistics planning, and natural language processing.
CS154 / Contemporary Applied Mathematics
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.
CS156 / Machine Learning for Science and Profit
Students learn to apply core machine learning techniques — such as classification, perceptron, neural networks, support vector machines, hidden Markov models, and nonparametric models of clustering — as well as fundamental concepts such as feature selection, cross-validation and over-fitting. Students program machine learning algorithms to make sense of a wide range of data, such as genetic data, data used to perform customer segmentation or data used to predict the outcome of elections.
CS162 / Software Development: Building Powerful Applications
This course is organized around the principle that the only way to learn software development is to develop software. Work together with a team to develop a significant software application. Examples include a spreadsheet application, a social media web application, or a distributed chat system. You will have the opportunity to apply and experience all aspects of software development, including requirements analysis, design, implementation, validation, deployment, documentation, and maintenance.
CS164 / Optimization Methods
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.
CS166 / Modeling, Simulation, and Decision Making
Learn how to apply advanced modeling techniques to analyze and predict the behavior of social, physical and economic systems. You will learn from specific examples applied to portfolio management, traffic flow management, and analyzing social networks. The course covers three modeling frameworks — cellular automata for modeling interactions on grids of cells, networks for more general interactions between nodes in a graph, and Monte Carlo simulations showing how we can use simulation to generate random numbers and how we can use random numbers to drive simulations of complex phenomena. The course covers the theoretical (mathematical) and practical (implementation) aspects of each of the three frameworks.
In their fourth year, Computational Sciences majors finish their Capstone Courses.