Course Summary

Course Description

Mathematics, statistics and decision sciences are, and will remain, key disciplines for analyzing and addressing complex problems. Students choosing the MSD concentration will be able to understand and appropriately apply methods and techniques from these disciplines.

Career Possibilities

  • Economic Forecaster
  • Engineer
  • Statistician
  • Financial Analyst
  • Corporate Strategist
  • Decision Scientist

Major Foundation Requirements

CS300 / Solving Problems with Algorithms

Learn how to design and analyze algorithms used to address complex problems. Solve problems ranging from logistics to route optimization to robotic arm control using algorithms such as hashing, searching, sorting, graph algorithms, dynamic programming, greedy algorithms, divide and conquer, backtracking, random number generation, and randomized algorithms.

CS301 / Bayesian Statistics in Practice

Bayes’ Theorem is a framework for combining prior information with new information to compute a posterior probability distribution. Gain insights into the differences between frequency-based statistics and Bayesian statistics by examining practical cases borrowed from such diverse fields as criminal justice, computer security and epidemiology. Also learn how to apply Bayesian approaches to learning from data

CS302 / Decision Science

Apply formal models of decision making to practical problems involving uncertainty, competition, complex systems, risk aversion, decision biases, and multiple objectives. Follow one principal case study throughout the course — for example, the decisions involved in pursuing the development of a drug. The case study incorporates decision trees, risk-adjusted calculations, optimization, and other methods.

Concentration Core Requirements

CS370 / Applications of Advanced Calculus

Utilize differentiation and integration, Taylor series, polar coordinates, partial derivatives, multiple integrals, and line and surface integrals (plus Gauss, Green and Stokes theorems) to frame and solve a broad range of practical problems.

CS470 / Applications of Advanced Linear Algebra

Implement matrix calculus and advanced concepts from linear algebra to frame and solve a broad range of problems. For example, study how Google’s PageRank is computed and suggest improvements. Assess the stability of complex ecological systems described by ordinary differential equations.

CS510 / Mathematical Foundations of Computer Science and Formal Logic

Analyze how to think about complex problems with the help of propositional logic and predicate calculus, formal proofs, and mathematical induction. Formalize deductive thought with symbolic logic, and examine the logical correctness of reasoning. Students review a range of practical applications of these foundational concepts, from calculating mathematical proofs to designing search algorithms.

Concentration Electives

CS371 / Intriguing and Incredibly Useful Applications of Ordinary Differential Equations

Discover how to use ordinary differential equations with an emphasis on mathematical modeling to frame and address a wide range of problems. Learn how to build ordinary differential equation models and solve them with analytical and computational techniques.

CS372 / Combinatorics and Graphs

Analyze how to use combinatorial concepts (for example, enumerative and analytic combinatorics, partition theory, probabilistic combinatorics, and generating functions) as well as graph theoretic concepts (such as trees, distance, cycles, coloring, route problems, subgraphs, giant component, covering, and visibility). Find highly diverse applications of combinatorics and graphs in food webs, industrial optimization and voting — illustrating the versatility and usefulness of concepts that may at first appear theoretical.

CS373 / Econometrics in Context

Explore how to use core econometric methods and statistical techniques to construct and test economic and social models in practical situations such as measuring the importance of peer pressure on teen smoking, estimating the elasticity of high end chocolate prices or evaluating the impact of mosquito bed nets against malaria. During in-class debates, students critically examine the assumptions, validity and outputs of the models.

CS411 / Building Useful and Usable Database Systems

Use data models, data description languages, query methods such as relational algebra and SQL, data normalization, and transaction and security protocols to design an efficient and secure database system for a real-world example. Also explore new trends in databases to sketch out what databases of the future may look like. For example, students examine how graph databases can be leveraged to process social network data or discover relationships between entities, with applications to biological and health care databases.

CS433 / Advanced Decision Science

Use advanced decision techniques such as real options and Monte Carlo simulation to address complex issues. Examples include project portfolio management, pharmaceutical drug development, and oil and gas investment decisions. Learn about philanthropic portfolio decisions requiring high-stake tradeoffs in highly uncertain environments and with complex, culturally and socially sensitive objectives.

CS471 / How to Make Partial Differential Equations Work for You

Solve partial differential equations using a combination of analytical and computational techniques, and apply partial differential equations to model the spread of epidemics, the dynamics of interest rates and patterns of highway traffic.

CS531 / Network Science

Understand how to use network concepts — from graph theory, mathematics, probability theory, and statistical physics — to analyze and predict the behavior of social, economic and transportation networks. Utilize properties such as centrality, diameter and effective distance; for example, model and predict the spread of an infectious disease and design interventions that can slow down or stop the epidemic.

CS552 / Causal Inference

Apply methods for establishing causation — from randomized controlled experiments to statistical approaches to infer causation from observational studies (matching methods and regression adjustments). Critically examine claims of causal links in such varied contexts as clinical trials (does a drug work better than a placebo?), economics (do incentives cause the desired behavior?), social sciences (does a friend’s happiness cause someone to be happy?), and program evaluation (do microloans reduce poverty?). Students conduct their own analysis on a topic of their choosing.

CS573 / Numerical Analysis

Solve scientific and engineering problems by calculating derivatives, integrals and differential equations using computational methods. Activities include modeling a complex social, economic or biological system numerically.

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