PhD Course List
Below are the pre-approved competencies as of Fall 2023. This list will be revised annually. Students may petition for alternative means to satisfy the competencies using other courses not on the list.
Methodology Core
Students are required to take at least five courses and must fulfill at least six of the eight competencies listed below. Note that a single course may satisfy multiple competencies.
Mathematical Foundations
CAS CS 531 4 credits.
Undergraduate Prerequisites: CAS MA 123 & 124, or equivalent and CAS CS 132 or equivalent; or conse nt of instructor. - Optimization algorithms, highlighting the fruitful interactions between discrete and continuous. Intended audience is advanced master students and doctoral students. Topics include gradient descent algorithms, online optimization, linear and semidefinite programming, duality, network optimization, submodular optimization, approximation algorithms via continuous relaxations.
CAS CS 538 4 credits.
Undergraduate Prerequisites: (CASCS131 & CASCS237 & CASCS357) or consent of instructor. - Graduate Prerequisites: (CASCS332) - Basic Algorithms to guarantee confidentiality and authenticity of data. Definitions and proofs of security for practical constructions. Topics include perfectly secure encryption, pseudorandom generators, RSA and Elgamal encryption, Diffie-Hellman key agreement, RSA signatures, secret sharing, block and stream ciphers.
CAS MA 576 4 credits.
Undergraduate Prerequisites: (CASMA575) or consent of instructor. - Covers topics in linear models beyond MA 575: generalized linear models, analysis of binary and polytomous data, log-linear models, multivariate response models, non-linear models, graphical models, and relevant model selection techniques. Additional topics in modern regression as time allows.
CAS MA 582 4 credits.
Undergraduate Prerequisites: : (CASMA 581 or ENGEK 381 or ENGEK 500) or consent of instructor. - Point estimation including unbiasedness, efficiency, consistency, sufficiency, minimum variance unbiased estimator, Rao-Blackwell theorem, and Rao-Cramer inequality. Maximum likelihood and method of moment estimations; interval estimation; tests of hypothesis, uniformly most powerful tests, uniformly most powerful unbiased tests, likelihood ratio test, and chi-square test.
CAS MA 588 4 credits.
Undergraduate Prerequisites: CASMA 582 or consent of instructor. - The theory and logic in the development of nonparametric techniques including order statistics, tests based on runs, goodness of fit, rank-order (for location and scale), measures of association, analysis of variance, asymptotic relative efficiency.
ENG EC 674 4 credits.
This course is an introduction to optimization problems and algorithms emphasizing problem formulation, basic methodologies and the underlying mathematical structures. We will cover the classical theory as well as the state of the art. The major topics we will cover are: 1. Theory and algorithms for linear programming. 2. Introduction to combinatorial problems and methods for handling intractable problems. 3. Introduction to nonlinear programming. 4. Introduction to network optimization. Optimization techniques have many applications in science and engineering. To name a few: * Optimal routing in communication networks. * Transmission scheduling and resource allocation in sensor networks. * Production planning and scheduling in manufacturing systems. * Fleet management. * Air traffic flow management by airlines. * Optimal resource allocation in manufacturing and communication systems. * Optimal portfolio selection. * Analysis and optimization of fluxes in metabolic networks. * Protein docking. Prerequisites: Working knowledge of Linear Algebra and some degree of mathematical maturity. Same as ENG EC 674, ENG SE 524, ENG EC 674. Students may not receive credits for both.
Statistical Modeling & Inference
CAS CS 542 4 credits.
Undergraduate Prerequisites: (CASCS365) - Introduction to modern machine learning concepts, techniques, and algorithms. Topics include regression, kernels, support vector machines, feature selection, boosting, clustering, hidden Markov models, and Bayesian networks. Programming assignments emphasize taking theory into practice, through applications on real-world data sets.
CAS MA 570 4 credits.
Undergraduate Prerequisites: (CASMA 225 or CASMA 230 or CDSDS 122) AND (CASMA 242 or CASMA4 42 or ENGEK 103 or CASCS 132) or consent of instructor) - Poisson processes, Markov chains, queuing theory. Matrix differential equations, differential-difference equations, probability-generating functions, single- and multiple-channel queues, steady-state and transient distributions.
CAS MA 575 4 credits.
Undergraduate Prerequisites: (CASMA 214 or CASMA 116) AND (CASMA 581 or ENGEK 381 or ENGEK 500 or CASCS 237) AND (CASMA 242 or ENGEK 103 or CDSDS 121 or CASMA 442 or CASCS 132) or consent of instructor. - Post-introductory course on linear models. Topics to be covered include simple and multiple linear regression, regression with polynomials or factors, analysis of variance, weighted and generalized least squares, transformations, regression diagnostics, variable selection, and extensions of linear models. Effective Fall 2019, this course fulfills a single unit in the following BU Hub area: Quantitative Reasoning II, Teamwork/Collaboration.
CAS MA 578 4 credits.
Undergraduate Prerequisites: CASMA 575 or consent of instructor. - The principles and methods of Bayesian statistics. Subjective probability, Bayes rule, posterior distributions, predictive distributions. Computationally based inference using Monte Carlo integration, Markov chain simulation. Hierarchical models, mixture models, model checking, and methods for Bayesian model selection.
CAS MA 582 4 credits.
Undergraduate Prerequisites: : (CASMA 581 or ENGEK 381 or ENGEK 500) or consent of instructor. - Point estimation including unbiasedness, efficiency, consistency, sufficiency, minimum variance unbiased estimator, Rao-Blackwell theorem, and Rao-Cramer inequality. Maximum likelihood and method of moment estimations; interval estimation; tests of hypothesis, uniformly most powerful tests, uniformly most powerful unbiased tests, likelihood ratio test, and chi-square test.
CAS MA 585 4 credits.
Undergraduate Prerequisites: CASMA 581 or ENGEK 381 or ENGEK 500 or consent of instructor. - Autocorrelation and partial autocorrelation functions; stationary and nonstationary processes; ARIMA and Seasonal ARIMA model identification, estimation, diagnostics, and forecasting. Modeling financial data via ARCH and GARCH models. Volatility estimation; additional topics, including long-range dependence and state-space models.
CAS MA 588 4 credits.
Undergraduate Prerequisites: CASMA 582 or consent of instructor. - The theory and logic in the development of nonparametric techniques including order statistics, tests based on runs, goodness of fit, rank-order (for location and scale), measures of association, analysis of variance, asymptotic relative efficiency.
ENG EC 505 4 credits.
Undergraduate Prerequisites: (ENGEC401 & CASMA142) or equivalent and either ENGEK381 or ENGEK500. - Introduction to discrete and continuous-time random processes. Correlation and power spectral density functions. Linear systems driven by random processes. Optimum detection and estimation. Bayesian, Weiner, and Kalman filtering.
QST DS 925 4 credits.
(Formerly SI 915) This course reviews tools and methods for drawing causal inferences from non-experimental data. The class emphasizes conceptual difficulties associated with establishing causality in observational settings, the strengths and weaknesses of statistical methods based on so-called natural experiments, and the practical problems that arise in the application of these tools. This course is designed to complement a traditional two-semester graduate sequence in econometrics.
Efficient & Scalable Algorithms
CAS CS 530 4 credits.
Undergraduate Prerequisites: (CASCS330) or consent of instructor. - Graduate Prerequisites: (CASCS330) or consent of instructor. - Studies the design and efficiency of algorithms in several areas of computer science. Topics are chosen from graph algorithms, sorting and searching, NP-complete problems, pattern matching, parallel algorithms, and dynamic programming.
CAS CS 565 4 credits.
Undergraduate Prerequisites: (CASCS112 & CASCS330 & CASCS365) - Introduction to data mining concepts and techniques. Topics include association and correlation discovery, classification and clustering of large datasets, outlier detection. Emphasis on the algorithmic aspects as well as the application of mining in real-world problems.
CAS MA 539 4 credits.
Undergraduate Prerequisites: (CASMA 225 or CASMA 230) & (CASMA 242 or CASMA 442) and programming experience or consent of instructor. - An introduction to topics including computational linear algebra, solutions of linear equations, numerical integration and solution of differential equations, finite element methods, and methods of stochastic simulation (i.e., Monte Carlo methods).
Predictive Analysis & ML
CAS CS 542 4 credits.
Undergraduate Prerequisites: (CASCS365) - Introduction to modern machine learning concepts, techniques, and algorithms. Topics include regression, kernels, support vector machines, feature selection, boosting, clustering, hidden Markov models, and Bayesian networks. Programming assignments emphasize taking theory into practice, through applications on real-world data sets.
CAS MA 575 4 credits.
Undergraduate Prerequisites: (CASMA 214 or CASMA 116) AND (CASMA 581 or ENGEK 381 or ENGEK 500 or CASCS 237) AND (CASMA 242 or ENGEK 103 or CDSDS 121 or CASMA 442 or CASCS 132) or consent of instructor. - Post-introductory course on linear models. Topics to be covered include simple and multiple linear regression, regression with polynomials or factors, analysis of variance, weighted and generalized least squares, transformations, regression diagnostics, variable selection, and extensions of linear models. Effective Fall 2019, this course fulfills a single unit in the following BU Hub area: Quantitative Reasoning II, Teamwork/Collaboration.
CAS MA 576 4 credits.
Undergraduate Prerequisites: (CASMA575) or consent of instructor. - Covers topics in linear models beyond MA 575: generalized linear models, analysis of binary and polytomous data, log-linear models, multivariate response models, non-linear models, graphical models, and relevant model selection techniques. Additional topics in modern regression as time allows.
ENG EC 503 4 credits.
Prerequisites: EK381 or equivalent; EK102 or equivalent; MA225 or equivalent; EK125 or equivalent.
This is an introductory graduate course in (classical) machine learning covering the basic principles and methods of four major non-sequential supervised and unsupervised learning problems namely, classification, regression, clustering, and dimensionality reduction. A variety of contemporary applications will be explored through homeworks and a project.
ENG EC 523 4 credits.
Feed-forward networks. Backpropagation. Training strategies for deep networks. Convolutional networks. Recurrent neural networks. Transformers. Diffusion Models. Deep unsupervised learning. Exposure to Pytorch and other modern programming tools. Other recent topics, time permitting. Same as CAS CS 523. Students may not receive credit for both.
Optimization Algorithms
CAS CS 531 4 credits.
Undergraduate Prerequisites: CAS MA 123 & 124, or equivalent and CAS CS 132 or equivalent; or conse nt of instructor. - Optimization algorithms, highlighting the fruitful interactions between discrete and continuous. Intended audience is advanced master students and doctoral students. Topics include gradient descent algorithms, online optimization, linear and semidefinite programming, duality, network optimization, submodular optimization, approximation algorithms via continuous relaxations.
CAS MA 569 4 credits.
Undergraduate Prerequisites: (CASMA 225 or CASMA 230 or CDSDS 122) AND (CASMA 242 or CASMA 442 or ENGEK 103 or CDSCS 132) or consent of instructor. - Graduate Prerequisites: graduate standing. - Optimization of linear functions: linear programming, simplex method; transportation, assignment, and network problems. Optimization of non-linear functions: unconstrained optima, constrained optima and Lagrange multipliers, Kuhn-Tucker conditions, calculus of variations, and Euler's equation.
ENG EC 524 4 credits.
Undergraduate Prerequisites: (ENGEK103 OR CASMA142) - Introduction to optimization problems and algorithms emphasizing problem formulation, basic methodologies, and underlying mathematical structures. Classical optimization theory as well as recent advances in the field. Topics include modeling issues and formulations, simplex method, duality theory, sensitivity analysis, large-scale optimization, integer programming, interior-point methods, non-linear programming optimality conditions, gradient methods, and conjugate direction methods. Applications are considered; case studies included. Extensive paradigms from production planning and scheduling in manufacturing systems. Other illustrative applications include fleet management, air traffic flow management, optimal routing in communication networks, and optimal portfolio selection. Same as ENG EC 674, ENG SE 524, ENG SE 674. Students may not receive credit for both.
ENG EC 674 4 credits.
This course is an introduction to optimization problems and algorithms emphasizing problem formulation, basic methodologies and the underlying mathematical structures. We will cover the classical theory as well as the state of the art. The major topics we will cover are: 1. Theory and algorithms for linear programming. 2. Introduction to combinatorial problems and methods for handling intractable problems. 3. Introduction to nonlinear programming. 4. Introduction to network optimization. Optimization techniques have many applications in science and engineering. To name a few: * Optimal routing in communication networks. * Transmission scheduling and resource allocation in sensor networks. * Production planning and scheduling in manufacturing systems. * Fleet management. * Air traffic flow management by airlines. * Optimal resource allocation in manufacturing and communication systems. * Optimal portfolio selection. * Analysis and optimization of fluxes in metabolic networks. * Protein docking. Prerequisites: Working knowledge of Linear Algebra and some degree of mathematical maturity. Same as ENG EC 674, ENG SE 524, ENG EC 674. Students may not receive credits for both.
Computational Complexity
CAS CS 530 4 credits.
Undergraduate Prerequisites: (CASCS330) or consent of instructor. - Graduate Prerequisites: (CASCS330) or consent of instructor. - Studies the design and efficiency of algorithms in several areas of computer science. Topics are chosen from graph algorithms, sorting and searching, NP-complete problems, pattern matching, parallel algorithms, and dynamic programming.
CAS CS 531 4 credits.
Undergraduate Prerequisites: CAS MA 123 & 124, or equivalent and CAS CS 132 or equivalent; or conse nt of instructor. - Optimization algorithms, highlighting the fruitful interactions between discrete and continuous. Intended audience is advanced master students and doctoral students. Topics include gradient descent algorithms, online optimization, linear and semidefinite programming, duality, network optimization, submodular optimization, approximation algorithms via continuous relaxations.
CAS CS 535 4 credits.
Undergraduate Prerequisites: (CASCS332) or consent of instructor. - Graduate Prerequisites: (CASCS332) - Covers topics of current interest in the theory of computation chosen from computational models, games and hierarchies of problems, abstract complexity theory, informational complexity theory, time-space trade-offs, probabilistic computation, and recent work on particular combinatorial problems.
CAS CS 538 4 credits.
Undergraduate Prerequisites: (CASCS131 & CASCS237 & CASCS357) or consent of instructor. - Graduate Prerequisites: (CASCS332) - Basic Algorithms to guarantee confidentiality and authenticity of data. Definitions and proofs of security for practical constructions. Topics include perfectly secure encryption, pseudorandom generators, RSA and Elgamal encryption, Diffie-Hellman key agreement, RSA signatures, secret sharing, block and stream ciphers.
Programming & Software Design
CAS CS 561 4 credits.
BU Hub Learn More Oral and/or Signed Communication Research and Information Literacy
Undergraduate Prerequisites: CAS CS 210 or equivalent and CAS CS 460/660. - Discusses the design of data systems that can address the modern challenges of managing and accessing large, ever-growing, diverse sets of data, often streaming from heterogenous sources, in the context of continuously evolving hardware and software. We use examples from several data management areas including relational systems, distributed database systems, key value stores, newSQL and NoSQL systems, data systems for machine learning (and machine learning for data systems), interactive analytics, and data management as a service. Effective Spring 2021, this course fulfills a single unit in each of the following BU Hub areas: Oral and/or Signed Communication, Research and Information Literacy.
ENG EC 523 4 credits.
Feed-forward networks. Backpropagation. Training strategies for deep networks. Convolutional networks. Recurrent neural networks. Transformers. Diffusion Models. Deep unsupervised learning. Exposure to Pytorch and other modern programming tools. Other recent topics, time permitting. Same as CAS CS 523. Students may not receive credit for both.
ENG EC 527 4 credits.
Considers theory and practice of hardware-aware programming. Key theme is obtaining a significant fraction of potential performance through knowledge of the underlying computing platform and how the platform interacts with programs. Studies architecture of, and programming methods for, contemporary high-performance processors. These include complex processor cores, multicore processors, and graphics processors. Laboratory component includes use and evaluation of programming methods on these processors through applications such as matrix operations and the Fast Fourier Transform.
Large-scale Data Management
CAS CS 561 4 credits.
BU Hub Learn More Oral and/or Signed Communication Research and Information Literacy
Undergraduate Prerequisites: CAS CS 210 or equivalent and CAS CS 460/660. - Discusses the design of data systems that can address the modern challenges of managing and accessing large, ever-growing, diverse sets of data, often streaming from heterogenous sources, in the context of continuously evolving hardware and software. We use examples from several data management areas including relational systems, distributed database systems, key value stores, newSQL and NoSQL systems, data systems for machine learning (and machine learning for data systems), interactive analytics, and data management as a service. Effective Spring 2021, this course fulfills a single unit in each of the following BU Hub areas: Oral and/or Signed Communication, Research and Information Literacy.
CAS CS 565 4 credits.
Undergraduate Prerequisites: (CASCS112 & CASCS330 & CASCS365) - Introduction to data mining concepts and techniques. Topics include association and correlation discovery, classification and clustering of large datasets, outlier detection. Emphasis on the algorithmic aspects as well as the application of mining in real-world problems.
Subject Core
To satisfy the subject core requirement, students must take a minimum of three courses in a single subject area.
Theoretical Foundations
CAS CS 530 4 credits.
Undergraduate Prerequisites: (CASCS330) or consent of instructor. - Graduate Prerequisites: (CASCS330) or consent of instructor. - Studies the design and efficiency of algorithms in several areas of computer science. Topics are chosen from graph algorithms, sorting and searching, NP-complete problems, pattern matching, parallel algorithms, and dynamic programming.
CAS CS 531 4 credits.
Undergraduate Prerequisites: CAS MA 123 & 124, or equivalent and CAS CS 132 or equivalent; or conse nt of instructor. - Optimization algorithms, highlighting the fruitful interactions between discrete and continuous. Intended audience is advanced master students and doctoral students. Topics include gradient descent algorithms, online optimization, linear and semidefinite programming, duality, network optimization, submodular optimization, approximation algorithms via continuous relaxations.
CAS CS 535 4 credits.
Undergraduate Prerequisites: (CASCS332) or consent of instructor. - Graduate Prerequisites: (CASCS332) - Covers topics of current interest in the theory of computation chosen from computational models, games and hierarchies of problems, abstract complexity theory, informational complexity theory, time-space trade-offs, probabilistic computation, and recent work on particular combinatorial problems.
CAS CS 538 4 credits.
Undergraduate Prerequisites: (CASCS131 & CASCS237 & CASCS357) or consent of instructor. - Graduate Prerequisites: (CASCS332) - Basic Algorithms to guarantee confidentiality and authenticity of data. Definitions and proofs of security for practical constructions. Topics include perfectly secure encryption, pseudorandom generators, RSA and Elgamal encryption, Diffie-Hellman key agreement, RSA signatures, secret sharing, block and stream ciphers.
CAS MA 576 4 credits.
Undergraduate Prerequisites: (CASMA575) or consent of instructor. - Covers topics in linear models beyond MA 575: generalized linear models, analysis of binary and polytomous data, log-linear models, multivariate response models, non-linear models, graphical models, and relevant model selection techniques. Additional topics in modern regression as time allows.
CAS MA 582 4 credits.
Undergraduate Prerequisites: : (CASMA 581 or ENGEK 381 or ENGEK 500) or consent of instructor. - Point estimation including unbiasedness, efficiency, consistency, sufficiency, minimum variance unbiased estimator, Rao-Blackwell theorem, and Rao-Cramer inequality. Maximum likelihood and method of moment estimations; interval estimation; tests of hypothesis, uniformly most powerful tests, uniformly most powerful unbiased tests, likelihood ratio test, and chi-square test.
CAS MA 588 4 credits.
Undergraduate Prerequisites: CASMA 582 or consent of instructor. - The theory and logic in the development of nonparametric techniques including order statistics, tests based on runs, goodness of fit, rank-order (for location and scale), measures of association, analysis of variance, asymptotic relative efficiency.
ENG EC 674 4 credits.
This course is an introduction to optimization problems and algorithms emphasizing problem formulation, basic methodologies and the underlying mathematical structures. We will cover the classical theory as well as the state of the art. The major topics we will cover are: 1. Theory and algorithms for linear programming. 2. Introduction to combinatorial problems and methods for handling intractable problems. 3. Introduction to nonlinear programming. 4. Introduction to network optimization. Optimization techniques have many applications in science and engineering. To name a few: * Optimal routing in communication networks. * Transmission scheduling and resource allocation in sensor networks. * Production planning and scheduling in manufacturing systems. * Fleet management. * Air traffic flow management by airlines. * Optimal resource allocation in manufacturing and communication systems. * Optimal portfolio selection. * Analysis and optimization of fluxes in metabolic networks. * Protein docking. Prerequisites: Working knowledge of Linear Algebra and some degree of mathematical maturity. Same as ENG EC 674, ENG SE 524, ENG EC 674. Students may not receive credits for both.
Software & Systems
CAS CS 561 4 credits.
BU Hub Learn More Oral and/or Signed Communication Research and Information Literacy
Undergraduate Prerequisites: CAS CS 210 or equivalent and CAS CS 460/660. - Discusses the design of data systems that can address the modern challenges of managing and accessing large, ever-growing, diverse sets of data, often streaming from heterogenous sources, in the context of continuously evolving hardware and software. We use examples from several data management areas including relational systems, distributed database systems, key value stores, newSQL and NoSQL systems, data systems for machine learning (and machine learning for data systems), interactive analytics, and data management as a service. Effective Spring 2021, this course fulfills a single unit in each of the following BU Hub areas: Oral and/or Signed Communication, Research and Information Literacy.
ENG EC 527 4 credits.
Considers theory and practice of hardware-aware programming. Key theme is obtaining a significant fraction of potential performance through knowledge of the underlying computing platform and how the platform interacts with programs. Studies architecture of, and programming methods for, contemporary high-performance processors. These include complex processor cores, multicore processors, and graphics processors. Laboratory component includes use and evaluation of programming methods on these processors through applications such as matrix operations and the Fast Fourier Transform.
Data Mining & Machine Learning
CAS CS 542 4 credits.
Undergraduate Prerequisites: (CASCS365) - Introduction to modern machine learning concepts, techniques, and algorithms. Topics include regression, kernels, support vector machines, feature selection, boosting, clustering, hidden Markov models, and Bayesian networks. Programming assignments emphasize taking theory into practice, through applications on real-world data sets.
CAS CS 565 4 credits.
Undergraduate Prerequisites: (CASCS112 & CASCS330 & CASCS365) - Introduction to data mining concepts and techniques. Topics include association and correlation discovery, classification and clustering of large datasets, outlier detection. Emphasis on the algorithmic aspects as well as the application of mining in real-world problems.
ENG EC 523 4 credits.
Feed-forward networks. Backpropagation. Training strategies for deep networks. Convolutional networks. Recurrent neural networks. Transformers. Diffusion Models. Deep unsupervised learning. Exposure to Pytorch and other modern programming tools. Other recent topics, time permitting. Same as CAS CS 523. Students may not receive credit for both.
AI and Human-Centered Computing
DS for Social & Behavioral Sciences