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Introduction to Information and Data Systems Research
1 unit (1-0-0)  | second term

This course will introduce students to research areas in IDS through weekly overview talks by Caltech faculty and aimed at first-year undergraduates. Others may wish to take the course to gain an understanding of the scope of research in computer science. Graded pass/fail. Not offered 2023-24.

Instructor: Staff
ACM/IDS 101 ab
Methods of Applied Mathematics
12 units (4-4-4)  | first, second terms
Prerequisites: Math 2/102 and ACM 95 ab or equivalent.

First term: Brief review of the elements of complex analysis and complex-variable methods. Asymptotic expansions, asymptotic evaluation of integrals (Laplace method, stationary phase, steepest descents), perturbation methods, WKB theory, boundary-layer theory, matched asymptotic expansions with first-order and high-order matching. Method of multiple scales for oscillatory systems. Second term: Applied spectral theory, special functions, generalized eigenfunction expansions, convergence theory. Gibbs and Runge phenomena and their resolution. Chebyshev expansion and Fourier Continuation methods. Review of numerical stability theory for time evolution. Fast spectrally-accurate PDE solvers for linear and nonlinear Partial Differential Equations in general domains. Integral-equations methods for linear partial differential equation in general domains (Laplace, Helmholtz, Schroedinger, Maxwell, Stokes). Homework problems in both 101 a and 101 b include theoretical questions as well as programming implementations of the mathematical and numerical methods studied in class.

Instructor: Bruno
Applied Linear Algebra
9 units (3-1-5)  | first term
Prerequisites: Ma 1 abc, some familiarity with MATLAB, e.g. ACM 11 is desired.

This is an intermediate linear algebra course aimed at a diverse group of students, including junior and senior majors in applied mathematics, sciences and engineering. The focus is on applications. Matrix factorizations play a central role. Topics covered include linear systems, vector spaces and bases, inner products, norms, minimization, the Cholesky factorization, least squares approximation, data fitting, interpolation, orthogonality, the QR factorization, ill-conditioned systems, discrete Fourier series and the fast Fourier transform, eigenvalues and eigenvectors, the spectral theorem, optimization principles for eigenvalues, singular value decomposition, condition number, principal component analysis, the Schur decomposition, methods for computing eigenvalues, non-negative matrices, graphs, networks, random walks, the Perron-Frobenius theorem, PageRank algorithm.

Instructor: Zuev
CMS/ACM/IDS 107 ab
Linear Analysis with Applications
12 units (3-0-9)  | first, second terms
Prerequisites: ACM/IDS 104 or equivalent, Ma 1b or equivalent.
Part a: Covers the basic algebraic, geometric, and topological properties of normed linear spaces, inner-product spaces and linear maps. Emphasis is placed both on rigorous mathematical development and on applications to control theory, data analysis and partial differential equations. Topics: Completeness, Banach spaces (l_p, L_p), Hilbert spaces (weighted l_2, L_2 spaces), introduction to Fourier transform, Fourier series and Sobolev spaces, Banach spaces of linear operators, duality and weak convergence, density, separability, completion, Schauder bases, continuous and compact embedding, compact operators, orthogonality, Lax-Milgram, Spectral Theorem and SVD for compact operators, integral operators, Jordan normal form. Part b: Continuation of ACM 107a, developing new material and providing further details on some topics already covered. Emphasis is placed both on rigorous mathematical development and on applications to control theory, data analysis and partial differential equations.Topics: Review of Banach spaces, Hilbert spaces, Linear Operators, and Duality, Hahn-Banach Theorem, Open Mapping and Closed Graph Theorem, Uniform Boundedness Principle, The Fourier transform (L1, L2, Schwartz space theory), Sobolev spaces (W^s,p, H^s), Sobolev embedding theorem, Trace theorem Spectral Theorem, Compact operators, Ascoli Arzela theorem, Contraction Mapping Principle, with applications to the Implicit Function Theorem and ODEs, Calculus of Variations (differential calculus, existence of extrema, Gamma-convergence, gradient flows) Applications to Inverse Problems (Tikhonov regularization, imaging applications).
Instructors: Leong, Stuart
Mathematical Optimization
12 units (3-0-9)  | first term
Prerequisites: ACM 11 and ACM 104, or instructor's permission.
This class studies mathematical optimization from the viewpoint of convexity. Topics covered include duality and representation of convex sets; linear and semidefinite programming; connections to discrete, network, and robust optimization; relaxation methods for intractable problems; as well as applications to problems arising in graphs and networks, information theory, control, signal processing, and other engineering disciplines.
Instructor: Chandrasekaran
Introduction to Probability Models
9 units (3-1-5)  | first term
Prerequisites: Ma 3 or EE 55, some familiarity with MATLAB, e.g. ACM 11, is desired.

This course introduces students to the fundamental concepts, methods, and models of applied probability and stochastic processes. The course is application oriented and focuses on the development of probabilistic thinking and intuitive feel of the subject rather than on a more traditional formal approach based on measure theory. The main goal is to equip science and engineering students with necessary probabilistic tools they can use in future studies and research. Topics covered include sample spaces, events, probabilities of events, discrete and continuous random variables, expectation, variance, correlation, joint and marginal distributions, independence, moment generating functions, law of large numbers, central limit theorem, random vectors and matrices, random graphs, Gaussian vectors, branching, Poisson, and counting processes, general discrete- and continuous-timed processes, auto- and cross-correlation functions, stationary processes, power spectral densities.

Instructor: Zuev
CS/IDS 121
Relational Databases
9 units (3-0-6)  | second term
Prerequisites: CS 1 or equivalent.

Introduction to the basic theory and usage of relational database systems. It covers the relational data model, relational algebra, and the Structured Query Language (SQL). The course introduces the basics of database schema design and covers the entity-relationship model, functional dependency analysis, and normal forms. Additional topics include other query languages based on the relational calculi, data-warehousing and dimensional analysis, writing and using stored procedures, working with hierarchies and graphs within relational databases, and an overview of transaction processing and query evaluation. Extensive hands-on work with SQL databases.

Instructor: Hovik
IDS/Ec/PS 126
Applied Data Analysis
9 units (3-0-6)  | first term
Prerequisites: Ma 3/103 or ACM/EE/IDS 116, Ec 122 or IDS/ACM/CS 157 or Ma 112 a.

Fundamentally, this course is about making arguments with numbers and data. Data analysis for its own sake is often quite boring, but becomes crucial when it supports claims about the world. A convincing data analysis starts with the collection and cleaning of data, a thoughtful and reproducible statistical analysis of it, and the graphical presentation of the results. This course will provide students with the necessary practical skills, chiefly revolving around statistical computing, to conduct their own data analysis. This course is not an introduction to statistics or computer science. I assume that students are familiar with at least basic probability and statistical concepts up to and including regression.

Instructor: Katz
EE/Ma/CS/IDS 127
Error-Correcting Codes
9 units (3-0-6)  | third term
Prerequisites: EE 55 or equivalent.
This course develops from first principles the theory and practical implementation of the most important techniques for combating errors in digital transmission and storage systems. Topics include highly symmetric linear codes, such as Hamming, Reed-Muller, and Polar codes; algebraic block codes, such as Reed-Solomon and BCH codes, including a self-contained introduction to the theory of finite fields; and low-density parity-check codes. Students will become acquainted with encoding and decoding algorithms, design principles and performance evaluation of codes.
Instructor: Kostina
EE/Ma/CS/IDS 136
Information Theory and Applications
9 units (3-0-6)  | third term
Prerequisites: EE 55 or equivalent.
This class introduces information measures such as entropy, information divergence, mutual information, information density, and establishes the fundamental importance of those measures in data compression, statistical inference, and error control. The course does not require a prior exposure to information theory; it is complementary to EE 126a.
Instructor: Kostina
Analysis and Design of Algorithms
12 units (3-0-9)  | first term
Prerequisites: Ma 2, Ma 3, Ma/CS 6 a, CS 21, CS 38/138, and ACM/EE/IDS 116 or CMS/ACM/EE 122 or equivalent.

This course develops core principles for the analysis and design of algorithms. Basic material includes mathematical techniques for analyzing performance in terms of resources, such as time, space, and randomness. The course introduces the major paradigms for algorithm design, including greedy methods, divide-and-conquer, dynamic programming, linear and semidefinite programming, randomized algorithms, and online learning.

Instructor: Mahadev
Ma/ACM/IDS 140 ab
9 units (3-0-6)  | second, third terms
Prerequisites: For 140 a, Ma 108 b is strongly recommended.

Overview of measure theory. Random walks and the Strong law of large numbers via the theory of martingales and Markov chains. Characteristic functions and the central limit theorem. Poisson process and Brownian motion. Topics in statistics. Part b not offered 2023-24.

Instructor: Vigneaux
CS/IDS 142
Distributed Computing
9 units (3-2-4)  | first term
Prerequisites: CS 24, CS 38.

Programming distributed systems. Mechanics for cooperation among concurrent agents. Programming sensor networks and cloud computing applications. Applications of machine learning and statistics by using parallel computers to aggregate and analyze data streams from sensors. Not offered 2023-24.

Instructor: Staff
Networks: Algorithms & Architecture
12 units (3-4-5)  | third term
Prerequisites: Ma 2, Ma 3, Ma/CS 6 a, and CS 38, or instructor permission.
Social networks, the web, and the internet are essential parts of our lives, and we depend on them every day. CS/EE/IDS 143 and CMS/CS/EE/IDS 144 study how they work and the "big" ideas behind our networked lives. In this course, the questions explored include: Why is an hourglass architecture crucial for the design of the Internet? Why doesn't the Internet collapse under congestion? How are cloud services so scalable? How do algorithms for wireless and wired networks differ? For all these questions and more, the course will provide a mixture of both mathematical analysis and hands-on labs. The course expects students to be comfortable with graph theory, probability, and basic programming.
Instructor: Wierman
Networks: Structure & Economics
12 units (3-4-5)  | second term
Prerequisites: Ma 2, Ma 3, Ma/CS 6 a, and CS 38, or instructor permission.
Social networks, the web, and the internet are essential parts of our lives, and we depend on them every day. CS/EE/IDS 143 and CMS/CS/EE/IDS 144 study how they work and the "big" ideas behind our networked lives. In this course, the questions explored include: What do networks actually look like (and why do they all look the same)?; How do search engines work?; Why do epidemics and memes spread the way they do?; How does web advertising work? For all these questions and more, the course will provide a mixture of both mathematical analysis and hands-on labs. The course expects students to be comfortable with graph theory, probability, and basic programming.
Instructor: Mazumdar
CS/IDS 150 ab
Probability and Algorithms
9 units (3-0-6)  | first, third terms
Prerequisites: part a: CS 38 and Ma 5 abc; part b: part a or another introductory course in discrete probability.

Part a: The probabilistic method and randomized algorithms. Deviation bounds, k-wise independence, graph problems, identity testing, derandomization and parallelization, metric space embeddings, local lemma. Part b: Further topics such as weighted sampling, epsilon-biased sample spaces, advanced deviation inequalities, rapidly mixing Markov chains, analysis of boolean functions, expander graphs, and other gems in the design and analysis of probabilistic algorithms. Parts a & b are given in alternate years. Not offered 2023-24.

Instructor: Schulman
CS/IDS 153
Current Topics in Theoretical Computer Science
9 units (3-0-6)  | first, second, third terms
Prerequisites: CS 21 and CS 38, or instructor's permission.

May be repeated for credit, with permission of the instructor. Students in this course will study an area of current interest in theoretical computer science. The lectures will cover relevant background material at an advanced level and present results from selected recent papers within that year's chosen theme. Students will be expected to read and present a research paper.

Instructors: Mahadev, Schulman, Umans
Inverse Problems and Data Assimilation
9 units (3-0-6)  | second term
Prerequisites: Basic differential equations, linear algebra, probability and statistics: ACM/IDS 104, ACM/EE 106 ab, ACM/EE/IDS 116, IDS/ACM/CS 157 or equivalent.

Models in applied mathematics often have input parameters that are uncertain; observed data can be used to learn about these parameters and thereby to improve predictive capability. The purpose of the course is to describe the mathematical and algorithmic principles of this area. The topic lies at the intersection of fields including inverse problems, differential equations, machine learning and uncertainty quantification. Applications will be drawn from the physical, biological and data sciences.

Instructors: Baptista, Carlson
Machine Learning & Data Mining
12 units (3-3-6)  | second term
Prerequisites: CS/CNS/EE 156 a. Having a sufficient background in algorithms, linear algebra, calculus, probability, and statistics, is highly recommended.
This course will cover popular methods in machine learning and data mining, with an emphasis on developing a working understanding of how to apply these methods in practice. The course will focus on basic foundational concepts underpinning and motivating modern machine learning and data mining approaches. We will also discuss recent research developments.
Instructor: Yue
Statistical Inference
9 units (3-2-4)  | third term
Prerequisites: ACM/EE/IDS 116, Ma 3.

Statistical Inference is a branch of mathematical engineering that studies ways of extracting reliable information from limited data for learning, prediction, and decision making in the presence of uncertainty. This is an introductory course on statistical inference. The main goals are: develop statistical thinking and intuitive feel for the subject; introduce the most fundamental ideas, concepts, and methods of statistical inference; and explain how and why they work, and when they don't. Topics covered include summarizing data, fundamentals of survey sampling, statistical functionals, jackknife, bootstrap, methods of moments and maximum likelihood, hypothesis testing, p-values, the Wald, Student's t-, permutation, and likelihood ratio tests, multiple testing, scatterplots, simple linear regression, ordinary least squares, interval estimation, prediction, graphical residual analysis.

Instructor: Zuev
Fundamentals of Statistical Learning
9 units (3-3-3)  | second term
Prerequisites: ACM/IDS 104, ACM/EE/IDS 116, IDS/ACM/CS 157.
The main goal of the course is to provide an introduction to the central concepts and core methods of statistical learning, an interdisciplinary field at the intersection of applied mathematics, statistical inference, and machine learning. The course focuses on the mathematics and statistics of methods developed for learning from data. Students will learn what methods for statistical learning exist, how and why they work (not just what tasks they solve and in what built-in functions they are implemented), and when they are expected to perform poorly. The course is oriented for upper level undergraduate students in IDS, ACM, and CS and graduate students from other disciplines who have sufficient background in linear algebra, probability, and statistics. The course is a natural continuation of IDS/ACM/CS 157 and it can be viewed as a statistical analog of CMS/CS/CNS/EE/IDS 155. Topics covered include elements of statistical decision theory, regression and classification problems, nearest-neighbor methods, curse of dimensionality, linear regression, model selection, cross-validation, subset selection, shrinkage methods, ridge regression, LASSO, logistic regression, linear and quadratic discriminant analysis, support-vector machines, tree-based methods, bagging, and random forests.
Instructor: Zuev
Advanced Topics in Machine Learning
9 units (3-0-6)  | third term
Prerequisites: CS 155; strong background in statistics, probability theory, algorithms, and linear algebra; background in optimization is a plus as well.

This course focuses on current topics in machine learning research. This is a paper reading course, and students are expected to understand material directly from research articles. Students are also expected to present in class, and to do a final project.

Instructor: Yue
Fundamentals of Information Transmission and Storage
9 units (3-0-6)  | second term
Prerequisites: EE 55 or equivalent.

Basics of information theory: entropy, mutual information, source and channel coding theorems. Basics of coding theory: error-correcting codes for information transmission and storage, block codes, algebraic codes, sparse graph codes. Basics of digital communications: sampling, quantization, digital modulation, matched filters, equalization.

Instructor: Hassibi
CS/IDS 162
Data, Algorithms and Society
9 units (3-0-6)  | second term
Prerequisites: CS 38 and CS 155 or 156 a.

This course examines algorithms and data practices in fields such as machine learning, privacy, and communication networks through a social lens. We will draw upon theory and practices from art, media, computer science and technology studies to critically analyze algorithms and their implementations within society. The course includes projects, lectures, readings, and discussions. Students will learn mathematical formalisms, critical thinking and creative problem solving to connect algorithms to their practical implementations within social, cultural, economic, legal and political contexts. Enrollment by application. Taught concurrently with VC 72 and can only be taken once as CS/IDS 162 or VC 72.

Instructor: Ralph
Foundations of Machine Learning and Statistical Inference
12 units (3-3-6)  | second term
Prerequisites: CMS/ACM/EE 122, ACM/EE/IDS 116, CS 156 a, ACM/CS/IDS 157 or instructor's permission.

The course assumes students are comfortable with analysis, probability, statistics, and basic programming. This course will cover core concepts in machine learning and statistical inference. The ML concepts covered are spectral methods (matrices and tensors), non-convex optimization, probabilistic models, neural networks, representation theory, and generalization. In statistical inference, the topics covered are detection and estimation, sufficient statistics, Cramer-Rao bounds, Rao-Blackwell theory, variational inference, and multiple testing. In addition to covering the core concepts, the course encourages students to ask critical questions such as: How relevant is theory in the age of deep learning? What are the outstanding open problems? Assignments will include exploring failure modes of popular algorithms, in addition to traditional problem-solving type questions.

Instructor: Anandkumar
Computational Cameras
12 units (3-3-6)  | third term
Prerequisites: ACM 104 or ACM 107 or equivalent.

Computational cameras overcome the limitations of traditional cameras, by moving part of the image formation process from hardware to software. In this course, we will study this emerging multi-disciplinary field at the intersection of signal processing, applied optics, computer graphics, and vision. At the start of the course, we will study modern image processing and image editing pipelines, including those encountered on DSLR cameras and mobile phones. Then we will study the physical and computational aspects of tasks such as coded photography, light-field imaging, astronomical imaging, medical imaging, and time-of-flight cameras. The course has a strong hands-on component, in the form of homework assignments and a final project. In the homework assignments, students will have the opportunity to implement many of the techniques covered in the class. Example homework assignments include building an end-to-end HDR (High Dynamic Range) imaging pipeline, implementing Poisson image editing, refocusing a light-field image, and making your own lensless "scotch-tape" camera.

Instructor: Bouman
Introduction to Data Compression and Storage
9 units (3-0-6)  | third term
Prerequisites: Ma 3 or ACM/EE/IDS 116.

The course will introduce the students to the basic principles and techniques of codes for data compression and storage. The students will master the basic algorithms used for lossless and lossy compression of digital and analog data and the major ideas behind coding for flash memories. Topics include the Huffman code, the arithmetic code, Lempel-Ziv dictionary techniques, scalar and vector quantizers, transform coding; codes for constrained storage systems. Given in alternate years; not offered 2023-24.

Mathematics of Signal Processing
12 units (3-0-9)  | third term
Prerequisites: ACM/IDS 104, CMS/ACM/EE 122, and ACM/EE/IDS 116; or instructor's permission.

This course covers classical and modern approaches to problems in signal processing. Problems may include denoising, deconvolution, spectral estimation, direction-of-arrival estimation, array processing, independent component analysis, system identification, filter design, and transform coding. Methods rely heavily on linear algebra, convex optimization, and stochastic modeling. In particular, the class will cover techniques based on least-squares and on sparse modeling. Throughout the course, a computational viewpoint will be emphasized. Not offered 2023-24.

Instructor: Hassibi
CS/IDS 178
Numerical Algorithms and their Implementation
9 units (3-3-3)  | third term
Prerequisites: CS 2.

This course gives students the understanding necessary to choose and implement basic numerical algorithms as needed in everyday programming practice. Concepts include: sources of numerical error, stability, convergence, ill-conditioning, and efficiency. Algorithms covered include solution of linear systems (direct and iterative methods), orthogonalization, SVD, interpolation and approximation, numerical integration, solution of ODEs and PDEs, transform methods (Fourier, Wavelet), and low rank approximation such as multipole expansions. Not offered 2023-24.

Instructor: Staff
ACM/IDS 180 ab
Multiscale Modeling
12 units (3-0-9)  | first, third terms
Prerequisites: CMS 107, CMS 117 or explicit email permission from instructor.

Part a: Multiscale methodology for partial differential equations (PDEs) and for stochastic differential equations (SDEs). Basic theory of underlying PDEs; basic theory of Gaussian processes; basic theory of SDEs; multiscale expansions. Part b: Transition from quantum to continuum modeling of materials. Schrodinger equation and semi-classical limit; molecular dynamics and kinetic theory; kinetic theory, Boltzmann equation and continuum mechanics. Not offered 2023-24.

Instructor: Stuart
ESE/Ge/Bi/IDS 184
Computational Tools for Decoding Microbial Ecosystems
9 units (3-0-6)  | second term
Microbes, the most diverse and abundant organisms on Earth, are critical to the daily functioning of humans as well as the life-sustaining biogeochemical cycles. This course provides an in-depth exploration of the fascinating world of environmental microbiology and genomics, with a special emphasis on computational approaches for systems-level analysis of microbial communities and their interactions. The course will delve into the diverse roles of microorganisms in environmental processes ranging from nutrient and biogeochemical cycling to predicting the impacts of climate change. It will introduce students to a wide range of computational tools and techniques used in the analysis of microbial genomic data. Topics covered include: microbial community structure and functioning; interactions among microbes and their environment; and the influence of the environment in shaping and driving microbial evolution. Through a combination of lectures, discussions, and hands-on computational exercises, students will gain skills in analyzing, interpreting and visualizing large scale community metagenomic (DNA) and metatranscriptomic (RNA) data from environmental ecosystems. Students will also explore how these computational approaches can be applied to address real-world environmental challenges, broaden understanding of the genetic and metabolic diversity of the microorganisms to better manage ecosystem function, the value of this biodiversity for adaptation to natural and anthropogenic perturbations. Prior experience in Environmental microbiology, shell scripting and python while encouraged is not required.
Instructor: Karthikeyan
IDS 197
Undergraduate Reading in the Information and Data Sciences
Units are assigned in accordance with work accomplished  | first, second, third terms
Prerequisites: Consent of supervisor is required before registering.

Supervised reading in the information and data sciences by undergraduates. The topic must be approved by the reading supervisor and a formal final report must be presented on completion of the term. Graded pass/fail.

Instructor: Staff
IDS 198
Undergraduate Projects in Information and Data Sciences
Units are assigned in accordance with work accomplished  | first, second, third terms
Prerequisites: Consent of supervisor is required before registering.

Supervised research in the information and data sciences. The topic must be approved by the project supervisor and a formal report must be presented upon completion of the research. Graded pass/fail.

Instructor: Staff
IDS 199
Undergraduate thesis in the Information and Data Sciences
9 units (1-0-8)  | first, second, third terms
Prerequisites: instructor's permission, which should be obtained sufficiently early to allow time for planning the research.

Individual research project, carried out under the supervision of a faculty member and approved by the option representative. Projects must include significant design effort and a written Report is required. Open only to upperclass students. Not offered on a pass/fail basis.

Instructor: Staff
Topics in Linear Algebra and Convexity
9 units (3-0-6)  | second term
Prerequisites: CMS 107a and CMS/ACM 122; or instructor's permission.

The content of this course varies from year to year among advanced subjects in linear algebra, convex analysis, and related fields. Specific topics for the class include matrix analysis, operator theory, convex geometry, or convex algebraic geometry. Lectures and homework will require the ability to understand and produce mathematical proofs. Not offered 2023-24.

Instructor: Tropp
Topics in Optimization
9 units (3-0-6)  | third term
Prerequisites: ACM/IDS 104, CMS/ACM/EE 122.

Material varies year-to-year. Example topics include discrete optimization, convex and computational algebraic geometry, numerical methods for large-scale optimization, and convex geometry. Not offered 2023-24.

Instructor: Staff
Markov Chains, Discrete Stochastic Processes and Applications
9 units (3-0-6)  | second term
Prerequisites: ACM/EE/IDS 116 or equivalent.

Stable laws, Markov chains, classification of states, ergodicity, von Neumann ergodic theorem, mixing rate, stationary/equilibrium distributions and convergence of Markov chains, Markov chain Monte Carlo and its applications to scientific computing, Metropolis Hastings algorithm, coupling from the past, martingale theory and discrete time martingales, rare events, law of large deviations, Chernoff bounds.

Instructor: Owhadi