Algorithmic Lower Bounds: Fun with Hardness Proofs

This course explores the mathematical concepts and techniques essential for the financial industry, blending theoretical mathematics with practical applications. Learners will study topics such as linear algebra, probability, statistics, and stochastic processes, guided by both MIT mathematicians and industry professionals.

This course offers a hands-on, project-based introduction to building scalable and high-performance software systems. Learners will explore performance analysis, algorithmic techniques, and optimizations to effectively utilize modern computing platforms.

This course covers the fundamentals of deep learning, including both theory and applications. Topics include neural net architectures (MLPs, CNNs, RNNs, graph nets, transformers), geometry and invariances in deep learning, backpropagation and automatic differentiation, learning theory and generalization in high dimensions, and applications to computer vision, natural language processing, and robotics.

This course covers fundamental discrete mathematics for computer science and engineering. It focuses on mathematical definitions, proofs, and applicable methods, covering various topics such as logic symbols, proof techniques, sets, relations, and graph theory.

This graduate course delves into the fundamental principles of Einstein's general theory of relativity, exploring topics such as differential geometry, black holes, and cosmology. Learners will engage with both the theoretical foundations and practical applications of general relativity.

Functional analysis explores the study and resolution of linear and nonlinear problems in normed spaces, extending beyond finite dimensions. Learners will delve into key concepts such as normed spaces, completeness, functionals, and the Spectral Theorem, gaining insights applicable to various mathematical and physical contexts.

This course covers the foundations of mathematical analysis. You will study the convergence of sequences and series, continuity, differentiability, Riemann integration, sequences and series of functions, uniformity, and the interchange of limit operations.

This course is intended for students with little to no programming experience and focuses on understanding the role of computers in problem-solving. Students will build confidence in writing simple programs using the Python 3 programming language.

This course covers elementary discrete mathematics for science and engineering, focusing on mathematical tools and proof techniques useful in computer science. Learners will explore topics such as logical notation, sets, relations, graph theory, state machines, and algorithms.

The Early Universe offers a comprehensive introduction to modern cosmology, exploring classical cosmology and the influence of contemporary particle physics on our understanding of the universe's origins.

Effective field theory is a fundamental framework for describing physical systems through quantum field theory. In this course, you will learn in depth about the general tools used in effective theories and Soft-Collinear Effective Theory (SCET) for hard interactions.

This course explores the transformative potential of blockchain technology in the realms of money and finance. Learners will study the fundamentals of blockchain, distributed ledgers, and smart contracts, with a focus on current and future applications in the financial sector.

This course focuses on learning several rules to improve speaking skills in important situations. Learners can master effective presentation methods for various contexts, such as interviews, thesis defenses, and oral exams.

This course introduces students to the mathematical concepts and techniques essential in the financial industry, blending theoretical mathematics with practical applications. Learners will explore topics such as probability, statistics, and linear algebra, all within the context of finance.

This course introduces the fundamental tools of game theory, the mathematical analysis of strategic interaction. Learners will learn how to use game theory to analyze various economic situations.

This course provides an introduction to analysis and aims to teach how to prove mathematical theorems and write proofs. It also covers how to rigorously prove the theorems of calculus.

This course surveys questions about human behavior and mental life, exploring topics such as perception, love, consciousness, and the nature of self. Students will engage with various theoretical perspectives, including biological, cognitive, and psychoanalytic, while experiencing psychology firsthand through demonstrations and discussions.

This course focuses on the practical aspects of designing and analyzing non-digital games. Learners will explore various game genres while collaborating in teams to create, develop, and test original games, gaining insights into game mechanics and rules.

This course provides an introduction to cellular and population-level systems biology with an emphasis on synthetic biology, modeling of genetic networks, cell-cell interactions, and evolutionary dynamics. Learners will explore genetic switches, network motifs, and models of pattern formation.

This course covers key macroeconomic questions such as economic recessions, inflation, and fluctuations in unemployment rates. Learners will gain a deep understanding of government policies and the determinants of economic growth.

Through this course, you can systematically learn core concepts such as Basic Sorting Algorithms, Advanced Sorting Algorithms, Special Purpose Sorting Algorithms, and Practical Considerations.

This course focuses on algorithms for analyzing and designing geometric folds. Students will learn about the reconfiguration of foldable structures, linkages and origami, and the unfolding and folding of 3D polyhedra.

Through this course, you can systematically learn core concepts such as basic search algorithms, graph search algorithms, tree search algorithms, advanced search techniques, performance optimization, and considerations.

This course covers the tools of probability theory and statistical inference, providing essential content for data analysis and understanding. Learners can acquire methods for utilizing data in various fields.

This course provides an introduction to analysis and aims to teach how to prove mathematical theorems and write proofs. It also covers how to rigorously prove the theorems of calculus.

Through this lecture, you can systematically learn core concepts such as the basic principles and implementation of stacks, stack applications: function calls (Call Stack), stack applications: expression evaluation, stack applications: parenthesis matching, and stack applications: implementing Undo/Redo functions.

This course introduces the mathematical modeling of computational problems. It covers common algorithms, algorithmic paradigms, and the data structures used to solve these problems.

This course introduces the mathematical modeling of computational problems and the common algorithms, algorithmic paradigms, and data structures used to solve them. It emphasizes the relationship between algorithms and programming, and introduces basic performance measurement and analysis techniques.

This course offers a hands-on, project-based introduction to building scalable and high-performance software systems. Learners will explore performance analysis, algorithmic techniques, and optimizations to effectively utilize modern computing platforms.