Numerical Methods Applied to Chemical Engineering

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 explores the practical aspects of proving that certain problems cannot be solved efficiently, focusing on reductions and techniques for demonstrating computational hardness across various complexity classes. Learners will engage with interesting problems and develop a deeper understanding of algorithmic limitations.

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 delves into projection theory, exploring how a set behaves under various orthogonal projections. Learners will engage with both classical techniques and contemporary applications across multiple mathematical disciplines, including harmonic analysis and analytic number theory.

This course introduces methods for harnessing data to answer questions of cultural, social, economic, and policy interest. Learners will study essential concepts in probability and statistics, along with modern data analysis techniques such as regression, econometrics, and data visualization.

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 covers the content necessary to understand and create machine learning algorithms, specifically deep learning and neural networks, through linear algebra concepts. It provides a comprehensive explanation of linear algebra, including applications in probability, statistics, and optimization.

This course provides an introduction to key concepts in electrical engineering and computer science through the lens of digital communication systems. Learners will explore the foundational layers of bits, signals, and packets that underpin modern communication technologies, including the Internet.

This course covers the fundamental principles of finite element analysis for solving complex static and dynamic problems. Learners will learn how to implement finite element procedures for linear and nonlinear analysis.

You will learn the concepts of ontology and their practical application methods, focusing on the secondary battery cathode material manufacturing process. You will learn how to transform fragmented process data into meaningful knowledge assets and build AI-based quality prediction and defect root-cause reasoning systems. You will acquire practical ontology engineering capabilities to lead the digital transformation (DX) and artificial intelligence transformation (AX) of manufacturing sites.

This course introduces major approaches to symbol-based music theory and musicology. Learners will explore various topics, including music theory algorithms, music generation, and machine learning.

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 covers the practical impact that quantitative methods have had on today's most important companies. Learners will study key quantitative methods that create a competitive advantage, such as data mining, dynamic optimization, and simulation.

This course is a collection of tutorial videos that visually explore various topics in materials science and engineering. Learners will discover how to use the Wolfram Mathematica programming system to easily understand complex concepts.

This course covers the scientific principles of quantitatively assessing the risk of airborne transmission of COVID-19. You can understand the factors of transmission in indoor spaces and their interactions.