Real Analysis

This course covers matrix theory and linear algebra, emphasizing topics useful in other disciplines such as physics, economics, social sciences, natural sciences, and engineering. It parallels the combination of theory and applications in Professor Strang’s textbook Introduction to Linear Algebra.

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 explores the principles of photoelectric conversion, focusing on charge excitation, conduction, separation, and collection. Learners will study both commercial and emerging photovoltaic technologies, alongside critical themes such as conversion efficiencies, loss mechanisms, and the societal impacts of solar energy.

This course explores the application of autonomy in real-world systems through the programming of cognitive robots. Learners will study advanced reasoning techniques and algorithms that enable robots to monitor themselves, schedule tasks, and collaborate with other agents.

This course provides a fast-paced introduction to deep learning, focusing on practical model-building for complex problems involving unstructured data. Learners will explore deep neural networks, convolutional networks, transformers, and generative models like ChatGPT and Midjourney.

This course covers essential mathematical concepts widely used in mechanical engineering, focusing on linear algebra and ordinary differential equations (ODEs). Learners will explore numerical methods for solving systems of equations and apply these techniques to real-world engineering problems.

This course immerses learners in an artificial intelligence programming contest where teams create virtual robots to compete in Battlecode, a real-time strategy game. Participants will enhance their programming skills through hands-on experience and optional lectures on relevant topics.

This course provides an introduction to the chemistry of biological, inorganic, and organic molecules. The emphasis is on basic principles of atomic and molecular electronic structure, thermodynamics, acid-base and redox equilibria, chemical kinetics, and catalysis.

This course delves into the essential poker and mathematical concepts necessary for mastering Texas Hold'em at a professional level. Learners will explore strategies and theories that elevate their gameplay and decision-making skills.

This course explores the fundamental role of data structures in computer science, emphasizing their importance in developing efficient algorithms. Learners will study advanced topics, including dynamic graphs, memory hierarchy, and hashing, while engaging with current research directions in the field.

This course focuses on the modeling and analysis of random phenomena and processes, emphasizing statistical inference and probabilistic thinking. Learners will explore essential models and tools that combine mathematical rigor with conceptual understanding.

This course delves into advanced principles of statistical mechanics, focusing on thermodynamics and modern statistical physics topics. Learners will explore concepts such as phase transitions, critical phenomena, and the hydrodynamic limit, building on foundational knowledge from the first term.

This course explores the art of improvisation in both solo and ensemble settings, examining its connections to composition and performance through various musical traditions. Students will engage in hands-on music-making while discussing the aesthetics of improvisation and learning from guest artists across diverse genres.

This course explores systematic methods for developing major innovations that can drive a firm's success. Learners will engage with practical idea generation techniques and real-world case studies presented by industry experts.

_Project Laboratory in Mathematics_ immerses students in the world of mathematical research, allowing them to collaboratively tackle complex problems and present their findings. This course emphasizes teamwork and the exploration of mathematical concepts through hands-on projects.

This course presents an innovative approach to teaching linear algebra, focusing on key concepts and their interconnections. Learners will explore foundational topics and gain insights into the structure and applications of linear algebra through engaging video content.

This course covers the essential techniques for modeling and solving differential equations, which are fundamental in expressing the laws of nature. Learners will explore both the theoretical and practical aspects of differential equations, focusing on their applications in science and engineering.

This course serves as the first semester of a four-part introduction to modern standard Chinese, or Mandarin. Learners will focus on mastering pronunciation, basic reading and writing skills, and engaging in simple conversations on everyday topics, all while exploring the cultural context of the language.

This course examines problems in the philosophy of film as well as literature studied in relation to their making of myths. The readings and films that are discussed in this course draw upon classic myths of the western world, emphasizing meaning and technique as the basis of creative value in both media.

This course explores key questions surrounding tariffs, focusing on their implications and effects through theoretical and data-driven lenses. Learners will gain insights into the complexities of tariffs and their role in the economy.

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.

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.