Category theory is a relatively new branch of mathematics that has transformed much of pure math research. The technical advance is that category theory provides a framework in which to organize formal systems and by which to translate between them, allowing one to transfer knowledge from one field to another. But this same organizational framework also has many compelling examples outside of pure math. In this course, we will give seven sketches on real-world applications of category theory.

This course covers empirical strategies for applied micro research questions. Our agenda includes regression and matching, instrumental variables, differences-in-differences, regression discontinuity designs, standard errors, and a module consisting of 8–9 lectures on the analysis of high-dimensional data sets a.k.a. “Big Data”.

The fact of scarcity forces individuals, firms, and societies to choose among alternative uses – or allocations – of its limited resources. Accordingly, the first part of this summer course seeks to understand how economists model the choice process of individual consumers and firms, and how markets work to coordinate these choices. It also examines how well markets perform this function using the economist’s criterion of market efficiency.
Overall, this course focuses on microeconomics, with some topics from macroeconomics and international trade. It emphasizes the integration of theory, data, and judgment in the analysis of corporate decisions and public policy, and in the assessment of changing U.S. and international business environments.

László Tisza was Professor of Physics Emeritus at MIT, where he began teaching in 1941. This online publication is a reproduction the original lecture notes for the course “Applied Geometric Algebra” taught by Professor Tisza in the Spring of 1976.
Over the last 100 years, the mathematical tools employed by physicists have expanded considerably, from differential calculus, vector algebra and geometry, to advanced linear algebra, tensors, Hilbert space, spinors, Group theory and many others. These sophisticated tools provide powerful machinery for describing the physical world, however, their physical interpretation is often not intuitive. These course notes represent Prof. Tisza’s attempt at bringing conceptual clarity and unity to the application and interpretation of these advanced mathematical tools. In particular, there is an emphasis on the unifying role that Group theory plays in classical, relativistic, and quantum physics. Prof. Tisza revisits many elementary problems with an advanced treatment in order to help develop the geometrical intuition for the algebraic machinery that may carry over to more advanced problems.
The lecture notes came to MIT OpenCourseWare by way of Samuel Gasster, ‘77 (Course 18), who had taken the course and kept a copy of the lecture notes for his own reference. He dedicated dozens of hours of his own time to convert the typewritten notes into LaTeX files and then publication-ready PDFs. You can read about his motivation for wanting to see these notes published in his Preface. Professor Tisza kindly gave his permission to make these notes available on MIT OpenCourseWare.

15.012 Applied Macro- and International Economics uses case studies to investigate the macroeconomic environment in which firms operate. The first half of the course develops the basic tools of macroeconomic management: monetary, fiscal, and exchange rate policy. The class discusses recent emerging market and financial crises by examining their causes and considering how best to address them and prevent them from recurring in the future. The second half evaluates different strategies of economic development. Topics covered in the second half of this course include growth, the role of debt and foreign aid, and the reliance on natural resources.

This course seeks to establish understanding of the development processes of societies and economies by studying several dimensions of sustainability (environmental, social, political, institutional, economy, organizational, relational, and personal) and the balance among them. It explores the basics of governmental intervention, focusing on areas such as the judicial system, environment, social security, and health, and builds skills to determine what type of policy is most appropriate. We also consider implications of new technologies on the financial sector: Internationalization of currencies, mobile payment systems, and cryptocurrencies, and discuss the institutional framework to ensure choices are sustainable across all dimensions and applications.

7.003 is an experimental biology course. You will spend most of your time in the teaching laboratory practicing fundamental techniques in molecular biology, genetics, and cell biology, and working with the model organism Saccharomyces cerevisiae (budding yeast). In addition to learning how to accurately and safely perform these techniques, we want to help you understand how and why they work and what scientific questions they can address. The goal is for you to be able to design your own experiments to perform by the end of the semester.

The topics covered under this course include elements of nuclear physics for engineering students, basic properties of the nucleus and nuclear radiations, quantum mechanical calculations of deuteron bound-state wave function and energy, n-p scattering cross-section, transition probability per unit time and barrier transmission probability. Also explored are binding energy and nuclear stability, interactions of charged particles, neutrons, and gamma rays with matter, radioactive decays, energetics and general cross-section behavior in nuclear reactions.

This course explores elements of nuclear physics for engineering students. It covers basic properties of the nucleus and nuclear radiations; quantum mechanical calculations of deuteron bound-state wave function and energy; n-p scattering cross section; transition probability per unit time and barrier transmission probability. It also covers binding energy and nuclear stability; interactions of charged particles, neutrons, and gamma rays with matter; radioactive decays; and energetics and general cross section behavior in nuclear reactions.

6.728 is offered under the department’s “Devices, Circuits, and Systems” concentration. The course covers concepts in elementary quantum mechanics and statistical physics, introduces applied quantum physics, and emphasizes an experimental basis for quantum mechanics. Concepts covered include: Schrodinger’s equation applied to the free particle, tunneling, the harmonic oscillator, and hydrogen atom, variational methods, Fermi-Dirac, Bose-Einstein, and Boltzmann distribution functions, and simple models for metals, semiconductors, and devices such as electron microscopes, scanning tunneling microscope, thermonic emitters, atomic force microscope, and others.

This course provides a phenomenological approach to superconductivity, with emphasis on superconducting electronics. Topics include: electrodynamics of superconductors, London’s model, flux quantization, Josephson Junctions, superconducting quantum devices, equivalent circuits, high-speed superconducting electronics, and quantized circuits for quantum computing. The course also provides an overview of type II superconductors, critical magnetic fields, pinning, the critical state model, superconducting materials, and microscopic theory of superconductivity.

This course details the quantitative treatment of chemical processes in aquatic systems such as lakes, oceans, rivers, estuaries, groundwaters, and wastewaters. It includes a brief review of chemical thermodynamics that is followed by discussion of acid-base, precipitation-dissolution, coordination, and reduction-oxidation reactions. Emphasis is on equilibrium calculations as a tool for understanding the variables that govern the chemical composition of aquatic systems and the fate of inorganic pollutants.
This course is offered through The MIT/WHOI Joint Program. The MIT/WHOI Joint Program is one of the premier marine science graduate programs in the world. It draws on the complementary strengths and approaches of two great institutions: the Massachusetts Institute of Technology (MIT) and the Woods Hole Oceanographic Institution (WHOI).

This 12 session course is designed for the beginning or novice archer and uses recurve indoor target bows and equipment. The purpose of the course is to introduce students to the basic techniques of indoor target archery emphasizing the care and use of equipment, range safety, stance and shooting techniques, scoring and competition.

This class investigates the use of computers in architectural design and construction. It begins with a pre-prepared design computer model, which is used for testing and process investigation in construction. It then explores the process of construction from all sides of the practice: detail design, structural design, and both legal and computational issues.

This is the second undergraduate design studio. It introduces a full range of architectural ideas and issues through drawing exercises, analyses of precedents, and explored design methods. Students will develop design skills by conceptualizing and representing architectural ideas and making aesthetic judgments about building design. Discussions regarding architecture’s role in mediating culture, nature and technology will help develop the students’ architectural vocabulary.

This studio will investigate the social, programmatic, tectonic and phenomenological performance and character of a student gathering place on the MIT campus. Whether it is simply for socializing or for more specific events, the student gathering place will serve as a refuge from the vigorous educational environment of the Institute, and it will reinforce a critical sense of “place” through the almost logical organization of its program. The place will foster a casual discovery of “being”: a reflection upon the student’s own existence based upon participation in group events and an intellectual attitude toward acting. To create a space that inspires, rather than imposes: such a discovery is the foremost challenge of this studio.

The theme that unites the Level II studios in the fall semester is a focus upon the ‘making of architecture and built form’ as a tectonic, technical and materially driven endeavor. It is a design investigation that is rooted in a larger culture of materiality and the associated phenomena, but a study of the language and production of built form as an integrated response to the conceptual proposition of the project. The studio will look to works of architecture where the material tectonic and its resultant technology or fabrication become instrumental to the realization of the ideas, in whatever form they may take. This becomes the ‘art of technology’ – suggesting a level of innovation and creative manipulation as part of the design process to transform material into a composition of beauty and poetry as well as environmental control. In this regard the studio will look to the works and design processes of a number of architects including Shigeru Ban, Peter Zumthor, Herzog and deMeuron, Kazuyo Sejima, Richard Horden, Rick Joy and Glenn Murcutt among others.

This semester students are asked to transform the Hereshoff Museum in Bristol, Rhode Island, through processes of erasure and addition. Hereshoff Manufacturing was recognized as one of the premier builders of America’s Cup racing boats between 1890’s and 1930’s. The studio, however, is about more than the program. It is about land, water, and wind and the search for expressing materially and tectonically the relationships between these principle conditions. That is, where the land is primarily about stasis (docking, anchoring and referencing our locus), water’s fluidity holds the latent promise of movement and freedom. Movement is activated by wind, allowing for negotiating the relationship between water and land.

The project for this studio is to design a demonstration project for a site near the French Quarter in New Orleans. The objectives of the project are the following:

To design more intense housing, community, educational and commercial facilities in four to six story buildings.
To explore the “space between” buildings as a way of designing and shaping objects.
To design at three scales - dwelling, cluster and overall.
To design dwellings where the owners may be able to help build and gain a skill for employment.
To provide/design facilities that can help the residents to gain education and skills.

This studio explores the notion of in-between by engaging several relationships; the relationship between intervention and perception, between representation and notation and between the fixed and the temporal. In the Exactitude in Science, Jorge Luis Borges tells the perverse tale of the one to one scale map, where the desire for precision and power leads to the escalating production of larger and more accurate maps of the territory. For Jean Baudrillard, “The territory no longer precedes the map nor survives it. …it is the map that precedes the territory… and thus, it would be the territory whose shreds are slowly rotting across the map.” The map or the territory, left to ruin-shredding across the ‘other’, beautifully captures the tension between reality and representation. Mediating between collective desire and territorial surface, maps filter, create, frame, scale, orient, and project. A map has agency. It is not merely representational but operational, the experience and discursive potential of this process lies in the reciprocity between the representation and the real. It is in-between these specific sets of relationships that this studio positions itself.