The study of abstract algebra grew out of an interest in knowing how attributes of sets of mathematical objects behave when one or more properties we associate with real numbers are restricted. The student will begin this course by reviewing basic set theory, integers, and functions in order to understand how algebraic operations arise and are used. The student then will proceed to the heart of the course, which is an exploration of the fundamentals of groups, rings, and fields. Upon successful completion of this course, the student will be able to: Describe and generate groups, rings, and fields; Relate abstract algebraic constructs to more familiar number sets and operations and see from where the constructs derive; Identify examples of specific constructs; Identify and differentiate between different structures and understand how changing properties give rise to new structures; Explain the theory behind relations and functions and identify domains and images of functions, based on the structures given; Explain how functions may relate seemingly dissimilar structures to each other and how knowing properties of one structure allows us to know the same properties in the related structure, if certain functions exist between them. (Mathematics 231)

Affect is to cognition and behavior as feeling is to thinking and acting or as values are to beliefs and practices. Subject considers these relations, both at the psychological level of organization and in terms of their neurobiological and sociocultural counterparts.

" Affect is to cognition and behavior as feeling is to thinking and acting, or as values are to beliefs and practices. Considers these relations, both at the psychological level of organization and also in terms of their neurobiological and sociocultural counterparts. In addition to attending weekly class sessions and doing regular homework Assignments and Labs, students are required to participate in small study groups that meet independently for two hours per week."

Subject consists of five sections. After a general survey of the field, students consider cases of stable civilian control, stable military rule (coups), and transitions from military to civilian rule. Cases are selected from around the world.

Examines political institutions from a rational choice perspective. The now burgeoning rational choice literature on legislatures, bureaucracies, courts, and elections constitutes the chief focus. Some focus on institutions from a comparative and/or international perspective. Graduate students are expected to pursue the subject in greater depth through reading and individual research. Advanced undergrads may take subject with faculty approval. This is an applied theory course covering topics in the political economy of democratic countries. This course examines political institutions from a rational choice perspective. The now burgeoning rational choice literature on legislatures, bureaucracies, courts, and elections constitutes the chief focus. Some focus will be placed on institutions from a comparative and/or international perspective.

This course analyzes the development of the United States Congress by focusing on the competing theoretical lenses through which legislatures have been studied. In particular, it compares sociological and economic models of legislative behavior, applying those models to floor decision-making, committee behavior, political parties, relations with other branches of the Federal government, and elections. Graduate students are expected to pursue the subject in greater depth through reading and individual research. This course analyzes the development of the United States Congress by focusing on the competing theoretical lenses through which legislatures have been studied. In particular, it compares sociological and economic models of legislative behavior, applying those models to floor decision-making, committee behavior, political parties, relations with other branches of the Federal government, and elections. Graduate students are expected to pursue the subject in greater depth through reading and individual research.

This course covered the mathematical topics most directly related to computer science. Topics included: logic, relations, functions, basic set theory, countability and counting arguments, proof techniques, mathematical induction, graph theory, combinatorics, discrete probability, recursion, recurrence relations, and number theory. Emphasis will be placed on providing a context for the application of the mathematics within computer science. The analysis of algorithms requires the ability to count the number of operations in an algorithm. Recursive algorithms in particular depend on the solution to a recurrence equation, and a proof of correctness by mathematical induction. The design of a digital circuit requires the knowledge of Boolean algebra. Software engineering uses sets, graphs, trees and other data structures. Number theory is at the heart of secure messaging systems and cryptography. Logic is used in AI research in theorem proving and in database query systems. Proofs by induction and the more general notions of mathematical proof are ubiquitous in theory of computation, compiler design and formal grammars. Probabilistic notions crop up in architectural trade-offs in hardware design.

In this class, food serves as both the subject and the object of historical analysis. As a subject, food has been transformed over the last 100 years, largely as a result of ever more elaborate scientific and technological innovations. From a need to preserve surplus foods for leaner times grew an elaborate array of techniques -- drying, freezing, canning, salting, etc -- that changed not only what people ate, but how far they could/had to travel, the space in which they lived, their relations with neighbors and relatives, and most of all, their place in the economic order of things. The role of capitalism in supporting and extending food preservation and development was fundamental. As an object, food offers us a way into cultural, political, economic, and techno-scientific history. Long ignored by historians of science and technology, food offers a rich source for exploring, e.g., the creation and maintenance of mass-production techniques, industrial farming initiatives, the politics of consumption, vertical integration of business firms, globalization, changing race and gender identities, labor movements, and so forth. How is food different in these contexts, from other sorts of industrial goods? What does the trip from farm to table tell us about American culture and history?

Explores the foundations of policy making in developing countries. Goal is to spell out various policy options and to quantify the trade-offs between them. Special emphasis on education, health, gender, fertility, adoption of technological innovation, and the markets for land, credit, and labor.

" This course explores the foundations of policy making in developing countries. The goal is to spell out various policy options and to quantify the trade-offs between them. We will study the different facets of human development: education, health, gender, the family, land relations, risk, informal and formal norms and institutions. This is an empirical class. For each topic, we will study several concrete examples chosen from around the world. While studying each of these topics, we will ask: What determines the decisions of poor households in developing countries? What constraints are they subject to? Is there a scope for policy (by government, international organizations, or non-governmental organizations (NGOs))? What policies have been tried out? Have they been successful?"

Mathematical tools and methods for computer science and engineering. Emphasis on development of rigorous thinking, analytical skills, and mathematical sophistication while learning elementary discrete mathematics. Topics: mathematical proofs; induction and well-ordering; divisibility and congruences; asymptotic notation and growth of functions; sets, relations, functions, and graphs; counting theory; recurrences and generating functions; and discrete probability. This is an introductory course in Discrete Mathematics oriented toward Computer Science and Engineering. The course divides roughly into thirds: Fundamental Concepts of Mathematics: Definitions, Proofs, Sets, Functions, Relations Discrete Structures: Modular Arithmetic, Graphs, State Machines, Counting Discrete Probability Theory.

This course covers elementary discrete mathematics for computer science and engineering. It emphasizes mathematical definitions and proofs as well as applicable methods. Topics include formal logic notation, proof methods; induction, well-ordering; sets, relations; elementary graph theory; integer congruences; asymptotic notation and growth of functions; permutations and combinations, counting principles; discrete probability. Further selected topics may also be covered, such as recursive definition and structural induction; state machines and invariants; recurrences; generating functions.

Mathematical tools and methods for computer science and engineering. Emphasis on development of rigorous thinking, analytical skills, and mathematical sophistication while learning elementary discrete mathematics. Topics: mathematical proofs; induction and well-ordering; divisibility and congruences; asymptotic notation and growth of functions; sets, relations, functions, and graphs; counting theory; recurrences and generating functions; and discrete probability.

This subject offers an introduction to Discrete Mathematics oriented toward Computer Science and Engineering. The subject coverage divides roughly into thirds: Fundamental concepts of mathematics: definitions, proofs, sets, functions, relations. Discrete structures: graphs, state machines, modular arithmetic, counting. Discrete probability theory. On completion of 6.042, students will be able to explain and apply the basic methods of discrete (noncontinuous) mathematics in Computer Science. They will be able to use these methods in subsequent courses in the design and analysis of algorithms, computability theory, software engineering, and computer systems.

In this video segment from Cyberchase, the CyberSquad learns how to read a thermometer as they try to keep their chocolate sculpture from melting.