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4434Computational Discrete Mathematics
http://www.merlot.org/merlot/viewMaterial.htm?id=519846
This online course comes from the Open Learning Initiative (OLI) by Carnegie Mellon. “The course includes self-guiding materials and activities, and is ideal for independent learners, or instructors trying out this course package.”״Discrete mathematics, also called finite mathematics or decision mathematics, is the study of mathematical structures that are fundamentally discrete in the sense of not supporting or requiring the notion of continuity. Objects studied in finite mathematics are largely countable sets such as integers, finite graphs, and formal languages. Concepts and notations from discrete mathematics are useful to study or describe objects or problems in computer algorithms and programming languages.״At this point only one of the planned 15 modules is currently available, that on Groups.14.11 Insights from Game Theory into Social Behavior (MIT)
http://www.merlot.org/merlot/viewMaterial.htm?id=884275
We will apply insights from game theory to explain human social behavior, focusing on novel applications which have heretofore been the realm of psychologists and philosophers—for example, why people speak indirectly, in what sense beauty is socially constructed, and where our moral intuitions come from—and eschewing traditional economic applications such as industrial organization or auctions. We will employ standard games such as the prisoners dilemma, coordination, hawk-dove, and costly signaling, and use standard game theory tools such as Nash Equilibria, Subgame Perfection, and Perfect Bayesian Equilibria. These tools will be taught from scratch and no existing knowledge of game theory, economics, or mathematics is required. At the same time, students familiar with these games and tools will not find the course redundant because of the focus on non-orthodox applications.14.12 Economic Applications of Game Theory (MIT)
http://www.merlot.org/merlot/viewMaterial.htm?id=884411
Game Theory, also known as Multiperson Decision Theory, is the analysis of situations in which the payoff of a decision maker depends not only on his own actions but also on those of others. Game Theory has applications in several fi…elds, such as economics, politics, law, biology, and computer science. In this course, I will introduce the basic tools of game theoretic analysis. In the process, I will outline some of the many applications of Game Theory, primarily in economics.6.254 Game Theory with Engineering Applications (MIT)
http://www.merlot.org/merlot/viewMaterial.htm?id=884346
This course is an introduction to the fundamentals of game theory and mechanism design. Motivations are drawn from engineered/networked systems (including distributed control of wireline and wireless communication networks, incentive-compatible/dynamic resource allocation, multi-agent systems, pricing and investment decisions in the Internet), and social models (including social and economic networks). The course emphasizes theoretical foundations, mathematical tools, modeling, and equilibrium notions in different environments.Computational Methods
http://www.merlot.org/merlot/viewMaterial.htm?id=884782
Standard topics in numerical linear algebra, interpolation, discrete differentiation, discrete integration, and approximate solutions to ordinary differential equations are treated in a context-based approach. Applications are drawn from hydrology, environmental modeling, geotechnical engineering, modeling of material behavior, and structural analysis.Discrete Structures
http://www.merlot.org/merlot/viewMaterial.htm?id=620073
This course describes discrete mathematics, which involves processes that consist of sequences of individual steps (as compared to calculus, which describes processes that change in a continuous manner). The principal topics presented in this course are logic and proof, induction and recursion, discrete probability, and finite state machines. This free course may be completed online at any time. See course site for detailed overview and learning outcomes. (Computer Science 202)SP.268 The Mathematics in Toys and Games (MIT)
http://www.merlot.org/merlot/viewMaterial.htm?id=884520
We will explore the mathematical strategies behind popular games, toys, and puzzles. Topics covered will combine basic fundamentals of game theory, probability, group theory, and elementary programming concepts. Each week will consist of a lecture and discussion followed by game play to implement the concepts learned in class.