limit theorems
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Concentrates on recognizing and solving convex optimization problems that arise in engineering. Topics include: Convex sets, functions, and optimization problems. Basics of convex analysis. Least-squares, linear and quadratic programs, semidefinite programming, minimax, extremal volume, and other problems. Optimality conditions, duality theory, theorems of alternative, and applications. Interiorpoint methods. Applications to signal proc...more
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This course is the second of a two-term sequence. The focus is on coding techniques for approaching the Shannon limit of additive white Gaussian noise (AWGN) channels, their performance analysis, and design principles. After a review of Principles of Digital Communication I and the Shannon limit for AWGN channels, the course begins by discussing small signal constellations, performance analysis and coding gain, and hard-decision and soft-d...more
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Topics covered in the first two or three semesters of college calculus. Everything from limits to derivatives to integrals to vector calculus. Should understand the topics in the pre-calculus playlist first (the limit videos are in both playlists).
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Parametric equations and polar coordinates. Vectors in 2- and 3-dimensional Euclidean spaces. Partial derivatives. Multiple integrals. Vector calculus. Theorems of Green, Gauss, and Stokes.
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This is a math course aimed at students with life science majors covering elementary probability, probability distributions, random variables, and limit theorems.
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By 1950, in most of the underdeveloped world, mortality had fallen to about half its pre-modern rate. The birth rate, however, had remained high and, by 1950, was about twice the death rate. For the rest of the century, both rates fell dramatically and in parallel, maintaining the gap. The enormous excess of births over deaths in this period is known as 'the population explosion.' By 1990, the world population was growing at almost 90 mill...more
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In addition to cultural controls acting to maximize fertility, there are important, and often competing, interests of individual families to limit fertility. Unwanted births are dealt with by infanticide in many cultures. Additionally, fertility is regularly controlled by limiting marriage within a culture. Another very important factor in population growth, especially in the tropics, is food availability. Heavy rains in the tropics wash n...more
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Until recently, the world population has been growing faster than exponentially. Although the growth rate has slowed somewhat, there are about 80 million more people each year and about 3 billion more will be added by 2050 (a 50% increase). Population will probably increase more beyond that. Such growth is unprecedented and we cannot predict its long-term effects. The environmental impact of this population increase is bound to be astronom...more
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Administrative Details, Exams - Time limit, Conflicts, Course Grade Breakdown, Assignment Details - Submission, Grading, Late Days, Course Email, Newsgroup, Facebook/Twitter, Mailing List, Course Prerequisites, Languages and Paradigms Taught - C++ vs. Pure C, Procedural Paradigm vs. Object-Oriented Paradigm, Assembly, Concurrent Programming Overview, Example of Data Sharing Issues with Concurrent Programming, Scheme, Functional Paradigm Ov...more
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This lecture continues the analysis of the Capital Asset Pricing Model, building up to two key results. One, the Mutual Fund Theorem proved by Tobin, describes the optimal portfolios for agents in the economy. It turns out that every investor should try to maximize the Sharpe ratio of his portfolio, and this is achieved by a combination of money in the bank and money invested in the "market" basket of all existing assets. The market basket...more
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Carol Bartz, CEO of Autodesk for many years, underlines the silver lining for many stagnating issues in the workplace. Making a plan for yourself is a good idea, but don't let it limit your scope. By bringing value to the organization, you are the one to benefit most. Learning is the most critical aspect of any job; if you're not growing, it's time to uproot. She also points out that bad managers are great teachers, as they are instructive...more
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Why does a dropped egg that spatters on the floor not rise back to your hands even though no laws prohibit it? The answer to such irreversibility resides in the Second Law of Thermodynamics which is explained in this and the next lecture. The Carnot heat engine is discussed in detail to show how there is an upper limit to the efficiency of heat engines and how the concept of entropy arises from macroscopic considerations.
