limit theorems
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Using the squeeze theorem to prove that the limit as x approaches 0 of (sin x)/x =1.
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More limit examples.
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Introduction to the Epsilon Delta Definition of a Limit.
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Limit theorems, Markovs inequality theorem, Chebyshevs inequality theorem, Law of large numbers.
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Limit theorems, Markovs inequality theorem, Chebyshevs inequality theorem, Law of large numbers.
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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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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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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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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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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
