Development of mathematical reasoning skills for problems that involve uncertainty. Counting and probability -- basic counting problems, probability definitions, mean, variance, binomial distribution, discrete random variables, continuous random variables, Markov and Chebyshev bounds, Laws of large numbers, and central limit theorem. Probabilistic reasoning -- conditional probability and odds, Bayes' Law, Markov Chains, Bayesian Networks.

Development of mathematical reasoning skills for problems that involve uncertainty. Counting and probability -- basic counting problems, probability definitions, mean, variance, binomial distribution, discrete random variables, continuous random variables, Markov and Chebyshev bounds, Laws of large numbers, and central limit theorem. Probabilistic reasoning -- conditional probability and odds, Bayes' Law, Markov Chains, Bayesian Networks.

Development of mathematical reasoning skills for problems that involve uncertainty. Counting and probability -- basic counting problems, probability definitions, mean, variance, binomial distribution, discrete random variables, continuous random variables, Markov and Chebyshev bounds, Laws of large numbers, and central limit theorem. Probabilistic reasoning -- conditional probability and odds, Bayes' Law, Markov Chains, Bayesian Networks.

Development of mathematical reasoning skills for problems that involve uncertainty. Counting and probability -- basic counting problems, probability definitions, mean, variance, binomial distribution, discrete random variables, continuous random variables, Markov and Chebyshev bounds, Laws of large numbers, and central limit theorem. Probabilistic reasoning -- conditional probability and odds, Bayes' Law, Markov Chains, Bayesian Networks.

Development of mathematical reasoning skills for problems that involve uncertainty. Counting and probability -- basic counting problems, probability definitions, mean, variance, binomial distribution, discrete random variables, continuous random variables, Markov and Chebyshev bounds, Laws of large numbers, and central limit theorem. Probabilistic reasoning -- conditional probability and odds, Bayes' Law, Markov Chains, Bayesian Networks.

Development of mathematical reasoning skills for problems that involve uncertainty. Counting and probability -- basic counting problems, probability definitions, mean, variance, binomial distribution, discrete random variables, continuous random variables, Markov and Chebyshev bounds, Laws of large numbers, and central limit theorem. Probabilistic reasoning -- conditional probability and odds, Bayes' Law, Markov Chains, Bayesian Networks.

Development of mathematical reasoning skills for problems that involve uncertainty. Counting and probability -- basic counting problems, probability definitions, mean, variance, binomial distribution, discrete random variables, continuous random variables, Markov and Chebyshev bounds, Laws of large numbers, and central limit theorem. Probabilistic reasoning -- conditional probability and odds, Bayes' Law, Markov Chains, Bayesian Networks.

Development of mathematical reasoning skills for problems that involve uncertainty. Counting and probability -- basic counting problems, probability definitions, mean, variance, binomial distribution, discrete random variables, continuous random variables, Markov and Chebyshev bounds, Laws of large numbers, and central limit theorem. Probabilistic reasoning -- conditional probability and odds, Bayes' Law, Markov Chains, Bayesian Networks.

Large-scale software systems like Google - deployed over a world-wide network of hundreds of thousands of computers - have become a part of our lives. These are systems success stories - they are reliable, available ("up" nearly all the time), handle an unbelievable amount of load from users around the world, yet provide virtually instantaneous results. On the other hand, many computer systems don't perform nearly as well as Google - hence the now-cliche "the system is down." In this class, we study the scientific principles behind the construction of high-performance, scalable systems.

Large-scale software systems like Google - deployed over a world-wide network of hundreds of thousands of computers - have become a part of our lives. These are systems success stories - they are reliable, available ("up" nearly all the time), handle an unbelievable amount of load from users around the world, yet provide virtually instantaneous results. On the other hand, many computer systems don't perform nearly as well as Google - hence the now-cliche "the system is down." In this class, we study the scientific principles behind the construction of high-performance, scalable systems.