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Lecture, discussion. Basic concepts of discrete mathematics useful to computer science: set theory, strings and formal languages, propositional and predicate calculus, relations and functions, basic number theory. Induction and recursion: interplay of inductive definition, inductive proof, and recursive algorithms. Graphs, trees, and search. Finite-state machines, regular languages, nondeterministic finite automata, Kleene's Theorem. Problem sets, 2-3 midterm exams, timed final.

Lecture, discussion. Basic concepts of discrete mathematics useful to computer science: set theory, strings and formal languages, propositional and predicate calculus, relations and functions, basic number theory. Induction and recursion: interplay of inductive definition, inductive proof, and recursive algorithms. Graphs, trees, and search. Finite-state machines, regular languages, nondeterministic finite automata, Kleene's Theorem. Problem sets, 2-3 midterm exams, timed final.

Lecture, discussion. Basic concepts of discrete mathematics useful to computer science: set theory, strings and formal languages, propositional and predicate calculus, relations and functions, basic number theory. Induction and recursion: interplay of inductive definition, inductive proof, and recursive algorithms. Graphs, trees, and search. Finite-state machines, regular languages, nondeterministic finite automata, Kleene's Theorem. Problem sets, 2-3 midterm exams, timed final.

Mathematical methods for dealing with uncertainty. Basic counting problems. Discrete probablitlity, expected value and variance. Random number generators and Monte Carlo simulation. Bayesian reasoning, naive Bayes classifiers. Markov processes. Programming projects.

Mathematical methods for dealing with uncertainty. Basic counting problems. Discrete probablitlity, expected value and variance. Random number generators and Monte Carlo simulation. Bayesian reasoning, naive Bayes classifiers. Markov processes. Programming projects.

Mathematical methods for dealing with uncertainty. Basic counting problems. Discrete probablitlity, expected value and variance. Random number generators and Monte Carlo simulation. Bayesian reasoning, naive Bayes classifiers. Markov processes. Programming projects.

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.

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.