EECS 70 Discrete Mathematics and Probability Theory Fall 2020 Two Killer Applications: Hashing and Load Balancing Note 18 In this note, we will see that the simple balls-and-bins process can be used to model a surprising range of phenomena. Recall that in this process we distribute k balls into n bins, where each ball is […]
EECS 70 Discrete Mathematics and Probability Theory Fall 2020 Continuous Probability Distributions Note 20 Up to now we have focused exclusively on discrete sample spaces Ω, where the number of sample points ω ∈ Ω is either finite or countably infinite (such as the integers). As a consequence, we have only been able to talk
EECS 70 Discrete Mathematics and Probability Theory Fall 2020 Finite Markov Chains Note 21 These notes explain the theory of finite Markov chains. For CS70, we do not cover the proofs that are discussed in Appendix 2. Introduction Markov chains are models of random motion in a finite or countable set. These models are powerful
EECS 70 Discrete Mathematics and Probability Theory Fall 2020 1 Proofs Note 2 In science, evidence is accumulated through experiments to assert the validity of a statement. Mathematics, in contrast, aims for a more absolute level of certainty. A mathematical proof provides a means for guar- anteeing that a statement is true. Proofs are very
EECS 70 Discrete Mathematics and Probability Theory Fall 2020 Review of Sets and Mathematical Notation Note 0 A set is a well defined collection of objects. These objects are called elements or members of the set, and they can be anything, including numbers, letters, people, cities, and even other sets. By convention, sets are usually
EECS 70 Discrete Mathematics and Probability Theory Fall 2020 1 The Stable Matching Problem Note 4 In the previous two notes, we discussed several proof techniques. In this note, we apply some of these techniques to analyze the solution to an important problem known as the Stable Matching Problem, which we now introduce. The Stable
EECS 70 Discrete Mathematics and Probability Theory Fall 2020 1 Modular Arithmetic Note 6 In several settings, such as error-correcting codes and cryptography, we sometimes wish to work over a smaller range of numbers. Modular arithmetic is useful in these settings, since it limits numbers to a prede- fined range {0, 1, . . .
EECS 70 Discrete Mathematics and Probability Theory Fall 2020 Error Correcting Codes Note 9 In this note, we will discuss the problem of transmitting messages across an unreliable communication chan- nel. The channel may cause some parts of the message (“packets”) to be lost, or dropped; or, more seriously, it may cause some packets to
EECS 70 Discrete Mathematics and Probability Theory Fall 2020 Polynomials Note 8 Polynomials constitute a rich class of functions which are both easy to describe and widely applicable in topics ranging from Fourier analysis, cryptography and communication, to control and computational geom- etry. You’ve seen them earlier in many contexts like Taylor approximation and other
CS 70 Spring 2018 PRINT Your Name: READ AND SIGN The Honor Code: Discrete Mathematics and Probability Theory Ayazifar and Rao , Final (Last) (First) As a member of the UC Berkeley community, I act with honesty, integrity, and respect for others. Signed: PRINT Your Student ID: WRITE your exam room: WRITE the name of
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