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 Graph Theory: An Introduction Note 5 One of the fundamental ideas in computer science is the notion of abstraction: capturing the essence or the core of some complex situation by a simple model. Some of the largest and most complex entities we might deal with
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 Note 7 This note is partly based on Section 1.4 of “Algorithms,” by S. Dasgupta, C. Papadimitriou and U. Vazirani, McGraw-Hill, 2007. Public Key Cryptography In this note, we discuss a very nice and important application of modular arithmetic: the RSA public-key cryptosystem, named after its
CS 70 Discrete Mathematics and Probability Theory Fall 2020 Course Notes Note 9 Error Correcting Codes 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
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
EECS 70 Discrete Mathematics and Probability Theory Fall 2020 Counting Note 10 The next major topic of the course is probability theory. Suppose you toss a fair coin a thousand times. How likely is it that you get exactly 500 heads? And what about 1000 heads? It turns out that the chances of 500 heads
CS 70 Spring 2019 PRINT Your Name: SIGN Your Name: PRINT Your Student ID: PRINT Your Exam Room: Name of the person sitting to your left: Discrete Mathematics and Probability Theory Ayazifar and Rao , Midterm 1 (last) (first) Name of the person sitting to your right: • After the exam starts, please write your
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