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
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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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 , Final Exam (last) (first) Name of the person sitting to your right: • After the exam starts, please write your
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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
EECS 70 Discrete Mathematics and Probability Theory Fall 2020 To Infinity And Beyond: Countability and Computability Note 11 This note ties together two topics that might seem like they have nothing to do with each other. The nature of infinity (and more particularly, the distinction between different levels of infinity) and the fundamental nature of
EECS 70 Discrete Mathematics and Probability Theory Fall 2020 Introduction to Discrete Probability Note 13 Probability theory has its origins in gambling — analyzing card games, dice, roulette wheels. Today it is an essential tool in engineering and the sciences. No less so in EECS, where its use is widespread in algorithms, systems, signal processing,