EECS 70 Discrete Mathematics and Probability Theory Fall 2021 1 Modular Arithmetic 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, . . . , N […]
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CS 70 Discrete Mathematics and Probability Theory Fall 2021 1 Stable Matching Consider the set of jobs J = {1, 2, 3} and the set of candidates C = {A, B, C} with the following preferences. Jobs Candidates 1 A>B>C 2 B>A>C 3 A>B>C Candidates Jobs A 2>1>3 B 1>3>2 C 1>2>3 Run the traditional
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CS 70 Discrete Mathematics and Probability Theory Fall 2021 1 Berlekamp- Up Let P(i), a polynomial applied to the input i, be the original encoded polynomial before sent, and let ri be the received info for the input i which may or may not be corrupted. (a) When does ri = P(i)? When does ri
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EECS 70 Discrete Mathematics and Probability Theory Fall 2021 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 packets to be corrupted.
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EECS 70 Discrete Mathematics and Probability Theory Fall 2021 Polynomials 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 contexts in
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EECS 70 Discrete Mathematics and Probability Theory Fall 2021 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 inventors ,
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CITS2002 Systems Programming 1 next ¡ú CITS2002 CITS2002 schedule The structure of C programs Let’s looks at the high-level structure of a short C program, rotate.c (using ellipsis to omit some statements for now). At this stage it’s not important what the program is supposed to do. Of note in this example: Characters such as
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CITS2002 Systems Programming 1 next ¡ú CITS2002 CITS2002 schedule Introducing functions C is a procedural programming language, meaning that its primary synchronous control flow mechanism is the procedure call. C names its procedures functions (in contrast, Java has a different mechanism -methods). In Mathematics, we apply a function, such as the trigonometric functioncos, to one
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FAMILY NAME: GIVEN NAMES: SIGNATURE: STUDENT NUMBER: SEMESTER 2, 2019 EXAMINATIONS Physics, Mathematics & Computing This paper contains: 6 Pages (including title page) INSTRUCTIONS: This paper contains 6 pages and 6 questions You are required to attempt ALL 6 questions Systems Programming Programming and Systems Time Allowed: 2:00 hours THIS IS A CLOSED BOOK EXAMINATION
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CITS2002 Systems Programming 1 next ¡ú CITS2002 CITS2002 schedule Allocating primary memory to processes The important task of allocating memory to processes, and efficiently ensuring that processes have their instructions and data in main memory when needed, is termed memory management. We’ll need to consider the role that memory plays from two (conflicting?) perspectives: the
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