Discrete Structures Computer Science Functions

Discrete Structures Lecture Notes Vladlen Koltun1 Winter 2008 1Computer Science Department, 353 Serra Mall, Gates 374, Stanford University, Stanford, CA 94305, USA email160protected. Contents 1 Sets and Notation 1 7 Relations and Functions 31

In computer science, we are very familiar with function composition. When the returned value of a function in the sense of a programming language is used as the input to another function, we have function composition. The following code segment shows the function composition of the previous example's real functions written in Python.

Discrete mathematics uses a range of techniques, some of which is sel-dom found in its continuous counterpart. This course will roughly cover the following topics and speci c applications in computer science. 1.Sets, functions and relations 2.Proof techniques and induction 3.Number theory aThe math behind the RSA Crypto system

CS243 Discrete Structures Functions Is l Dillig Is l Dillig, CS243 Discrete Structures Functions 135 Functions I Afunction f from a set A to a set B assigns each element of A to exactly one element of B . I A is calleddomainof f, and B is calledcodomainof f. I If f maps element a 2 A to element b 2 B , we write fa b

Later courses in the computer science curriculum build on the mathematical foundations covered here. Particular emphasis is placed on inductive definitions and proofs, with application to problems in computer science. Special topics such as finite state automata and modular arithmetic will be discussed. The course covers 6 major topics.

Why functions? Sets rigorous way to talk about collections of objects Logic rigorous way to talk about conditions and decisions Relations rigorous way to talk about how objects can relate to each other Function a relation in which each element of the domain is related to exactly one element in the codomain

This course builds the mathematical foundation of computer science. It introduces the elements of mathematics like sets, functions, relations that form the basics of almost the entirety of computer science. It gives a clear understanding about the formal statements and their proofs and the counting techniques.

This subject offers an interactive introduction to discrete mathematics oriented toward computer science and engineering. The subject coverage divides roughly into thirds 1. Fundamental concepts of mathematics Definitions, proofs, sets, functions, relations. 2. Discrete structures graphs, state machines, modular arithmetic, counting. 3. Discrete probability theory. On completion of 6.042J

This course is an introduction to the essential discrete structures used in Computer Science, with emphasis on their applications. Topics to be covered include binary number representation and arithmetic, sets, relations, functions, formal propositional logic and proofs, digital logic and combinational circuits, finite state machines, regular expressions and formal grammars.

following functions. a.The function that determines the number of zeros in some bit string b.The function that maps an English word to its two rightmost letters c. The function that assigns to an integer the sum of its individual digits Problem 2 Suppose 0 is a function from ! to quot and is a function from quot to 5. Prove that if and 0 are