tailieunhanh - Lecture Notes for CS120: Computing 1 Subhashis Banerjee S. Arun-Kumar

Technology is the making, modification, usage, and knowledge of tools, machines, techniques, crafts, systems, methods of organization, in order to solve a problem, improve a preexisting solution to a problem, achieve a goal, handle an applied input/output relation or perform a specific function. It can also refer to the collection of such tools, machinery, modifications, arrangements and procedures. Technologies significantly affect human as well as other animal species' ability to control and adapt to their natural environments. The word technology comes from Greek τεχνολογία (technología); from τέχνη (téchnē), meaning "art, skill, craft", and -λογία (-logía), meaning "study of-".[1] The term. | Lecture Notes for CS120 An Introduction to Computing1 Subhashis Banerjee S. Arun-Kumar Department of Computer Science and Engineering Indian Institute of Technology New Delhi 110016 email suban sak @ August 2 2003 1Copyright 1997-2003 Subhashis Banerjee and S. Arun-Kumar. All Rights Reserved. These notes may be used in an academic course with the prior consent of the authors. 2 Contents I Models of computation 5 1 Introduction 7 2 Mathematical preliminaries 9 Sets. 9 Relations and Functions. 11 Principle of Mathematical Induction. 11 3 A functional model of computation 17 The primitive expressions. 18 Substitution of functions. 20 Substitution using let. 21 Definition of functions using conditionals. 23 Functions as inductively defined computational processes . 24 Recursive processes. 26 Analysis of correctness and efficiency. 28 Correctness. 28 Efficiency . 28 Efficiency Why and How . 29 In the long run Asymptotic analysis and Orders of growth . 30 More examples of recursive algorithms. 31 Scope rules. 41 Tail-recursion and iterative processes. 43 Correctness of an iterative process. 45 More examples of iterative processes. 46 4 The Imperative model of computation 53 The primitives for the imperative model . 53 Variables and the assignment instruction . 54 Assertions . 56 The if then else instruction. 58 The while do instruction. 61

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