'Elementary number theory' presentation slideshows

Outline

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3 Gallon Jug

Greatest Common Divisor. 3 Gallon Jug. 5 Gallon Jug. Lecture 8: Sep 29. This Lecture. In this lecture we will learn the Euclidean algorithm for computing greatest common divisor (GCD), which is one of the earliest important

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Chapter 3

Chapter 3. Elementary Number Theory and Methods of Proof. 3.1. Direct Proof and Counterexample 1 Integers. Mathematical Proof. A mathematical proof is a carefully reasoned argument to convince a skeptical listener. (pg 125) Example: How would you prove if 5x + 3 = 33 then, x = 6?

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Discrete Structures

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Discrete Structures

Discrete Structures. Chapter 4: Elementary Number Theory and Methods of Proof 4.1 Direct Proof and Counter Example I: Introduction.

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Discrete Structures

Discrete Structures. Chapter 4: Elementary Number Theory and Methods of Proof 4.2 Direct Proof and Counter Example II: Rational Numbers.

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Chapter 3

Chapter 3. Elementary Number Theory and Methods of Proof. 3.4. Direct Proof and Counterexample 4 Division into Cases and the Quotient-Remainder Theorem. Quotient-Remainder Theorem. Theorem 3.4.1 The Quotient-Remainder Theorem

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Chapter 3

Chapter 3. Elementary Number Theory and Methods of Proof. 3.6. Indirect Argument. Reductio Ad Absurdum. Argument by contradiction Illustration in proof of innocence Suppose I did commit the crime. Then at the time of the crime, I would have had to be at the scene of the crime.

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Chapter 3

Chapter 3. Elementary Number Theory and Methods of Proof. 3.5. Direct Proof and Counterexample 5 Floor & Ceiling. Floor & Ceiling. Definition Floor Given any real number x , the floor of x , denoted ? x ?, is defined as: ? x ? = n ? n ? x < n + 1. Ceiling

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Chapter 3

Chapter 3. Elementary Number Theory and Methods of Proof. 3.2. Direct Proof and Counterexample 2 Rational Numbers. Rational Numbers. Definition

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Discrete Structures

Discrete Structures. Chapter 4: Elementary Number Theory and Methods of Proof 4.6 Indirect Argument: Contradiction & Contraposition.

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Security in Distributed Systems

Security in Distributed Systems. Introduction and Design Issues Threats to security systems Security Mechanisms Design Issues: Focus of Data Control, Layering of security mechanisms and Simplicity Cryptography Basics of Cryptography

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