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# Background Knowledge

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### Background Knowledge

1. 1. Information Safe Background Hoang V.Nguyen Mail: startnewday85@gmail.com Department of Computer Science Faculty of Information Technology – Hanoi University of Agriculture
2. 2. Background • Set theory and functions • Probability and Information theory • Complexity theory • Abstract Algebra • Number theory
3. 3. Set theory and functions • Set theory A B • Functions - Relations: 1-1, 1-n, n-1, n-n - functions: • domain vs codomain • preimage vs image • injective, onto, bijective • inverse • permutation A B
4. 4. Probability theory • a language for “randomness” • How: - experiment - simple events, event - sample space: discrete vs continous - probability distribution - conditional probability and Bayes’ theorem - random variables - expected value or mean - cumulative distribution function, probability function, density function - some distributions: normal, binomial, … .
5. 5. Information theory • What’s information, how to measure? • 1940s, Claude Shannon: Entropy n H ( A)   pi log pi i 1
6. 6. Complexity theory • What are the mathematical models of computation? Automata theory • What problems can(not) computers solve? Computability theory • What makes some problems computationally hard and other easy? Complexity theory
7. 7. Complexity theory • Rate of growth/Order of growth • Classify problems - P, NP, NPC, NP_hard - PSPACE - FP
8. 8. Abstract Algebra • Group - is a set with a binary operation such that: associate, identity element and inverse element - is abelian group: cummutative - subgroup, generator element, cyclic group • Ring -is a set(R) with two binary operations(+, x) such that: -(R,+) is abelian group with identify denoted by 0 -x operation is associate with identify is 1 ≠ 0 -The operation x is distributive over + operation - commutative ring: x operation is commutative • Field - is a commutative ring which all non-zero elements have multiplicative inverses
9. 9. Number theory • What’s number? • Characters of numbers • Integer numbers - divisibility - prime numbers - modulo