Algor ithms and Integ ers - Columbia University Computer

Section 3.0 3.0.1

Chapter 3Algorithmsand Integers

3.1 Algorithms

3.2 Growth of Functions

3.3 Complexity of Algorithms

3.4 The Integers and Division

3.5 Primes and GCD’s

3.6 Integers and Algorithms

3.7 Applications of Number Theory

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 3.1 Algorithms 3.1.1

3.1 ALGORITHMS


3.1.2 Chapter 3 Algorithms and Integers

Algo 3.1.1:



Algo 3.1.2:



Algo 3.1.3:



Algo 3.1.4:



Algo 3.1.5:


Section 3.2 Growth of Functions 3.2.1

3.2 GROWTH OF FUNCTIONS

BIG OH CLASSES





WITNESSES

CLASSROOM EXERCISE







BIG-THETA CLASSES


Section 3.3 Complexity 3.3.1

3.3 COMPLEXITY



Algo 3.1.1:



Algo 3.1.2:



Algo 3.1.3:



Algo 3.1.4:





Algo 3.1.5:



COMPLEXITY JARGON


Section 3.4 The Integers and Division 3.4.1

3.4 THE INTEGERS AND DIVISION



AXIOMS for the NATURAL NUMBERS



ARITHMETIC OPERATIONS



DIVISION



DIVISION THEOREM

Algo 3.4.1:





MODULAR ARITHMETIC



CAESAR ENCRYPTION


Section 3.5 Primes and GCD’s 3.5.1

3.5 PRIMES AND GCD’S

Algo 3.5.1:



Algo 3.5.2:



MERSENNE PRIMES



Fundamental Theorem of Arithmetic



GREATEST COMMON DIVISORS

Algo 3.5.3:



Algo 3.5.4:



RELATIVE PRIMALITY


Section 3.6 Integers and Algorithms 3.6.1

3.6 INTEGERS AND ALGORITHMS

POSITIONAL REPRESENTATION of INTEGERS



NUMBER BASE CONVERSION



EVALUATION OF MONOMIALS

EVALUATION OF POLYNOMIALS



EUCLIDEAN ALGORITHM



Algo 3.6.1:




Section 3.7 Number Theory 3.7.1

3.7 NUMBER THEORY

EXTENDED EUCLIDEAN ALGORITHM



EXPONENTIATION MOD a PRIME


Section 3.7 Number Theory 3.7.3


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Algor ithms and Integ ers - Columbia University Computer

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