Algor ithms and Integ ers - Columbia University Computer
Transcript of 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
coursenotes by Prof. J. L. Gross for Rosen 6th Edition
3.1.2 Chapter 3 Algorithms and Integers
Algo 3.1.1:
coursenotes by Prof. J. L. Gross for Rosen 6th Edition
Section 3.1 Algorithms 3.1.3
Algo 3.1.2:
coursenotes by Prof. J. L. Gross for Rosen 6th Edition
3.1.4 Chapter 3 Algorithms and Integers
Algo 3.1.3:
coursenotes by Prof. J. L. Gross for Rosen 6th Edition
Section 3.1 Algorithms 3.1.5
Algo 3.1.4:
coursenotes by Prof. J. L. Gross for Rosen 6th Edition
3.1.6 Chapter 3 Algorithms and Integers
Algo 3.1.5:
coursenotes by Prof. J. L. Gross for Rosen 6th Edition
Section 3.2 Growth of Functions 3.2.1
3.2 GROWTH OF FUNCTIONS
BIG OH CLASSES
coursenotes by Prof. J. L. Gross for Rosen 6th Edition
3.2.2 Chapter 3 Algorithms and Integers
coursenotes by Prof. J. L. Gross for Rosen 6th Edition
Section 3.2 Growth of Functions 3.2.3
WITNESSES
CLASSROOM EXERCISE
coursenotes by Prof. J. L. Gross for Rosen 6th Edition
3.2.4 Chapter 3 Algorithms and Integers
coursenotes by Prof. J. L. Gross for Rosen 6th Edition
Section 3.2 Growth of Functions 3.2.5
coursenotes by Prof. J. L. Gross for Rosen 6th Edition
3.2.6 Chapter 3 Algorithms and Integers
BIG-THETA CLASSES
coursenotes by Prof. J. L. Gross for Rosen 6th Edition
Section 3.3 Complexity 3.3.1
3.3 COMPLEXITY
coursenotes by Prof. J. L. Gross for Rosen 6th Edition
3.3.2 Chapter 3 Algorithms and Integers
Algo 3.1.1:
coursenotes by Prof. J. L. Gross for Rosen 6th Edition
Section 3.3 Complexity 3.3.3
Algo 3.1.2:
coursenotes by Prof. J. L. Gross for Rosen 6th Edition
3.3.4 Chapter 3 Algorithms and Integers
Algo 3.1.3:
coursenotes by Prof. J. L. Gross for Rosen 6th Edition
Section 3.3 Complexity 3.3.5
Algo 3.1.4:
coursenotes by Prof. J. L. Gross for Rosen 6th Edition
3.3.6 Chapter 3 Algorithms and Integers
coursenotes by Prof. J. L. Gross for Rosen 6th Edition
Section 3.3 Complexity 3.3.7
Algo 3.1.5:
coursenotes by Prof. J. L. Gross for Rosen 6th Edition
3.3.8 Chapter 3 Algorithms and Integers
COMPLEXITY JARGON
coursenotes by Prof. J. L. Gross for Rosen 6th Edition
Section 3.4 The Integers and Division 3.4.1
3.4 THE INTEGERS AND DIVISION
coursenotes by Prof. J. L. Gross for Rosen 6th Edition
3.4.2 Chapter 3 Algorithms and Integers
AXIOMS for the NATURAL NUMBERS
coursenotes by Prof. J. L. Gross for Rosen 6th Edition
Section 3.4 The Integers and Division 3.4.3
ARITHMETIC OPERATIONS
coursenotes by Prof. J. L. Gross for Rosen 6th Edition
3.4.4 Chapter 3 Algorithms and Integers
DIVISION
coursenotes by Prof. J. L. Gross for Rosen 6th Edition
Section 3.4 The Integers and Division 3.4.5
DIVISION THEOREM
Algo 3.4.1:
coursenotes by Prof. J. L. Gross for Rosen 6th Edition
3.4.6 Chapter 3 Algorithms and Integers
coursenotes by Prof. J. L. Gross for Rosen 6th Edition
Section 3.4 The Integers and Division 3.4.7
MODULAR ARITHMETIC
coursenotes by Prof. J. L. Gross for Rosen 6th Edition
3.4.8 Chapter 3 Algorithms and Integers
CAESAR ENCRYPTION
coursenotes by Prof. J. L. Gross for Rosen 6th Edition
Section 3.5 Primes and GCD’s 3.5.1
3.5 PRIMES AND GCD’S
Algo 3.5.1:
coursenotes by Prof. J. L. Gross for Rosen 6th Edition
3.5.2 Chapter 3 Algorithms and Integers
Algo 3.5.2:
coursenotes by Prof. J. L. Gross for Rosen 6th Edition
Section 3.5 Primes and GCD’s 3.5.3
MERSENNE PRIMES
coursenotes by Prof. J. L. Gross for Rosen 6th Edition
3.5.4 Chapter 3 Algorithms and Integers
Fundamental Theorem of Arithmetic
coursenotes by Prof. J. L. Gross for Rosen 6th Edition
Section 3.5 Primes and GCD’s 3.5.5
GREATEST COMMON DIVISORS
Algo 3.5.3:
coursenotes by Prof. J. L. Gross for Rosen 6th Edition
3.5.6 Chapter 3 Algorithms and Integers
Algo 3.5.4:
coursenotes by Prof. J. L. Gross for Rosen 6th Edition
Section 3.5 Primes and GCD’s 3.5.7
RELATIVE PRIMALITY
coursenotes by Prof. J. L. Gross for Rosen 6th Edition
Section 3.6 Integers and Algorithms 3.6.1
3.6 INTEGERS AND ALGORITHMS
POSITIONAL REPRESENTATION of INTEGERS
coursenotes by Prof. J. L. Gross for Rosen 6th Edition
3.6.2 Chapter 3 Algorithms and Integers
NUMBER BASE CONVERSION
coursenotes by Prof. J. L. Gross for Rosen 6th Edition
Section 3.6 Integers and Algorithms 3.6.3
EVALUATION OF MONOMIALS
EVALUATION OF POLYNOMIALS
coursenotes by Prof. J. L. Gross for Rosen 6th Edition
3.6.4 Chapter 3 Algorithms and Integers
EUCLIDEAN ALGORITHM
coursenotes by Prof. J. L. Gross for Rosen 6th Edition
Section 3.6 Integers and Algorithms 3.6.5
Algo 3.6.1:
coursenotes by Prof. J. L. Gross for Rosen 6th Edition
3.6.6 Chapter 3 Algorithms and Integers
coursenotes by Prof. J. L. Gross for Rosen 6th Edition
Section 3.7 Number Theory 3.7.1
3.7 NUMBER THEORY
EXTENDED EUCLIDEAN ALGORITHM
coursenotes by Prof. J. L. Gross for Rosen 6th Edition
3.7.2 Chapter 3 Algorithms and Integers
EXPONENTIATION MOD a PRIME
coursenotes by Prof. J. L. Gross for Rosen 6th Edition
Section 3.7 Number Theory 3.7.3
coursenotes by Prof. J. L. Gross for Rosen 6th Edition