MATH2400
Finite Mathematics
Term 2 - 2021
Arithmetic
- Ring
- Ring with Identity
- Non-Unital Ring
- GF(2)
- Division Algorithm
- Divisibility
- Greatest Common Divisor for Integers
- Properties of the GCD
- Bezout Identity
- Euclidean Algorithm
- Prime Number
- Fundamental Theorem of Arithmetic
- Infinitude of Primes
- Twin Prime Conjecture
- Goldbach Conjecture
- Sophie Germain Prime
- Mersenne Primes
- Fermat Prime
Rational and Real Arithmetic
- Place Value System
- Base b Algorithm
- Binary GCD Algorithm
- Continued Fraction
- Continued Fraction Algorithm
- Simplifying Recurring Continued Fractions
- Periodic Continued Fractions
- Terminating Continued Fraction
- Approximations of Real Numbers Using Continued Fractions
Modular Arithmetic
- Modulo Operation
- Modular Arithmetic
- Operations Respected by Modulo Congruences
- Cancelling in Linear Congruences
- Cayley Table
- Multiplicative Group
- Multiplicative Group of Integers Modulo \(n\)
- Integers Modulo Prime Finite Field
- Group
- Abelian Group
- Base 10 Divisibility Rules
Solving Linear Equations
- Diophantine Equation
- Chinese Remainder Theorem
- Chinese Remainder Theorem Algorithm
- Chinese Remainder Theorem with Non-Coprime Moduli
Powers and Primitive Roots
- Quadratic Residue
- Fermat's Little Theorem
- Euler's Totient Function
- Order (Group Theory)
- Order of Element Divides Order of Group
- Primitive Root
- Efficiently Calculating Primitive Roots
- Cyclic Group
- Discrete Logarithm
- Diffie-Hellman Key Exchange Protocol
Applications
- Sieve of Eratosthenes
- Primality Testing by Trial Division
- Fermat's Test for Primality
- Fermat Pseudoprime
- Carmichael Number
- Lucas' Test for Primality
- AKS Primality Test
- RSA Encryption
- Exploiting RSA With Twin Primes
- Exploiting RSA With Mersenne Primes
- Parity Check Code
- Repetition Codes
- Information Rate
- Hamming Code
Polynomials
- Polynomial
- Polynomial Ring
- Polynomial Division Algorithm
- Polynomial Long Division
- Unique Factorisation Domain
- Irreducible Element
- Prime Element
- Unit
- Associates
- Polynomial Quotient Ring Construction of Finite Fields
- Polynomial Formal Derivative
- Fundamental Theorem of Algebra
- Primitive Polynomial