Math 300: Introduction to Mathematical Reasoning

Midterm: here
Solutions: here
Final: here
Solutions: here

Week # Topic Reading Homework
Intro to Math Reasoning
1.
  • Definitions, proofs, the language of math. Connectives
  • => and <=>
2.
  • truth tables, Negations, 3 proofs methods
  • Three proof methods
  • proof by contradiction, induction
3.
  • More induction
  • Strong induction, recursive definitions
  • Fibonacci's numbers
4.
  • sets
  • sets continued
  • Cartesian Product, Power set
5.
  • Nested Quantifiers, Fucntions
  • Injections, Surejections, Bijections
  • More on Functions
6.
  • Cardinality
  • Denumerability Proofs
  • More Cardinality Proofs
7.
  • Division th, gcd, Euclidean algorithm, diophantine equations
  • Congruence, classes, mod m
8.
  • Modular Arthmetic
  • Zm, Cancellation laws, Linear congruence
  • Linear congruence cont.
9.
  • inverses in zm
  • Equivalence Relations, Equivalence Classes
  • No Class Thanksgiving
  • Prime Numbers
10.
  • Psuedo Primes, Eulers function
  • RSA Algorithm