> See also:
> - Reference
# COT 3100 - Discrete Structures
induction is recursion flipped on its head
early exam grades raised by half distance to final exam grade (cuts off at 80%)
open book open notes (no screens)
You can use the laws of logic in equivalence proofs but you can’t use the rules of inference for
## Exam Objectives
### Exam 1
- [[Fundamentals of Logic]]
- [ ] Boolean operators
- [ ] Laws of Logic
- [ ] Implication Basics
- [ ] Contrapositive, Inverse, Converse
- [ ] Rules of Inference
- [ ] Nested Quantifiers
- [ ] When order matters ($\forall \exists$ vs $\exists \forall$)
- [ ] How to disprove
- [[Proof Techniques]]
- [ ] Choosing the right proof technique
- [ ] Direct
- [ ] Contradiction
- [ ] Contrapositive
- [ ] Cases
- [[Set Theory]]
- [ ] Operator Definitions
- [ ] Laws of Set Theory
- [ ] Inclusion/Exclusion Principles (2 & 3)
- **Math/Arithmetic**
- [ ] Logarithms
- [ ] D=RT
- [ ] Managing variables in problems
- [ ] Completing the square
- [ ] Factoring/Algebraic Techniques
### Exam 2
> [!summary]+ Recitation Problems (15 pts)
> - [ ] Using integers information to restrict possibilities
> - [ ] Factorial prime factorization
> - [ ] Number of divisors of an integers
> - [ ] Factoring formula, using for divisibility, divisors
> - [ ] Age problems
> - [ ] Work problems
> - [ ] Clock problems
> - [ ] Mixture problems (hell no)
> [!summary]+ [[Number Theory]] (25 pts)
> - [[Divisibility and Modular Arithmetic]]
> - [[Integers]]
> ---
> - [ ] Definition of Division/Modulo (Modular Arithmetic)
> - [ ] Logical properties of division
> - [ ] Divisibility Proofs
> - [ ] Euclid's Algorithm
> - [ ] Extended Euclid's Algorithm
> - [ ] Full Solution to $ax+by=c$ for integers given $a,b,c$
> - [ ] Finding Modular Inverses
> - [ ] Pi Notation
> - [ ] Fundamental Theorem of Algebra
> - [ ] Least common multiple (LCM)
> - [ ] Connection between LCM and GCD
> - [ ] Calculating # of divisors of an integer
> - [ ] Calculating the number of times prime p divides into n!
> [!summary]+ [[Mathematical Induction]] (35 pts)
> - [ ] Arithmetic & Geometric Series
> - [ ] Solving for terms, sums, etc.
> - [ ] How to recursively define sequences
> - [ ] Definition of Summation Notation
> - [ ] Summation Rules
> - [ ] Telescopic Sum Idea
> - [ ] Matrix Addition, Subtraction, Multiplication
> - [ ] Solving Induction Problems
> - [ ] Base Case
> - [ ] Inductive Hypothesis
> - [ ] Inductive Step
> - [ ] Not all induction problems use summations
> - [ ] How to deal with inequalities during induction (inequality steps)
> - [ ] Strong Induction
> - [ ] Induction divisibility problems
> - [ ] Induction matrix exponentiation problems
> - [ ] Induction problems with recursively defined sequences
> - [ ] Induction problems with Harmonic numbers
> - [ ] Other
> - [ ] NIM, Chicken Nuggets, Trominos
> [!example] Reference Sheet Planning
> - Euclidian Algorithm Example
> - Arithmetic Series Definition
> - Geometric Series Definition
> - Proving divisibility techniques
> - Summation notation
> - Summation rules
> - Pi notations
### Exam 3
> [!summary] Counting
> - [ ] Definition of "n choose k"
> - [ ] Algebraic vs Combinatorial Proofs
> - [ ] Binomial Theorem (+ Corollaries)
> - [ ] "4 Types of Counting Situations"
> - Combinations
> - Permutations
> - Repeat Items
> - Unique/Distinct Choices
> - [ ] Counting "Operators"
> - +, -, /, *
> - Concept of "splitting up choices"
>
TODO:
- Finding the possible events for a given problem
- Finding event space sizes
The sample space size for a given even is the chance of that event happening out of all of the event spaces that could possibly occur?
pizza