MATH1004 Summary Notes (83)

Description

Discrete maths is packed with content. This subject requires significant time to excel in. These notes will give you a summary of every week and define concepts. Ultimately giving you the guide for HD on all assessments. Week 1 – Defining Discrete Math’s + Catalan Numbers Dots, Strings (brackets), Catalan Paths & Triangulations Week 2 – Set Theory Basics: Subsets, Equality of Sets, Cardinality & Operations 
Properties (incl. De Morgan’s Law) 
Power Sets 
Functions Between Sets: Injective, Surjective & Bijections 
 Week 3 – Functions 
 Contrapositives 
Bijections (injective + surjective) 
Compositions (incl. Identity Function) 
Binomial Coefficients (incl. Pascal Triangle) 
Pigeonhole Principle 
Week 4 – Counting Principles 
 Additive + Multiplicative Principal 
Permutations 
4 x Counting Methods o Ordered (repetition + no repetition) o Unordered (repetition + no repetition) Multinomial Coefficients (TB pg. 53-56) 
Binomial Theorem
 Week 5 – Principle of Inclusion-Exclusion 
 Counting Surjective Functions with Inclusion-Exclusion Weeks 5 & 6 – All things Boolean Functions, Variables and Notation 
Circuit Diagrams & Expressions 
Algebra Rules, Lemmas & De Morgan’s Laws 
Propositional Logic (Incl. Implication, Equivalence, Theorems, Contradictions, Quantifiers & Predicate Logic) 
 Week 7 & 8 – Proofs 
 Direct, Contrapositive & Contradiction 
Induction (incl. Well-Ordering & Number Theory) Week 9 – TWO PARTS: 
Euclid’s Lemma, Theorem of Arithmetic
Generating Functions, Closed Form & Recurrence Relation 
 Working with Generating Functions
 Week 10 & 11 – Process from Recurrence Relation to Exact Formula METHOD 1: BIG Process (incl. Partial Fractions & Geometric Series) 
 METHOD 2: Second Order Linear Recurrence Relation à Characteristic 
Equation (TB pg. 105-106) 
 Week 11-12 – Catalan Numbers 
 Dividing our Catalan Path into subsets (incl. a bijection from path to sub paths) 
Form a Closed Form Final Week - Revision