Week 7

This week we worked on proof by cases, review of proofs and we began to see some content about algorithms.
Proof by cases has simple steps to get to a solution first we must split our argument into different cases then we prove the conclusion for each case.

During the review of proofs we saw some content about proof pattern. Pattern of inference has two categories of inference rules: introduction and elimination.
Consider:
ss-->smaller statement
ls--> larger statement

Introduction: when the smaller statement is equal or larger than the larger statement
(ss => ls)
elimination: when the larger statement is equal or larger than the smaller statement (ls => ss)

Introduction has some rules as: negation introduction, conjuction introduction, disjunction introduction, implication introduction, equivalence introduction, universal introduction, existencial introduction

Elimination rules: negation elimination, conjuction elimination, disjunction elimination,
implication elimination,implication elimination,equivalence elimination, universal elimination, existencial elimination

Tip: how to be good at proofs:
become familiar with these patters, by lots of practice
recognize these patters in your proof, use the manipulation rules to get closer to your target.

After that was time to start the content about Algorithm Analysis and Asymptotic Notation
among several subjects inside this content we looked at how analyse the time complexity of a program specifically through linear search we also saw the worst-case time complexity, best-case and average-case.

with it we finished this week anxious waiting for learn more about asymptotic notation and algorithm analysis.