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.

Week 6

This week was an important one. We got our results and they were very nice, the class average was pretty high and i got a good score. :D
During the class we keep talking about proofs including:
Proof about non-boolean functions, proof something false, proof about limits.
The proofs became a little confusing to me I have to read the content again to really get all the informations.
Remember we have to make sure that we fully understand the definition of the function otherwise we will proof it wrong. As we are manipulating the expression we have to try put them as closer as possible to those in the definition since the definition is all we have to use.

Tips for disprove a statement:
First make sure to negate it correctly, then prove the negated statement and draw examples to obtain intuition. The main point about all those weird letters that when you take a look you get nervous and confuse is, do not freak out, keep calm and try to solve the question following all the rules they only seems hard but with a good practice they will become more easier to solve

We are going to finish up proofs next week and according with the time that we have
we might start a new subject, algotithm runtime.

Week 5

The Week 5 was right after our midterm, i was a bit apprehensive because i did not know if i had gone well on the test, so, was kind of hard to concentrate/put the head on the place right after a test. Although all this facts the class was fine so let's see what's happened and get into the rhythm of study again.
We continued to talk about proofs this week covering several kinds of proofs including:
Proof using contrapositive, proof using contradiction, proof for existence, proof about a sequence. These proofs techniques are very interesting. The professor gave us severals tips during the lecture about how to do the work of proof become easier
Haaa and just to remember:
One proof may consist of  several different structures and another important part is that with multiple quantifiers, we should do a zoom into the smaller and smaller part of the statement, layer by layer to better prove the statement.

Week 4

Hey guys, the past weeks have been hard to me with a lot of assignments and midterms going on but now i'm back to present you whats happened at week 4.

The main subjects of this week were Bi-implication, Transitivity and Mix quantifiers.
With these subjects we finished all the content about the language of math.
The content was very extensive but I was able to understand it. Once the exercises during the week helped me to do that. Once we finished the content about math language we start to talk about Proofs. The professor gave us an nice introduction regarding to why do we use proofs, why are they important, what is proofs and how to prove. To end up we solved some questions together to better understand the structure of proofs.
Just to remember this was our last lecture before the so waited midterm