Week 5 ,Lecture#1, #2

I believe week five lectures were about recursion concept .
The slide # 8, 9 from week #5 , lecture#2, I could not get them at all. If I am right, It should be chapter four materials related to set.

The closed-form concept is cumbersome job. I think first, I have to do unwinding on general given function after analyzing the output of function I have to derive closed-form formula from the output of general function. Then I have to prove it that the closed-form formula works.

I hope, I am right here.

Recursion

In recursion, is zero always the base case?

Well-Ordering

I got the concept about well ordering but I could not figure out how to connect it with the simple induction. I beleive it should be simple since all we learned about well ordering was a set must have smallest element. Okay, If a set has smallest element does this mean that the smallest element is true then the rest of the element must be true unless I assume that all elements including the smallest element belong to some group.
Here I get confused, How can I prove that my assumption is hundred percent correct.
Otherwise, it would be very clear and self explanatory to say that my assumption is true due to blah... mathematic proof therefore my smallest number belong to blah.. group and therefore the n+1 number following the smallest number also belong to blah... group and vallah there we go my proof is done. May be I am missing something here. I think I should talk to prof about this matter.

Induction is working for me now

Hi;

I would like to start with few suggestions.

1) it would be very helpful if professor post the lecture slides ahead of the lecture.This will be like a preview of lecture for us. Also we will be able to get the insight of the material and then we can effectively write down all his explanations and comments about the material during the lecture promptly.


2)I think it would be great if any solution get posted for the exercises of each chapter.

I found this course very demanding since the nature of materials involves handling a lot assumptions and algebraic tricks that we have to apply on different problems.

In the first two weeks, I could not convince my self that Induction proof works. It seemed to me just bunch of self evident statements and manipulations of statements (Black Magic). It was not till to yesterday , after reading few books on Induction such as the CSC165 book, "Learning to reason" by Nancy Rogers and the "Calculus " by Michael Spivack and also after reading more than two times the current course text book for CSC236.

For sure I have to learn the patterns and practice all exercises available in order to acquaintance my self with different kind of proofs.

I am just wondering is there any good book available for improving algebraic skills. I think for me it is the big hassle and I need to improve this area as soon as possible.