Stanford online Real Analysis course --- comments?

[desimba]

I have been trying to improve my understanding of math proofs and have been using a book by Vellman called "How to Prove it: A Structured Approach". For someone who has an engineering undergrad (and a fair bit of math that goes with that), Vellman hasn't been an easy read. Nevertheless I have been patient with it and trying to plod through the material. Anyone who has used Vellman would like to comment on its usefulness for courses like Math for Economists and the Microeconomics sequence?

[rcwlhk]

double post - delete

[rcwlhk]

Hey there,

I also used the Vellman book to go along side with my math proof / intro analysis course.

Here are my two cents about this book:

PROS
-Definitely good intro into the basics of logic

-I actually find reading their chapter on "3. Proofs" to be the greatest value out of this book. Perhaps its just the course that I took or the instructor himself, but we started the class by saying "here are the names for the various methods of proof but we'll show you what it means and how it works as we progress in the class." Hence, I struggled so much at the beginning just trying to understand "what" exactly am I trying to do.


CONS
-The notations they use are somewhat annoying, but I can deal with it

-If I recall correctly, they advocate this "two column" what-do-you-want vs. what-do-you-need approach. I tried doing this for a while and eventually I just gave up. It works well if you have a very well structured theorem / lemma that you want to show (i.e. If A, B, C, then D, E, F). But it's almost useless for those one-liner theorems (i.e. (Division Theorem) There exist unique integers q and r such that a = qd + r and 0 ≤ r < | d |, where | d | denotes the absolute value of d.)

-The biggest con that I have for this book is that it the scope of material is quite limited (i.e. they don't even touch on sequences, series, etc.)

SUGGESTIONS & COMMENTS
-Take a look at Amazon.ca: An Introduction to Mathematical Reasoning: Numbers, Sets and Functions: Peter J. Eccles: Books. I find it to be a decent book too and it goes into good detail compared to Velleman. But I'd say Velleman is slightly more "user friendly"

-It might sound awkward to most people on TM, but I actually find taking ANOTHER non-analysis based proof course first to be a better preparation for the subsequent analysis courses. Namely, I found taking Number Theory to be quite useful. And yes, I'm well aware that Number Theory has little to no applications in Economics (right?). But this is my takeaway after taking Number Theory and comparing to my initial struggles with analysis ---- let's face it, analysis is very abstract, even at the very elementary level. So, as a beginner, not only do you struggle with the concepts of analysis, you ALSO have to struggle with the methods of proof --- bad combination! However, number theory is quite different. You pretty much "know" all the concepts they teach you in number theory since elementary school (i.e. divisibility, remainders, primes, composites, etc.) so at the very least, you won't have to struggle with the concepts. And it is here, where you can practice your proofing skills before moving on to analysis.

Originally Posted by desimba

I have been trying to improve my understanding of math proofs and have been using a book by Vellman called "How to Prove it: A Structured Approach". For someone who has an engineering undergrad (and a fair bit of math that goes with that), Vellman hasn't been an easy read. Nevertheless I have been patient with it and trying to plod through the material. Anyone who has used Vellman would like to comment on its usefulness for courses like Math for Economists and the Microeconomics sequence?

[philecon]

Originally Posted by desimba

I have been trying to improve my understanding of math proofs and have been using a book by Vellman called "How to Prove it: A Structured Approach". For someone who has an engineering undergrad (and a fair bit of math that goes with that), Vellman hasn't been an easy read. Nevertheless I have been patient with it and trying to plod through the material. Anyone who has used Vellman would like to comment on its usefulness for courses like Math for Economists and the Microeconomics sequence?

My intro to proofs class used Bridge to Abstract Mathematics by Ronald Morash. It was very helpful, but there were times that I was getting lost (especially when he discussed cardinality - the material was brief), so I bought Velleman's book (and I was confused with this book at times because it used different notation), and Solow's book as references. I also borrowed Eccles' book from my college library.

If I'm going to rank the three, it would be like this: Solow > Eccles > Velleman.