# Real Analysis - Study Group

1. Sep 22, 2011

### estro

Anyone interested in opening online study group on Real Analysis?
I want to use https://www.amazon.com/gp/product/0486469131" for the study group.

Method: Some time will be given for self study then, group will discuss concepts and solve exercises from the book. [each phrase will be limited in time]

Please let me know if someone is interested.
I'm looking to start it around mid november.

Last edited by a moderator: May 5, 2017
2. Sep 22, 2011

### boaz

Sounds good, just what are the prerequisites? Judging by the cover of the book, it seems more than just Analysis.
Anyway, more details regarding the online study group are welcome.

3. Sep 22, 2011

### estro

By chance you know someone named Naftaly?=)

4. Sep 22, 2011

### boaz

Hehehe, good guess. What are the odds?
I see you have gotten some reputation here. :-)

5. Sep 22, 2011

### estro

If no one else will be interested we can make this study group offline.
I suggest OU Ra'anana, [Although never been there] what do you think?

6. Sep 22, 2011

### boaz

The location is great. The problem is how one, who doesn't own a car, can get there.
By the way, when does it start?

7. Sep 22, 2011

### estro

If someone else join us we will make it online, if it will be only me and you there is absolutly no problem. [You live in Ra'anana, I work in Ra'anana [very close to OU] so it shouldn't be a problem.]
We can start it when we will decide. =)

8. Sep 22, 2011

### micromass

If the study group is online, then I'd be willing to offer support

9. Sep 22, 2011

### estro

Thanks Micromass, I appreciate it very much!

10. Sep 23, 2011

### Bacle

Make it a study monoid , and I'm in!.

11. Sep 23, 2011

### micromass

Don't lose your *identity*

12. Oct 17, 2011

### h323t1q

I'm taking a class on Real Analysis, so I would like to contribute using a different book (as well as several programming languages!)

13. Oct 19, 2011

### drc4rd1n

Hello there,

I am interested to join into this great discussion (about: Real Analaysis) !

I heard that this particular field (Real Analysis) is the toughest field in Pure Mathematics. Isn't?

14. Oct 19, 2011

### drc4rd1n

May I know, what books you are using?

I've been used 'Fundamentals of Mathematical Analysis' 2nd Ed by Rod Haggarty &
'A Friendly Intro to Analaysis Single and Multivariable' by Witold A.J Kosmala

These two books are just nice

15. Oct 19, 2011

### h323t1q

Well, I have a large collection of analysis in pdf format - I've been reading wikis, and Mathematical Analyis, Apostol whenever things get hairy.

The course book is Vector Calculus, Linear Algebra, and Differential Forms by the Hubbards; the authors are a married couple who, oddly enough, write math books together.

The class I'm taking covers linear algebra, multi-variable calculus, and real analysis over two semesters. Right now we're studying row reduction, and how row reduction can be used as a proof method. It's interesting because, from my understanding, it's uncommon to use row reduction in proofs. Apparently, this can be used to prove that only square matrices are invertible.

Some proofs I've learned:

Proof of the intermediate value theorem.

Prove, using continuity and the Bolzano Weiestrass theorem that a compact, real valued continuous function has a supremum M, and is continuous at a point a such that f(a) = M.

http://en.wikipedia.org/wiki/Bolzano–Weierstrass_theorem

Prove that a function f is continuous at a point x_0 if and only if for all sequences x_i converging to x_0, the limit i approaches infinity for f(x_i) = f(x_0) is true.

If we want to do this, perhaps we could narrow the collaboration down to common proofs, and syntax/semantics of analysis. What proofs do your books cover? Perhaps I could obtain a pdf copy of the books others are using.

My background is in computer science. I've committed quite a bit of time to getting scheme with scmutils up and running. It's used with this book:
http://mitpress.mit.edu/SICM/

I also have prolog, but haven't spent as much time with it. I'd like to use prolog to develop a functional interpretation of analysis; I'm not a fan of how everything is so rigorous, yet everything is typically presented in not so rigorous notation.

16. Oct 19, 2011

### diracy

I'd be interested in the group if it is done online.

17. Oct 19, 2011

### Dr. Seafood

Sounds good to me too, I can contribute online if possible. Feel free to inbox me.

I have no background in analysis -- my first complex analysis course begins in January and I'll take Real Analysis I in May. Right now I'm taking my third calculus course in which we're discussing partial differentiability, linear approximations and Taylor polynomials. I'm also taking an "enriched" version of the calculus 3 course, in which we've covered a variety of topics. Here they are if you're interested:

• Some analysis of $\mathbb{R}^n$: norms, convergent and Cauchy sequences in $\mathbb{R}^n$, Bolzano-Weierstrass theorem. Open/closed sets, compactness. Sequences in closed sets. Supremums and infimums.
• Continuity, sequential continuity, uniform continuity. Theorem: a continuous function on a compact domain is also uniformly continuous. Intermediate value theorem, extreme value theorem.
• Integrability: Rectangles in $\mathbb{R}^n$, partitions, sequences of divisions, refinements. Upper and lower Darboux sums and Riemann integrals. Criteria for integrability, the algebra of bounded and integrable functions.

18. Oct 22, 2011

### diligence

I'd love to contribute to this group if it's online. I'm currently taking my second course in real analysis. Over the summer I took Advanced Calculus, which is my school's title for the first analysis course. The texts used were Understanding Analysis by Abbott (easy, but still good), Intro to Real Analysis by Bartle (tougher than Abbott, great for it's problems), and Baby Rudin.

I survived the summer course with my pride intact, then had the wise idea to take graduate level introductory analysis this semester. It's mostly the same material I had over the summer, but with more focus on general metric spaces and functions of several variables. We use Baby Rudin and Elementary Classical Analysis by Marsden/Hoffman.

Anyway, the point is that I'm struggling in the higher level class and it would probably be a great idea to join a study group. Please inbox me the info if this is still going on...thanks.

19. Oct 22, 2011

### MarlyK

Hey -
I would also be interested. I haven't worked with online study groups before though. I've got about the same background as Dr. Seafood - have taken a multivariable calculus course and now taking a calculus course in R^n that covers most of the topics he has listed. Not sure what pace you want to go at...I'll be getting busy around mid-November, but will free up again mid-December after exams.

20. Oct 22, 2011