Tagged Questions

2
votes
1answer
41 views

Helpful to review certain calculus topics before first real analysis course?

This is my first time posting, so I apologize in advance if my question is inappropriate here. I wanted to know if it would be beneficial for me to review certain calculus topics before I take my ...
1
vote
3answers
106 views

Is there a problem in studying analysis before calculus? [closed]

Is there a problem in studying analysis before calculus? Most people say that analysis is rigorous calculus, the university I'm studying teaches calculus first because they believe it's better for the ...
2
votes
3answers
78 views

Lebesgue covering theorem

I am having trouble understanding Lebesgue covering theorem as stated in Mathematical Encyclopedia. First of all I think I have confusion with the definition of "finite subsystem". Is it finite ...
1
vote
1answer
133 views

Sternberg's Advanced Calculus [closed]

I have taken an analysis course using baby Rudin as the text, and I would like to keep up by analysis skills while developing on them. As such, I want to work through Sternberg's Advanced Calculus on ...
2
votes
1answer
102 views

Doubt - Proof of completeness of number system [duplicate]

Possible Duplicate: Choice of $q$ in Baby Rudin’s Example 1.1 I am going through Walter S. Rudin - Introduction to Mathematical Analysis,3rd Edition. In his proof of the existence of real ...
6
votes
5answers
810 views

Advice for benefits to directly use analysis textbook to replace calculus

Main purpose: For self-learning performance, neither for exam nor degree courses. Calculus textbook using now[1]: Calculus I, Weinstein&Marsden, UTM, Springer Question Description: I've been ...
11
votes
2answers
339 views

Choice of $q$ in Baby Rudin's Example 1.1

First, my apologies if this has already been asked/answered. I wasn't able to find this question via search. My question comes from Rudin's "Princicples of Mathematical Analysis," or "Baby Rudin," ...
0
votes
1answer
865 views

Can “How to Prove It” replace Baby Rudin for me?

I am an engineer with tons of math courses behind me. However, all of them were applied wherein instead of giving us intuition, they gave us a toolbox. (If you encounter this then use that to solve.) ...
1
vote
1answer
389 views

Help me find a book for self-study Calculus/Analysis

I read here all the recommendations but looking at tables of contents of each book none satisfies what I need.I am given a book series that has 4 volumes and 2800 pages but it is very hard to follow.I ...
5
votes
2answers
1k views

Just how much proof knowledge is necessary to begin Spivak's Calculus?

I bought Spivak's classic Calculus a month or so ago, and after doing a few problems from the first chapter, it's become apparent that some type of foundational knowledge in formal maths and proofs ...
1
vote
1answer
185 views

Undergraduate Research question

I've just finished my first analysis course, unfortunately I will not be able to continue studying as my family needs me to work for income. I was wondering if there is any meaningful research I can ...
1
vote
0answers
165 views

Are Specific Facts about the Riemann Integral Logically Required?

This question is somewhat in the spirit of this one in that I am trying to understand the most efficient path to the major integral theorems (Fubini, change of variables, etc). My question is this: ...
13
votes
9answers
4k views

Good book for self study of real analysis

Does anyone have a recommendation for a book to use for the self study of real analysis? Several years ago when I completed about half a semester of Real Analysis I, the instructor used "Introduction ...
4
votes
1answer
147 views

field properties

I decided to learn analysis over the summer for fun, but I'm really confused by the field properties. Why is the 2 element set of 0 and 1 a field? Addition wouldn't be satisfied, because 1 + 1 = 2, ...