13 events
when toggle format what by license comment
Dec 24 '17 at 2:22 review Close votes
Dec 30 '17 at 3:06
Jul 21 '15 at 14:42 comment added Nate C-K Well the real question is, what's the best use of your time? You can read another calculus book now but it will cost you extra time, and it seems like you're in a hurry. Speaking of being in a hurry: does it make sense to self-study real analysis while enrolled at a university that teaches the course? Why not start reading an analysis book right now (not all of them) for your research background and then take the course next year? The first 4 chapters of Apostol's MA cover the topics you mention; start reading and see how you feel.
Jul 21 '15 at 1:47 comment added MathWanderer Study the basics of analysis (real number system, basic topology, limits, and continuity) from the basic analysis (Rudin-PMA) and jump directly into those real analysis books I mentioned above and study them in a "non-linear, backward" manner, studying the necessary topics from basic analysis books as necessary. He said that he studied on that way and finished both Rudin-PMA and Folland at the same time. Is this actually a possible plan?
Jul 21 '15 at 1:46 comment added MathWanderer I just got a mathematics undergraduate research in the computational complexity theory. Although the research mainly involves in the abstract algebra and linear algebra, my research project will also involve e measure theory, approximation theory, optimization, and real analysis. My research adviser told me that the real analysis books such as Royden, Folland, Rudin-RCA, Lang (RCA), and Stein/Shakarchi will be a good reading. I told him of my lack of background in the analysis and multivariable calculus, and he devised a following plan for me:
Jul 21 '15 at 1:43 comment added MathWanderer Also by "transitional analysis course", do you mean at the level of Rudin-PMA, Apostol (MA), and Pugh (RMA)?
Jul 21 '15 at 1:42 comment added MathWanderer Dear Chris C: Do you mean Apostol's Calculus vol.1-2, not his Mathematical Analysis? I did not read his calculus books, but I bought his analysis book, Rudin-PMA, and Pugh (Real Mathematical Analysis). I actually like them all three, especially Apostol and Pugh. I heard Pugh is at the same level as Rudin-PMA, but Pugh has a better exposition throughout. My plan is to read either Apostol or Pugh as a main text, and use Rudin for the problem sets.
Jul 21 '15 at 1:36 comment added Chris C I found it challenging to tackle Folland, Rudin, or Royden without many of the ideas in a transitional analysis course.
Jul 21 '15 at 1:35 comment added Chris C I would skim Apostol and read Baby Rudin. Apostol's construction of calculus mirrors its construction in real/complex analysis while Baby Rudin gives you many analytic tricks and basic topology that you will find you will need later.
Jul 20 '15 at 23:19 comment added MathWanderer Dear Nate C-K: I did not take the multivariable calculus yet, which I am planned to take on Spring 2016 after taking the theoretical linear algebra on this Fall (I assume that the linear algebra will be very helpful to understand the multivariable calculus). However, my understanding is that the 1-variable analysis does not require the knowledge from the vector calculus. I had taken a look at Rudin, Apostol (Mathematical Analysis), and Pugh, and I could understand their expositions.
Jul 20 '15 at 22:43 comment added Nate C-K I notice that you don't say you've studied multivariate calculus. That's probably a more important priority than redoing single variable calculus in a more rigorous fashion, don't you think? One option that comes to mind is Friedman's Advanced Calculus: it covers both single-variable and multivariate calculus and does so in a more rigorous fashion than Lang (e.g. using sup and inf).
Jul 19 '15 at 20:27 comment added Santiago Canez Can you clarify the distinction you're making between a rigorous calculus course and real analysis? In the US at least, what most universities offer as an introductory real analysis course is a rigorous proof-based calculus course. In particular, I don't know of any "advanced calculus" books by Rudin or Pugh which are not the same as their intro "real analysis" books.
Jul 19 '15 at 16:29 comment added user5402 In my country, there's no calculus courses outside high school. We start our 1st year with introductory real analysis.
Jul 18 '15 at 19:10 history asked MathWanderer CC BY-SA 3.0