#6 in Mathematical analysis books
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Reddit mentions of Introduction to Analysis (Dover Books on Mathematics)
Sentiment score: 8
Reddit mentions: 15
We found 15 Reddit mentions of Introduction to Analysis (Dover Books on Mathematics). Here are the top ones.
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Height | 8.5 Inches |
Length | 5.32 Inches |
Number of items | 1 |
Release date | February 1985 |
Weight | 0.65697754076 Pounds |
Width | 0.52 Inches |
You are in a very special position right now where many interesing fields of mathematics are suddenly accessible to you. There are many directions you could head. If your experience is limited to calculus, some of these may look very strange indeed, and perhaps that is enticing. That was certainly the case for me.
Here are a few subject areas in which you may be interested. I'll link you to Dover books on the topics, which are always cheap and generally good.
Basically, don't limit yourself to the track you see before you. Explore and enjoy.
The most important thing you can do is memorize the definitions. I mean seriously have them down cold. The next thing I would recommend is to get another couple of analysis books (go cheap by getting old books, it isn't like the value of epsilon has changed over the past two hundred years) and look at their explanations, work those problems. Having a different set can be enlightening. Be prepared to spend a lot of time on it all.
Good luck!
EDIT: Back home now and able to put in some specific books. I used Rosenlicht and you wouldn't believe how happy I was to buy a textbook that, combined with a slice of pizza and a coke, was still less than $20. One of my books that I looked at for a different view point was Sprecher.
I also got a great deal of value out of Counterexamples in Analysis because after seeing things go wrong (a function that is continuous everywhere but nowhere differentiable? Huh?) I started to get a better feel for what the definitions really meant.
I hope you're also sensing a theme: Dover math books rock!
Really interested, actually! But I'm curious about a few things:
When exactly will it start in January? And when will it end? Will it be in the evenings? Which days of the week?
Will we need a text book? I have a Dover book on basic analysis already which I haven't cracked open.
Where will the class be held?
I had an incredibly hard time with calculus as a university student. I took it 5 times because I kept dropping it or withdrawing or not getting a passing grade. I almost got kicked out of my program because I pushed the limits of how many times I could repeat the course. There was a general disinterest on my part, but now, almost 10 years later, I am much more fascinated and genuinely interested in math, number theory, and also in many ways, analysis.
I started reading a book recently that finally explained what calculus actually was in simple terms. I feel like it's the first time that was ever done for me and I can say that helped my interest.
Anyway, I'd really hope to attend your class! The reason I'm curious about exact start date is that I'll be away from the HRM until mid-January. And it's a bummer to miss the first few classes of anything!
It mentions Rosenlicht at the bottom. Lucky you, that book's only 8 bucks! It's a good book, too.
You might like Rosenlicht's book, Introduction to Analysis. Google Books will show you the first 2 chapters for free. It's a Dover book, so it's good and also cheap. I believe that it is often used as the text for the first "serious" real analysis course.
We used this one in my undergraduate analysis class, and I found it pretty straightforward to read and understand. And it's only $13.
Introduction to Analysis (Dover Books on Mathematics) https://www.amazon.com/dp/0486650383/ref=cm_sw_r_cp_api_i_WTGPCbM6P2N4H
It’s actually a pretty decent book for a first look at Real Analysis.
Apologies for the serious comment on /r/funny.
I am not a big fan of Rudin. The tone is incredibly stuffy and his style is fairly loose.
I would recommend the small Dover book Introduction to Analysis by Rosenlicht. It's a very small book, hardly 200 pages, but the style is much nicer. It doesn't cover nearly as much (there is no introduction to Fourier Analysis, differential forms, or the gamma function), but that's a good thing for an introductory book, since you can expect to master everything in it.
We used Abbott in a class I audited. I skimmed bits of it, and it seemed pretty nice. Very expository, which is always nice to have when self-studying.
I would eventually pick up a copy of Rudin, just because it's a cultural icon. But it's just very brutal for an introduction to the subject.
This is a pretty good book too. http://www.amazon.com/Introduction-Analysis-Dover-Books-Mathematics/dp/0486650383/ref=sr_1_1?ie=UTF8&qid=1323212337&sr=8-1
I don't know why more people on here don't recommend it, especially considering how cheap it is.
If you're comfortable with some calculus and proofs, analysis would be a logical next step in the same direction. In analysis, you pretty much rigorously build up to all the results from calculus, starting from the construction of the real numbers (or at least its introduction as a field). It would be a great way to apply your proof skills. I found Introduction to Analysis by Rosenlicht to be a great intro. An other classic is Rudin's Principles of Mathematical Analysis, which I like very much, but is arguably a more difficult text.
If you're looking for something in a different direction, linear and abstract algebra are very accessible.
Yes. However, you should probably read something that introduces you to proofs. My Intro to Higher Math classes (commonly called Intro to Proof-Writing or Intro to Analysis, the class or series of classes that introduce you to higher math and proofwriting skills) used this book alongside a prepackaged set of detailed lecture notes. I'd say that'd be a good place to start before reading about Abstract Algebra, plus the book is dirt cheap.
Here is the mobile version of your link
For real analysis, I would avoid Rudin. I think it's overrated as a good book to learn from, especially for people who aren't math majors. I'd go with Introduction to Analysis by Rosenlicht. It's basically a friendlier version of Rudin, and a heck of a lot cheaper.
https://www.amazon.com/Introduction-Analysis-Dover-Books-Mathematics/dp/0486650383
If you really want to understand probability then you'll need to learn measure theory, which will require some background knowledge in real analysis. This is the book I used, which I highly recommend (and it's cheap!): http://www.amazon.com/Introduction-Analysis-Dover-Books-Mathematics/dp/0486650383/ref=sr_1_1?ie=UTF8&qid=1414974523&sr=8-1&keywords=introduction+to+analysis
As for an actual book on probability, I'm not too sure since my probability course was based on lecture notes provided by the professor, although I just ordered this book because it looked decent: http://www.amazon.com/Graduate-Course-Probability-Dover-Mathematics-ebook/dp/B00I17XTXY/ref=sr_1_1?ie=UTF8&qid=1414974533&sr=8-1&keywords=graduate+book+on+probability