Reddit reviews Elementary Analysis: The Theory of Calculus (Undergraduate Texts in Mathematics)
We found 8 Reddit comments about Elementary Analysis: The Theory of Calculus (Undergraduate Texts in Mathematics). Here are the top ones, ranked by their Reddit score.
Springer
Here's my radical idea that might feel over-the-top and some here might disagree but I feel strongly about it:
In order to be a grad student in any 'mathematical science', it's highly recommended (by me) that you have the mathematical maturity of a graduated math major. That also means you have to think of yourself as two people, a mathematician, and a mathematical-scientist (machine-learner in your case).
AFAICT, your weekends, winter break and next summer are jam-packed if you prefer self-study. Or if you prefer classes then you get things done in fall, and spring.
Step 0 (prereqs): You should be comfortable with high-school math, plus calculus. Keep a calculus text handy (Stewart, old edition okay, or Thomas-Finney 9th edition) and read it, and solve some problem sets, if you need to review.
Step 0b: when you're doing this, forget about machine learning, and don't rush through this stuff. If you get stuck, seek help/discussion instead of moving on (I mean move on, attempt other problems, but don't forget to get unstuck). As a reminder, math is learnt by doing, not just reading. Resources:
math on irc.freenode.net
Here are two possible routes, one minimal, one less-minimal:
Minimal
Less-minimal:
NOTE: this is pure math. I'm not aware of what additional material you'd need for machine-learning/statistical math. Therefore I'd suggest to skip the less-minimal route.
I thought Elementary Analysis by Kenneth Ross was pretty accessible. As others have said, though, your goal seems somewhat unrealistic.
Hello, I think you're spot on about it making your life easier after struggling, and by taking this class and putting in the time, it will make other math courses much easier for you. Because of what you gain from the struggle, I would really recommend you take this over 142, if you have the time. I took 140A last fall, and although I only got a C, it took an immense amount of effort to even get that. The class is set up so that if you put in the hard work to understand the concepts, the homework, the proofs and so forth, you're gonna do well, and If you truly understand how to solve the homework problems, then the tests will be familiar (doesn't mean it will be easy).
Expect to put a lot of work in. This statement needs to be taken seriously for this class, I've talk to some people in the class who say they put in 40 hours a week. This is usually because the concepts do not come immediately and you have to constantly repeat and approach at different angles to find a good understanding.
I recommend having a supplementary text while you are studying from the dreaded Rudin. For 140A, you should be looking at compactness and chapter 2 very early on as this is a big hurdle in that class. Other concepts will be more familiar but still challenging.
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Some recommended texts (definitely find your own that works for you)
https://www.amazon.com/Real-Analysis-Lifesaver-Understand-Princeton/dp/0691172935 (If you prefer "casual" explanations of the concepts, this help me survive chapter 2 of Rudin. There are useful book recommendations in the very back)
https://www.amazon.com/Elementary-Analysis-Calculus-Undergraduate-Mathematics/dp/1461462703 (Ross is used for the 142 series, and I find it is very helpful if you are struggling. If you are having trouble, start with the easier version of a problem and build up from there. The book mainly stays within the R\^2 metric, which is what makes it simpler)
https://minds.wisconsin.edu/handle/1793/67009 (at some point, you're gonna get stuck and you will have to look at the solutions. This is ok, but don't become reliant on it, that really hurt me in the end when I did that. Some of the questions are fuccckkkiiinngg hard, so when you hit that wall, take a look here. They give solutions that skips over a ton of steps, or might not be that good of a way to solve the problem, but this is a great resource)
https://www.math.ucla.edu/~tao/preprints/compactness.pdf (Who doesn't know who Terence Tao is? This is very helpful for giving an answer to "what is compactness used for?". It gives some intuition about what it is, and you should read it a couple times during 140A.)
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So this is advice that I would give myself when entering the course, and maybe it won't apply to you. Since you got an A in 109 without too much trouble, you are definitely very ready for 140, and you have a very chance of succeeding. Stay curious, and don't stop at just the solution. Really question why it is true. You probably won't have this problem, but when it hits you (probably when you get to chapter 2) you have to keep at it and don't give up. Abuse office hours, ask lots of questions, study everyday etc. and you'll do well. If you want to get better at math then the pain is worth it.
I was an undergraduate majoring in mathematics. But due to health problems I am not attending any school currently. I have became unfamiliar with much of what I had learned/worked through when as an undergraduate. So I just genuinely wish and try to seriously re-study mathematics.
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Question about Spivak's Calculus and Ross' Elementary Classical Analysis:
Are they books treating mathematics on the same level? Do they treat the rigorous theoretical foundation and computational techniques equally well? Can each one be an alternative to the other? Could someone please give brief comparative reviews/comments on them?
This question is also on r/learnmath: HERE.
I wish I was only taking those two. I've also got Abstract Algebra II (Ring Theory), and teaching the one class on top of that. This is my "tough" semester. The next two I'll probably only be taking 2 classes each semester, plus teaching.
What book are you using for Topo? We're using Munkres.
And what are you using for Real Analysis? I know Baby Rudin is sort of the standard, but we're using Ross.
I believe abstract algebra will be more useful. It'll teach you useful skills regardless of the field of physics. Analysis on the other hand will just make you a wizard with limits. You shouldn't need analysis for things like differential geometry. I would recommend this textbook for analysis though. While a deep understanding of calculus is nice to have, it's not often useful. Abstract algebra allows you to explore a whole new world of math.
I liked the one by Ross
http://www.amazon.com/Elementary-Analysis-Calculus-Undergraduate-Mathematics/dp/1461462703/ref=cm_cr_arp_d_product_top?ie=UTF8
Oh also forgot to mention, I have taken a RA class that covered through roughly chapter ~35 of Elementary Analysis - Ross