omg I just took a look at Apostol's "Mathematical Analysis"

[InquilineKea]

<p>My god that book is fun to read.</p>

<p>Why is it so fun to read? Because it’s not Rudin. Apostol is still terse - most of the math books really have little fluff.</p>

<p>Um yeah - that should be really fun. I wish I could carry it along with me. </p>

<p>But eh - screw the other books I’m reading. I’ll just read this.</p>

<p>==</p>

<h1>oh and by the way - it’s excellent reading for high school students. It’s supposedly at the senior undergraduate level but the knowledge it assumes isn’t that much at all. Just make sure that you’re comfortable with the epsilon/delta definition of a limit.</h1>

<p>(and I need to get a hand on Griffiths “Introduction to Electrodynamics”. Why did I just stop reading that? Ugh - I want to read Pinker too. Then I want to read Koch. And Artin’s Algebra. And …)</p>

<p>edit: omg the typesetting is a pain >: (</p>

[InquilineKea]

<p>

The Riemann integral .f(x)dx, as developed in Chapter 7, is well motivated,
simple to describe, and serves all the needs of elementary calculus. However, this
integral does not meet all the requirements of advanced analysis. An extension,
called the Lebesgue integral, is discussed in this chapter. It permits more general
functions as integrands, it treats bounded and unbounded functions simultaneously,
and it enab]es us to replace the interval [a, b] by more general sets.

</p>

<p>I love this explanation :)</p>

[InquilineKea]

<p>holy ****</p>

<p>this is understandable
<a href=“http://en.wikipedia.org/wiki/Sigma-algebra[/url]”>http://en.wikipedia.org/wiki/Sigma-algebra&lt;/a&gt;&lt;/p&gt;

<p>screw neurobiology - I’m going to read real analysis for fun
(and I still want to study that…)</p>

<p>==</p>

<p>As for what revitalized my interest in pure mathematics</p>

<p>“Where Mathematics Comes From”</p>

<ul>
<li>a look at mathematics from the way people conceptualize things.</li>
</ul>

[fizix2]

<p>Wikipedia’s math articles make me want to cry.</p>

[InquilineKea]

<p><a href=“http://en.wikipedia.org/wiki/Category_of_topological_spaces[/url]”>http://en.wikipedia.org/wiki/Category_of_topological_spaces&lt;/a&gt; makes me want to die</p>

[LesOs]

<p>I’m crying and wanting to die simultaneously now.</p>

[ChaosTheory]

<p>I have Apostol’s Mathematical Analysis, too. I have Rudin as well, and I presume you do, too. I’m using [my physical copy of :D] Shilov for R&C A, at the moment. It’s nice. </p>

<p>

and I need to get a hand on Griffiths “Introduction to Electrodynamics”.

</p>

<p>I have that. :D</p>

[snoopyiscool]

<p>The library doesn’t have any of it. My mother has never heard of amazon.com. I feel screwed.</p>

[InquilineKea]

<p>

I have that.

</p>

<p>So do I. I have a copy of the 3rd edition as pdf and 2nd edition as checked-out book. But gaah I want to read everything!</p>

<p>…if only I knew it was possible for a 9th grader to read those books… (well, kinda, I sucked at math when I was in 9th grade - :p)</p>

[LesOs]

<p>Ugh. I suck at physics. Biology and Chem = lovvveeeee.</p>

[ChaosTheory]

<p>I really need to try to stick to one book and one subject. Do you have this problem as well, IK?</p>

[CountingDown]

<p>DS LOVES Spivak’s Calculus. He got it after someone on another CC thread suggested it and is using it for proof work. As for more than one book at a time…Spivak, Communication Complexity by Eyal Kushilevitz, Intro to the Theory of Computation by Sipser, several David Weber novels, and a paper on writing math papers by Donald Knuth.</p>

<p>DS1 has inherited the multiple book reading gene from his father and I…</p>

<p>Edit: Wiki Math ROCKS as far as DH is concerned…</p>

[ChaosTheory]

<p>OmgRudinisawsum!!!</p>

[InquilineKea]

<p>

I really need to try to stick to one book and one subject. Do you have this problem as well, IK?

</p>

<p>Yes - I definitely do. Read the OP lol.</p>

<p>Ultimately, I think I’m going to have to quit reading analysis. =( I have to study off Lang Complex Analysis and then a partial differential equations textbook in preparation for a couple of grad-lvl courses next year.</p>

[ChaosTheory]

<p>Use Rudin. I started reading it a couple hours ago and I find it amazing.</p>

[InquilineKea]

<p>

Use Rudin. I started reading it a couple hours ago and I find it amazing.

</p>

<p>Rudin is known for its lack of diagrams and its lack of “user-friendliness”. Mathwonk of physicsforums.com does not recommend it - at least for the first time around. ;)</p>

[ChaosTheory]

<p>Are you talking about Principles of Analysis or R&C A? </p>

<p>Lack of clarity? He just leaves a lot of things out. It allows the reader to explore the missing parts on his own, giving him a more thorough understanding of the topic. If you think “Hold up. How did he go from that step to that one?” and work it out by yourself [and understand everything correctly], it is very satisfying [and even enlightening]. </p>

<p>Which textbooks does Ben recommend? I’ll take a look at Apostol’s. Perhaps he is more user-friendly. </p>

<p>Eh, I can understand Mathwonk’s concerns. I’ve seen that thread.</p>

[InquilineKea]

<p>

It allows the reader to explore the missing parts on his own, giving him a more thorough understanding of the topic. If you think “Hold up. How did he go from that step to that one?” and work it out by yourself [and understand everything correctly], it is very satisfying [and even enlightening].

</p>

<p>That’s contingent upon the assumption that you can work everything out by yourself. However - it is flawed pedagogy. It assumes that the student can do everything that mathematicians took decades to develop, which isn’t very realistic. yes you will get a more thorough understanding of the topic if you can work everything out - however - that is contingent upon the assumption that the reader is able to explore all the missing parts on his own - and most students won’t - so they’d be better served by books like Apostol (at least initially). They can work out Rudin later. Most real analysis textbooks don’t have much fluff anyhow (even Apostol is very succinct)</p>

<p>If you merely want light and enjoyable reading and don’t want to derive everything yourself, then you probably don’t want Rudin. Yes some math books can be light and enjoyable reading - it’s an excellent habit to pick up. ^_^</p>

<p>For a course syllabi, try
<a href=“http://www.math.caltech.edu/courses/06ma108a.html[/url]”>http://www.math.caltech.edu/courses/06ma108a.html&lt;/a&gt;&lt;/p&gt;

<p>Caltech uses Carothers. ^_^</p>

<p><a href=“http://www.amazon.com/gp/cdp/member-reviews/ATN0BSFQQTEQI?ie=UTF8&display=public&sort_by=MostRecentReview&page=3[/url]”>http://www.amazon.com/gp/cdp/member-reviews/ATN0BSFQQTEQI?ie=UTF8&display=public&sort_by=MostRecentReview&page=3&lt;/a&gt;&lt;/p&gt;

<p>

this book was written by an expert in analysis, whose goal in writing a book is to provide the most concise possible proof of every result. This is what many expert analysts revere, but unfortunately is not what most students appreciate nor benefit from.</p>

<p>Hence this book remains the text of choice for most analysis professors, but not for most students learning the topic.</p>

<p>George Simmons’ books are much better liked by learners, and for very strong students the books of Dieudonne are much more highly recommended.

</p>

<p>==
Another complaint on Rudin:
<a href=“http://talk.collegeconfidential.com/showthread.php?p=2616798&highlight=rudin#post2616798[/url]”>http://talk.collegeconfidential.com/showthread.php?p=2616798&highlight=rudin#post2616798&lt;/a&gt;&lt;/p&gt;

[InquilineKea]

<p>LOL AT MATHWONK’S REVIEW OF PRINCIPIA MATHEMATICA</p>

<p>

I have not read this book. I tried, having been fascinated by logic and mathematics since high school, but it has absolutely nothing to offer most people. in fact I find it hard to believe anyone has ever read this book. The 4 and 5 star reviews on this page should be taken as evidence there are some people out there with very different taste from mine, and I bet yours. In fact I have difficulty believing they are serious.</p>

<p>I think only a fanatic could enjoy reading this book, certainly not a budding mathematician. If you are attracted by a book that proves 1+1 = 2 somewhere after 100 pages, this is the book for you!</p>

<p>I admit I have been surprized before at what some people find interesting, but the idea that anyone would pay 5 or 6 hundred dollars for the set! the publishers seem to me to be sniffing glue. (I have a PhD in mathematics, a mathematical library costing thousands of dollars, and tried to read this work at Harvard as a young math student.)</p>

<p>To call this book influential, is to me really ridiculous, since I suspect few people have even looked at it in the last half of the 20th century, nor would want to do so at any length, in my opinion.</p>

<p>But don’t take my word for it, go to your scientific library and check it out for yourself. You might like it, but I seriously doubt it. I did not intend to review this book, but some of the reviews here really defy belief. I could not let them pass without comment.</p>

<p>One must assume those reviewers here are serious who praise it, but I suggest almost no mathematics student need give it more than a passing look. The review that stated something like “if you do not already know you want this book, then you do not” is pretty accurate.</p>

<p>OK, a quick re reading of reviews here shows many of them say truthfully that this book is only appropriate for a very small group of readers. However I would suggest that group does not even include most mathematicians. The ones who like it are apparently philosophers, and some are the sort who resort to calling people stupid who disagree with them.

</p>

[InquilineKea]

<p>Hey ChaosTheory - what is your post count on AoPS? :p</p>

<p>I’m thinking of defecting CC for AoPS or PF, but somehow I became too comfortable here. ;p</p>