Timeline for A Learning Roadmap request: From high-school to mid-undergraduate studies
Current License: CC BY-SA 2.5
60 events
| when toggle format | what | by | license | comment | |
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| Feb 25 at 4:18 | review | Close votes | |||
| Mar 2 at 3:06 | |||||
| Dec 4, 2017 at 8:26 | review | Close votes | |||
| Dec 4, 2017 at 12:07 | |||||
| Oct 23, 2012 at 11:41 | comment | added | user9072 | Contributing a vote as no longer relevant. The questions seems to have run its course; later answers seem to have hardly attracted attention anymore. | |
| Mar 11, 2012 at 18:58 | comment | added | Unknown | @Max, I think it was because you did not write as @Solomon, that the comment did not reach me. However, after two years, I ended up reading this post again. I meant as you said. I wish you all the best in your mathematical adventure. | |
| May 30, 2011 at 9:38 | answer | added | vonjd | timeline score: 2 | |
| May 29, 2011 at 16:28 | answer | added | Koundinya Vajjha | timeline score: 4 | |
| Oct 18, 2010 at 13:21 | answer | added | Brian | timeline score: 2 | |
| Oct 18, 2010 at 13:04 | answer | added | Jim Conant | timeline score: 1 | |
| Oct 18, 2010 at 12:23 | history | edited | Max Lonysa Muller | CC BY-SA 2.5 |
edited body; edited body; deleted 9 characters in body
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| Aug 4, 2010 at 1:57 | answer | added | Matt Calhoun | timeline score: 2 | |
| Aug 4, 2010 at 0:39 | answer | added | user12345678 | timeline score: 3 | |
| Jul 20, 2010 at 21:26 | answer | added | Paolo Ketter-Umbanza | timeline score: 3 | |
| Jul 20, 2010 at 19:12 | history | edited | Max Lonysa Muller | CC BY-SA 2.5 |
improved formatting
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| Jul 18, 2010 at 12:00 | answer | added | Justin Curry | timeline score: 4 | |
| Jul 18, 2010 at 7:23 | answer | added | Vectornaut | timeline score: 5 | |
| Jul 17, 2010 at 2:45 | answer | added | Zen Harper | timeline score: 2 | |
| Jun 16, 2010 at 12:52 | answer | added | Thomas Riepe | timeline score: 4 | |
| Jun 16, 2010 at 11:50 | answer | added | Lennart Meier | timeline score: 4 | |
| Jun 16, 2010 at 10:21 | answer | added | Konrad Voelkel | timeline score: 6 | |
| Jun 15, 2010 at 23:32 | answer | added | Noah Stein | timeline score: 14 | |
| Jun 15, 2010 at 16:43 | comment | added | Boyarsky | @Harry: Bourbaki's motivation via physics is not in the main text, just in historical notes at the end. Bourbaki only provides (some historical) motivation in appendices, and not for all main notions introduced in the text itself (as would be appropriate for beginners). Andrew L. is correct: the style in which the actual Bourbaki texts are written (not the appendices) has zero motivation. As a test case for the irrelevance of much motivation, please read Chapter IV--VI of Bouraki Lie algebras and then discuss what you "learned" with your professors who know representation theory. | |
| Jun 15, 2010 at 15:34 | answer | added | Colin Pratt | timeline score: 5 | |
| Jun 15, 2010 at 11:54 | answer | added | Tom Boardman | timeline score: 20 | |
| Jun 15, 2010 at 10:26 | comment | added | Max Lonysa Muller | @ Mister Solomon: Do you mean 'best' post? Thanks anyhow, as I think I should consider your comment as a compliment;) | |
| Jun 15, 2010 at 9:00 | answer | added | bc919 | timeline score: 10 | |
| Jun 15, 2010 at 7:12 | comment | added | Unknown | Good Max, keep on studying and wondering in math. This is one of the most posts I've ever read on MO! | |
| Jun 15, 2010 at 7:10 | answer | added | Unknown | timeline score: 3 | |
| Jun 15, 2010 at 6:17 | comment | added | The Mathemagician | @Harry I just said they were bad books for the beginner,that's all. I don't like them in general,but they do give a complete overview of mathematics with complete rigor and modernity.By the way,Harry-filters and uniformities can be found in Willard and Engelking as well-and easier to break into.I first learned general convergence myself from Bartle's classic paper "Nets and filters in topology". | |
| Jun 15, 2010 at 5:27 | answer | added | J W | timeline score: 3 | |
| Jun 15, 2010 at 5:09 | comment | added | Harry Gindi | Also, @Op: Bourbaki's book on topology is one of the most modern and comprehensive treatments of point-set topology. It makes use of filters and uniformities, something that most other books do not cover at all. Don't listen to Andrew L, he basically thinks that Bourbaki is the devil. | |
| Jun 15, 2010 at 4:57 | comment | added | Harry Gindi | @Andrew L: I'm sure this will rather surprise you, but I actually picked up Bourbaki's book on integration, and guess how they motivate the idea of a measure! Physics! It turns out that people who don't actually read Bourbaki and just say things based on preconceived notions oftentimes look rather siily.... | |
| Jun 15, 2010 at 3:57 | answer | added | Unknown | timeline score: 6 | |
| Jun 15, 2010 at 0:33 | comment | added | Peter Samuelson | I looked at the table of contents for the book the OP linked to ("Introductory Mathematics:...") and they define things like sets, functions, injective, bijective, complex numbers, vector spaces, etc. I think it would be considerate if people kept this in mind when suggesting books. Some people have not done this, and I would agree with Mike Benfield that you shouldn't be discouraged if a randomly chosen book from the answers is too difficult to understand right now. Many of them will still be difficult after several years of studying math. | |
| Jun 15, 2010 at 0:28 | comment | added | Emerton | Dear Max, I learnt (rigorous) calculus and some basic topological concepts when I was in high-school, via self-study, from The elements of real analysis, by Bartle. It is a (very!) long time since I looked at it, but it had a careful treatment of concepts like continuity and limits in terms of epsilons and deltas, and also in the more topological language of open and closed sets. If I remember correctly, it introduced concepts such as connectedness and compactness (in the context of subsets of $\mathbb R^n$). It also gave a nice treatment of lots of classical analysis topics. | |
| Jun 14, 2010 at 23:24 | answer | added | bhwang | timeline score: 4 | |
| Jun 14, 2010 at 22:46 | answer | added | Bman | timeline score: 5 | |
| Jun 14, 2010 at 22:44 | answer | added | Akhil Mathew | timeline score: 11 | |
| Jun 14, 2010 at 22:39 | history | edited | Dmitri Pavlov | CC BY-SA 2.5 |
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| Jun 14, 2010 at 22:24 | answer | added | SandeepJ | timeline score: 13 | |
| Jun 14, 2010 at 22:23 | comment | added | Boyarsky | The Spivak book "Calculus" is well-suited to self-study since it has lots of exercises (theory and computation). The Steenrod-Chinn book mentioned below will open your eyes to the topology of the real line (I read it before I learned rigorous calculus, and loved it; but lacks enough exercises). Another fun book is Gerald Edgar's undergraduate book "Measure, Topology, and fractal geometry". It has many exercises/examples and will lead you into first steps of metric spaces, measure, and topology in concrete settings. Don't rush. Weyl & Serre & category theory can wait for later in life. :) | |
| Jun 14, 2010 at 22:10 | comment | added | Theo Johnson-Freyd |
Aack! If you want italics, on MO put underscores _ or asterisks * on either side, not dollar signs. In TeX, use {\em text }. Dollar signs make the computer process whatever's inside as math, as if you had all those variables to multiply together. The classic example is $difference$ versus difference — notice the spacing around the f s. (In the default TeX font, the correct look is $\textit{difference}$.) The spacing is even weirder for words with ffi: $spiffier$, $\textit{spiffier}$, spiffier.
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| Jun 14, 2010 at 22:10 | comment | added | Michael Benfield | 1. Some of the answers you have received are a little odd, IMO. I see some fairly difficult graduate level books being recommended for a high school student who knows some calculus. (Homological algebra? Really?) I honestly don't know what to make of this. 2. Generic advice that may or may not be something you need to hear: Don't get discouraged. Math is hard for everybody. Be persistent, but if you have a book you can't make progress on, don't feel the least bit of shame in turning to a more elementary treatment or going back to learn prerequisite topics or whatever it takes. | |
| Jun 14, 2010 at 22:08 | answer | added | Daniel Barter | timeline score: 8 | |
| Jun 14, 2010 at 22:04 | answer | added | Dmitri Pavlov | timeline score: 6 | |
| Jun 14, 2010 at 21:56 | comment | added | Vladimir Dotsenko | Well, some real analysis is a prerequisite for topology, but not algebra. The book by Steenrod and Chinn I mention in my answer below is a great example of an introductory topology book for which, at least up to some point, you don't need much except for enthusiasm... | |
| Jun 14, 2010 at 21:56 | answer | added | Gerhard Paseman | timeline score: 5 | |
| Jun 14, 2010 at 21:56 | comment | added | The Mathemagician | @Max Depends on how the topology book is organized,Max.If it has a mainly geometric approach,like the McCleary book for example-then you should definitely learn algebra first. If the emphasis is on point-set methods-then you need to master calculus/real analysis first and some basic set theory. | |
| Jun 14, 2010 at 21:53 | answer | added | Vladimir Dotsenko | timeline score: 7 | |
| Jun 14, 2010 at 21:41 | comment | added | Max Lonysa Muller | Oh ok, thanks for the advice, mister Dotsenko. But don't you think it's better to read a book on algebra $first$ and $then$ read a book on Topology? Or isn't it that important? | |
| Jun 14, 2010 at 21:34 | comment | added | Vladimir Dotsenko | Max, I think that the sooner you stop worrying about questions like "But isn't Topology more of a graduate subject?", the better. Most Bourbaki's books do not make good first reading for the subject, that's true, but there are topology books that can, and should be, read while still undergraduate. There is no such thing as undergraduate/graduate subject, there is mathematics and something else. | |
| Jun 14, 2010 at 21:24 | answer | added | The Mathemagician | timeline score: 9 | |
| Jun 14, 2010 at 21:21 | answer | added | Charles Matthews | timeline score: 6 | |
| Jun 14, 2010 at 21:21 | comment | added | Max Lonysa Muller | @Andrew L: I understand what you mean, now... Mister Gindi: I think the Bourbaki Books are (far) too difficult at the moment, for me. | |
| Jun 14, 2010 at 21:12 | comment | added | Max Lonysa Muller | @Harry Gindi: These books look nice, too. But isn't Topology more of a graduate subject? | |
| Jun 14, 2010 at 21:11 | history | made wiki | Post Made Community Wiki by Max Lonysa Muller | ||
| Jun 14, 2010 at 21:10 | comment | added | The Mathemagician | Please take what Harry says with a grain of salt,Max.He thinks anything with motivation is not mathematics and that's not good for beginners. | |
| Jun 14, 2010 at 21:00 | comment | added | Harry Gindi | Walter Rudin's Principles of Mathematical analysis, Nicolas Bourbaki's Topologie Generale (part I&II), and his Algebre (part I). Do not waste your time with Bourbaki's book on set theory. | |
| Jun 14, 2010 at 20:54 | answer | added | Eric Rowell | timeline score: 13 | |
| Jun 14, 2010 at 20:27 | history | edited | Max Lonysa Muller | CC BY-SA 2.5 |
fixed grammar
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| Jun 14, 2010 at 20:18 | history | asked | Max Lonysa Muller | CC BY-SA 2.5 |