Timeline for A Learning Roadmap request: From high-school to mid-undergraduate studies
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14 events
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| Oct 19, 2010 at 2:15 | comment | added | Brian | @Andrew L: Thanks a lot for your comments! I definitely need to look up Jacobson's book since many people talk about it. @Max: I hope you've been reading our comments. Since I'm only an undergraduate, one implication is that I have no idea about how to teach so that people can learn effectively. That means you would probably be much better off listening to what Andrew L has to say. The list above is more of my personal list so far and all I know is that I enjoyed working with those books. Good luck! | |
| Oct 18, 2010 at 22:42 | comment | added | The Mathemagician | @Brian,Max continued: And of course,I'd be remiss talking about graduate algebra texts without mentioning the great classic by Nathan Jacobson,BASIC ALGEBRA,which has miraculously been reissued by Dover in 2 beautiful cheap paperbacks.There's absolutely no excuse not to have it now.The only real drawback of Jacobson is a dearth of examples,but this is easily remedied by supplementing it with Knapp or Ash's book (also in cheap Dover). | |
| Oct 18, 2010 at 22:38 | comment | added | The Mathemagician | @Brian,Max: Algebra is a critical course for a beginner and I think Lang would be way too discouraging. I don't HATE Lang-although many people I know do.In fact,it's worth having simply because of the treasure of examples present in it's pages and nowhere else.I just think Lang makes the book unnecessarily hard and abstract;some of the exercises are just ludicrously difficult.Moreover,in the last 20 years,the backlash against Lang has produced some outstanding graduate algebra texts which will be much more pleasant for the student:Rotman,Rowen,Knapp and Grillet,just to name a few I love. | |
| Oct 18, 2010 at 17:06 | comment | added | Brian | Lang's definitely hard for a beginner, including myself. I struggled hard with it, but it's worth the effort. The way everything formulated is amazing, especially the part on Galois Theory. I read the book for my first abstract algebra course (which is only 2 years ago), and it was hard. But in the end, I got prepared. I think "having pain" this way is a good way to learn. ForCA, reading and doing all exercises in Atiyah Macdonald is good since it's not too long . Eisenbud's book is definitely good, if one has the time to read through it (admittedly, I only looked here and there in the book). | |
| Oct 18, 2010 at 17:00 | comment | added | The Mathemagician | @Brain And yes,for the record,I WAS talking about "baby Rudin"-which I reviewed for the MAA Online.You may want to check that review out to see my further comments on the book. | |
| Oct 18, 2010 at 16:59 | comment | added | The Mathemagician | @Brain concluded: Most mathematicians were either gifted students or they've been professionals too long to remember what it was like to struggle with math for the first time.As a result,they generally have very unrealistic recommendations for beginners. | |
| Oct 18, 2010 at 16:58 | comment | added | The Mathemagician | @Brain Continued: And disregard Hartshorne unless you can read Shafaravich completely first. That's a ludicrous recommendation for any student that hasn't mastered commutative algebra first.To that end,David Eisenbud's COMMUTATIVE ALGEBRA WITH A VIEW TOWARDS ALGEBRAIC GEOMETRY is very much worth a look. And of course,Miles Ried's UNDERGRADUATE ALGEBRAIC GEOMETRY should come before any of those. | |
| Oct 18, 2010 at 16:53 | comment | added | The Mathemagician | @Brian continued: Now your algebra recommendations are really where i have to take issue. LANG?!? Ok,Max-completely disregard that last suggestion. Instead,I recommend heartily I.M.Herstein's TOPICS IN ALGEBRA,2nd ed(a near perfect text where a whole generation of mathematicians cut thier teeth,including me),M.Artin's ALGEBRA(now in it's 2nd edition,hopefully better organized now) and the beautiful A COURSE IN ALGEBRA by E.B.Vinberg(a gorgeous tour through algebra for the talented beginner with a Russian bent i.e. many applications). | |
| Oct 18, 2010 at 16:53 | comment | added | Brian | Thanks for your comment! I like the books by M. Lee too, even though I haven't really gone through them. For the Analysis book, are you talking about Rudin's Principles of Mathematical Analysis? I really liked this book when I took the first course in Analysis. For the other books, I haven't read them, so I don't know. | |
| Oct 18, 2010 at 16:49 | history | edited | Brian | CC BY-SA 2.5 |
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| Oct 18, 2010 at 16:41 | comment | added | The Mathemagician | Several modifications to be suggested to your list,Brian-it's WAY too ambitious as usual. For real analysis,Rudin is the usual rubber-stamp recommendation,but I much prefer Charles Chapman Pugh's REAL MATHEMATICAL ANALYSIS and Kenneth Hoffman's ANALYSIS IN EUCLIDEAN SPACE.They are much more geometric and have very deep insights while not sacrificing rigor or exercise difficulty.Your topology and differential geometry recommendations are good,but to that list I'd add Klaus Janich's TOPOLOGY,John McCleary's A FIRST COURSE IN TOPOLOGY:CONTINUITY AND DIMENSION and all 3 books by John M.Lee. | |
| Oct 18, 2010 at 14:34 | history | edited | Brian | CC BY-SA 2.5 |
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| Oct 18, 2010 at 13:35 | history | edited | Brian | CC BY-SA 2.5 |
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| Oct 18, 2010 at 13:21 | history | answered | Brian | CC BY-SA 2.5 |