I've been retraining myself concepts of college level mathematics for fun mostly. Thus far, I've progressed past the fundamentals of Calculus, and have just recently finished the CALC III texts my school uses. Yet, I kind have come to a fork in the road without definitive knowledge of what lies ...
12-01-2008, 10:41 PM
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| ἀλήθεια  Humanist while (1) 
| Those with graduate experience in Mathematics I've been retraining myself concepts of college level mathematics for fun mostly. Thus far, I've progressed past the fundamentals of Calculus, and have just recently finished the CALC III texts my school uses. Yet, I kind have come to a fork in the road without definitive knowledge of what lies ahead. This is where you --whomever you may be-- come into play. What fields of mathematics should I further tune myself towards? So far, I've got the following, but without much knowledge of their application: Linear Algebra Mathematical Analysis - Complex Analysis - Non-standard Analysis (many other facets as well, these two seemed to be the most interesting) Topology Chaos Mathematics Any suggestions on fields to pursue and books to use?
__________________ History is a nightmare from which I'm trying to awake. --Stephen Dedalus (by way of Joyce) | ||||
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12-01-2008, 11:01 PM
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| Lurker  Independent
| If you're truly retraining rather than learning for the first time, I probably would have skipped the Calculus sequence altogether and started with Adv. Calc at the level of, say, Apostol or Baby Rudin. The Calculus 1-3 sequence does help build intuition but it's not very useful for a mathematician, near as I can tell. How much math have you studied previously? | ||||
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12-01-2008, 11:07 PM
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| ἀλήθεια Humanist while (1)
| Originally Posted by khari Sadly, just as much as my high school had admitted, which is intro level Calculus (precalc II-CALC I in College). At that point I had been blithely inculcated to hate mathematics. So professionally, none. I had reread the CALC books to reintroduce myself to the concepts as well as propel my learning.
Past that, nothing. | ||||
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12-01-2008, 11:26 PM
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| Lurker Independent
| Originally Posted by HughRuss Ah, you're at the foot of the mountain. It's the most exciting part, where you don't yet wake up in a cold sweat after nightmares of epsilons and deltas.
I'm not a graduate mathematician by any stretch, just a lowly physics/math major. With that in mind, I'll give you my thoughts on it. I think Linear Algebra is a great way to build a little bit of mathematical maturity, and a great place to start. My second year class used Axler's book () which I think is a fantastic book. However the meat of Undergraduate math is real Analysis. Mastering a text like Apostol () is absolutely essential to understanding pretty much every other topic you listed. However, if your background is high school calculus you're in for a culture shock when you open it. A more reasonable path is probably starting with a book like Bartle (). Here at least you get to stick to the real line, where everything is nice. Then you can decide to go further in real analysis or not, as you like. | ||||
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12-01-2008, 11:29 PM
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| Lurker Independent
| Woah, that's a pretty cool feature. I was just thinking those long links I had copied and pasted were going to make my post unreadable, but that's pretty neat. | ||||
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12-01-2008, 11:37 PM
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| ἀλήθεια Humanist while (1)
| Base of the mountain? Is that common mathematical parlance? Or are you dougabug from Orangevale, CA?  Thank you for the suggestions! Now the time is prime for me to get working. | ||||
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12-01-2008, 11:40 PM
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| Lurker Independent
| Also, save yourself a fortune and buy your textbooks used (AbeBooks Official Site - New & Used Books, New & Used Textbooks, Rare & Out of Print Books). I bought the second edition of Bartle's book for some $20 including shipping to canada, versus the $140 they wanted for the third edition in the campus book store, and it's basically identical. | ||||
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12-01-2008, 11:41 PM
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| Lurker Independent
| Originally Posted by HughRuss Pfft, you hillbilly yanks just aren't hip to the jive like us Canucks.
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12-01-2008, 11:58 PM
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| ἀλήθεια Humanist while (1)
| Originally Posted by khari Jive is one way to describe it...
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12-02-2008, 07:01 AM
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| For those about to rock...  libertarian Atlanta, GA
| Every math major I've ever known (undergrad or grad level) did a lot of combinatorics. Personally, I found combo to be retarded... but then, they say that's the stopping point for a lot of people. It's also where math majors and computer science majors cross paths. For some reason, they make CS people take combo (something about logic training for your brain). Quick story: Early in college, I had made friends with these three chick math graduate students. They were nice people, and like most grad students, drank like fish. However, when a big assignment due date was nearing, they would basically lock themselves away, not to be seen. One time, a due date was nearing and I hadn't seen them in a few days. Walking across campus I saw the three of them sitting outside (I assume to get some sunlight). The one I knew the best was a girl named Patty, who I saw first and I walked near and said "hey Patty!" She looked up at me, square in the face, never said a word, then looked back down at her books. I was like "ok" and walked off. That weekend I saw her again and me, not one to hold grudges, had mostly forgotten the interchange (or lack thereof), but she came over and said "Josh, I am SOOOOO sorry about the other day. I looked up at you and in my head, I said 'hey' but after you left, the other two girls told me I was horribly mean to you just then. At first I didn't believe I hadn't actually said 'hey' to you, because I really thought I had!" It was at that point that I wrote off ever being a math major. | ||||
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12-02-2008, 09:22 AM
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| Humanitarian and musician  Independent Bradford, PA
| I had to take Algebra in high school in the 1970's. I hated math in general and Algebra even more. I found it boring, had trouble understanding the concepts, and I thought to myself "I'll never use this shit so why do I have to learn it?" Then in 1978, I bought my first microcomputer (a TRS-80, for those who remember that far back) and I started learning how to write code and do programming. Computer code was full of Algebra, and I had a V8 moment  and I finally got it. For me, having some way to actually APPLY what I was learning was the magic bullet, and made Algebra so much more interesting and easier to learn. The feedback was immediate. If you did it right, the computer program worked. If you made a mistake, it didn't work...or at least not the way you intended. I still hate math. But at least now I get it.
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12-02-2008, 09:21 PM
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| *insert uninteresting nomenclature here*  Independent Unfortunately, Michigan
| I've found that if you smack yourself in the left side of the head kinda hard, the math part of the brain seems to work better.  | ||||
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12-04-2008, 11:17 AM
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| Dirty Liberal  Democrat South Jersey
| Originally Posted by Dispatcher I had a similar experience. My first "attempt" at college was not very successful. It started off strong with mostly A's and B's but went downhill after that. I could never see an application for any of it and as such it could never hold my interest. My grades slipped to the point that I was in danger of failing out. I left school.
Five years later, after entering the work force and spending some time in the trenches, I decieded to go back to school. Now having some work experience, I saw application in the stuff I was learning so it was interesting. I have straight A's now. ( and one A-  ) | ||||
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