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User:Revolver

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This is an old revision of this page, as edited by Robbot (talk | contribs) at 10:10, 23 March 2004 (Andre Engels - Robot-assisted disambiguation: Function). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

My name is Darin Brown. I am a graduate student in mathematics at University of California, Santa Barbara. If all goes as planned, I should be filing my Ph.D. in June 2004. My advisor is Jeffrey Stopple (check out his new number theory book), and my research interests lie in algebraic number theory and Fuchsian groups. In particular, I study prime geodesics in the fundamental domain, and how these geodesics lift to higher surfaces.

My interests and areas of knowledge include mathematics, music, film, poker, chess, comics, and baseball. This list is not exhaustive.

My Wikipediholic Test score on 18 January 2004 was 65.

"There is no terror in the bang, only in the anticipation of it." Alfred Hitchcock

"General Turgidson, I am becoming less and less interested in your estimates of what is possible and impossible." President Mervin Muffley

"Good artists copy; great artists steal." Pablo Picasso

Mathematics

Almost disjoint sets, Banach-Mazur game, Base (topology), Compact space, Curve, Descriptive set theory, Disjoint sets, Fermat number, Isoperimetry, Jordan curve theorem, Limit point, Lindemann-Weierstrass theorem, Locally cyclic group, Kuratowski closure axioms, Modular arithmetic, Modular group Gamma, Partial fraction decomposition over R, Proof that e is irrational, Proof that the sum of the reciprocals of the primes diverges, PSL(2,7), Pythagorean theorem, Quotient group, Sierpinski space, Stark-Heegner theorem, Subbase, Subgroup, Topological space, Trigonometric function, Wilson's theorem

Not mathematics

Alfred Hitchcock, Hoop Dreams, North by Northwest, Fundamental theorem of poker, Texas hold'em, Baseball slang, Bunt

Pages to work on

Algebraic number theory, Baseball, California State University, Stanislaus, Discrete valuation, Discrete valuation ring, Finite field, Fuchsian group, Function, Fundamental domain, Isomorphism, Mersenne prime, Ordered ring, p-adic number, Prime geodesic, Quadratic field, Vector space, On the Number of Primes Less Than a Given Magnitude

Unfinished projects

Fermat number, Basel problem, Modular group Gamma, Poker probability (Texas hold 'em), Vitali set, Proof that the sum of the reciprocals of the primes diverges

Useful things

Relax, Wikipedia is young

Wikipedia is still in its infancy. Most topics and articles are still at an "information-gathering" stage. Few articles have reached a stage that could be considered remotely close to "stable" or "complete". I think this is something to keep in mind when confronted with critics. Some apparently intrinsic pessimists like to shoot down the wiki by claiming it doesn't live up to its goal of being a "complete and accurate" encyclopedia. Well, that's true. But that's kind of like saying when Tiger Woods was a toddler, that he would never amount to much, because he couldn't yet drive the ball over 200 yards.

Math notation suggestions

Here are some suggestions for wikipedia math notation:

  • When writing in HTML (not math) mode, don't use '-', use '& minus;', (without the space). This produces a longer minus sign, not a hyphen.
  • I've been ignorant of this one for a long time, apparently: when writing out function abbreviations in math mode (i.e. sin, cos, exp, ln, etc.) use '\sin', '\cos', etc. If the function isn't standard, use '\operatorname{xyz}' to write xyz. If you have some text to write in math mode that isn't a function abbreviation, you can use '\mbox{...}'.
  • Write the cyclic group with n elements as Z/nZ (or even Z/n if you get tired of seeing too many Z's..., although I prefer Z/nZ), not as Zn. I know the latter is used by a lot of people and textbooks, but I have more than one good reason for asking for this. First of all, and most importantly, when n = p is prime, Zp is the standard notation for the ring of p-adic integers, and the cyclic group is not isomorphic to this (indeed, one notation stands for a group, the other for a ring, so they can hardly even be compared to each other. We could think of the quotient ring, but this isn't ring-isomorphic, either.) To make matters even worse, some people use Zp to denote the localization of the integers at the prime ideal (p). The correct relationship between these is that the ring of p-adic integers is the completion of the localization. So, the best way to notate this is really to let the localization be Z(p) and reserve Zp for the p-adic integers. I hope this amount of potential confusion is enough to persuade people that we should use Z/nZ or Z/n for cyclic groups. Another reason to do this is that the Z/nZ notation is unambiguous -- it can mean only one thing. Lastly, this notation explicitly realises the nature of the finite cyclic group as a quotient group of the integers. For my comments on the notation Cn (often used by group theorists and geometers, as opposed to number theorists), see Talk:Cyclic group
  • I think the notation Fpn or Fq should be used for finite fields. It's much more common than the GF notation. That's just my opinion.
  • If you're going to use 'log' to mean 'log base 10', write out the base explicitly, or at least mention at the start of the article what the base will be throughout the article. I lost the war on this one ('ln' vs 'log' for natural logarithm) but maybe I can win this battle. Lots of people use 'log' for both base 10 and base 2 (and some of us, even for base e!, although I'll surrender and use 'ln'), so it's important to know. Don't just assume everyone knows that 'log' means 'log base 10'.

20 favorite math books

The following are 20 of my favorite math books. These are not necessarily the books I've found most useful, but they are the ones I've found most fun and the ones that had the most influence on me going into mathematics. This list will probably give you a good idea of my mathematical tastes. Unfortunately, many of these books are no longer in print.

  1. Asimov on Numbers, Isaac Asimov, ASIN 067149404X
  2. Counterexamples in Topology, Steen and Seebach, ISBN 048668735X
  3. Disquisitiones Arithmeticae, Gauss, ISBN 0300094736
  4. Fourier Analysis, Korner, ISBN 0521389917
  5. The Higher Arithmetic, H. Davenport, ISBN 0521634466
  6. The Historical Development of the Calculus, C. H. Edwards, ISBN 0387943137
  7. How to Solve It, Polya, ISBN 0691023565
  8. Introduction to General Topology, K. D. Joshi, ASIN 0470275561
  9. Introduction to Set Theory, J. D. Monk, ASIN 0898740061
  10. Introduction to the Theory of Numbers, Hardy and Wright, ISBN 0198531710
  11. Introduction to the Theory of Numbers, Niven, ISBN 0471625469
  12. Irrational Numbers, Niven, ASIN 0883850117
  13. The Mathematical Experience, Davis and Hersh, ISBN 0395929687
  14. Mathematics and the Unexpected, Ivar Ekeland, ISBN 0226199908
  15. Measure and Category, John Oxtoby, ISBN 0387905081
  16. Primes of the Form x2 + ny2, David Cox, ISBN 0471190799
  17. Proofs From the Book, ed. Aigner and Ziegler, ISBN 3540678654
  18. Theory of Algebraic Integers, Dedekind (Stillwell preface), ISBN 0521565189
  19. Visual Complex Analysis, Tristan Needham, ISBN 0198534469
  20. The World of Mathematics, J. R. Newman, ISBN 0671829505
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