Jan 31, 2012

Hungarian Mathematical Olympiad



  1. [PDF] 

    Hungarian Mathematical Olympiad 2001/02

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    Hungarian Mathematical Olympiad 2001/02. Final Round. Grades 11 and 12 – technical schools. 1. The perpendicular from vertex A of the rectangle ABCD to ...
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    Hungarian Mathematical Olympiad 2005/06

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    Hungarian Mathematical Olympiad 2005/06. Final Round. High Schools. 1. For each nonnegative integer n, define t(0) = t(1) = 0, t(2) = 1 and for n > 2 define f(n) ...
    You visited this page on 1/31/12.
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    Hungarian Mathematical Olympiad 2000/01

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    Hungarian Mathematical Olympiad 2000/01. Final Round. Grades 11 and 12. 1. Let S denote the number of 77-element subsets of H = {1, 2,..., 2001} ...
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    Hungarian Mathematical Olympiad 1997/98

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    Hungarian Mathematical Olympiad 1997/98. Final Round. Grades 11 and 12. 1. Prove that the arithmetic mean of the numbers 2sin2◦, 4 sin 4◦, 6 sin 6◦, ...
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    Hungarian Mathematical Olympiad 1999/2000

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    Hungarian Mathematical Olympiad 1999/2000. Final Round. Grades 11 and 12. 1. Let H be a set of 2000 nonzero real numbers. How many negative elements ...
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    Hungarian Mathematical Olympiad 1998/99

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    Hungarian Mathematical Olympiad 1998/99. Final Round. Grades 11 and 12. 1. Find all solutions 0 < x, y, z ≤ 1 of the equation x. 1 + y + zx. + y. 1 + z + xy. + ...
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    Eötvös Mathematical Competition 1905

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    Eötvös Mathematical Competition 1905. 1. Find the necessary and sufficient conditions on positive integers n, p for the system of equations x + py = n, x + y = pz ...
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    Eötvös Mathematical Competition 1897

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    Eötvös Mathematical Competition 1897. 1. If α,β,γ are the angles of a right triangle, prove the relation: sin α sin β sin(α − β) + sinβ sinγ sin(β − γ) + sin γ sin α sin(γ ...
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    Eötvös Mathematical Competition 1900

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    Eötvös Mathematical Competition 1900. 1. Let a, b, c, d be fixed integers with d not divisible by 5. Assume that there is an integer m for which am3 + bm2 + cm+ d ...
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    Kürschák Mathematical Competition 1982

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    Kürschák Mathematical Competition 1982. 1. For any five points A, B, P, Q, R in a plane, prove that. AB + PQ + QR + RP ≤ AP + AQ + AR + BP + BQ + BR. 2. ...
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    Eötvös Mathematical Competition 1903

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    Eötvös Mathematical Competition 1903. 1. Suppose that 2p. − 1 is a prime number. Prove that the sum of all positive divisors of n = 2p−1(2p. − 1) (excluding n) is ...
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    Eötvös Mathematical Competition 1899

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    Eötvös Mathematical Competition 1899. 1. The points A0,A1,A2,A3,A4 divide a unit circle into five equal parts. Prove that the chords A0A1 and A0A2 satisfy ...
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    Kürschák Mathematical Competition 1981

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    Kürschák Mathematical Competition 1981. 1. The points of space are colored with five colors, all colors being used. Prove that some plane contains four points ...
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    Eötvös Mathematical Competition 1896

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    Eötvös Mathematical Competition 1896. 1. If k is the number of distinct prime divisors of a natural number n, prove that log n ≥ k log 2. 2. Prove that the ...
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    Eötvös Mathematical Competition 1902

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    Eötvös Mathematical Competition 1902. 1. Consider an arbitrary quadratic polynomial Q(x) = Ax2 + Bx + C. (a) Prove that Q(x) can be written in the form. Q(x) = k ...
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    Kürschák Mathematical Competition 1986

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    Kürschák Mathematical Competition 1986. 1. The convex (n + 1)-gon P0P1 ...Pn is partitioned into triangles by n − 2 nonintersecting diagonals. Prove that the ...
  17. Eötvös Mathematical Competition 1909

    Eötvös Mathematical Competition 1909. 1. Consider any three consecutive natural numbers. Prove that the cube of the largest number cannot be the sum of the ...
  18. Eötvös Mathematical Competition 1939

    Eötvös Mathematical Competition 1939. 1. Let a1,a2,b1,b2,c1,c2 be real numbers for which a1a2 > 0, a1c1 ≥ b2. 1 and a2c2 > b2. 2. Prove that. (a1 + a2)(c1 + ...
  19. Eötvös Mathematical Competition 1936

    Eötvös Mathematical Competition 1936. 1. Prove that for all positive integers n,. 1. 1 · 2. +. 1. 3 · 4. + ···. 1. (2n − 1)2n. = 1 n + 1. +. 1 n + 2. + ··· +. 1. 2n. 2. A point S ...
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    Kürschák Mathematical Competition 1984

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    Kürschák Mathematical Competition 1984. 1. Rational numbers x, y and z satisfy the equation x3 + 3y3 + 9z3. − 9xyz = 0. Prove that x = y = z = 0. 2. ...
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    Eötvös Mathematical Competition 1911

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    Eötvös Mathematical Competition 1911. 1. Show that, if the real numbers a, b, c, A,B,C satisfy. aC − 2bB + cA = 0 and ac − b2 > 0, then AC − B2 < 0. 2. Let Q be ...
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    Eötvös Mathematical Competition 1938

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    Eötvös Mathematical Competition 1938. 1. Prove that an integer n has a representation as a sum of two squares if and only if so does 2n. 2. Prove that for all ...
  23. [PDF] 

    Eötvös Mathematical Competition 1894

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    Eötvös Mathematical Competition 1894. 1. Let x and y be integers. Prove that one of the expressions. 2x + 3y and 9x + 5y is divisible by 17 if and only if so is the ...
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    Eötvös Mathematical Competition 1937

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    Eötvös Mathematical Competition 1937. 1. Let a1,a2,...,an be positive integers and k be an integer greater than the sum of the ai's. Prove that a1!a2! ··· an! < k!. 2. ...
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    Eötvös Mathematical Competition 1904

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    Eötvös Mathematical Competition 1904. 1. Prove that if an inscribed pentagon has equal angles then its sides are equal. 2. If a is a natural number, show that the ...
  26. [PDF] 

    Eötvös Mathematical Competition 1898

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    Eötvös Mathematical Competition 1898. 1. Determine all positive integers n for which 2n + 1 is divisible by 3. 2. Prove the following statement: If two triangles ...
  27. [PDF] 

    Eötvös Mathematical Competition 1907

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    Eötvös Mathematical Competition 1907. 1. If p and q are odd integers, prove that the equation x2 + 2px +2q = 0 has no rational roots. 2. Let P be a point inside ...
  28. [PDF] 

    Eötvös Mathematical Competition 1895

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    Eötvös Mathematical Competition 1895. 1. Prove that there are exactly 2 (2n−1. − 1) ways of dealing n cards to two persons. (The persons may receive unequal ...
  29. [PDF] 

    Eötvös Mathematical Competition 1906

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    Eötvös Mathematical Competition 1906. 1. Prove that if tan α. 2 is rational (or undefined) then so are cosα and sin α;. Conversely, if cosα and sinα are rational ...
  30. [PDF] 

    Eötvös Mathematical Competition 1901

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    Eötvös Mathematical Competition 1901. 1. Prove that, for any positive integer n, 1n + 2n + 3n + 4n is divisible by 5 if and only if n is not divisible by 4. 2. If u = cot ...
  31. [PDF] 

    Eötvös Mathematical Competition 1910

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    Eötvös Mathematical Competition 1910. 1. If real numbers a, b, c satisfy a2 + b2 + c2 = 1, prove the inequalities. −. 1. 2. ≤ ab + bc + ca ≤ 1. 2. Let a, b, c, d and u ...
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    Hungarian Mathematical Olympiad 2002/03

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    Hungarian Mathematical Olympiad 2002/03. Final Round. Category 1. 1. Solve the equation (x2 + 5x + 1)(x2 + 4x) = 20(x + 1)2 in R. 2. The medians sa,sb,sc and ...
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    Kürschák Mathematical Competition 1983

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    Kürschák Mathematical Competition 1983. 1. A cube of integer edge lengths is given in space so that all four vertices of one of the faces are lattice points. ...
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    Kürschák Mathematical Competition 1985

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    Kürschák Mathematical Competition 1985. 1. Writing down the first 4 rows of the Pascal triangle in the usual way and then adding up the numbers in vertical ...
  35. Eötvös Mathematical Competition 1908

    Eötvös Mathematical Competition 1908. 1. If a and b are odd integers, prove that a3. −b. 3 is divisible by 2n if and only if so is a − b. 2. Let n > 2 be an integer. ...

Jan 26, 2012

The American Mathematical Monthly related resources (I)

http://www.maa.org/pubs/monthly.html

  1. [PDF] 

    Hypatia and Her Mathematics

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    by MAB Deakin - 1994 - Cited by 17 - Related articles
    The American Mathematical Monthly, March 1994, Volume 101,. Number 3, pp. 234–243. 1. INTRODUCTION. The first woman mathematician of whom we have ...
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    Reprinted from the AMERICAN MATHEMATICAL MONTHLY, Vol ...

    codeblab.com/wp-content/uploads/2011/10/weierstrass.pdf
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    Reprinted from the AMERICAN MATHEMATICAL MONTHLY,. Vol. LX, No. 10, December 1953. AN EVERYWHERE CONTINUOUS NOWHERE ...
  3. [PDF] 

    The Toilet Paper Problem Donald E. Knuth The American ...

    gi.cebitec.uni-bielefeld.de/teaching/2007summer/.../toiletPaper.pdf
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    by DE Knuth - 1984 - Cited by 16 - Related articles
    3 Jul 2007 – The American Mathematical Monthly is currently published by Mathematical Association of America. Your use of the JSTOR archive indicates ...
    You visited this page on 1/27/12.
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    An Introduction to Matroid Theory R. J. Wilson The American ...

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    by RJ Wilson - 1973 - Cited by 29 - Related articles
    10 Mar 2008 – The American Mathematical Monthly is currently published by Mathematical Association of America. Your use of the JSTOR archive indicates ...
    You visited this page on 1/27/12.
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    On Infinite Radicals Aaron Herschfeld The American Mathematical ...

    pballew.net/1935Herschfeld.pdf
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    by A Herschfeld - 1935 - Cited by 18 - Related articles
    The American Mathematical Monthly is currently published by Mathematical Association of America. Your use of the JSTOR archive indicates your acceptance of ...
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  6. [PDF] 

    The Role of Logic in Teaching Proof

    condor.depaul.edu/sepp/monthly886-899.pdf
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    by SS Epp - Cited by 54 - Related articles
    The Role of Logic in Teaching Proof. Susanna S. Epp. 1. INTRODUCTION. Over the past several decades, many of those involved with mathematics education ...
    You visited this page on 1/27/12.
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    Responding to Calls for Change in High School Mathematics ...

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    by HL Schoen - Cited by 22 - Related articles
    Responding to Calls for Change in High. School Mathematics: Implications for. Collegiate Mathematics. Harold L. Schoen and Christian R. Hirsch. 1.
    You visited this page on 1/27/12.
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    AMERICAN MATHEMATICAL MONTHLY.

    poncelet.math.nthu.edu.tw/disk5/js/biography/farkas.pdf
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    THE. AMERICAN. MATHEMATICAL MONTHLY. Entered at the Post-ofiice at Springfield, Missouri, as Second-class Mail Matter. VoL. III. JANUARY, 1896. No. 1. ...
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    AMERICAN MATHEMATICAL MONTHLY

    apollonius.math.nthu.edu.tw/d1/disk5/js/history/music.pdf
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    by RC ARCHIBALD - 1923 - Cited by 16 - Related articles
    AMERICAN. MATHEMATICAL MONTHLY. MATHEMATICIANS AND MUSIC. By R. O. ARCHIBALD, Brown University. Presidential Address 1 delivered' before ...
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    The American Mathematical Monthly, Vol. 81, No. 8 (Oct., 1974), 876 ...

    math.claremontmckenna.edu/moneill/Math188/papers/Gale2.pdf
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    by D Gale - 1974 - Cited by 39 - Related articles
    6 Mar 2005 – The American Mathematical Monthly is currently published by Mathematical Association of America. Your use of the JSTOR archive indicates ...
    You visited this page on 1/27/12.
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    Cryptography in an Algebraic Alphabet Lester S. Hill The American ...

    f09.middlebury.edu/FYSE1280Z/lectures/.../hill1.pdf
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    by LS Hill - 1929 - Cited by 133 - Related articles
    The American Mathematical Monthly is currently published by Mathematical Association of America. Your use of the JSTOR archive indicates your acceptance of ...
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    Rational Values of Trigonometric Functions J. M. H. Olmsted The ...

    yaroslavvb.com/papers/olmsted-rational.pdf
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    by JMH Olmsted - 1945 - Cited by 13 - Related articles
    The American Mathematical Monthly is currently published by Mathematical Association of America. Your use of the JSTOR archive indicates your acceptance of ...
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    The Mathematics of Sentence Structure Joachim Lambek The ...

    ling.umd.edu/~alxndrw/CGReadings/lambek-58.pdf
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    by J Lambek - 1958 - Cited by 1238 - Related articles
    11 Mar 2008 – The American Mathematical Monthly is currently published by Mathematical Association of America. Your use of the JSTOR archive indicates ...
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    The Dynamics of Monopoly G. C. Evans The American Mathematical ...

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    by GC Evans - 1924 - Cited by 82 - Related articles
    9 Feb 2008 – The American Mathematical Monthly is currently published by Mathematical Association of America. Your use of the JSTOR archive indicates ...
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    Digital Topology Azriel Rosenfeld The American Mathematical ...

    turing.iimas.unam.mx/~elena/CompVis/Topology-Rosenfeld79.pdf
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    by A Rosenfeld - 1979 - Cited by 216 - Related articles
    18 Sep 2007 – The American Mathematical Monthly is currently published by Mathematical Association of America. Your use of the JSTOR archive indicates ...
  16. HowtoWriteYourFirst Paper

    by SG Krantz - Related articles
    While it is okay to publish a “Letter to the Editor” in the Notices, or a recreational problem in the. American Mathematical Monthly, the hard fact of the matter is that ...
  17. The American Mathematical Monthly

    by BF FINKEL
    The American. Mathematical Monthly. Beginning with Volume XX (January, 1913), the AMERICAN. MATHEMATICAL MONTHLY will be in charge of an Editorial ...
  18. [PDF] 

    Binomial Identities and Hypergeometric Series Ranjan Roy The ...

    web.cs.dal.ca/~jborwein/Preprints/Books/MbyE/...Ed/.../roy-maa.pdf
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    by R Roy - 1987 - Cited by 42 - Related articles
    6 Sep 2007 – The American Mathematical Monthly is currently published by Mathematical Association of America. Your use of the JSTOR archive indicates ...
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    Rational Reciprocity Laws Emma Lehmer The American ...

    math.mit.edu/~brubaker/rationalreciprocity.pdf
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    by E Lehmer - 1978 - Cited by 8 - Related articles
    26 Oct 2007 – The American Mathematical Monthly is currently published by Mathematical Association of America. Your use of the JSTOR archive indicates ...
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    Conway's Tiling Groups Author(s): William P. Thurston Source: The ...

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    by WP Thurston - Cited by 215 - Related articles
    Source: The American Mathematical Monthly, Vol. 97, No. 8, Special Geometry Issue (Oct.,. 1990), pp. 757-773. Published by: Mathematical Association of ...
  21. [PDF] 

    The American Mathematical Monthly, Vol. 64, 1957, pp. 688-689.

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    688. RECENT PUBLICATIONS. [November modular functions, the generalized principal ideal theorem, and the cohomology of algebraic number fields. ...
  22. [PDF] 

    Sums of Squares Olga Taussky The American Mathematical Monthly ...

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    by O TAUSSKY - 1970 - Cited by 37 - Related articles
    28 Apr 2007 – The American Mathematical Monthly is currently published by Mathematical Association of America. Your use of the JSTOR archive indicates ...
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    The Kakeya Problem

    cfa-www.harvard.edu/~jdevor/links/needle.pdf
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    by S Kakeya - 1963 - Cited by 23 - Related articles
    The Kakeya Problem. A. S. Besicovitch. The American Mathematical Monthly, Volume 70, Issue 7 (Aug. - Sep., 1963), 697-706. Stable URL: ...
  24. [PDF] 

    The Fundamental Theorem of Linear Algebra Gilbert Strang The ...

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    by G Strang - 1993 - Cited by 24 - Related articles
    5 Feb 2008 – The American Mathematical Monthly is currently published by Mathematical Association of America. Your use of the JSTOR archive indicates ...
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    American Mathematical Monthly (11/99)

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    American Mathematical Monthly (11/99). Problem 10762 [1999,864]. Let x1 = 1 and for m ≥ 1 let xm+1 = (m+3/2)−1 ∑m k=1 xkxm+1−k. Evaluate limm→∞ ...
  26. [PDF] 

    All Games Bright and Beautiful J. H. Conway The American ...

    maths.dur.ac.uk/~dma0hg/all_games.pdf
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    by JH Conway - 1977 - Cited by 30 - Related articles
    13 Jun 2007 – The American Mathematical Monthly is currently published by Mathematical Association of America. Your use of the JSTOR archive indicates ...
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    American Mathematical Monthly Problem 11409 by Paolo Perfetti ...

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    American Mathematical Monthly Problem 11409 by Paolo Perfetti. Let α and β be positive reals such that β>α. Let. S (α,β,N) = N. ∑ n=2 n(log n)(−1) n n. ∏ k=2 ...
  28. [PDF] 

    American Mathematical Monthly Problem 11403 by Yaming Yu ...

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    American Mathematical Monthly. Problem 11403 by Yaming Yu (edited). For every integer n ≥ 0, define a polynomial fn ∈ Q[x] by fn (x) = n. ∑ i=0. (n i. ) (−x) n−i ...
  29. [PDF] 

    Recounting the Rationals Neil Calkin; Herbert S. Wilf The American ...

    math.univ-lyon1.fr/~altinel/Master/.../recountingtherationals.pdf
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    by N Calkin - 2000 - Cited by 80 - Related articles
    13 Mar 2008 – The American Mathematical Monthly is currently published by Mathematical Association of America. Your use of the JSTOR archive indicates ...
  30. [PDF] 

    Is Mathematical Truth Time-Dependent Judith V. Grabiner The ...

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    by JV Grabiner - 1974 - Cited by 92 - Related articles
    2 Nov 2007 – The American Mathematical Monthly is currently published by Mathematical Association of America. Your use of the JSTOR archive indicates ...
  31. [PDF] 

    On Intervals, Transitivity = Choas Michel Vellekoop; Raoul Berglund ...

    pb.math.univ.gda.pl/chaos/pdf/on_intervals.pdf
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    by M Vellekoop - 1994 - Cited by 121 - Related articles
    14 Apr 2007 – The American Mathematical Monthly is currently published by ... In an earlier article in the American Mathematical Monthly a redundancy was ...
  32. [PDF] 

    The Factorial Function and Generalizations Author(s): Manjul ...

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    by M Bhargava - Cited by 45 - Related articles
    The Factorial Function and Generalizations. Author(s): Manjul Bhargava. Source: TheAmerican Mathematical Monthly, Vol. 107, No. 9 (Nov., 2000), pp. 783-799 ...
  33. [PDF] 

    What is a Stochastic Process? J. L. Doob American Mathematical ...

    chagall.med.cornell.edu/BioinfoCourse/PDFs/Lecture4/doob.pdf
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    by JL Doob - 1942 - Cited by 18 - Related articles
    American Mathematical Monthly, Volume 49, Issue 10 (Dec., 1942), 648-653. ...American Mathematical Monthly is published by Mathematical Association of ...
  34. [PDF] 

    Well-Distributed Measurable Sets Walter Rudin The American ...

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    by W Rudin - 1983 - Cited by 5 - Related articles
    25 Oct 2005 – The American Mathematical Monthly is currently published by Mathematical Association of America. Your use of the JSTOR archive indicates ...
  35. [PDF] 

    Abelian Forcing Sets Joseph A. Gallian; Michael Reid The American ...

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    by JA Gallian - 1993 - Cited by 3 - Related articles
    20 Feb 2008 – The American Mathematical Monthly is currently published by Mathematical Association of America. Your use of the JSTOR archive indicates ...
  36. [PDF] 

    Orders for Finite Noncommutative Rings D. B. Erickson The ...

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    by DB Erickson - 1966 - Cited by 9 - Related articles
    25 Feb 2008 – The American Mathematical Monthly is currently published by Mathematical Association of America. Your use of the JSTOR archive indicates ...
  37. [PDF] 

    More on Fresnel Integrals I. E. Leonard The American Mathematical ...

    202.120.1.3/new/course/fourier/supplement/Fresnel%20integral.pdf
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    by IE Leonard - 1988 - Cited by 10 - Related articles
    7 Mar 2008 – The American Mathematical Monthly is currently published by Mathematical Association of America. Your use of the JSTOR archive indicates ...
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    College Admissions and the Stability of Marriage D. Gale; L. S. ...

    athens.src.uchicago.edu/.../gale_shapley_AMM62_...
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    by D Gale - 1962 - Cited by 2209 - Related articles
    The American Mathematical Monthly is published by Mathematical Association of America. Please contact the publisher for further permissions regarding the ...
  39. [PDF] 

    Improvement of a Problem from American Mathematical Monthly 1 ...

    awesomemath.org/wp-content/uploads/reflections/.../JMI-0533.pdf
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    Improvement of a Problem from American Mathematical Monthly. Abstract. In this note we give an improvement to a problem that was published in the American ...
  40. [PDF] 

    The Plane Symmetry Groups: Their Recognition and Notation

    File Format: PDF/Adobe Acrobat - Quick View
    by D Schattschneider - 1978 - Cited by 161 - Related articles
    American Mathematical Monthly, Volume 85, Issue 6 (Jun. - Jul., 1978) ... American Mathematical Monthly is published by Mathematical Association of America.
  41. [PDF] 

    Fair Dice Persi Diaconis; Joseph B. Keller The American ...

    www-stat.stanford.edu/~cgates/PERSI/papers/fairdice.pdf
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    by P Diaconis - 1989 - Cited by 7 - Related articles
    13 Jul 2007 – The American Mathematical Monthly is currently published by Mathematical Association of America. Your use of the JSTOR archive indicates ...
  42. [PDF] 

    Some Probabilistic Aspects of Set Partitions

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    by J Pitman - 1997 - Cited by 39 - Related articles
    The American Mathematical Monthly, Volume 104, Issue 3 (Mar., 1997), 201-209. ...The American Mathematical Monthly is published by Mathematical ...
  43. [PDF] 

    The Banach-Tarski Paradox Karl Stromberg The American ...

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    by K Stromberg - 1979 - Cited by 54 - Related articles
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