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Liouville number
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#	Item
41	USA Mathematical Talent Search Round 2 Grading Criteria Year 25 — Academic Year 2013–2014 www.usamts.org IMPORTANT NOTE: On all problems, the graders have the discretion to deduct 1 Add to Reading List Source URL: usamts.org Language: English - Date: 2014-01-03 17:21:15 Trigonometry Equations Fibonacci number Trigonometric functions Plus-minus sign Ordinary differential equations Sturm–Liouville theory Catalan number Mathematics Elementary mathematics Mathematical analysis
42	On the log-concavity of the degenerate Bernoulli numbers Florian Luca Instituto de Matem´aticas Universidad Nacional Aut´onoma de M´exico C.P[removed], Morelia, Michoac´an, M´exico Add to Reading List Source URL: youngp.people.cofc.edu Language: English - Date: 2011-10-07 14:23:41 Spectral theory Number theory Operator theory Bernoulli number Topology Binomial coefficient Λ-ring Sturm–Liouville theory Mathematics Mathematical analysis Integer sequences
43	Journal of Statistical Physics, Vol. 34, Nos. 1/2, 1984 Functional Equations for Circle Homeomorphisms with Golden Ratio Rotation Number Oscar E. Lanford III 1 Add to Reading List Source URL: www.math.harvard.edu Language: English - Date: 2013-12-22 12:53:21 Ordinary differential equations Functional equations Operator theory Spectral theory Recurrence relation Continuous function Spectral theory of ordinary differential equations Sturm–Liouville theory Mathematical analysis Mathematics Calculus
44	UIUC UNDERGRADUATE MATH CONTEST April 8, [removed]Determine, without numerical calculations, which of the two numbers √ Add to Reading List Source URL: www.math.illinois.edu Language: English - Date: 2006-04-08 17:58:20 Ring theory Elementary mathematics Combinatorics Elementary number theory Integer Liouville number Binomial coefficient Mathematics Abstract algebra Algebraic number theory
45	2011 U OF I UNDERGRAD MATH CONTEST 1. Given distinct points a1 < a2 < Pa3 < · · · < a100 on the real line, determine, with proof, the exact set of real numbers x for which the sum 100 i=1 \|x − ai \| takes its minimal Add to Reading List Source URL: www.math.illinois.edu Language: English - Date: 2011-03-11 18:02:38 Mathematical notation Sequence Number theory Summation Integer Pi Liouville number Thue–Morse sequence Mathematics Abstract algebra Elementary mathematics
46 $Algebra / Polynomials / Analytic number theory / Partial fraction / Liouville number / Mathematics / Combinatorics / Permutation$	Seniors (Grades 11 & 12) Add to Reading List Source URL: www.math.toronto.edu Language: English - Date: 2004-11-29 08:35:22 Algebra Polynomials Analytic number theory Partial fraction Liouville number Mathematics Combinatorics Permutation
47	Proceedings of the International Congress of Mathematicians Vancouver, 1974 Add to Reading List Source URL: www.mathunion.org Language: English - Date: 2012-04-18 10:37:24 Diophantine approximation Thue–Siegel–Roth theorem Thue equation Subspace theorem Polynomial Rational function Transcendental number Liouville number Number theory Mathematics Algebra Abstract algebra
48	PDF Document Add to Reading List Source URL: www.renyi.hu Language: English - Date: 2006-11-05 15:16:09 Transcendental numbers Liouville number Limit superior and limit inferior Binomial coefficient Peetre theorem Mathematics Mathematical analysis Diophantine approximation
49	Joseph Liouville’s construction of a transcendental number Topmatter: Some ideas pulled from exercises 6.6 – 6.8 in, Galois Theory (second edition) by Ian Stewart, Add to Reading List Source URL: deanlm.com Language: English - Date: 2012-10-25 18:20:47 Field theory Elementary mathematics Transcendental numbers Group theory Polynomials Liouville number Algebraic number Irrational number Real number Abstract algebra Mathematics Algebra
50	ON THE IRRATIONALITY OF CERTAIN SERIES : PROBLEMS AND RESULTS P. Erdős Add to Reading List Source URL: www.renyi.hu Language: English - Date: 2006-11-05 15:16:25 Algebraic number theory Prime-counting function Liouville number Number theory Mathematics Analytic number theory

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