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456/ INDEX TO VOLUME 40, 2014 INDEX TO VOLUME 40, 2014 The Contest Corner Robert Bilinski, Kseniya Garaschuk, Olga Zaitseva January No. 21 ................................................................. 4 February No. 22 ............................................................... 51 March No. 23 ............................................................... 96 April No. 24 .............................................................. 142 May No. 25 .............................................................. 188 June No. 26 .............................................................. 234 September No. 27 .............................................................. 276 October No. 28 .............................................................. 319 November No. 29 .............................................................. 368 December No. 30 .............................................................. 413 The Olympiad Corner Nicolae Strungaru, Carmen Bruni January No. 319 ............................................................... 9 February No. 320 .............................................................. 56 March No. 321 ............................................................. 102 April No. 322 ............................................................. 147 May No. 323 ............................................................. 194 June No. 324 ............................................................. 240 September No. 325 ............................................................. 282 October No. 326 ............................................................. 326 November No. 327 ............................................................. 374 December No. 328 ............................................................. 417 Book Reviews John Grant McLoughlin, Robert Bilinski Undiluted Hocus-Pocus : The Autobiography of Martin Gardner, with foreword by Persi Diaconis and an afterword by James Randi Reviewed by Chelluri C.A. Sastri ............................................. 17 Solving Mathematical Problems: a personal perspective by Terence Tao Reviewed by Robert Bilinski.................................................... 63 Will You Be Alive 10 Years from Now? And Numerous Other Curious Ques- tions in Probability by Paul J. Nahin Reviewed by Ed Barbeau....................................................... 110 Borges and Mathematics by Guillermo Martinez Reviewed by Robert Bilinski................................................... 154 Across the Board : the Mathematics of Chessboard Problems by John J. Watkins Reviewed by Robert Bilinski................................................... 201 The proof and the pudding: What Mathematicians, Cooks, and You Have in Common by Jim Henle Reviewed by Robert Bilinski................................................... 246 Single digits : in praise of small numbers Crux Mathematicorum, Vol. 40(10), December 2014 INDEX TO VOLUME 40, 2014 /457 by Marc Chamberland Reviewed by Robert Bilinski................................................... 333 What if? Serious Scientific Answers to Absurd Hypothetical Questions by Randall Munroe Reviewed by Robert Bilinski................................................... 424 Focus On ... Michel Bataille No. 10, Some Sequences of Integrals ............................................... 21 No. 11, The Partial Sums of some Divergent Series ............................... 112 No. 12, Intersecting Circles and Spiral Similarity ................................. 218 No. 13, The Dot Product ......................................................... 289 No. 14, Solutions to Exercises from Focus On... No. 6 – 11 ....................... 380 Articles Robert Dawson, Kseniya Garaschuk ASquare from Similar Triangles, Olga Zaitseva ................................................................... 25 Ramsey’s Theory Through Examples, Exercises, and Problems: Part 1 Veselin Jungi´c .................................................................. 65 Excerpt from The Math Olympian Richard Hoshino ................................................................ 70 Apples, Oranges, and Bananas Warut Suksompong ............................................................. 116 Ramsey’s Theory Through Examples, Exercises, and Problems: Part 2, Veselin Jungi´c ................................................................. 157 Excerpt from The Math Olympian Richard Hoshino ............................................................... 161 ALaboratory on Cubic Polynomials Arkady Alt ..................................................................... 207 Exercises in Inductive Processes Olga Zaitseva .................................................................. 255 Partially Ordered Sets Bill Sands ...................................................................... 293 Variations on a theme: The sum of equal powers of natural numbers (I) Arkady Alt ..................................................................... 340 From the Adequality of Fermat to Nonstandard Analysis Paul Deguire ................................................................... 386 Variations on a theme: The sum of equal powers of natural numbers (II) Arkady Alt ..................................................................... 431 From the archives Kseniya Garaschuk Sums of equal powers of natural numbers c Copyright Canadian Mathematical Society, 2015 458/ INDEX TO VOLUME 40, 2014 V. S. Abramovich .............................................................. 248 Chebyshev polynomials and recursive relations (I) N. Vasiliev and A. Zelevinskiy .................................................. 335 Chebyshev polynomials and recursive relations (II) N. Vasiliev and A. Zelevinskiy .................................................. 426 Problems January 3901–3910 ............................................................ 28 February 3911–3920 ............................................................ 73 March 3921–3930 ........................................................... 120 April 3931–3940 ........................................................... 163 May 3941–3950 ........................................................... 212 June 3951–3960 ........................................................... 259 September 3961–3970 .......................................................... 299 October 3971–3980 ........................................................... 345 November 3981–3990 .......................................................... 391 December 3991–4000 .......................................................... 435 Solutions January 3801–3810 ............................................................ 32 February 3811–3820 ............................................................ 77 March 3821–3830 ........................................................... 125 April 3831–3840 ........................................................... 167 May 3841–3850 ........................................................... 217 June 3851–3860 ........................................................... 263 September 3861–3870 .......................................................... 303 October 3871–3880 ........................................................... 349 November 3881–3890 .......................................................... 407 December 3891–3900 .......................................................... 439 Miscellaneous Unsolved Crux Problems: 1615 and 2399 ..........................................253 Crux Mathematicorum Founding Editors / R´edacteurs-fondateurs: L´eopold Sauv´e & Frederick G.B. Maskell Former Editors / Anciens R´edacteurs: G.W. Sands, R.E. Woodrow, Bruce L.R. Shawyer, Shawn Godin Crux Mathematicorum with Mathematical Mayhem Former Editors / Anciens R´edacteurs: Bruce L.R. Shawyer, James E. Totten, V´aclav Linek, Shawn Godin Crux Mathematicorum, Vol. 40(10), December 2014
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