By Stephen F. Kennedy, Donald J. Albers, Gerald L. Alexanderson, Della Dumbaugh, Frank A. Farris, Deanna B. Haunsperger, Paul Zorn

The MAA used to be based in 1915 to function a house for The American Mathematical Monthly. The project of the Association-to improve arithmetic, particularly on the collegiate level-has, even though, continually been greater than simply publishing world-class mathematical exposition. MAA participants have explored greater than simply arithmetic; now we have, as this quantity attempts to make glaring, investigated mathematical connections to pedagogy, background, the humanities, expertise, literature, each box of highbrow pastime. Essays, all commissioned for this quantity, contain exposition by way of Bob Devaney, Robin Wilson, and Frank Morgan; background from Karen Parshall, Della Dumbaugh, and invoice Dunham; pedagogical dialogue from Paul Zorn, Joe Gallian, and Michael Starbird, and cultural observation from Bonnie Gold, Jon Borwein, and Steve Abbott.

This quantity comprises 35 essays via all-star writers and expositors writing to have a good time a rare century for mathematics-more arithmetic has been created and released due to the fact that 1915 than in all of past recorded background. we have now solved age-old mysteries, created whole new fields of analysis, and altered our notion of what arithmetic is. lots of these tales are instructed during this quantity because the individuals paint a portrait of the vast cultural sweep of arithmetic through the MAA's first century. arithmetic is the main exciting, the main human, quarter of highbrow inquiry; you will discover during this quantity compelling evidence of that claim.

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Le calcul intégral : Des nombres, en somme...

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Extra info for A Century of Advancing Mathematics

Sample text

The red regions are the preimages of B . 30 A Century of Advancing Mathematics around the time the Mandelbrot set was first observed (although, as noted above, Cremer anticipated Herman rings in the early 1930s), these regions are (eventually) periodic annular regions of period n in which all points rotate around distinct simple closed curves under a given irrational rotation. The reasons these types of Fatou domains do not occur for polynomials is that there has to be a pole inside one of these Herman rings; otherwise, all points inside these annuli would be mapped to corresponding points inside the image annuli.

L. Devaney, D. M. Look, and D. Uminsky, The escape trichotomy for singularly perturbed rational maps. Indiana Univ. J. 54 (2005), 1621–1634. [12] A. Douady, and J. Hubbard, It´eration des polynomes quadratiques. C. R. Acad. Sci. Paris 294 (1985), 123–126. [13] P. Fatou, Sur les solutions uniformes de certaines e´ quations fonctionnelles. C. R. Acad. Sci. Paris 143 (1906), 546–548. [14] ———, Sur les substitutions rationnelles. C. R. Acad. Sci. Paris 164 (1917), 806–808. [15] ———, Sur les substitutions rationnelles.

Ann. Math. 147 (1987), 225-267. [43] C. L. Siegel, Iterations of analytic functions. Ann. Math. 43 (1942), 607–612. [44] W. Sierpinski, Sur une courbe Cantorienne qui contient une image biunivoque et continue de toute courbe donn´ee. C. R. Acad. Sci. 162 1916, 629–632. 34 A Century of Advancing Mathematics [45] D. Sullivan, Quasiconformal homeomorphisms and dynamics I: Solution of the Fatou-Julia problem on wandering domains. Ann. Math. 122 (1985), 401–418. edu Robert L. edu Map-Coloring Problems Robin Wilson Open University, UK Dedicated to the memory of Kenneth Appel In 1852 Augustus De Morgan was asked whether all plane maps can be colored with just four colors in such a way that neighboring countries are always colored differently.