The Best Writing on Mathematics 2015
Format: PDF / Kindle (mobi) / ePub
This annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2015 makes available to a wide audience many articles not easily found anywhere else--and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates.
Here David Hand explains why we should actually expect unlikely coincidences to happen; Arthur Benjamin and Ethan Brown unveil techniques for improvising custom-made magic number squares; Dana Mackenzie describes how mathematicians are making essential contributions to the development of synthetic biology; Steven Strogatz tells us why it's worth writing about math for people who are alienated from it; Lisa Rougetet traces the earliest written descriptions of Nim, a popular game of mathematical strategy; Scott Aaronson looks at the unexpected implications of testing numbers for randomness; and much, much more.
In addition to presenting the year's most memorable writings on mathematics, this must-have anthology includes a bibliography of other notable writings and an introduction by the editor, Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us--and where it is headed.
indispensable in a discipline as vast and quickly changing as mathematics. For while the basic steps of mathematical arguments are often shared among specialists in related areas, the nuances and particularities of a single mathematician’s work can be opaque even to recent collaborators. A proof may be true or valid universally, but mathematicians must make sense of it in their own particular ways. So blackboards offer a means of communication in both the obvious sense—as things on which to
example, suppose a researcher is interested in how Democrats and Republicans perform differently in a short mathematics test when it is expressed in two different contexts, involving either healthcare or the military. The question may be framed nonspecifically as an investigation of possible associations between party affiliation and mathematical reasoning across contexts. The null hypothesis is that the political context is irrelevant to the task, and the alternative hypothesis is that context
it out so that the heights in the final siteswap are all the same. At each step, you may interchange any two adjacent numbers and then transfer a “unit” of height from the right digit to the left digit (we’ll call this process a height swap). For instance, to apply a height swap to the adjacent pair 62, switch it to 26 and then transfer a unit of height from right to left, yielding 35. It is important to recall that a siteswap represents a periodic sequence, so the last digit in a siteswap is
Rougetet traces the earliest written descriptions of the popular game of Nim to a treatise written at the beginning of the sixteenth century by Luca Pacioli and follows the subsequent European developments of the game since then. Jan von Plato considers the context of mathematical ideas and the personalities that shaped German mathematician Gerhard Gentzen’s ordinal proof theory—and how this work relates (or does not!) with a theorem by Reuben Goodstein. James Franklin illustrates with several
math. The reason, according to a graduate student in the United States, is “because it’s easier for teachers to teach reading. Some of them don’t know math well.” CLASSROOM: SERIOUS LEARNING PLACE VS. SOCIAL CENTER. The classroom environment is quite different in the two countries. Given the fact that there are about as many elementary and high school students in China as there are people in the United States, one will not be surprised that the size of a Chinese class is usually more than twice