**What's Happening in the Mathematical Sciences**

Volume: 10;
2015;
111 pp;
Softcover
**Print ISBN: 978-1-4704-2204-2
Product Code: HAPPENING/10**

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# What’s Happening in the Mathematical Sciences, Volume 10

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*Dana Mackenzie; Barry Cipra*

What's Happening in the Mathematical
Sciences is a collection of articles highlighting some of the most
recent developments in mathematics. These include important
achievements in pure mathematics, as well as its fascinating
applications.

On the pure mathematics side, “Prime Clusters and Gaps:
Out-Experting the Experts” talks about new insights into the
distribution of prime numbers, the perpetual source of new problems,
and new results. Recently, several mathematicians (including Yitang
Zhang and James Maynard) significantly improved our knowledge of the
distribution of prime numbers. Advances in the so-called
Kadison-Singer problem and its applications in signal processing
algorithms used to analyze and synthesize signals are described in
“The Kadison-Singer Problem: A Fine Balance”. “Quod Erat
Demonstrandum” presents two examples of perseverance in
mathematicians' pursuit of truth using, in particular, computers to
verify their arguments. And “Following in Sherlock Holmes' Bike
Tracks” shows how an episode in one of Sir Arthur Conan Doyle's
stories about Sherlock Holmes naturally led to very interesting
problems and results in the theory of completely integrable systems.

On the applied side, “Climate Past, Present, and
Future” shows the importance of mathematics in the study of
climate change and global warming phenomena. Mathematical models help
researchers to understand the past, present, and future changes of
climate, and to analyze their consequences. “The Truth Shall Set
Your Fee” talks about algorithms of information exchange in
cyberspace. Economists have known for a long time that trust is a
cornerstone of commerce, and this becomes even more important nowadays
when a lot of transactions, big and small, are done over the
Internet. Recent efforts of theoretical computer scientists led to the
development of so-called “rational protocols” for
information exchange, where the parties in the information exchange
process find that lies do not pay off.

Over the last 100 years
many professional mathematicians and devoted amateurs contributed to
the problem of finding polygons that can tile the plane, e.g., used as
floor tiles in large rooms and walls. Despite all of these efforts,
the search is not yet complete, as the very recent discovery of a new
plane-tiling pentagon shows in “A Pentagonal Search Pays
Off”. Mathematics can benefit coaches and players in some of
the most popular team sports as shown in “The Brave New World of
Sports Analytics”. The increased ability to collect and process
statistics, big data, or “analytics” has completely
changed the world of sports analytics. The use of modern methods of
statistical modeling allows coaches and players to create much more
detailed game plans as well as create many new ways of measuring a
player's value. Finally, “Origami: Unfolding the Future”
talks about the ancient Japanese paper-folding art and origami's
unexpected connections to a variety of areas including mathematics,
technology, and education.

#### Readership

General mathematical audience.