## March Mathness Winner

Davidson College student, Jane Gribble, was our March Mathness winner this year. Below she explains how she filled in her bracket.

I love basketball – Davidson College basketball. As a Davidson College cheerleader I have an enormous amount of school pride, especially when it comes to our basketball team. However, outside of Davidson College I know little to nothing about college basketball. I knew that UNC Chapel Hill was having a tough season because this is my sister’s alma mater. Also, I knew that New Mexico, Gonzaga, Duke, and Montana were all likely teams for the NCAA tournament because we had played these non-conference teams during our season and these were the most talked about non-conference games around campus. My name is Jane Gribble. I am a junior mathematics major and this is the first year I completed a bracket.

In Dr. Tim Chartier’s MAT 210 – Mathematical Modeling course we discussed sports ranking using the Colley method and the Massey method. We were given the opportunity to apply our new knowledge of sports ranking in the NCAA Tournament Challenge. Since Davidson College was participating in the tournament my focus was on one game, the Davidson/Marquette game in Lexington, KY. When we traveled to KY I thought I had missed my opportunity to fill out a bracket, but one of my classmates was also traveling for the game with the Davidson College Pep Band and had the modeling program on his computer. We completed our brackets in the hotel lobby in Kentucky the night before our game.

My bracket used the Massey method because in previous years it has had better success than the Colley method. I decided to submit only one bracket, a bracket solely based on math (partially because I know little about college basketball). As a cheerleader and a prideful student it upset me to have Davidson losing against Marquette the following night, but I wasn’t going to let a math model crush my personal dreams of success in the tournament.  The home games were weighted as .5 (it would have been 1 if it was an unweighted model) to take into account home court advantage. Similarly, away games were weighted as 1.5 and neutral games as 1. Also, the season was segmented into 6 equal sections. I believe games at the end of the season are more important than games at the beginning of the season because teams change throughout the year and the last games give the best perspective of the teams going into the tournament. There was no real reason for the numbers chosen, other than they increased each segment. The 6 equal sections were weighted: .4, .6, .8, 1, 1.5, and 2. With these weights in the Massey method my model correctly predicted the Minnesota upset, but missed the Ole Miss, LaSalle, Harvard, and Florida Gulf upsets.

After Davidson’s tragic loss I could not watch anymore basketball for a while. I even forgot that my bracket was in the competition. I only started paying attention to the brackets when a friend in the same competition congratulated me on being second going into the Elite 8; my math based bracket was in the top 10 percent of all the brackets. Once he told me my bracket had a chance of winning, I paid attention to the rest of the games to see how my bracket was doing in the competition. After Davidson’s loss against Louisville last year in the tournament I never wanted to cheer for Louisville. To my surprise, I went into the final game this year cheering for Louisville because my model had Louisville winning it all. I was not cheering for Louisville because of any connections with the team, but was cheering to receive a free ice cream cone, a prize that our local Ben and Jerry’s donates to the winner of  Dr. Chartier’s class pool.

Next year I hope to compete in the NCAA tournament challenge again. This year I greatly enjoyed the experience and want to continuing submitting brackets for the tournament. Next year I will submit one bracket that uses the exact weightings of my bracket this year to see how it compares from year to year. This year I wanted to submit a math bracket that looked at teams who had injuries throughout the season. My motivation for this was Davidson’s player Clint Mann. Clint had to sit out many games towards the end of the season because of a concussion, but he had recovered in time for the NCAA tournament. I thought that our wins during the time without Clint showed our strengths as a team. Unfortunately this year I ran out of time to code this additional weighting. Hopefully next year my submissions will include a bracket using the weights from this year, a bracket that includes weights for teams with injured team members, and another bracket with varying weights.

## Leonhard Euler’s 306th Birthday Present is a Google Doodle

Today’s Google homepage is a doodle dedicated to the celebrated mathematician Leonhard Euler whose 306th birthday is today. While you may not know a lot about Euler, if you have ever taken a math class you have been exposed to his mathematical contributions. Among his many contributions, he has two numbers named after him- Euler’s Number (in calculus e) and Euler’s Constant (gamma). He is also the man behind ‘ f(x)’ and the use of the Greek letter π. Euler’s contributions do not end here and they have paved the way for today’s leading mathematicians and physicists.

Celebrate Euler’s birthday with some readings from PUP!

1. Dr. Euler’s Fabulous Formula: Cures Many Mathematical Ills by Paul J. Nahin

In the mid-eighteenth century, Swiss-born mathematician Leonhard Euler developed a formula so innovative and complex that it continues to inspire research, discussion, and even the occasional limerick. Dr. Euler’s Fabulous Formula shares the fascinating story of this groundbreaking formula–long regarded as the gold standard for mathematical beauty–and shows why it still lies at the heart of complex number theory.

This book is the sequel to Paul Nahin’s An Imaginary Tale: The Story of I [the square root of -1], which chronicled the events leading up to the discovery of one of mathematics’ most elusive numbers, the square root of minus one. Unlike the earlier book, which devoted a significant amount of space to the historical development of complex numbers, Dr. Euler begins with discussions of many sophisticated applications of complex numbers in pure and applied mathematics, and to electronic technology. The topics covered span a huge range, from a never-before-told tale of an encounter between the famous mathematician G. H. Hardy and the physicist Arthur Schuster, to a discussion of the theoretical basis for single-sideband AM radio, to the design of chase-and-escape problems.

The book is accessible to any reader with the equivalent of the first two years of college mathematics (calculus and differential equations), and it promises to inspire new applications for years to come. Or as Nahin writes in the book’s preface: To mathematicians ten thousand years hence, “Euler’s formula will still be beautiful and stunning and untarnished by time.”

Paul J. Nahin is the author of many best-selling popular math books, including An Imaginary Tale, Digital Dice, Chases and Escapes, When Least Is Best, Duelling Idiots and Other Probability Puzzlers, and Mrs. Perkins’s Electric Quilt (all Princeton). He is professor emeritus of electrical engineering at the University of New Hampshire.

2. Gamma: Exploring Euler’s Constant by Julian Havil

Among the myriad of constants that appear in mathematics, p, e, and i are the most familiar. Following closely behind is g, or gamma, a constant that arises in many mathematical areas yet maintains a profound sense of mystery.

In a tantalizing blend of history and mathematics, Julian Havil takes the reader on a journey through logarithms and the harmonic series, the two defining elements of gamma, toward the first account of gamma’s place in mathematics.

Introduced by the Swiss mathematician Leonhard Euler (1707-1783), who figures prominently in this book, gamma is defined as the limit of the sum of 1 + 1/2 + 1/3 + . . . up to 1/n, minus the natural logarithm of n–the numerical value being 0.5772156. . .. But unlike its more celebrated colleagues p and e, the exact nature of gamma remains a mystery–we don’t even know if gamma can be expressed as a fraction.

Among the numerous topics that arise during this historical odyssey into fundamental mathematical ideas are the Prime Number Theorem and the most important open problem in mathematics today–the Riemann Hypothesis (though no proof of either is offered!).

Sure to be popular with not only students and instructors but all math aficionados, Gamma takes us through countries, centuries, lives, and works, unfolding along the way the stories of some remarkable mathematics from some remarkable mathematicians.

3. Euler’s Gem: The Polyhedron Formula and the Birth of Topology by David S. Richeson

Leonhard Euler’s polyhedron formula describes the structure of many objects–from soccer balls and gemstones to Buckminster Fuller’s buildings and giant all-carbon molecules. Yet Euler’s formula is so simple it can be explained to a child. Euler’s Gem tells the illuminating story of this indispensable mathematical idea.

From ancient Greek geometry to today’s cutting-edge research, Euler’s Gem celebrates the discovery of Euler’s beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. In 1750, Euler observed that any polyhedron composed of V vertices, E edges, and F faces satisfies the equation V-E+F=2. David Richeson tells how the Greeks missed the formula entirely; how Descartes almost discovered it but fell short; how nineteenth-century mathematicians widened the formula’s scope in ways that Euler never envisioned by adapting it for use with doughnut shapes, smooth surfaces, and higher dimensional shapes; and how twentieth-century mathematicians discovered that every shape has its own Euler’s formula. Using wonderful examples and numerous illustrations, Richeson presents the formula’s many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map.

Filled with a who’s who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem’s development, Euler’s Gem will fascinate every mathematics enthusiast.

David S. Richeson is associate professor of mathematics at Dickinson College.

## HP & PUP: Ravenclaw’s PUP Reading List

This week we have a couple of PUP books for any prospective Hogwarts student seeking placement in the Ravenclaw house. What would a Ravenclaw read? Chances are, a Ravenclaw would want to read everything due to their devotion to intelligence, knowledge, and wit. Here we have some books on philosophy of mind, cognitive science, and mathematics that would interest any Ravenclaw.

1. Worldly Philosopher: The Odyssey of Albert O. Hirschman by Jeremy Adelman- Ravenclaw students would sink their teeth into a biography about one of the most important thinkers of the twentieth century.

Worldly Philosopher chronicles the times and writings of Albert O. Hirschman, one of the twentieth century’s most original and provocative thinkers. In this gripping biography, Jeremy Adelman tells the story of a man shaped by modern horrors and hopes, a worldly intellectual who fought for and wrote in defense of the values of tolerance and change.

Born in Berlin in 1915, Hirschman grew up amid the promise and turmoil of the Weimar era, but fled Germany when the Nazis seized power in 1933. Amid hardship and personal tragedy, he volunteered to fight against the fascists in Spain and helped many of Europe’s leading artists and intellectuals escape to America after France fell to Hitler. His intellectual career led him to Paris, London, and Trieste, and to academic appointments at Columbia, Harvard, and the Institute for Advanced Study in Princeton. He was an influential adviser to governments in the United States, Latin America, and Europe, as well as major foundations and the World Bank. Along the way, he wrote some of the most innovative and important books in economics, the social sciences, and the history of ideas.

Throughout, he remained committed to his belief that reform is possible, even in the darkest of times.

This is the first major account of Hirschman’s remarkable life, and a tale of the twentieth century as seen through the story of an astute and passionate observer. Adelman’s riveting narrative traces how Hirschman’s personal experiences shaped his unique intellectual perspective, and how his enduring legacy is one of hope, open-mindedness, and practical idealism.

2. The Golden Ticket: P, NP and the Search for the Impossible by Lance Fortnow- The Ravenclaw house would be most likely to produce the P-NP problem without magic.

The P-NP problem is the most important open problem in computer science, if not all of mathematics. Simply stated, it asks whether every problem whose solution can be quickly checked by computer can also be quickly solved by computer. The Golden Ticket provides a nontechnical introduction to P-NP, its rich history, and its algorithmic implications for everything we do with computers and beyond. In this informative and entertaining book, Lance Fortnow traces how the problem arose during the Cold War on both sides of the Iron Curtain, and gives examples of the problem from a variety of disciplines, including economics, physics, and biology. He explores problems that capture the full difficulty of the P-NP dilemma, from discovering the shortest route through all the rides at Disney World to finding large groups of friends on Facebook. But difficulty also has its advantages. Hard problems allow us to safely conduct electronic commerce and maintain privacy in our online lives.

The Golden Ticket explores what we truly can and cannot achieve computationally, describing the benefits and unexpected challenges of this compelling problem.

3. Invisible in the Storm: The Role of Mathematics in Understanding Weather by Ian Roulstone & John Norbury- Their aptitude for mathematics would draw Ravenclaws to this book.

Invisible in the Storm is the first book to recount the history, personalities, and ideas behind one of the greatest scientific successes of modern times–the use of mathematics in weather prediction. Although humans have tried to forecast weather for millennia, mathematical principles were used in meteorology only after the turn of the twentieth century. From the first proposal for using mathematics to predict weather, to the supercomputers that now process meteorological information gathered from satellites and weather stations, Ian Roulstone and John Norbury narrate the groundbreaking evolution of modern forecasting.

The authors begin with Vilhelm Bjerknes, a Norwegian physicist and meteorologist who in 1904 came up with a method now known as numerical weather prediction. Although his proposed calculations could not be implemented without computers, his early attempts, along with those of Lewis Fry Richardson, marked a turning point in atmospheric science. Roulstone and Norbury describe the discovery of chaos theory’s butterfly effect, in which tiny variations in initial conditions produce large variations in the long-term behavior of a system–dashing the hopes of perfect predictability for weather patterns. They explore how weather forecasters today formulate their ideas through state-of-the-art mathematics, taking into account limitations to predictability. Millions of variables–known, unknown, and approximate–as well as billions of calculations, are involved in every forecast, producing informative and fascinating modern computer simulations of the Earth system.

4. The Milky Way: An Insider’s Guide by William H. Waller- Ravenclaws would want to know everything about the wizarding world, the muggle world, and beyond.

This book offers an intimate guide to the Milky Way, taking readers on a grand tour of our home Galaxy’s structure, genesis, and evolution, based on the latest astronomical findings. In engaging language, it tells how the Milky Way congealed from blobs of gas and dark matter into a spinning starry abode brimming with diverse planetary systems–some of which may be hosting myriad life forms and perhaps even other technologically communicative species.

William Waller vividly describes the Milky Way as it appears in the night sky, acquainting readers with its key components and telling the history of our changing galactic perceptions. The ancients believed the Milky Way was a home for the gods. Today we know it is but one galaxy among billions of others in the observable universe. Within the Milky Way, ground-based and space-borne telescopes have revealed that our Solar System is not alone. Hundreds of other planetary systems share our tiny part of the vast Galaxy. We reside within a galactic ecosystem that is driven by the theatrics of the most massive stars as they blaze through their brilliant lives and dramatic deaths. Similarly effervescent ecosystems of hot young stars and fluorescing nebulae delineate the graceful spiral arms in our Galaxy’s swirling disk. Beyond the disk, the spheroidal halo hosts the ponderous–and still mysterious–dark matter that outweighs everything else. Another dark mystery lurks deep in the heart of the Milky Way, where a supermassive black hole has produced bizarre phenomena seen at multiple wavelengths.

5. Odd Couples: Extraordinary Differences between the Sexes in the Animal Kingdom by Daphne J. Fairbairn- On their quest for knowledge, learning about all types of animals is pertinent- sadly, magical creatures are not covered in this book.

While we joke that men are from Mars and women are from Venus, our gender differences can’t compare to those of other animals. For instance, the male garden spider spontaneously dies after mating with a female more than fifty times his size. Female cichlids must guard their eggs and larvae–even from the hungry appetites of their own partners. And male blanket octopuses employ a copulatory arm longer than their own bodies to mate with females that outweigh them by four orders of magnitude. Why do these gender gulfs exist? Introducing readers to important discoveries in animal behavior and evolution, Odd Couples explores some of the most extraordinary sexual differences in the animal world. From the fields of Spain to the deep oceans, evolutionary biologist Daphne Fairbairn uncovers the unique and bizarre characteristics–in size, behavior, ecology, and life history–that exist in these remarkable species and the special strategies they use to maximize reproductive success. Fairbairn describes how male great bustards aggressively compete to display their gorgeous plumage and large physiques to watching, choosey females. She investigates why female elephant seals voluntarily live in harems where they are harassed constantly by eager males. And she reveals why dwarf male giant seadevils parasitically fuse to their giant female partners for life. Fairbairn also considers humans and explains that although we are keenly aware of our own sexual differences, they are unexceptional within the vast animal world.

## LA Times Article with Tim Chartier

Davidson math professor, PUP author and bracketology expert, Tim Chartier, discusses the math behind March Madness with the LA Times.

Mathematician Tim Chartier has the best job on Earth once a year: when the NCAA men’s basketball tournament begins, so does March Mathness.

His telephone rings, he’s on the radio, he’s talking to ESPN, and for once he can explain what exactly he does for a living at North Carolina’s Davidson College.

“For the first time in my life I can talk about what I’m doing, on a higher level, and people understand,” Chartier said.

What Chartier does is use complex math to win the Final Four pool on a regular basis. How regular a basis? He’s been in the top 3%  of the 4 million submissions to ESPN’s March Madness tournament challenge, which is arguably the major league of sports prognostication.

“That’s when we said, whoa, this thing really works,” Chartier said of his brush with sports handicapping superstardom.

Blame it on tiny Butler College. Chartier’s math class was among those to recognize that fifth-seeded Butler was destined for the finals in 2010. That was the second year Chartier started making bracketology — the art and science of picking winners among 68 teams in a single-elimination tournament — part of his syllabus. That’s right: take Chartier’s course and you’ll be deep into basketball come March.

Source: Los Angeles Times, “March Madness puts Davidson math professor in a bracket of his own”  http://touch.latimes.com/#section/-1/article/p2p-74922641/

Skipping to the good stuff — who is going to win March Madness this year? At least according to the math?

So, who did Chartier pick? With a simplified Massey method (which gives his students a fighting chance), he agrees with Dick Vitale: Louisville wins it all, in this case beating Florida, then Indiana, which beats Gonzaga.

By the Colley method, the Final Four are Duke, Kansas, New Mexico and Miami, with New Mexico winning.

Which system will do the best?

“That’s the madness for us in the math!” Chartier said.

Read the complete article here: http://touch.latimes.com/#section/-1/article/p2p-74922641/

## Who’s #1? Kyle Snipes’ bracket after the Round of 32

After the Round of 32, Kyle Snipes was #1 on our leaderboard. Below he gives us an update on his bracket.

As the scores continued to roll in Friday and Saturday afternoon, I was left echoing the words of many bracketologists around the country- “Dang, thanks to ___________, my bracket is totally busted!” For me, FGCU, Oregon, and Ole Miss dealt the harshest blows. When the second round was said and done, my mathematical methods had correctly predicted 2 of the 10 first round upsets (lower seed over higher seed) while incorrectly predicting victories by Missouri and St. Mary’s over their higher seeded opponents. Once the madness of the first weekend had subsided, however, I came out looking relatively strong. As of the first weekend of the tournament, my best bracket (based on the Massey method) was sitting at the 97.2 percentile in ESPN’s nationwide pool.

While my method was unable to recognize strong teams on the lower seed lines, it did a great job of telling me which teams were strong out of the teams that everyone thought would be strong (with the exception of Gonzaga). Looking forward, I still have 7 out of 8 teams remaining in the Elite Eight, and 3 out of 4 Final Fours teams, including my National Championship participants. I’m excited to see if my bracket is able to remain near the top as the tournament plays itself, but more importantly, I’m ready for some more March Madness!

## Princeton Students Learn Magical Math

I had a friend who used to always do the whole “Pick a card, any card” charade and flip through every card until he got to the right one, at which he point he flamboyantly touted “I knew it all along!” Maybe if he took this freshman seminar course here at Princeton, he would have actually known it all along.

A freshman seminar course “The Mathematics of Magic Tricks and Games” teaches its students the magic behind tricks like the one my friend so desperately tried to get right. Students learn the mathematical principles behind games and magic tricks in this class giving math a fun and engaging application. Princeton mathematics professor Manjul Bhargava employs Magical Mathematics: The Mathematical Ideas That Animate Great Magic Tricks to teach his students how to do fun magic tricks.

Bhargava actually studied with Persi Diaconis who is one of the co-authors of the book and is also a professor of mathematics and professional magician. Bhargava’s course is designed to show freshman students the creative and artistic side of mathematics that they would probably not see in any of their past high school geometry or calculus classes.

Magical Mathematics can teach you some tricks that Bhargava teaches in his classes. Not only will you enjoy doing math, but it will make also give you fun tricks to show your friends.

Also, if you’re interested in this book, you may also be interested in The Ultimate Book of Saturday Science which gives various fun and astounding backyard science experiments.

## How did they create their brackets? Two Davidson students explain.

Maddie Parrish is senior Economics major with a Communications Studies concentration at Davidson College. She plays Division I field hockey.

March Madness. 65 elite NCAA Division I Basketball teams competing to win it all, the NCAA Tournament Championship. Every year fans from across the nation create brackets to predict who will ultimately be #1. I am one of those fans, and I’m excited to share my story. My name is Maddie Parrish and I am a senior Economics major with a Communication Studies concentration at Davidson College, a small, highly selective liberal arts school twenty minutes north of Charlotte, NC.  We are also the alma mater to such basketball phenoms as John Belk ’43, Terrence Holland ’65, Kenneth Wilson ’84, Mike Maloy, and Stephen Curry.  My hometown is Chester, VA, a suburb of Richmond and I have interests in economics, communications, sports, and many other topics. In the fall of 2012, I wrapped up my fourth and final season as a member of the Davidson Wildcats NCAA Division I Field Hockey Team. Being a student-athlete at Davidson has clearly shaped my college experience. It has made me who I am today by teaching me many lessons about dedication, respect, passion, heart, and life in general.

As a student-athlete, the pride I have in my school and its’ athletic teams is enormous. I am a huge fan of college basketball and I am close friends with many of the Davidson Basketball Team members.  Our boys just won the 2013 Southern Conference Championship for a second year in a row and the entire school is supporting them in their March Madness journey to the NCAA Championship. My personal connections and interest in Davidson basketball are my main reasons for completing a March Madness bracket this year.

I am an athlete, a sports-lover, and a passionate sports enthusiast. Although a rookie to Bracketology, I know that using mathematic strategies is the best way to create a successful bracket. Being an Economics major, math comes easily to me and I find it very enjoyable. This Spring I am taking Dr. Tim Chartier’s MAT 110 – Finite Math course here at Davidson in which we spend a good chunk of class time learning about linear systems and how to solve them. The concepts of linear systems are the key behind ranking the right teams in our bracket by using matrices and weighted values. In class, we learned about the Colley Method for sports ranking, which utilizes winning percentage to determine each team’s ranking. Another method of sports ranking is the Massey Method, which utilizes actual game scores in the regular season to determine each team’s ranking. With both methods, there is an opportunity to choose your own weighted values for specific times during the season. For example, it is possible to weight games that occurred in the beginning of the season less than games mid-way through the season and at the end of the season. If games at the end of the season are weighted more than 1 game, say each game counts as 2 games; the weight is capturing a team’s final push or momentum. A team’s momentum is explained by their ability to win games at the end of the season, which is admirable because the season is so long and competition may be very tough.

For my March Madness bracket this year, I am choosing to use the Colley Method because I am curious to use my newly learned knowledge from class in a life application and see how well it really works. I split the season into four even intervals, one for games at the beginning of the

season, one for games leading up to mid-way through the season, one for games in the second half of the season, and one for games at the very end of the season. I am creating my weights for each season interval based on the hypothesis that as a basketball team plays more games, it gains momentum and wins more frequently. I also am using the Davidson Men’s Basketball schedule results from this year to create my weights. In the first two intervals of the season, the team lost a good number of games. However, they have not yet lost a game in the third and fourth intervals of this year’s season. Using this intuition, I am weighting the first interval at 0.5/1 game, the second interval at 0.75/1 game, the third interval at 1.25/1 game, and the fourth interval at 2/1 games. This means that games played in the beginning of the season are only worth half of a game and games at the end of the season are worth two games. Therefore, if a team is winning more at the end of the season due to momentum then those wins will be worth more in my ranking method.

I understand that using the Colley Method may not factor in specific scores of games and because of this will not capture strength of opponents throughout the season. Yet, I am confident that using the Colley Method and the particular weights I have chosen will produce solid results. After the 65 teams (1 play-in) were announced on Selection Sunday, I filled in my bracket according my method rankings. Of course, I ranked Davidson higher due to the success of their season thus far and due to my personal bias.

As a student-athlete, I have always been interested in how we can harness the talents of individual teams throughout the nation and celebrate sports through common mediums such as love for the game, competition, and passion for your school. The NCAA Division I Men’s Basketball Tournament provides a venue for all of these values. It also allows for fans to express their passion for the game, pride for their school, and their intuitive math sense in a fun way. Using my intuition as an athlete and my knowledge of math, I have created a bracket that I hope will perform well during the March Madness basketball tournament. I am curious to see how it turns out and wish the best of luck to all of the teams who have the honor and privilege of participating in the tournament! Here at Davidson, we have a saying that runs throughout campus each day that follows “It’s a Great Day to be a Wildcat!” Hopefully, my bracket will sing this tune throughout the tournament! Go ‘Cats!

Kyle Snipes is a senior Math major at Davidson College. He is from Indian Trail, NC. He is a volunteer Younglife leader and a lifelong basketball fan. He will be spending this March Madness season cheering on the Davidson Wildcats!

I have competed in bracket pools for a long as I can remember. In the past I have picked games based on what I know about basketball with a fairly high success rate. Since my senior year of high school, I have won at least one of the couple of pools that I have competed in. This will be my first year applying mathematics to my March Madness selections.

I will use ranking methods adapted from the Colley and Massey ranking methods. Since all NCAA tournament games are played at neutral sites, I will count road and neutral site games as a full game, while weighting home games as partial games to account for any homecourt advantage a team might have during the regular season.

I will weigh different portions of the season differently. Generally teams will play the toughest part of their nonconference schedule in preseason tournaments and standalone nonconference games early in the season. On the other hand, a team’s performance early of the season is less likely to be representative of their performance at the end of the season. Therefore, I will give games during the first quarter of the season a weight of 0.7. The second quarter of the season is still a bit early to be representative of a team’s performance come tournament time. Since there are generally fewer nonconference games during this part of the season, I will give these games a weight of 0.6. Teams begin playing the important part of their nonconference during the third quarter of the season. It is also the point in the season where teams poised to make a deep run in the tournament will begin hitting their stride. I will give the games during this quarter of the season a weight of 0.85. Teams that succeed during the last quarter of the regular season are the teams that will be hot coming into the tournament. I will give these games a weight of 1. I have noticed that teams that rely solely on winning their conference tournaments to get to the Big Dance will be burnt out by the time they play the next weekend. Furthermore, teams that have already secured a spot in the Big Dance may have more of an incentive to rest players and avoid injury than to perform to the best of their potential during their conference tournament, making these games even more illegitimate. Therefore, I will only use data from regular season games in my rankings.

One last idea I would like to implement into my ranking is to reward teams who go on long winning streaks as well as teams who are able to beat teams on long winning streaks. I imagine that this will help pick out teams who are able to win successive games, as they must do in the tournament, as well as the giant killers who are able to beat teams that are in the middle of a strong run. If I have the time, I will do this by incrementing a game’s weight by 0.05 for each game in the winning streak for whichever team comes into the game with a longer winning streak. I will cap this at a weight of 1.5 games to avoid over-rewarding strong teams playing in weak conferences in which long winning streaks are common. I plan on submitting three bracket– two using different ranking methods and one where I will synthesize the math with my intuition. I’m excited to see how my picks stand up against the rest of the country!

## How are we doing after the round of 32?

##### Sportscaster-John Hussey

The first weekend of the NCAA tournament was as surprising as ever, with Florida Gulf Coast’s sweet 16 appearance topping the list. FGCU put the largest dent into my bracket knocking out Georgetown, which eliminated a team from the finals for me, essentially ending what chance I had at a good score. Even though the game was a big upset, it wasn’t “entirely” a shock. Going into the tourney, I knew that FGCU had a win over Miami on their resume and Georgetown’s Princeton offense makes them susceptible to low scoring games, which makes them vulnerable. There is a reason that Georgetown lost to South Florida this year.

Out West, I had the right idea picking against Gonzaga in the second round–I just picked the wrong team in Wichita State. In the South, the basketball gods must really love Florida. This is the second straight year that Florida gets to play a 15 seed in round 2 or later. For perspective, Florida has now played a 14, 11, and 15 in their first three games, while #1 seed Kansas has played a 16, 8, and now a 4. Talk about luck of the draw for the Gators! I wish someone would have told me that would happen!

I had a near miss with Illinois over Miami (FL), which really torched my East Region. It will be interesting to see who wins that Indiana/Syracuse matchup down in Washington DC. I’ll be in attendance to see what happens.

Overall, with three Final Four teams alive (and my champion), the first weekend wasn’t a completely disaster. But it was pretty close!

##### Math Geek-Vickie Kearn

This was definitely a weekend of hits and misses for me. There were some big surprises from a math point of view, especially FGCU, Oregon and Ole Miss. However, I still have 7 of 8 teams scheduled to go to the Elite Eight (assuming they survive the Sweet 16). Although I was sad to see my math off track, I did love seeing some personal favorites (Temple and Lasalle) and underdogs (FGCU) go further than I expected.

After riding high the first day of play my sister, who made her picks based on the color of the team jerseys, is rethinking that strategy. Her color is blue and she did pick Duke so she may be flying high again soon.

## The Sportscaster versus the Math Geek

John Hussey and Vickie Kearn both work at Princeton University Press. John is the assistant sales director and national accounts manager and Vickie is the mathematics editor. We thought it would be fun to see how they filled out their March Madness brackets. The conversation that follows took place on March 20 at our PUP offices. To get things started, we asked a single question: How did you fill out your bracket?

Vickie: You may have figured out I am the math geek. After getting my math degree at the University of Richmond, I taught math for 8 years and then ventured into publishing math books. Although I am a huge sports fan, my true love is football. I didn’t watch basketball until we began March Mathness a couple of years ago. Now I will be glued to the TV for the next few weeks. I really don’t know much about the game at all but I love watching the numbers and the great upsets, especially those we have seen so far this year.

Now to my bracket. Because of the many upsets this year, I decided to ignore the seeds.

I looked at four things when I filled in my bracket:

1. Strength of schedule (pulled from RPI). I gave this figure a weight of 1.
2. Winning percentage for the regular season earned a weight of 1.
3. The sum of the posts season wins over the past three years plus the coach’s winning record with their current team also got a weight of 1.
4. Then each team received the following bonus points.

-One point if they were the leader in their conference in the regular season.
-One point if they are a major team and if they are in a tested basketball conference like the ACC, Big East, and Big10.
-One point if they won their conference championship season
-One point for the leaders in points per game/rebounds per game/scoring offense and scoring defense

Bonus points are weighted as 2 because they reflect how the teams were playing at the end of the season.

John: What about style of play?

Vickie: I don’t know that much about basketball, I’m in March Madness for the math. I’m interested in the data and stats.

John: To get an understanding of my approach, here’s my background: I went to Syracuse University for sports broadcasting. I have friends that still work in sports. My picks are based on a personal study of the game; I watch about 20 hours of sports/week and college basketball is my favorite. My picks are similar to Vickie’s, but from a different point of view. I’m not distinguishing between conference tournament and how a team plays through the stretch of the season. I’ve been watching teams play and deciding on style of play. For example, if one team tends to make a lot of 3-pointers and they’re up against a team with a strong zone defense, the zone defense is not going to do well. Where things get tricky is making decisions about Syracuse. Since that’s my team I’m pretty biased. When you watch teams extensively, you have seen them in the good times and bad but the bad times stick in your mind. For example, Kansas’ loss at TCU or Michigan’s loss at Penn State. I also know a lot about upset histories. This year there are no #1 seeds in my final bracket because this year no one team dominated. The possibilities are wider this year…could be a five seed that wins.

Vickie: I only have one #1 seed in my final 4. We both picked #2 seed Duke as the 2013 champion.

John: Player experience is also a big factor. Some game style doesn’t translate into a tournament setting. Duke is a great team, but sometimes flakes out super early. They lost to Lehigh last year but they make lot of deep runs. It’s interesting that Miami is in Vickie’s final 4 but I have them flaming out in the 2nd round. They’re too reliant on 3pt shooting. They’re not an intelligent team and play up and down.

What does the math say the biggest upset will be in the first round?

Vickie: New Mexico State over St. Louis is a 13 over 4 and San Diego State over Michigan is a 13 over 4. California over UNLV is a 12 over 5.

John: Any upsets in your Elite 8? No major upsets but I do have 2, 3, and 4 seeds.

Vickie: No major upsets but I do have 1, 2, 3, and 4 seeds.

John: I don’t have any top seeds in my final four because they have been losing lately, but the math is backing up the top seeds.

Vickie: But here’s the real question: will we beat the president?

John: Obama takes the smart, safe approach to the bracket. Historically he has been very good, because he is conservative in his picks and doesn’t bet on upsets. Generally that’s a good way to go. This year is going to be odd since the tops aren’t doing so well. It really could be a 5, 6,or 7 that wins. Nothing crazy based on the math?

Vickie: No, but that doesn’t mean I wouldn’t like to see an upset.

John: Gonzaga has a great RPI, but they’re not ranked high. Their defense metrics must be off . They have a great winning percentage but not necessarily the RPI.

Vickie: But seriously, will we beat the president?

John: He’s playing smart and safe. I want to win, but in an interesting way. It’s a little riskier when you don’t have any #1 seeds in the final 4.

Vickie: Well it’s interesting how similar our brackets are even though we had different strategies! I just got a text from my sister who picked her teams by the color of their uniforms. Blue is her color so she also picks Duke to win this year.

In case you are wondering, the odds of having a perfect bracket are 9.2 Quadrillion to 1. Good luck and have fun.

Don’t forget to join our ESPN bracket challenge group before Thursday, March 21st!

Use the widget below to explore Tim Chartier’s lectures on March Mathness and to find more advice on how to fill out your brackets this year.

## Celebrate Pi Day with Princeton University Press

Happy Pi Day, everyone!  In honor of the day, we’ve come up with a reading list that includes some of our favorite Einstein books at Princeton University Press, along with some free chapter excerpts. Celebrate Pi Day and Einstein’s birthday with a great book — we’ve got plenty to choose from!

Einstein’s Jury: The Race to Test Relativity
Jeffrey Crelinsten
This book tells the dramatic story of how astronomers in Germany, England, and America competed to test Einstein’s developing theory of relativity.

The Ultimate Quotable Einstein
Collected and edited by Alice Calaprice
“Without the belief that it is possible to grasp reality with our theoretical constructions, without the belief in the inner harmony of our world, there could be no science. This belief is and will remain the fundamental motive for all scientific creation.” 1938; p. 390
Want more quotes? Check out The Ultimate Quotable Einstein’s Facebook page.

The Meaning of Relativity, Fifth Edition: Including the Relativistic Theory of the Non-Symmetric Field
by Albert Einstein, with a new introduction by Brian Greene

The Collected Papers of Albert Einstein, Volume 13: The Berlin Years: Writings & Correspondence, January 1922 – March 1923 (Documentary Edition)
Edited by Diana Kormos Buchwald, József Illy, Ze’ev Rosenkranz, & Tilman Sauer
Check out Chapter 1
Here’s all of the Collected Papers of Albert Einstein

Einstein’s Miraculous Year: Five Papers That Changed the Face of Physics
Edited and introduced by John Stachel
Far more than just a collection of scientific articles, this book presents work that is among the high points of human achievement and marks a watershed in the history of science.

Albert Einstein, Mileva Maric: The Love Letters
Edited by Jürgen Renn & Robert Schulmann, Translated by Shawn Smith
Informative, entertaining, and often very moving, this collection of letters captures for scientists and general readers alike a little known yet crucial period in Einstein’s life.

The Curious History of Relativity: How Einstein’s Theory of Gravity Was Lost and Found Again
Jean Eisenstaedt
Written with flair, this book poses – and answers – the difficult questions raised by Einstein’s magnificent intellectual feat.

Einstein for the 21st Century: His Legacy in Science, Art, and Modern Culture
Edited by Peter L. Galison, Gerald Holton & Silvan S. Schweber
Check out Chapter 1
In this wide-ranging collection, eminent artists, historians, scientists, and social scientists describe Einstein’s influence on their work, and consider his relevance for the future.

The Little Book of String Theory
Steven S. Gubser
A short, accessible, and entertaining introduction to one of the most talked-about areas of physics today.

The Nature of Space and Time
Stephen Hawking & Roger Penrose
Einstein said that the most incomprehensible thing about the universe is that it is comprehensible. But was he right? On this issue, two of the world’s most famous physicists – Stephen Hawking and Roger Penrose – disagree. Here they explain their positions in a work based on six lectures with a final debate.

Traveling at the Speed of Thought: Einstein and the Quest for Gravitational Waves
Daniel Kennefick
Check out Chapter 1
Daniel Kennefick’s landmark book takes readers through the theoretical controversies and thorny debates that raged around the subject of gravitational waves after the publication of Einstein’s theory.

The Extravagant Universe: Exploding Stars, Dark Energy, and the Accelerating Cosmos
by Robert P. Kirshner
Check out Chapter 1
One of the world’s leading astronomers, Robert Kirshner, takes readers inside a lively research team on the quest that led them to an extraordinary cosmological discovery: the expansion of the universe is accelerating under the influence of a dark energy that makes space itself expand.

Quantum Generations: A History of Physics in the Twentieth Century
Helge Kragh
Combining a mastery of detail with a sure sense of the broad contours of historical change, Kragh has written a fitting tribute to the scientists who have played such a decisive role in the making of the modern world.

Philosophy of Physics: Space and Time
Tim Maudlin
Tim Maudlin’s broad historical overview examines Aristotelian and Newtonian accounts of space and time, and traces how Galileo’s conceptions of relativity and space-time led to Einstein’s special and general theories of relativity.

It’s About Time: Understanding Einstein’s Relativity
by N. David Mermin
Check out Chapter 1
The book reveals that some of our most intuitive notions about time are shockingly wrong, and that the real nature of time discovered by Einstein can be rigorously explained without advanced mathematics.

Dynamics and Evolution of Galactic Nuclei
David Merritt
Deep within galaxies like the Milky Way, astronomers have found a fascinating legacy of Einstein’s general theory of relativity: supermassive black holes. This is the first comprehensive introduction to dynamical processes occurring in the vicinity of supermassive black holes in their galactic environment.

Einstein Before Israel: Zionist Icon or Iconoclast?
by Ze’ev Rosenkranz
Rosenkranz explores a host of fascinating questions, such as whether Zionists sought to silence Einstein’s criticism of their movement, whether Einstein was the real manipulator, and whether this Zionist icon was indeed a committed believer in Zionism or an iconoclast beholden to no one.

Einstein on Politics: His Private Thoughts and Public Stands on Nationalism, Zionism, War, Peace, and the Bomb
Edited by David E. Rowe & Robert Schulmann
Check out Chapter 1
A vivid firsthand view of how one of the twentieth century’s greatest minds responded to the greatest political challenges of his day, this work will forever change our picture of Einstein’s public activism and private motivations.

Einstein’s German World
Fritz Stern
At once historical and personal, provocative and accessible, this book illuminates the issues that made Germany’s and Europe’s past and present so important in a tumultuous century of creativity and violence.

Einstein Gravity in a Nutshell
A. Zee
This unique textbook provides an accessible introduction to Einstein’s general theory of relativity, a subject of breathtaking beauty and supreme importance in physics.
Check out the In a Nutshell series

## BOOK FACT FRIDAY – Trigonometric Delights

BOOK FACT excerpted from Trigonometric Delights by Eli Maor:

It is no coincidence that trigonometry up until the sixteenth century was developed mainly by astronomers. Aristarchus and Hipparchus, who founded trigonometry as a distinct branch of mathematics, were astronomers, as was Ptolemy, the author of the Almagest. During the Middle Ages, Arab and Hindu astronomers, notably Abul-Wefa, al-Battani, Aryabhata, and Ulugh Beg of Samarkand (1393-1449), absorbed the Greek mathematical heritage and greatly expanded it, especially in spherical trigonometry. And when this combined heritage was passed on to Europe, it was again an astronomer who was at the forefront: Johann Muller, known as Regiomontanus.

Regiomontanus was the first publisher of mathematical and astronomical books for commercial use. In 1474 he printed his Ephemerides, tables listing the position of the sun, moon, and planets for each day from 1475 to 1506. This work brought him great acclaim; Christopher Columbus had a copy of it on his fourth voyage to the New World and used it to predict the famous lunar eclipse of February 29, 1504. Regiomontanus’s most influential work was his De triangulis omnimodis (On triangles of every kind), a work in five parts (“books”) modeled after Euclid’s Elements. As he states in his introduction, Regiomontanus’s main goal in On Triangles was to provide a mathematical introduction to astronomy. Regiomontanus completed writing On Triangles in 1464, but it was not published until 1533, more than half a century after his death.

We are pleased to announce a new paperback edition is now available:
Trigonometric Delights
by Eli Maor

Trigonometry has always been an underappreciated branch of mathematics. It has a reputation as a dry and difficult subject, a glorified form of geometry complicated by tedious computation. In this book, Eli Maor draws on his remarkable talents as a guide to the world of numbers to dispel that view. Rejecting the usual arid descriptions of sine, cosine, and their trigonometric relatives, he brings the subject to life in a compelling blend of history, biography, and mathematics. He presents both a survey of the main elements of trigonometry and a unique account of its vital contribution to science and social development. Woven together in a tapestry of entertaining stories, scientific curiosities, and educational insights, the book more than lives up to the title Trigonometric Delights.

Maor also sketches the lives of some of the intriguing figures who have shaped four thousand years of trigonometric history. We meet, for instance, the Renaissance scholar Regiomontanus, who is rumored to have been poisoned for insulting a colleague, and Maria Agnesi, an eighteenth-century Italian genius who gave up mathematics to work with the poor–but not before she investigated a special curve that, due to mistranslation, bears the unfortunate name “the witch of Agnesi.” The book is richly illustrated, including rare prints from the author’s own collection. Trigonometric Delights will change forever our view of a once dreaded subject.

Eli Maor teaches the history of mathematics at Loyola University in Chicago. He is the author of To Infinity and Beyond, e: The Story of a Number, Venus in Transit, and The Pythagorean Theorem: A 4,000-Year History.