Using math for March Madness bracket picks

The countdown to fill out your March Madness brackets is on! Who are you picking to win it all?

Today, we hear from Liana Valentino, a student at the College of Charleston who works with PUP authors Amy Langville and Tim Chartier. Liana discusses how math can be applied to bracket selection.

court chalk

What are the chances your team makes it to the next round?

The madness has begun! Since the top 64 teams have been released, brackets are being made all over the country. As an avid college basketball fan my entire life, this is always my favorite time of the year. This year, I have taken a new approach to filling out brackets that consist of more than my basketball knowledge, I am using math as well.

To learn more about how the math is used to make predictions, information is available on Dr. Tim Chartier’s March Mathness website, where you can create your own bracket using math as well!

My bracket choices are decided using the Colley and Massey ranking methods; Colley only uses wins and losses, while Massey integrates the scores of the games. Within these methods, there are several different weighting options that will change the ratings produced. My strategy is to generate multiple sets of rankings, then determine the probability that each particular team will make it to a specific round. Using this approach, I am able to combine the results of multiple methods instead of having to decide on one to use for the entire bracket.

Choosing what weighting options to use is a personal decision. I will list the ones I’ve used and the reasoning behind them using my basketball awareness.

(1)

Winning games on the road should be rewarded more than winning games at home. Because of that, I use constant rates of .6 for a winning at home, 1.6 for winning away, and 1 for winning at a neutral location; these are the numbers used by the NCAA when determining RPI. I incorporate home and away weightings when performing other weighting methods as well.

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Margin of victory is another factor, but a “blow out” game is defined differently depending on the person. With that in mind, I ran methods using the margin of victory to be both 15 and 20. This means if the margin of victory if 15, then games with a point differential of 15 or higher are weighed the same. These numbers are mainly from personal experience. If a team wins by 20, I would consider that a blowout, meaning the matchup was simply unfair. If a team loses by 15, which in terms of the game is five possessions, the game wasn’t necessarily a blow out, but the winning team is clearly defined as better than the opposition.

In addition to this, I chose to weight games differently if they were close. I defined a close game as a game within one possession, therefore three points. My reasoning behind this was if a team is blowing out every opponent, it means those games are obviously against mismatched opponents, so that does not say very much about them. On the other hand, a team that constantly wins close games shows character. Also, when it comes tournament time, there aren’t going to be many blow out games, therefore teams that can handle close game situations well will excel compared to those who fold under pressure. Because of this, I weighted close games, within three points, 1.5, “blow out” games, greater than 20 points, .5, and any point differential in between as 1.

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Games played at different points in the season are also weighted differently. Would you say a team is the same in the first game as the last? There are three different methods to weight time, as provided by Dr. Chartier using his March Mathness site, linearly, logarithmically, and using intervals. Linear and logarithmic weights are similar in the fact that both increase the weight of the game as the season progresses. These methods can be used if you believe that games towards the end of the season are more important than games at the beginning.

Interval weighting consists of breaking the season into equal sized intervals and choosing specific weightings for each. In one instance, I weighted the games by splitting the season in half, down weighting the first half using .5, and up weighting the second half using 1.5 and 2. These decisions were made because during the first half of the season, teams are still getting to know themselves, while during the second half of the season, there are fewer excuses the make. Also, the second half of the season is when conference games are played, which are generally considered more important than non-conference games. For the people that argue that non conference play is more important because it is usually more difficult than in conference play, I also created one bracket where I up weight the first half of the season and down weight the second half.

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The last different weighting method used was incorporating if a team was on a winning streak. In this case, we would weight a game higher if one team breaks their opponents winning streak. Personally, I defined a winning streak as having won four or more games in a row.

I used several combinations of these various methods and created 36 different brackets that I have used to obtain the following information. Surprisingly, Kentucky only wins the tournament 75% of the time; Arizona wins about 20%, and the remaining 5% is split between Wisconsin and Villanova. Interestingly enough, the only round Kentucky ever loses in is the Final Four, so each time they do make it to the championship, they win. Duke is the only number 1 seed never predicted to win a championship.

Villanova makes it to the championship game 70% of the time, where the only team that prevents them from doing so is Duke, who makes it 25% of the time. The remaining teams for that side of the bracket that make it are Stephen F. Austin and Virginia, both with a 2.5% chance. Kentucky makes it to the championship game 75% of the time, while Arizona makes it 22%, and Wisconsin makes it 3%. However, if Arizona makes it the championship game, they win it 88% of the time. Furthermore, Wisconsin is predicted to play in the championship game once, which they win.

The two teams Kentucky loses to in the Final Four are Arizona, and Wisconsin. During the final four, Kentucky has Arizona as an opponent 39% of the time, where Arizona wins 50% of those matchups. Kentucky’s only other opponent in the final four is Wisconsin, where Wisconsin wins that game only 5% of the time. On the other side, Villanova makes it to the final four 97% of the time, where the one instance they did not was a loss to Virginia. Villanova’s opponent in the Final Four is made up of Duke 72%, Gonzaga 19%, Stephen F. Austin 6%, Utah at 3%. The only seeds that appear in the Final Four are 1, 2, and one 12 seed, Stephen F. Austin one time.

During the Elite 8, Duke is the only number 1 seed that does not make it 100% of the time, with Utah upsetting them in 17% of their matchups. The other Elite 8 member is Gonzaga 97% of the time. Kentucky’s opponent in this round is Notre Dame 47% and Kansas 53% of the time.

In the Sweet 16, there are eight teams that make it every time: Kentucky, Wisconsin, Villanova, Duke, Arizona, Virginia, Gonzaga, and Notre Dame. Kansas is the only number 2 seed not on the list as Wichita State is predicted to beat them in 8% of their matchups. Kentucky’s opponent in the Sweet 16 is Maryland 39%, West Virginia 36%, Valparaiso 14%, and Buffalo 11%. Valparaiso is the only 13 seed predicted to make it to the Sweet 16. Villanova’s opponent is either Northern Iowa 61% or Louisville 38%. Duke appears to be facing either Utah 67%, Stephen F. Austin 19%, or Georgetown 14%.

Now, for the teams that make it into the third round. I’m not sure how many people consider a 9 seed beating an 8 seed an upset, but the number 9 seeds that are expected to progress are Purdue, Oklahoma State, and St. John’s. In regards to the 10 seed, Davidson is the most likely to continue with a 47% chance to move past Iowa, which is the highest percentage for an upset not including the 8-9 seed matchups. Following them is 11 seed Texas, who have a 42% of defeating Butler. For the 12 seeds, Buffalo is the most likely to continue with a 36% chance of beating Virginia. The 13 seed with the best chance of progressing is Valparaiso with 19% over Maryland. Lastly, the only 14 seeds that move on are Georgia State and Albany, which only happens a mere 8% of the time.

In general, Arizona seems to win the championship when using Massey and linear or interval weighting without home and away. This could be because most of their losses happen during the beginning of the season, while they win important games towards the end. Using the Colley method is when most of the upsets are predicted. For example, Stephen F. Austin making it to the championship game happens using the Colley logarithmic weighting. Davidson beating Iowa in the second round is also found many times using different Colley methods.

Overall, there are various methods that include various factors, but there are still qualitative variables that we don’t include. On the other hand, math can do a lot more than people expect. Considering Kentucky is undefeated, I presumed the math would never show them losing, but there is a lot more in the numbers than you think. Combining the various methods on 36 different brackets, I computed the probabilities of teams making it to specific rounds and decided to make a bracket using the combined data. This makes it so I don’t have to decide on solely one weighting that determines my bracket; instead, I use the results from several methods. Unfortunately, there is always one factor we cannot consider, luck! That is why we can only make estimates and never be certain. From my results, I would predict to see a Final Four of Kentucky, Arizona, Villanova, Duke; a championship game of Kentucky, Villanova; and the 2015 national champion being Kentucky.

 

 

Cinderella stories? A College of Charleston student examines March Madness upsets through math

Drew Passarello, a student at the College of Charleston, takes a closer look at how math relates to upsets and predictability in March Madness.

balls

The Madness is coming. In a way, it is here! With the first round of the March Madness tournament announced, the craziness of filling out the tournament brackets is upon us! Can math help us get a better handle on where we might see upsets in March Madness? In this post, I will detail how math helps us get a handle on what level of madness we expect in the tournament. Said another way, how many upsets do we expect? Will there be a lot? We call that a bad year as that leads to brackets having lower accuracy in their predictions. By the end of the article, you will see how math can earmark teams that might be on the cusp of upsets in the games that will capture national attention.

Where am I learning this math? I am taking a sports analytics class at the College of Charleston under the supervision of Dr. Tim Chartier and Dr. Amy Langville. Part of our work has been researching new results and insights in bracketology. My research uses the Massey and Colley ranking methods. Part of my research deals with the following question: What are good years and bad years in terms of March Madness? In other words, before the tournament begins, what can we infer about how predictable the tournament will be?

One way of answering this question is to see how accurate one is at predicting the winners of the tournaments coupled with how high one’s ESPN score is. However, I also wanted to account for the variability of the level of competition going into the tournament, which is why I also looked at the standard deviation of the ratings of those in March Madness. A higher standard deviation implies the more spread out the playing level is. Ultimately, a good year will have a high tournament accuracy, high ESPN score, and a high standard deviation of ratings for those competing in March Madness. Similarly, a bad year will have low tournament accuracy, low ESPN score, and a low standard deviation of the ratings. This assessment will be relative to the ranking method itself and only defines good years and bad years solely in terms of past March Madness data.

I focused on ratings from uniformly weighted Massey and Colley ranking methods as the weighting might add some bias. However, my simple assessment can be applied for other variations of weighting Massey and Colley. I found the mean accuracy, mean ESPN score, and mean standard deviation of ratings of the teams in March Madness for years 2001 – 2014, and I then looked at the years which rested below or above these corresponding means. Years overlapping were those deemed to be good or bad, and the remaining years were labeled neutral. The good years for Massey were 2001, 2004, 2008, and 2009, and the bad years were 2006, 2010 – 2014. Neutral years were 2002, 2003, and 2007. Also, for Colley, the good years were 2005, 2007 – 2009; bad years were 2001, 2006, and 2010 – 2014; neutral years were 2002 – 2004. A very interesting trend I noticed from both Massey and Colley was that the standard deviation of the ratings of those in March Madness from 2010 to 2014 were significantly lower than the years before. This leads me to believe that basketball has recently become more competitive in terms of March Madness, which would also partially explain why 2010 – 2014 were bad years for both methods. However, this does not necessarily imply 2015 will be a bad year.

In order to get a feel for how accurate the ranking methods will be for this year, I created a regression line based on years 2001 – 2014 that had tournament accuracy as the dependent variable and standard deviation of the ratings of those in March Madness as the independent variable. Massey is predicted to have 65.81% accuracy for predicting winners this year whereas Colley is predicted to have 64.19%accuracy. The standard deviation of the ratings for those expected to be in the tournament was 8.0451 for Massey and 0.1528 for Colley, and these mostly resemble the standard deviation of the ratings of the March Madness teams in 2002 and 2007.

After this assessment, I wanted to figure out what defines an upset relative to the ratings. To answer this, I looked at season data and focused on uniform Massey. Specifically for this year, I used the first half of the season ratings to predict the first week of the second half of the season and then updated the ratings. After this, I would use these to predict the next week and update the ratings again and so on until now. For games incorrectly predicted, the median in the difference of ratings was 2.2727, and the mean was 3.0284. I defined an upset for this year to be those games in which the absolute difference in the ratings is greater than or equal to three. This definition of an upset is relative to this particular year. I then kept track of the upsets for those teams expected to be in the tournament. I looked at the number of upsets each team had and the number of times each team gets upset, along with the score differential and rating differences for these games. From comparing these trends, I determined the following teams to be upset teams to look for in the tournament: Indiana, NC State, Notre Dame, and Georgetown. These teams had a higher ratio of upsets over getting upset when compared to the other teams. Also, these teams had games in which the score differences and rating differences were larger than those from the other teams in March Madness.

I am still working on ways to weight these upset games from the second half of the season, and one of the approaches relies on the score differential of the game. Essentially, teams who upset teams by a lot of points should benefit more in the ratings. Similarly, teams who get upset by a lot of points should be penalized more in the ratings. For a fun and easy bracket, I am going to weight upset games heavily on the week before conference tournament play and a week into conference tournament play. These two weeks gave the best correlation coefficient in terms of accuracy from these weeks and the accuracy from March Madness for both uniform Massey and Colley. Let the madness begin!

 

May the odds be in your favor — March Mathness begins

Let the games begin! After the excitement of Selection Sunday, brackets are ready for “the picking.” Have you started making your picks?

Check out the full schedule of teams selected yesterday, and join the fun by submitting a bracket to the official Princeton University Press March Madness tournament pool.

Before you do, we recommend that you brush up on your bracketology by checking out PUP author Tim Chartier’s strategy:

 

 

For more on the math behind the madness, head over to Dr. Chartier’s March Mathness video page. Learn three popular sport ranking methods and how to create March Madness brackets with them. Let math make the picks!

Be sure to follow along with our March Mathness coverage on our blog, and comment below with your favorite strategy for making March Madness picks.

Pi Day Recipe: Apple Pie from Jim Henle’s The Proof and the Pudding

Tomorrow (March 14, 2015) is a very important Pi Day. This year’s local Princeton Pi Day Party and other global celebrations of Albert Einstein’s birthday look to be truly stellar, which is apt given this is arguably the closest we will get to 3.1415 in our lifetimes.

Leading up to the publication of the forthcoming The Proof and the Pudding: What Mathematicians, Cooks, and You Have in Common by Jim Henle, we’re celebrating the holiday with a recipe for a classic Apple Pie (an integral part of any Pi Day spread). Publicist Casey LaVela recreates and photographs the recipe below. Full text of the recipe follows. Happy Pi Day everyone!


Notes on Jim Henle’s Apple Pie recipe from Publicist Casey LaVela

The Proof and the Pudding includes several recipes for pies or tarts that would fit the bill for Pi Day, but the story behind Henle’s Apple Pie recipe is especially charming, the recipe itself is straightforward, and the results are delicious. At the author’s suggestion, I used a mixture of baking apples (and delightfully indulgent amounts of butter and sugar).

Crust:

All of the crust ingredients (flour, butter, salt) ready to go:

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After a few minutes of blending everything together with a pastry cutter, the crust begins to come together. A glorious marriage of flour and butter.

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Once the butter and flour were better incorporated, I dribbled in the ice water and then turned the whole wonderful mess out between two sheets of plastic wrap in preparation for folding. The crust will look like it won’t come together, but somehow it always does in the end. Magical.

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Now you need to roll out and fold over the dough a few times. This is an important step and makes for a light and flaky crust. (You use a similar process to make croissants or other viennoiserie from scratch.)

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I cut the crust into two (for the top crust and bottom crust) using my handy bench scraper:

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Apples:

The apples cored, peeled, and ready to be cut into slices. I broke out my mandolin slicer (not pictured) to make more even slices, but if you don’t own a slicer or prefer to practice your knife skills you can just as easily use your favorite sharp knife.

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Beautiful (even) apple slices:

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Action shot of me mixing the apple slices, sugar, and cinnamon together. I prefer to prepare my apple pie filling in a bowl rather than sprinkling the dry ingredients over the apple slices once they have been arranged in the bottom crust. I’m not sure if it has much impact on the flavor and it is much, much messier, but I find it more fun.

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Assembly:

The bottom crust in the pie plate:

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Arrange the apple slices in the bottom crust:

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Top with the second crust, seal the top crust to the bottom with your fingers, and (using your sharp knife) make incisions in the top crust to allow steam to escape:

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The apple pie before going into the oven (don’t forget to put a little extra sugar on top):

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The finished product:

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There was a little crust left over after cutting, so I shaped it into another pi symbol, covered it in cinnamon and sugar, and baked it until golden brown. I ate the baked pi symbol as soon as it had cooled (before thinking to take a picture), but it was delicious!

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Apple Pie

The story of why I started cooking is not inspiring. My motives weren’t pure. Indeed, they involved several important sins.

I really am a glutton. I love to eat. As a child, I ate well; my mother was a wonderful cook. But I always wanted more than I got, especially dessert. And of all desserts, it was apple pie I craved most. Not diner pies, not restaurant pies, and not bakery pies, but real, homemade apple pies.

When I was six, I had my first homemade apple pie. It was at my grandmother’s house. I don’t remember how it tasted, but I can still recall the gleam in my mother’s eye when she explained the secret of the pie. “I watched her make it. Before she put on the top crust, she dotted the whole thing with big pats of butter!”

Several times as I was growing up, my mother made apple pie. Each one was a gem. But they were too few—only three or four before I went off to college. They were amazing pies. The apples were tart and sweet. Fresh fall apples, so flavorful no cinnamon was needed. The crust was golden, light and crisp, dry when it first hit the tongue, then dissolving into butter.

I grew up. I got married. I started a family. All the while, I longed for that pie. Eventually I set out to make one.

Success came pretty quickly, and it’s not hard to see why. The fact is, despite apple pie’s storied place in American culture, most apple pies sold in this country are abysmal. A pie of fresh, tart apples and a crust homemade with butter or lard, no matter how badly it’s made, is guaranteed to surpass a commercial product.

That means that even if you’ve never made a pie before, you can’t go seriously wrong. The chief difficulty is the crust, but I’ve developed a reliable method. Except for this method, the recipe below is standard.

For the filling:
5 cooking apples (yielding about 5 cups of pieces)
1/4 to 1/3 cup sugar
2 Tb butter
1/2 to 1 tsp cinnamon
lemon juice, if necessary
1 tsp flour, maybe

For the crust:
2 cups flour
1 tsp salt
2/3 cup lard or unsalted butter (1 1/3 sticks)
water

The crust is crucial. I’ll discuss its preparation last. Assume for now that you’ve rolled out the bottom crust and placed it in the pie pan.

Core, peel, and slice the apples. Place them in the crust. Sprinkle with sugar and cinnamon. Dot with butter. Roll out the top crust and place it on top. Seal the edge however you like. In about six places, jab a knife into the crust and twist to leave a hole for steam to escape. Sprinkle the crust with the teaspoon of sugar.

Bake in a preheated oven for 15 minutes at 450° and then another 35 minutes at 350°. Allow to cool. Serve, if you like, with vanilla ice cream or a good aged cheddar.

Now, the crust:

Mix the flour and salt in a large bowl. Place the lard or butter or lard/butter in the bowl. Cut it in with a pastry cutter.

Next, the water. Turn the cold water on in the kitchen sink so that it dribbles out in a tiny trickle. Hold the bowl with the flour mixture in one hand and a knife in the other. Let the water dribble into the bowl while you stir with the knife. The object is to add just enough water so that the dough is transformed into small dusty lumps. Don’t be vigorous with the knife, but don’t allow the water to pool. If the water is dribbling too fast, take the bowl away from the faucet from time to time. When you’re done, the dough will still look pretty dry.

Recipes usually call for about 5 tablespoons of water. This method probably uses about that much.

Actually, the dough will look so dry that you’ll think it won’t stick together when it’s rolled out. In fact, it probably won’t stick together, but trust me. This is going to work.

Tear off a sheet of plastic wrap and lay it on the counter. Place a bit more than half the dough on the sheet and cover it with a second sheet of plastic.

With a rolling pin, roll the dough out between the two sheets. Roll it roughly in the shape of a rectangle.

It won’t look great and it probably would fall apart if you picked it up.

Don’t pick it up. Remove the top sheet of plastic wrap and fold the bottom third up, and fold the top third down, then do the same horizontally, right and left.

Now replace the top sheet of plastic wrap and roll the dough out gently into a disk.

This time it should look pretty decent. This time the dough will stick together.

You should be able to remove the top sheet of plastic and, using the bottom sheet, turn it over into the pie pan. The crust should settle in nicely without breaking.

Form the top crust the same way.

This method rolls each crust twice—usually not a good idea because working the dough makes it tough. But remarkably, crusts produced this way are tender and light. I’m not sure why but I suspect it’s because the dough is fairly dry.

Notes:
• Cooking apples are tart apples. The best I know is the Rhode Island Greening, but they’re hard to find. Baldwins and Jonathans are decent, but they’re hard to find too. The British Bramleys are terrific. I’ve made good pies from the French Calville Blanc d’Hiver. But we’re not living in good apple times. Most stores don’t sell apples for cooking. When in doubt, use a mixture.
• The lemon juice and the larger quantity of cinnamon are for when you have tired apples with no oomph. The cheese also serves this purpose. It should be a respectable old cheddar and it should be at room temperature.
• Consumption of too many commercial pies makes me loath to add flour or cornstarch to pie filling. The flour is here in case you fear your apples will be too juicy. I don’t mind juice in a pie, in moderation. If adding flour, mix the apples, sugar, cinnamon, and flour in a bowl before pouring into the crust.
• Lard is best. Its melting point is higher than butter’s. It successfully separates the flour into layers for a light, crispy crust. Butter is more likely to saturate the flour and produce a heavy crust. Some like half butter/half lard, preferring butter for its flavor. But the flavor of lard is nice too, and its porkiness is wonderful with apple.


This recipe is taken from:

Henle_TheProof_S15

The Proof and the Pudding

What Mathematicians, Cooks, and You Have in Common

Jim Henle

“If you’re a fan of Julia Child or Martin Gardner—who respectively proved that anyone can have fun preparing fancy food and doing real mathematics—you’ll enjoy this playful yet passionate romp from Jim Henle. It’s stuffed with tasty treats and ingenious ideas for further explorations, both in the kitchen and with pencil and paper, and draws many thought-providing parallels between two fields not often considered in the same mouthful.”—Colm Mulcahy, author of Mathematical Card Magic: Fifty-Two New Effects

Spotlight on…Mathematicians

John Napier, by Julian Havil

John Napier
by Julian Havil

Mathematics has long been a specialty of the Press, and mathematicians have been the subjects of many of our biographies. Julian Havil’s John Napier: Life, Logarithms and Legacy describes the life and thought of the inventor of logarithms. Napier’s work on logarithms, first published in 1614, established the efficient method of calculation that remained in widespread use until the development of computers over three hundred years later. Napier lived in an age when the boundaries between mathematics, science, religion and the occult were less clearly drawn: he attempted to predict the Apocalypse on the basis of the Book of Revelations and the Sibylline oracles, and was even alleged to be an alchemist and a necromancer.

A century later Leonhard Euler continued development of logarithms, but for Euler this was only one among dozens of mathematical innovations over the course of a brilliant and prolific career. Ronald Calinger’s Leonhard Euler: Mathematical Genius in the Enlightenment is the first full-scale biography of one of the great figures in mathematics. His tireless devotion to his work while at the court of Frederick the Great earned him the mockery of Voltaire, but his collected writings on topics ranging from calculus, number theory, and geometry to astronomy and optics are an extraordinary treasure trove of ideas. Despite near total blindness in the last two decades of his life, Euler’s prodigious memory and skill at mental calculation allowed him to continue working to his death, dictating to a team of scribes. He remains the only mathematician to have given his name to two numbers: the transcendental number (and base of natural logarithms) e, known as Euler’s number, and the Euler-Mascheroni constant.

Theoretical ability doesn’t always translate into practical applications, and Frederick the Great was unimpressed with Euler as an engineer. By contrast, Henri Poincaré worked in the French Corps des Mines throughout his life, eventually attaining the rank of Inspector General, while continuing to pursue his work in multiple fields in mathematics, physics and philosophy. Jeremy Gray’s Henri Poincaré: A Scientific Biography analyzes the lasting influence of a man that some argue was the true discoverer of relativity. Poincaré did not shy away from involvement in public affairs, acting as an expert witness to counter spurious claims by the prosecution in the Dreyfus trials that convulsed France.

Unusually for brilliant theoreticians, Euler and Poincaré also wrote for a popular audience – Letters of Euler on Different Subjects in Natural Philosophy Addressed to a German Princess was a bestseller in its time. In Undiluted Hocus-Pocus one of the great popularizers of our time, Martin Gardner, writes with characteristic wit about his own life. Gardner’s column in Scientific American, Mathematical Games, ran for 25 years – Cambridge University Press are currently working on a new edition of the fifteen volumes of the collected columns. No stranger to controversy, Gardner devoted much energy to combating pseudo-science, but is perhaps best known for the Annotated Alice, in which he explained in detail the mathematical trickery and literary wordplay of Lewis Carroll’s classic Alice books.

The math behind March Madness

It’s almost that time again. The beginning of the March Madness basketball tournament is a few days away, and here at PUP, we cannot wait!

We’re marking our calendars (find the schedule here) and going over our bracketology, with a little help from PUP author Tim Chartier.

To kick off the countdown, we bring you an article from the Post and Courier, who checked in with Dr. Chartier about how numbers can be the best strategy in bracketology.

College basketball fans seeking to cash in on March Madness need to turn on their calculators and turn off their allegiances.

That was the message Dr. Tim Chartier, a math professor at Davidson and published author, brought to cadets at The Citadel on Monday night.

“The biggest mistake people make in bracketology is they go with their heart no matter what the data says,” said Chartier, who has made studying the mathematics of the NCAA basketball tournament part of his students’ course work at Davidson. “They just can’t let a certain team win or they just have to see their team do well.

“It’s hard not to do that, because that is part of the fun.”

Chartier has made it easier for the average fan to use math in filling out their own brackets at the March Mathness website marchmathness.davidson.edu. The site will get a lot of traffic after the NCAA tournament field is announced on March 15.

 

Read the full article on the Post and Courier website.

Dr. Tim Chartier is a numbers guy, and not only during basketball season. He likes to show students how math can apply outside of the classroom. How can reposting on Twitter kill a movie’s opening weekend? How can you use mathematics to find your celebrity look-alike? What is Homer Simpson’s method for disproving Fermat’s Last Theorem? Dr. Chartier explores these and other questions in his book Math Bytes.

(Photo courtesy of Davidson College)

(Photo courtesy of Davidson College)

 

As Dr. Chartier and others gear up for basketball lovers’ favorite time of year, PUP reminds you to mark your calendars for these key dates.

Check back here soon for more hoop scoop!

• Selection Sunday, March 15, ESPN

• First and Second Rounds, March 20, 22 or March 21, 23

• Greensboro Regional, March 27, 29, Greensboro Coliseum (Greensboro, North Carolina)

• Oklahoma City Regional, March 27, 29, Chesapeake Energy Arena (Oklahoma City, Oklahoma)

• Albany Regional, March 28, 30, Times Union Center (Albany, New York)

• Spokane Regional, March 28, 30, Spokane Veterans Memorial Arena (Spokane, Washington)

• National Semifinals, April 5, Amalie Arena (Tampa Bay, Florida)

• Championship Game, April 7, Amalie Arena (Tampa Bay, Florida)

Calculus predicts more snow for Boston

Are we there yet? And by “there,” we mean spring and all the lovely weather that comes with it. This winter has been a tough one, and as the New York Times says, “this winter has gotten old.”

snow big[Photo Credit: John Talbot]

Our friends in Boston are feeling the winter blues after seven feet of precipitation over three weeks. But how much is still to come? You may not be the betting kind, but for those with shoveling duty, the probability of more winter weather may give you chills.

For this, we turn to mathematician Oscar Fernandez, professor at Wellesley College. Professor Fernandez uses calculus to predict the probability of Boston getting more snow, and the results may surprise you. In an article for the Huffington Post, he writes:

There are still 12 days left in February, and since we’ve already logged the snowiest month since record-keeping began in 1872 (45.5 inches of snow… so far), every Bostonian is thinking the same thing: how much more snow will we get?

We can answer that question with math, but we need to rephrase it just a bit. Here’s the version we’ll work with: what’s the probability that Boston will get at least s more inches of snow this month?

Check out the full article — including the prediction — over at the Huffington Post.

Math has some pretty cool applications, doesn’t it? Try this one: what is the most effective number of hours of sleep? Or — for those who need to work on the good night’s rest routine — how does hot coffee cool? These and other answers can be found through calculus, and Professor Fernandez shows us how in his book, Everyday Calculus: Discovering the Hidden Math All around Us.

This book was named one of American Association for the Advancement of Science’s “Books for General Audiences and Young Adults” in 2014. See Chapter One for yourself.

For more from Professor Fernandez, head over to his website, Surrounded by Math.

 

Photo Credit: https://www.flickr.com/photos/laserstars/.

Q&A with Michael Harris, author of Mathematics without Apologies

What do pure mathematicians do, and why do they do it? Looking beyond the conventional answers—for the sake of truth, beauty, and practical applications—Michael Harris offers an eclectic panorama of the lives and values and hopes and fears of mathematicians in the twenty-first century, assembling material from a startlingly diverse assortment of scholarly, journalistic, and pop culture sources.

Princeton University Press catches up with Michael Harris, author of Mathematics without Apologies, to talk about the culture of math and what writing has to do with the pace of innovation.

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PUP: What is the book about? 

MH: The preface claims the book is “about how hard it is to write a book about mathematics.” This becomes less self-referential and paradoxical if the sentence is completed: “… without introducing distortions that transform the book into one about certain conventional images of mathematics.” One thing I had to learn when I started trying to explain what it means to be a mathematician was that the point of an  activity like mathematics doesn’t speak for itself through the products of the activity. If you try to find a simple definition of mathematics you’ll see it’s not so easy. As a first approximation we might say that “mathematics is what mathematicians do, plus the stories that are told about that.” The book is then about mathematics in that sense, with an emphasis on the stories, and not only the conventional ones, nor only the stories told by mathematicians.

Why did you write this book?

MH: For a long time I have been hoping to see a book about mathematics, for the non-specialist public, that broke with stereotypes and clichés and a predictable stock of references, and instead reflected the values to which mathematicians refer when we talk to one another. At the same time, I hoped the book, while not being a historical study, would at least acknowledge that these values have a history, and would take seriously the idea that mathematics also belongs to cultural history, by exploring the roots of some of the notions and habits of thought that mathematicians take for granted, using the tools of cultural analysis—but without adopting the elevated tone that is too common in this kind of exercise.

I have written a few book reviews and articles with these hopes in mind, waiting for someone to take the hint. In recent years several mathematicians have made a valiant effort to challenge stereotypes by writing about mathematics as a living activity, and a few writers have examined mathematics through the lens of cultural criticism; but it’s still sadly the case that when mathematicians write the word “culture” the reader can nearly always expect a dose of uplift. Soon enough I realized I would have to write the book myself.

There’s a more selfish reason as well:  I thought it would be prudent to develop a second skill, to prepare for the dire moment when the pace of  new developments in my mathematical specialty began to outstrip my ability to keep up with them, and I would need to find a different way to keep my brain occupied. Writing was the only plausible option. Strangely enough, when I reached the end of the book I found I could still function reasonably well as a mathematician, even though the pace of innovation in my field has suddenly accelerated—but that’s another story.

The text refers to any number of controversies and polemics, historical or contemporary. But you don’t come down clearly in favor of a solid position on anything. Is this a “postmodern” book?

MH: I am certainly opinionated about a great many things, and it is my considered opinion that most of the sharpest controversies—like platonism vs. nominalism, or positions on what Wigner called “the unreasonable effectiveness of mathematics”—miss the features that make it really interesting to be a mathematician. To avoid distracting the reader with pointless polemics, I consciously chose to present those features with a minimum of ideological adornment, and to allude to controversies only obliquely. I’m told there’s a risk that some will find it disorienting to read a book about mathematics that doesn’t tell them what to think; but it’s a risk I’m willing to take.

What’s with all the endnotes?

MH: Two of the blurbs describe the author as “erudite,” which is a kind thing to write but is unfortunately far from the truth.  It’s amazing how easy the internet has made it to look well-read; it helps to think of asking questions different from the ones that are usually asked. The endnotes and the extensive bibliography are there, in the first place, to convince the reader, that mathematics really does deal intimately with an extraordinarily varied range of experience. I hope in particular that genuine scholars can use this material to expand their sense of what’s relevant in writing about mathematics.

In the second place, the notes are there to convince the reader that I didn’t make things up. But please don’t get the impression that I actually read more than a few pages of most of the references quoted.

The notes are also a convenient hiding place for the author’s true opinions. But what do they matter?

Describe your writing process. How long did it take you to finish your book? Where do you write?

MH: Each chapter started with a clear-cut theme, though some of them led me in unexpected directions. Chapter 8, for example, was supposed to be an exploration of why it’s so important for mathematics to appear to be serious, and specifically why so much is written about the supposed affinity between mathematics and classical music. The “trickster” theme was supposed to serve as an indirect way of introducing the question of mathematical seriousness. But mathematical “tricks” turned out to have such a rich and unfamiliar history that they tricked themselves into the chapter’s main theme.

Each chapter’s theme evolved as I collected relevant material. Some of the material organized itself into a plausible narrative outline. Then the actual writing began.   The individual paragraphs were easy enough to complete, but assembling them in a coherent order often enough presented an impossible mathematical problem: I need to talk about B before I can explain C, and B is incomprehensible until I talk about A; but it makes no sense to bring up A without having already mentioned C. Resolving this kind of problem is what took up most of the time between when I started writing in early 2011 and when I submitted a completed manuscript three years later. Usually it was only possible in a state of total isolation, which I could only maintain for a few days at most.

At the end I found myself discarding enough material for at least two books the same length. But there’s no reason to write them, because they would say the same thing!

Who do you see as the audience for this book?

MH: Anyone who is willing to take seriously the idea that mathematics deserves respect, not only because it can be used to provide efficient solutions to practical problems (though that is eminently worthy of respect), but also as a living community, a cultural form, an autonomous domain of experience.

Check out the introduction to Mathematics without Apologies here. The book was recently reviewed at Library Journal and Peter Woit’s Not Even Wrong.

Q&A with the authors of The Fascinating World of Graph Theory

The fascinating world of graph theory goes back several centuries and revolves around the study of graphs—mathematical structures showing relations between objects. With applications in biology, computer science, transportation science, and other areas, graph theory encompasses some of the most beautiful formulas in mathematics—and some of its most famous problems. For example, what is the shortest route for a traveling salesman seeking to visit a number of cities in one trip? What is the least number of colors needed to fill in any map so that neighboring regions are always colored differently?

Princeton University Press catches up with Arthur Benjamin, Gary Chartrand, and Ping Zhang, authors of The Fascinating World of Graph Theory, to discuss just what it is that makes graph theory so fascinating.

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PUP: What is graph theory?

AB, GC & PZ: Graph theory is the study of objects, some pairs of which are related in some manner. Since there are no restrictions on what the objects might be and no restrictions on how two objects might be related, applications of graph theory are only limited by one’s imagination.

PUP: Why is graph theory important?

AB, GC & PZ: There are problems and questions that occur in a wide variety of settings that can be visualized with the aid of graphs and which can often be understood more clearly. Understanding the theoretical nature of graph theory can, in many instances, lead us to solutions of these problems and answers to these questions.

PUP: Where do you see graph theory in action in the real world?

AB, GC & PZ: Because graph theory has been shown to be so useful with problems in transportation, communication, chemistry, computer science, decision-making, games and puzzles, among other things, there are few aspects of life where graphs do not enter in.

PUP: Who needs to understand graph theory? And why does understanding the theoretical underpinnings help us?

AB, GC & PZ: Whether it’s mathematics or some other scholarly endeavor, a key element to understanding is not only becoming aware of what others have accomplished but developing a knack of being curious and asking relevant questions. Because graph theory has applications in so many areas, it is an ideal area within mathematics to become familiar with.

PUP: Why did you write this book?

AB, GC & PZ: There have been numerous reports of American students doing poorly in mathematics in recent years. Furthermore, we believe that mathematics has acquired an under-served reputation of being boring and difficult. While gaining a good understanding of any subject requires effort, we know that many aspects of mathematics are interesting. Since we felt it was likely that many people are not familiar with graph theory, we decided to illustrate how interesting and useful mathematics can be by writing a book on graph theory with this goal in mind. While we wanted to include some real mathematics, showing how certain facts can be verified, we primarily wanted to show where mathematics comes from, discussing some of the people responsible for this, and how mathematics can assist us, often in many unexpected and fascinating ways.

Read the preface of The Fascinating World of Graph Theory here!

Andrew Hodges honored with Scripter Award

 

Andrew Hodges, author of ALAN TURING: THE ENIGMA

Andrew Hodges, author of Alan Turing: The Enigma

Congratulations to PUP author Andrew Hodges, who along with The Imitation Game screenwriter Graham Moore, has been awarded the USC Libraries Scripter Award. Hodges’s book, Alan Turing: The Enigma, was used as the basis for the screenplay of the Oscar-nominated film.

Calling bookworms and movie-goers alike — this award has something for all of you. Established in 1988, the USC Libraries Scripter Award is an honor that recognizes the best adaptation of word to film. The award is given to both the author and the screenwriter.

Alan Turing: The Enigma — a New York Times–bestselling biography of the founder of computer science — is the definitive account of an extraordinary mind and life. Capturing both the inner and outer drama of Turing’s life, Andrew Hodges tells how Turing’s revolutionary idea of 1936 — the concept of a universal machine — laid the foundation for the modern computer and how Turing brought the idea to practical realization in 1945 with his electronic design.

The book also tells how this work was directly related to Turing’s leading role in breaking the German Enigma ciphers during World War II, a scientific triumph that was critical to Allied victory in the Atlantic. Turing’s work on this is depicted in The Imitation Game, which stars Benedict Cumberbatch and Keira Knightley.

Benedict Cumberbatch plays Alan Turing in THE IMITATION GAME © 2014 THE WEINSTEIN COMPANY

Benedict Cumberbatch plays Alan Turing in THE IMITATION GAME © 2014 The Weinstein Company

At the same time, Alan Turing: The Enigma is the tragic account of a man who, despite his wartime service, was eventually arrested, stripped of his security clearance, and forced to undergo a humiliating treatment program — all for trying to live honestly in a society that defined homosexuality as a crime. Alan Turing: The Enigma is a gripping story of mathematics, computers, cryptography, and homosexual persecution.

Check out Chapter 1 of Alan Turing: The Enigma for yourself here.

The other four finalists for the Scripter award included:

  • Gillian Flynn, author and screenwriter of Gone Girl
  • Novelist Thomas Pynchon and screenwriter Paul Thomas Anderson for Inherent Vice
  • Jane Hawking, author of Travelling to Infinity: My Life With Stephen, and screenwriter Anthony McCarten for The Theory of Everything
  • Screenwriter Nick Hornby for Wild, adapted from Cheryl Strayed’s memoir Wild: From Lost to Found on the Pacific Crest Trail

 

“A Brief History” of Stephen Hawking’s work

As we near February, and Oscars month (our calendars are marked for Feb. 22!), PUP takes a look at The Theory of Everything. The best-picture nominee, which stars Eddie Redmayne and Felicity Jones, depicts the love story and life story of Stephen Hawking and Jane Wilde. The beginning of the film is set in Cambridge, where Hawking is a brilliant graduate student. For movie-goers looking for a deeper look at Hawking’s scholarly work, PUP brings you a “Brief History” of books by Stephen Hawking.

Liam Daniel / Focus Features Eddie Redmayne stars as Stephen Hawking in THE THEORY OF EVERYTHING.

Liam Daniel / Focus Features
Eddie Redmayne stars as Stephen Hawking in THE THEORY OF EVERYTHING.

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A Brief History of Time

“A landmark volume in science writing by one of the great minds of our time, Stephen Hawking’s book explores such profound questions as: How did the universe begin—and what made its start possible? Does time always flow forward? Is the universe unending—or are there boundaries? Are there other dimensions in space? What will happen when it all ends?

Told in language we all can understand, A Brief History of Time plunges into the exotic realms of black holes and quarks, of antimatter and “arrows of time,” of the big bang and a bigger God—where the possibilities are wondrous and unexpected. With exciting images and profound imagination, Stephen Hawking brings us closer to the ultimate secrets at the very heart of creation.”

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On the Shoulders of Giants

“In On the Shoulders of Giants, Stephen Hawking brings together the greatest works by Copernicus, Galileo, Kepler, Newton and Einstein, showing how their pioneering discoveries changed the way we see the world.

From Copernicus’ revolutionary claim that the earth orbits the sun and Kepler’s development of the laws of planetary motion to Einstein’s interweaving of time and space, each scientist built on the theories of their predecessors to answer the questions that had long mystified humanity.

Hawking also provides fascinating glimpses into their lives and times – Galileo’s trial in the Papal inquisition, Newton’s bitter feuds with rivals and Einstein absent-mindedly jotting notes that would lead to his Theory of Relativity while pushing his baby son’s pram. Depicting the great challenges these men faced and the lasting contributions they made, Hawking explains how their works transformed the course of science – and gave us a better understanding of the universe and our place in it.”

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The Nature of Space and Time

Princeton University Press

By Stephen Hawking and Roger Penrose

“Einstein said that the most incomprehensible thing about the universe is that it is comprehensible. But was he right? Can the quantum theory of fields and Einstein’s general theory of relativity, the two most accurate and successful theories in all of physics, be united in a single quantum theory of gravity? Can quantum and cosmos ever be combined? On this issue, two of the world’s most famous physicists–Stephen Hawking (A Brief History of Time) and Roger Penrose (The Emperor’s New Mind and Shadows of the Mind)–disagree. Here they explain their positions in a work based on six lectures with a final debate, all originally presented at the Isaac Newton Institute for Mathematical Sciences at the University of Cambridge.

How could quantum gravity, a theory that could explain the earlier moments of the big bang and the physics of the enigmatic objects known as black holes, be constructed? Why does our patch of the universe look just as Einstein predicted, with no hint of quantum effects in sight? What strange quantum processes can cause black holes to evaporate, and what happens to all the information that they swallow? Why does time go forward, not backward? In this book, the two opponents touch on all these questions.”

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The Universe in a Nutshell

“In this new book Hawking takes us to the cutting edge of theoretical physics, where truth is often stranger than fiction, to explain in laymen’s terms the principles that control our universe.

Like many in the community of theoretical physicists, Professor Hawking is seeking to uncover the grail of science — the elusive Theory of Everything that lies at the heart of the cosmos. In his accessible and often playful style, he guides us on his search to uncover the secrets of the universe — from supergravity to supersymmetry, from quantum theory to M-theory, from holography to duality.

He takes us to the wild frontiers of science, where superstring theory and p-branes may hold the final clue to the puzzle. And he lets us behind the scenes of one of his most exciting intellectual adventures as he seeks ‘to combine Einstein’s General Theory of Relativity and Richard Feynman’s idea of multiple histories into one complete unified theory that will describe everything that happens in the universe.'”

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The Grand Design

“When and how did the universe begin? Why are we here? What is the nature of reality? Is the apparent ‘grand design’ of our universe evidence for a benevolent creator who set things in motion? Or does science offer another explanation? In The Grand Design, the most recent scientific thinking about the mysteries of the universe is presented in language marked by both brilliance and simplicity.

The Grand Design explains the latest thoughts about model-dependent realism (the idea that there is no one version of reality), and about the multiverse concept of reality in which there are many universes. There are new ideas about the top-down theory of cosmology (the idea that there is no one history of the universe, but that every possible history exists). It concludes with a riveting assessment of m-theory, and discusses whether it is the unified theory Einstein spent a lifetime searching for.”

See more books by Stephen Hawking here. Which of these have you read, and which are on your “to-read” list?

Princeton University Press’s best-selling books for the last week

These are the best-selling books for the past week.

Alan Turing: The Enigma, The Book That Inspired the Film The Imitation Game by Andrew Hodges
The Original Folk and Fairy Tales of the Brothers Grimm edited by Jack Zipes
Irrational Exuberance: Revised and Expanded Third edition by Robert J. Shiller
Mastering ’Metrics: The Path from Cause to Effect by Joshua D. Angrist & Jörn-Steffen Pischke
1177 BC: The Year Civilization Collapsed by Eric H. Cline
Mostly Harmless Econometrics: An Empiricist’s Companion by Joshua D. Angrist & Jörn-Steffen Pischke
On Bullshit by Harry Frankfurt
How to Solve It: A New Aspect of Mathematical Method by G. Polya
Privilege: The Making of an Adolescent Elite at St. Paul’s School by Shamus Rahman Khan
The Age of the Crisis of Man: Thought and Fiction in America, 1933–1973 by Mark Greif