March Mathness Winner

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

 


 

Gribble

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.

 

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.

chartierMathematician 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.

SnipesAs 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!

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.

Maddie Parrish - DCFH

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!

Snipes

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?

John_Hussey[1]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!

 

vickie_kearn[1]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.

The Madness begins!

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

To learn more about March Mathness this year and to glean tips from years’ past, please visit the March Mathness site.

 
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.

A Better Way to Score the Olympics

This excerpt from Towing Icebergs, Falling Dominoes, and Other Adventures in Applied Mathematics
Robert B. Banks
brings up  some questions to consider when thinking about how to score the Olympics. Read the complete chapter in our new Princeton Puzzlers edition of this book, available in February 2013.

 

Chapter 8

“In response to the sports reporter’s question, the coach replied, “Well, we don’t know for sure, of course, but based on the results of our statistical analysis, there is a 90% probability that the team will set a new Olympics record, perhaps even a new world record.” The sport reporter replied, “well, good luck, coach.”

Key words: for sure, of course, statistical analysis, about, probability, perhaps, luck.

____________________________________________________________________________________

The subjects of probability and statistics are extremely important areas of the broad field of mathematics. In this chapter, and those that follow, we shall look at several topics which show how statistics and probability are used to analyze many kinds of phenomena and events. A complete list of the practical applications of statistics and probability would be endless: everything from the probability that it will rain tomorrow to your likelihood of winning at Las Vegas and from the annual cost of your life insurance to your chances of being kicked in the head by a horse or struck by lightning or attacked by killer bees.

From an almost infinitely long list of applications, we shall consider only a few. We start with an analysis of the medal scores of the 1992 Summer Olympic Games held in Barcelona. In subsequent chapters, we go on to fantastically interesting things like dropping a needle on a table to compute the numerical value of π, determining the probability that two people, within a certain size group of people, have the same birthday, calculating the minimum cost of having all your teeth extracted, counting the number of rice grains on a chessboard, and seeing how well a great many chimpanzees do behind a great many typewriters. But, for now, Jet’s go to the Olympics!

We Need a Better Scorekeeper for the Olympics

In recent years we have observed that the Olympic Games have become increasingly nationalized, politicized, and commercialized. In addition, we have noted that preparation for and participation in the Games has become almost a whole new science. Wind tunnel studies are conducted to attempt to reduce the drag coefficients of bicycle riders and ski jumpers; mathematical models are devised to improve the biomechanics of high jumpers and pole vaulters; high-speed photography is employed to analyze the movements of gymnasts and relay racers; computer analyses are carried out to optimize the performance of kayak rowers and long-distance runners; and so on.

It seems as if everything relating to the Olympic Games is improving except for one thing: the system of final scoring of the participants. After all the incredibly hard work by the athletes and coaches and the countless hours of television viewing by billions of people around the world, all we get at the end is simply a dull column of numbers that tabulates how many medals each country has been awarded. A great many people believe that this denouement-this final outcome-is entirely inadequate.

We also read and hear a lot about the need for “level playing fields” in all kinds of arenas, especially economic and political. In no arena is this need greater than in the matter of determining the final scores of the Olympics. To illustrate this need, the following points and questions are raised:

1. The annual gross domestic products per capita (GDP/cap) of China, Nigeria, and Ghana are nearly identical (about $350). We can say that the three countries are equally “poor”. However, China has a population of 1,180 million, Nigeria 100 million, and Ghana 17 million. Thus, China has 70 times more people than Ghana from wh1ch to draw its athletes.

2. By the same token, the GDP/cap of the United States, Canada, and Norway are about the same ($20,000). So they are equally “rich.” But the population of the U.S. is 260 million, Canada 28 million, and Norway about 4 million. We note that the U.S. has a pool of athletes 65 times larger than Norway’s.

3. Indonesia has a population of 195 million and GOP /cap of $700. Cuba has a population of 11 million and GDP/cap of $1,400. Qatar has a population of 0.50 million and GDP/cap of $17.000. Which country would be expected to receive the most Olympic medals: that country which is the poorest but most populous, that country which is the richest but least populous, or a country in between?

 

Tim Chartier on how to use math to win gold at the Olympics

Tim Chartier, co-author of Numerical Methods: Design, Analysis, and Computer Implementation of Algorithms with Anne Greenbaum, explains how to take home the gold using math.

A free-surface simulation of the forces experienced when diving, provided by Speedo® in their press release for the Fastskin Racing System®
http://anss.client.shareholder.com/releasedetail.cfm?ReleaseID=681886

Math can help win gold in London!  From air passing over an athlete’s body, whether that person be running or biking, to water streaming along a swimsuit or the hull of a boat, many events benefit from numerical analysis and its role, in particular, in computer simulation. For example, aerodynamic research can improve a swimmer’s suit and shave off time that would otherwise be taken with added friction.  Such numerics can also inform a biker on a more efficient body position.

Such work involves computing numerical solutions of partial differential equations.  Two important stages occur in such work.  First, one must develop and utilize appropriate mathematical models.  If the model is too simple, its solution will not accurately reflect the real-world phenomenon.  In such a case, the swimmer could end up with a suit that isn’t minimizing friction with the water.  The second stage is solving the numerical solution to the model, which is performed on a computer with finite precision. As such, numerical methods that can efficiently and accurately solve the mathematical model are needed.

From sports science to the laboratory, modeling and numerics often complement each other, giving modern science a power, not possible without such digital resources.  As such, learning the strengths and limitations of numerical methods, often coming through mathematical analysis, enables one to appropriately utilize such tools and leverage them to explore today’s difficult and important problems.

So, as you watch the Olympics, keep in mind that the body mechanics and equipment we see were often informed by mathematics.  Such tools play an important role in training and the innovations that contribute to the feats we will witness in the coming weeks.

Math and the Olympics

After 69 days of traveling, the Flame crossed the River Thames on Friday to reach its final destination at London’s Olympic Stadium. There are many reasons to be excited about the Olympics, but here at Princeton University Press, we can’t help but think about the abundance of equations and mathematical modeling taking place during the summer games. From the design of the Olympic logo and the sports equipment, to the actual athletics, math is taking place everywhere during the Olympics. For example, watch for the swimmers who win a race by .001 of a second!

We’re not the only ones excited about it either. Cambridge University’s math education initiative, The Millennium Mathematics Project has been running the Math and Sport: Countdown to the Games for the last 18 months. Check out their website for fun activities that celebrate both math and the Olympics: http://sport.maths.org/content/.

As the games continue, we’ll be hearing from PUP authors, excerpting from our books and staying up-to-date with the math and science of the Olympics. Stay tuned.

How Mathematical Models Make Sense of Big Data

Tim Chartier, co-author with Anne Greenbaum of Numerical Methods: Design, Analysis, and Computer Implementation of Algorithms, explains how to make sense of big data with numerical analysis.

 

You submit a query to Google or watch football bowl games as we enter a new year. In either case, you benefit from mathematical methods that can garner meaningful information from large amounts of data. Such techniques fall in the field of data mining.

Massive datasets are available with every passing minute in our world. For example, during the Oscars in February, the Cirque du Soleil performance resulted in 18,718 tweets in one minute according to TweetReachBlog. While tweets cannot exceed 140 characters in length, their average length is 81.9 characters according to MediaFuturist. So, in one minute, approximately 1.5 million characters zoomed through Twitter. From Wikipedia, we’ll take the average length of a word (in English) to be 5.1 characters. Assuming these Oscar tweets are written in English and conform to the standard length of words, 300,000 words were tweeted in one minute. This is approximately the number of words contained in the entire Hunger Games Trilogy!

Mathematical models and numerical analysis play important roles in data mining. For example, a foundational part of Google’s search engine algorithm is a method called PageRank. In Anne Greenbaum and my book, Numerical Methods: Design, Analysis, and Computer Implementation of Algorithms, published by Princeton University Press, we discuss the PageRank method– both its underlying mathematical model and how it is computed on a computer.

In an exercise in the text, you can develop a system of linear equations in a manner similar to that used by the Bowl Championship Series to rank college football teams (editor – or college basketball teams for March Madness). An important part of this problem is developing the linear system. Our text also discusses the computation challenges of such problems and what numerical methods result in the most accurate results.

Many techniques utilized to solve the large linear systems of data mining are also utilized in engineering and science. The book discusses how large linear systems (containing millions of rows) can derive from problems involving partial differential equations. Again, the book analyzes the efficiency and accuracy of the methods utilized to solve such systems. Such techniques led to the computed animated figures we enjoy in modern movies and aid in simulating the aerodynamics of a car created with computer-aided design.

As stated at the opening of Chapter 1 of the text, “Numerical methods play an important role in modern science. Scientific exploration is often conducted on computers rather than laboratory equipment. While it is rarely meant to completely replace work in the scientific laboratory, computer simulation often complements this work.” As such modern science demands the use and understanding of numerical methods.

 

 

 

Guesstimation #3

We have another Guesstimation special for you. As a reminder, we are posting these problems in support of Math Awareness Month which this year is celebrating Mathematics, Statistics, and the Data Deluge. One way anyone can deal with huge amounts of data is estimating — a skill that is examined and taught in much greater detail in Lawrence Weinstein and John Adam’s book, Guesstimation: Solving the World’s Problems on the Back of a Cocktail Napkin.

Question #3

On average, how many people are airborne over the US at any given moment?

Hint: Don’t choose 3:00 AM, choose sometime during the day.


If you like this, try your hand at the other Guesstimation problems: