AKPotW: Showing that the group generated by an element of G is a subgroup of G [Algebra]

Check out this AKPotW.

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Solution below.

Math Organizations from JMM 2018

JMM 2018 was a fun math filled event and a great way to start the year. After meeting so many new people and seeing so many different math related organization, we thought we'd share some of our favorites. Here is a list of some of cool math organizations we learned about.

AWM - Association for Women in Mathematics
AWM works to help encourage interest in mathematics among women, as well as advocates for equality among genders in the mathematics. Formed in 1971, the society has held lectures series honoring notable female mathematicians and have given out medals such as the Alice T. Schafer for undergraduate women who have shown themselves to be exceptional mathematicians. They have notable members too, such as their current president Ami Radunskaya, who is a professor of mathematics at Pomona College.

CoCalc - Collaborative Calculation in the Cloud
CoCalc is part of the Sage Project, an expansive tool created by the mathematics professor William Stein. CoCalc is a powerful environment made to carry out mathematical calculations, and can also be used to help organize courses. Over 200 courses have used CoCalc; it has proven itself to be invaluable to classroom learning.

Project Gutenburg - Free eBooks
Project Gutenburg makes easily accessible old eBooks from notable authors, many of which have expired copyrights. On Project Gutenburg you can find works by Max Planck, Albert Einstein, Felix Klein, and many more. Project Gutenburg has books from a wide range of topics, which they digitize and proofread with the help of many volunteers.

Edfinity - Affordable Resource for Problems
It is well known that solving problems is key to progressing in mathematics, and Edfinity is working to make textbook problems more accessible to students. Edfinity provides problems and solutions from textbooks or other sources for students to solve to help further their education, and helps educators by making grading more automated. It is a convenient place for students to hone their problem solving abilities.

Welcome to the Center: New Introduction videos on Facebook and YouTube

If you are familiar with the center of math, you probably know us by one or two avenues: you read our blog, which produces problems of the week and talks about math related news; or you have used one of our textbooks, and watched the videos that came along with it. Behind our mission, to bring accessible math materials into the world, is a community of mathematicians of all sorts. We would like to invite you to explore the Center of Math, and take some time to make that community grow. With new Facebook and YouTube introduction videos, finding your way around our little corner of the worldwide web has never been easier. The videos outline some features of the Worldwide Center of Mathematics' Facebook and Youtube pages, that you may want to know about. 

Our Facebook page primarily serves as a place for our community to gather, and a hub to navigate around the Center of Math with ease. Visit the Facebook page and join the collective! Once on the page, you can click the learn more button to go to our main site, or use the menu on the left to explore more. Don't forget to like us on FB to stay in the loop.

The YouTube video helps serve as a starting point to our overwhelming library of math videos. Check it out yourself, and don't hesitate to dive right into our content! If you need some more direction, our 'playlists' tab is a great place to start, or just use the spotlight search to find a specific topic. Drop a subscribe if you like what you see, to never miss another math video.

These features are explained in greater detail in the welcome videos, so give them a watch, and we'll see you soon!

-Worldwide Center of Math.

WCoM Donates Statistics Textbooks

The Worldwide Center of Mathematics recently had some winter weather make its way into a stock room and slightly damage a number of Introduction to Statistics: Think & Do (Stevens).

The damaged books will not be sold and instead will be donated.

The recipient(s) include: Siem Reap at Life and Hope Association and Phnom Penh at People Improvement Organization. Both organizations are in Cambodia.

Water-damaged books prepared for donation.

The Career Mathematician, Vol. 1 — Dr. Walter Sun

So you love mathematics. What next? The Career Mathematician highlights interesting and relevant work and insights offered by professional mathematicians, statisticians, logicians and more.

The Career Mathematician, Vol. 1 -- Dr. Walter Sun

Ever wonder how predictive technology works? Click here to learn how the Principal Applied Science Manager and Bing Predicts Team Lead, Dr. Walter Sun, leverages technology and some careful calculations to improve Microsoft's "Bing Predicts" feature.

Not sure this is the career for you? Click the image below for some inspiration.

Using Math to Create Something Beautiful

                   Think back to when you were first introduced to functions, thin lines depicting a single value output for each input in a domain.

A Function

For many people, the idea of what a function ‘looks’ like does not change much from this bland depiction of data. However, data can be crafted into something that carries much more information than just inputs and outputs, and in the right hands an enormous and messy set of data can be presented in a powerful way. Indeed, data representation is an important part of any scientific field.

            Compacting more data into inputs and outputs provides not only more information, but also a more stunning visualization of data. In a vector field, a single point can contain information about location, strength and direction of a force.  The more information a function tracks, the more stunning the display becomes, with 4 or even 5 dimensions represented on a graph of three-dimensional space and color.

Vectors depicting the strength and direction
of a magnetic field at discrete points.

A 3D graph, with a 4th color dimension

 Vector fields can even represent information that cannot be easily compiled into a simple function, which allows for out-of-the-ordinary occurrences in nature to be studied more carefully.

With developments in technologies that offer efficient data manipulation, the possibilities of what we can do with functions and data are more far-reaching than ever. Anne M. Burns of Long Island University Uses computers to create beautiful representations of functions.

Burns plots complex valued functions as a vector field, seen here.

The advantages of this technique transcend aesthetic purpose, and can be used to find roots of functions at a glance.

Attributing more dimensions to an occurrence is useful and can be beautiful, but what if the object or function in question is impossible to make sense of as it is? It is often handy to project or unfold an N-dimensional surface onto an (N-1)-dimensional surface. Most of the time, in calculus, a three-dimensional surface will be looked at as a two-dimensional projection on the xy, yz, or xz plane in order to set up an integral to find the volume of the object. In theoretical physics, this technique of reducing the dimension of mysterious happenings is used to speculate the nature of the universe. A common example, and perhaps the most accessible way to think of this process is the unfolding of a four-dimensional cube, the tesseract.

The nets of a 3D cube and a 4D hypercube above.

Dali's Corpus Hypercubus (1954)

This way of thinking about higher dimensions caught more than just the eyes of mathematicians and scientists. Salvador Dali, the great surrealist painter, was fascinated by the advances in science during the twentieth-century. In the 1950’s Dali was fascinated by nuclear physics and quantum mechanics, and found inspiration for many paintings in mathematics.

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At its core, mathematics does not only seek knowledge, but also pursues beauty in the natural world.

Works Cited

• The Function graphic was found on the page of Maret School's BC calculus page, and is spliced with Charlie Brown of Peanuts, created by Charles M. Schulz.
• The Magnetic field graphic was found on Vassar College's Wordpress blog, under a lecture by Prof. Magnes.
• 4D graph curtesy of user Blue7 on math.stackexchange. 
• Find all of Anne M. Burn's Work here.
• The Cube net image was found here. 

Any unwanted images in this article will be removed at the request of the owner.

Meet the New Co-ops!

The Center of Math would like to introduce two new students from Northeastern University, Kelsey (left) and Ben (right)! They will be with the center until December 23rd, working on giving you blog posts, Problems of the Week, YouTube content, Advanced Knowledge Problems of the Week, and much more.

Kelsey has just completed her second year of studying Physics with a minor in Mathematics. In addition to a love of learning how the universe works, she enjoys playing music, digital art, and board games. Florence + the Machine is her favorite band, and How to Train Your Dragon is her favorite movie. Before coming here, she worked as a research assistant at Northeastern University's nanophysics lab. If you ever need a recommendation for an interesting, informative book about physics, she has many!

Ben has also just completed his second year studying both Physics and Mathematics. He enjoys rock climbing, traveling, and playing with his nephew. Ben is also an Eagle scout and enjoys camping and the outdoors. In addition to this, he fascinated by space and rocketry and hopes to one day enter the space industry.

The two of them are very excited to create quality content on topics viewers, like you, want to see! Let us know what you would like covered and they'd be happy to make blog posts or videos about it.

Everyday Math: Architecture

Throughout this series, we have discovered mathematics posing as a character on your favorite television show, hiding in your favorite pieces of art, and starring in your favorite big-screen productions. We have even uncovered math in the baseball diamond, at the casino table, and on the soccer pitch.. but we aren't done yet. This Everyday Math blog post goes even further to examine the mathematics behind the very building you are sitting in, and the people who designed it.

That's right– let's take a look at the math behind architecture!

According to the dictionary, architecture is the art or practice of designing or constructing buildings. While this is common knowledge, the close correlation between mathematics and architecture might go unrecognized. The connections between the two disciplines are almost innumerable, especially when you realize that both, in a way, are the study of patterns and systems. Throughout history, some of the greatest architectural feats have been based in the realm of mathematics. This post will further explore some of these buildings, as well as the connection between math and architecture.


The first instance in history that demonstrates a mathematical association to architecture involves, not surprisingly, Pythagoras. Known for being the mind behind the Pythagorean theorem, numbers held a special significance to the Greek mathematician. This significance was mainly geometrical, as Pythagoras spoke of square, oblong, and triangular numbers. He also placed an importance on the aesthetic qualities of numbers and proportions. After Pythagoras's death, his followers– the Pythagoreans– carried on his ideas and utilized them in 447 BC when rebuilding the Parthenon. The ratio 3 : 4 : 5 was used throughout the building of the Parthenon, and later was notated as one of the Pythagorean Triples. Further, the ratio between the height and width (4 : 9), is the same as the ratio between the width and length (4:9). This may not seem significant but Berger, a mathematician, examined that the ratio 4:9 is used in the creation of the columns, as well as the inner area of the temple. Many argue that this consistent ratio accounts for the aesthetic beauty of the temple.

Let's turn the history book ahead a few hundred years. Time– 27 BC. Place– Ancient Rome. In case you dosed off during a few months of History class, there are many consistencies between the societies of Ancient Greece and Ancient Rome. Like Ancient Greece, Rome focused on education, the arts, and beauty. This sets the stage for more architectural accomplishments, and with that more mathematical connections. In fact, in his series of books titled De Architectura, Virtruvius outlines the practical applications of mathematics that are necessary for building design.  The Classical age again mirrored the former great civilizations in Greece and Rome, creating buildings that relied again on the importance of proportions, ratios, and perspective. The Classical age brings us Brunellischi, Alberti, and Leonardo da Vinci– all fascinated with mathematics. 

London City Hall– Created by Foster + Partners
Note the helical staircase inside

After that nice history lesson, you may be wondering.. Why should I care? Throughout history, math was needed to properly structure buildings. As we mentioned, the two areas of study were completely intertwined. Today, technological advancements (like calculators!) help architects with some of the work load. However, in many architectural projects, these technological advancements are still set in place through mathematics. 

One of today's most famous architecture studio is Foster + Partners. The company is famous for constructing enormous structure that dwarf their surrounding buildings. With the added size, comes more of a need for math. The buildings need to be made secure, aesthetically pleasing, comply with building regulations, and maximize a budget. A series of equations and programs help to ensure all of these categories are fulfilled. The Special Modeling Group's (SMG) was created to maximize the efforts of architects. SMG's often build larger shapes from smaller shapes. Makes sense, right? In order to do this, they create equations for various sections of a building. Examples of this are pictured below. 

Has this post convinced you of the connections between mathematics and architecture? 

In case it hasn't, here are some testimonials from architects further explaining their personal opinions.

(Testimonials gathered from http://www.lifeofanarchitect.com/architecture-and-math/)  



Jes Stafford
"Architects should be math ninjas. The aspiring architect should rush headlong into math as if charging into a field of battle. Math is an education in problem solving and of knowing what is asked. There are few stronger parallels to all the the variables in the Builder-Architect-Client dynamic. All math puns intended."

Andrew Hankins
"Math is important to my daily tasks as an Architect. It mostly involves simple calculations, but for me, it is necessary to be able to do them quickly in my head.  And they are mostly simple equations, but it definitely helps if you can do them in your head and on the fly."

Evan Troxel
"That said, it is better if you are decent at math. Here are some examples people usually don’t think of as math, but are things architects use all the time: We are constantly adding and subtracting measurements, thicknesses, volumes and areas. We are responsible for budgets. We work with spreadsheets that tally sizes of spaces and everything has to all add up. We do TONS of geometry, and we love it. Geometry is math, right? Yes it is. Drawing + Math = Awesome. That’s one reason we’re architects and not artists."


Sources: http://www-groups.dcs.st-and.ac.uk/history/HistTopics/Architecture.html
https://plus.maths.org/content/perfect-buildings-maths-modern-architecture
http://www.lifeofanarchitect.com/architecture-and-math/

April: Math Awareness Month

Each year, in an effort to increase understanding and appreciation for mathematics, the Joint Policy Board for Mathematics (JPBM) sponsors April as Math Awareness Month. The JPBM is comprised of various mathematical associations, including the AMA, ASA, MAA, and the Society for Industrial and Applied Mathematics. In a collaborative effort, the JPBM has denoted each Math Appreciation Month with a certain theme each year. Last year, the theme was Math Drives Careers. This year, April is centered on "The Future of Prediction". With this title, comes a focus on how mathematics and statistics can be used to predict innovations and patterns for the future.

History

Math Awareness Week began in 1986, and was set into play by President Ronald Reagan. He aimed to increase the appreciation and public understanding of mathematics by the public. In a speech, Reagan proclaimed, 

                     

"Despite the increasing importance of mathematics to the progress of our  economy and society, enrollment in mathematics programs has been declining at all levels of the American educational system. Yet the application of mathematics is indispensable in such diverse fields as medicine, computer sciences, space exploration, the skilled trades, business, defense, and government. To help encourage the study and utilization of mathematics, it is appropriate that all Americans be reminded of the importance of this basic branch of science to our daily lives."

In 1986, Math Awareness Month was celebrated on a national basis, with national exhibits and advertising. However, today colleges, institutions, regions, and states have all taken the responsibility of directing focus to mathematics. Mathematics Awareness Week has also been transformed into Mathematics Awareness Month.

Essays and Posters

The connections between mathematics and predictions can be explored throughout various mediums and topics. The predictive nature of math can be utilized to examine various disciplines– from economics to the environment. Through the month, the JPBM will publish essays and posters that help illuminate the theme of the month. 

So far, a few essays and visualizations have been made available on www.mathaware.org, a website dedicated to Math Appreciation Month.

Predicting U.S Industrial Production with Oil and Natural Gas Prices

Matthew L. Higgins

http://www.mathaware.org/mam/2016/essay/MAM2016_theme_Essay1.pdf 

To Your Health!

Joe Kincaid

http://www.mathaware.org/mam/2016/essay/MAM_Essay2.pdf

Great expectations: The past, present and future of prediction from ancient oracles to statistical models. 

Coming Soon in April 2016 Significance Magazine

Click here for a closer look at The Future of Prediction poster

Activities

This list will be updated with events throughout the month. 

Spark 101: Spark 101 is a program that allows for students to walk in the shoes of STEM professionals. Through video case studies, students will use problem solving capabilities to face challenges that will lead to future innovation. Resources are free to faculty members and align with curriculum to teach students about working in STEM. 

Social Media

Twitter: @mathaware
This twitter account is active every April, posting information that coincides with the theme of each particular Math Awareness Month. The Math Aware twitter shares activities planned throughout the country and essays that have been submitted. Follow the page to stay updated on the latest Math Awareness Month updates!

 Facebook: Mathematics Awareness Month

The JPBM also maintains a Facebook page that works to inform the public about Math Awareness Month events and happenings. The Facebook page also publishes images and posters that go along with the theme of the month. Check it out!

sources: http://www.mathaware.org/mam/2016/
http://www.mathaware.org/mam/2015/about/

Women in STEM

Women in STEM: Bridging the Gap

     With Women's History Month winding to a close, will the conversation about STEM education for females also dwindle to a mere whisper? We have already written about the accomplished women in the STEM fields, but what about the young mathematicians and scientists that are trying to break into the male-dominated area of study? While the disparity between males and females in STEM is easy to spot, the root of the problem is not as obvious. For years, researchers have made efforts to determine what exactly causes females to shy away from careers in math and science. Pinpointing specific problems would allow for an effective solution to take shape. This post is aiming to inform people about the obstacles that stand in the way for women in STEM, as well the work that has been done to bridge the gender gap.

So, what's the problem? And why does it matter?

     In the general workforce, females are only slightly outnumbered by men. Men encompass 52% of the workforce, while females make up the other 48%. However, in the fields of science, technology, engineering, and mathematics (STEM), woman make up only 24% of the workforce. This statistic shows that as most industries are closing the gender gap, the STEM field is making much less progress. This is significant to women, because in the STEM field the wage gap between men and women is actually much smaller. In STEM, the wage gap is only 14%, whereas is all other fields the gap is 21%. In addition to this, STEM careers have higher salaries in general, averaging over $10 more an hour. There is also a greater chance for career advancements. More importantly, in an era of global competition and technology, shouldn't we be utilizing all possible talent in the important fields of math and science? The gender gap in STEM shows that a significant supply of intelligent and capable female workers are not being used efficiently. 

Disparity in Higher Education

     New studies show that females are actually more likely to earn a college degree than males are. However, this trend does not translate into the fields of math and science. In fact, the opposite seems to be true, as a smaller share of STEM degrees are going to females. Between 2004 and 2014, the percent of STEM degrees earned by women decreased in each discipline area. On average, only 35% of STEM degrees are earned by females, and 65% are earned by males. The fields with the greatest discrepancy between men and women are computer science and engineering. Each only confer about 18% of degrees to females. Interestingly enough, the gap grows throughout college. In other words, there is a lower retention rate for females in STEM. This is particularly true in the fields dominated by men, such as engineering. Out of 100 female students, only 12 will graduate with a stem degree.

Perception and Stereotypes 

     Picture it. A stereotypically "nerdy" male with a female friend that struggles with basic math–a twist on the classic, "Beauty and the Geek". How many shows follow this plot line?  I can think of a few off the top of my head. Even in the modern era, our culture is pervaded with the idea that young boys should play with legos, while girls should play with Barbies. It may seem trivial, but even simple toy or show choices can impact the decisions young children make, and set into motion their likes and dislikes. According to the Organization for Economic Co-operation and Development, at age 9 the gender gap in science and math starts to widen. About 2/3 of girls under the age of 12 claim to like science, yet by the time they reach high school, opt out of advanced level math and science courses. What causes them to diverge from their original interests? Around age 12, girls start to lose confidence in their mathematical abilities. In a survey, a 15 year-old females were more likely to"get nervous when doing a math problem", or "worry that they will get low marks" than their male counterparts. This does not necessarily reflect their grades, but instead shows the mindset that young girls assume when it comes to learning in the STEM fields.
     Unfortunately, some teachers fail to reassure these students. In a NBER study, a researcher found that when grading math, teachers who knew the gender of the test taker were more likely to show a bias favoring male students. When they were unaware of gender, the exams were scored more evenly. This information seems to show that students and teachers alike are likely to adhere to the gender stereotypes set forth in the past. In fact, students in entry level college biology classes were asked to guess which students in their class had the highest grade. The answers showed that male students overwhelmingly selected other males, while females selected males and females equally. Could this be a reason why more females don't continue taking STEM classes after beginner courses?

What's being done to help?

     Many researchers agree that part of the issue plaguing females in STEM is the lack of mentors. If there aren't a plethora of women in STEM, there is less encouragement for young girls to work in that field. Therefore, in the next generation, there are still less women in STEM, and the cycle continues. In order to put an end to the cyclic imbalance of the STEM fields, organizations like Million Women Mentors are forming. Million Women Mentors encourages both men and women to sign up as mentors, and then match these mentors with young women. They strive to not only get students interested in STEM, but to further the initial interest through encouragement, job-shadowing, internships, and sponsorships. Larger corporations, such as the Huffington Post, also have initiatives in place to encourage and support women in STEM. President Obama and the White House have also dedicated time and resources to the improvement in STEM. A new 15 million dollar is being proposed that would grant money to mentoring programs, as well as new curriculum for k-12 STEM education.
     Getting to the root of the problem, however, involves a change in mindset from educators, students, and STEM professionals alike. In an article by Tech Crunch, Erin Sawyer explains the importance of incorporating STEm education at an early age and continuing to foster a connection to math and science. This involves showing young girls practical uses of STEM. For an example, Kids' Vision is an after-school program that brings girls into Silicon Valley and exposes them to the tech industry. Likewise, Technovation is placing leadership in young girls' hands, holding competitions to build confidence and familiarity with the STEM field. These programs can help initiate an interest in STEM, and broaden the career opportunities that young women see.

So what can you do?

Becoming aware of the issue is one of the first steps towards finding a solution. Changing your own mindset about females in STEM is a way to ensure you are doing your part. Whether it's signing up to become a mentor, staying up to date on new programs, or simply encouraging your child to follow their interests, any step is good if it's in the right direction.

sources:
http://www.verizon.com/about/responsibility/girls-in-stem 

http://www.seattletimes.com/education-lab/new-bill-would-encourage-support-women-and-minorities-in-stem-fields/
http://www.goodcall.com/news/study-shows-male-students-underestimate-their-female-peers-in-early-stem-courses-05106
http://techcrunch.com/2016/01/05/why-stems-future-rests-in-the-hands-of-12-year-old-girls/

http://www.esa.doc.gov/sites/default/files/womeninstemagaptoinnovation8311.pdf

Everyday Math: Math in the Movies

Coming soon to theaters near you: Mathematics

You may not run to the nearest theater to watch a mathematician prove a theorem, but math may be starring in your favorite movie without your recognition. This installation of Everyday Math features big screen hits that would not be possible without mathematics. Usually a math story line is intertwined with a romance, mystery, or comedy, which can make it easier to miss. Don't worry! We're here to point out our favorite films that carry a heavy dose of real math information. Grab your popcorn and make your next movie night a math-themed experience!

The Classic: A Beautiful Mind

A Beautiful Mind is based loosely on the real life story of John Nash, a Nobel Prize winner. Russell Crowe plays John Nash, a mathematical genius that specialized in game theory, differential geometry, and differential equations. Game theory can be utilized in fields such as economics and political science. In fact, Nash won his Nobel Prize in economics. In a famous scene, the film dramatizes Nash's discovery of the Nash equilibrium, a term used in economics and game theory. The film is said to take artistic interpretation of Nash's real life, but the mathematics in the movie are based on real theorems and theories. The director of A Beautiful Mind enlisted the help of a mathematics consultant, Dave Bayer of Columbia University, to ensure the mathematics were correct throughout the film. The movie contains some math jokes and facts that may only be clear to those well versed in mathematics. For an example, at the end of the film, a student wants to show Nash a proof exploring the idea that "finite Galois extensions are the same as covering spaces", which is actually a true statement. Along with his prowess in mathematics, A Beautiful Mind also demonstrates Nash's story of mental illness and schizophrenia. His schizophrenia initially impacts his career, but he is able to recover and take his place as one of the leading mathematical and economic minds of his time.

Watch the dramatized discovery of Nash's Equilibrium here!

The Romantic Drama: Proof

Proof, starring Gwenyth Paltrow and Anthony Hopkins, ties in universal themes with the backdrop of mathematics. The movie tells the story of 2 mathematicians, father and daughter, fighting mental illness and attempting to prove various mathematical theorems. Before he dies, Robert (the father) makes note of the interesting characteristics of the number 1729. The daughter eventually takes the place of her ailing father and dedicates herself to mathematics, even though she lacks formal training. Critics explain that the film realistically expresses the field of mathematics. It shows the nuances of proving a theorem, as well as the work and studying that are involved. Paltrow's character, Catherine, describes how she feels when she is attempting to solve a difficult problem, comparing "elegant proofs" to music. Proof also makes reference to other real mathematicians that may or may not be known to the public, such as Sophie Germain and Carl Friedrich Gauss. The director of the film consulted heavily with Timothy Gowers, a Fields medalist from Cambridge University.

For the Sport's Enthusiast: Moneyball

Watch a mental math scene here

Moneyball is the perfect flick for sports enthusiasts and statisticians alike. Starring Brad Pitt, Moneyball takes a twist on the average sports film, incorporating mathematics into the strategy of baseball. The movie is adapted from a book of the same name, written by Michael Lewis. The plot is based on the 2002 Oakland A's and General Manager Billy Beane. Billy Beane took a different route when gathering players, in order to deal with the economic impositions placed on the team. He searched for undervalued players, and looked specifically at statistical analysis in order to determine who was worth the cost. Other 'risky' plays like stealing bases and bunting were thrown out the window under Beane's guidance. The heavy dose of mathematics in the movie is centered on the Pythagorean Expectation, which is used to calculate wins based on runs scored and allowed. The sabermetric approach to baseball is placed head to head against more traditional methods, and definitely makes for an entertaining film.

Pythagorean Expectation

The Teen Rom-Com: Mean Girls

This may be an outlier of the group, as the movie is geared towards teenage girls and features all the facets of your typical high-school movie. Mean Girls star Lindsey Lohan plays a homeschooled girl who tries her luck at navigating high school for the first time. She comes across some new friends, and they attempt to steer her in the right direction. Cady Herring, Lohan's character, has an aptitude for math and even joins the math club. Her math teacher, played by Tina Fey, is featured several times in the movie explaining various high-school math concepts. Late in the movie, Cady attends a mathlete competition and is faced with a limits problem. There are also scenes where she is being tutored in calculus, and the math errors showed are typical errors a high school student would make. This movie is perhaps the epitome of teen-movies circa 2004 but the mathematics represented, although correct, definitely correspond with the high school setting.

Click here to watch the scene!

The Story of An Underdog: Good Will Hunting

Known as a classic math movie, Good Will Hunting is a must-see. This underdog tale has a romantic twist and stars both Matt Damon and Robin Williams. Matt Damon's character, Will Hunting is a troubled young adult who's life path weaved in and out of foster homes and trouble with the law. While working as a janitor at MIT, he is able to solve two math problems that were created for graduate students. A professor at MIT took interest in Will, noticing his affinity towards mathematics and genius-level ability. Along his journey, Will faces his inner struggles with the help of a therapist (Robin Williams), and meets a romantic interest who helps to shape his life. The math problem that Will faces on the board is actually a real problem, although not as difficult as it is made out to be. The problem involves a feature of graph theory, homeomorphically irreducible trees. Pictured below is the problem that sent Will into the realm of academia. Interestingly enough, the math brains behind the movie actually appeared on screen as well. Patrick O'Donnell, who had a minor roll in the bar scene, actually ran the math department at University of Toronto at the time. O'Donnell and John Mighton, who plays the professor's assistant, chose the equations and theorems used in the movie. 

See the solution here!