Many ways to approach the Riemann Hypothesis have been proposed during the past 150 years, but none of them have led to conquering the most famous open problem in mathematics. A new paper in the Proceedings of the National Academy of Sciences (PNAS) suggests that one of these old approaches is more practical than previously realized.
The Riemann Hypothesis is one of seven Millennium Prize Problems, identified by the Clay Mathematics Institute as the most important open problems in mathematics. Each problem carries a $1 million bounty for its solvers.
Starting Fall 2019, Math 313 (Elementary Linear Algebra) courses will be discontinued. The curriculum will be split between Math 213, a 2 credit course which focuses on the theory of linear algebra, and Math 215, a 1 credit lab course which focuses on its computational applications. Note that concurrent or previous enrollment in Math 213, Math 313, or Math 302 is a requirement for taking Math 215.
For mathematics majors:
Math majors who have not completed Math 313 before Fall 2019 will instead be required to take Math 213 and Math 215.
For other majors that also formerly required Math 313:
In most cases, Math 313 will be replaced with Math 213 and Math 215, but please contact the academic advisor for your major to confirm whether you are required to take Math 213, Math 215, or both.
Problems to Be Solved: Applied Math in South America
By Lilian Whitney
In Spring of 2018, students took their study of math equations from the orderly classrooms of BYU campus to a much larger classroom: South America.
Dr. Michael Dorff, chair of BYU’s Department of Mathematics, led the three-week study abroad tour through four South American countries: Brazil, Chile, Peru, and Argentina. The trip allowed sixteen STEM students to study math in a real-world, culturally diverse setting. Students toured various companies including Itaú Bank, Walmart, General Motors, and Laureate.
In addition to learning about applied math, students rafted below the thundering waters of Iguazu Falls, explored the vibrant streets of Rio de Janeiro, and hiked the lush mountains to Machu Picchu. Though the stunning sites of South America were memorable, what students remember most is seeing applied math combat poverty, strengthen businesses, and change lives.
Making a Difference
Seeing the growth students experience in new cultures inspired Dorff to lead the first applied math study abroad in Europe in 2017. Dorff decided to lead the 2018 program in South America, allowing students to connect with alumni who live and work there. Dorff believes enabling students to see math applied in unfamiliar cultures increases their capacity to work and serve others both at home and internationally. Each visit was made possible through connecting with BYU alumni, a unique aspect of the program which reflects the diverse opportunities available to BYU graduates.
“The goal is for students to see how math and data analytics are used in different companies that you probably wouldn’t expect,” Dr. Dorff said. “When people think of tech stuff they probably think of companies like Google and Microsoft, but they might not think of Walmart or General Motors. For students to see that these types of companies use data to improve their services and production is really important. When students graduate and are looking for a job, they don’t have to restrict themselves to the standard tech companies. I also want them to see opportunities outside of the United States. It’s part of BYU’s famous catchphrase: Enter to Learn, Go Forth to Serve.”
Visiting the Walmart headquarter in São Paulo, Brazil helped many students realize how much of a difference math can make for families in poor economic circumstances. Paulo, a BYU alum who is a native Brazilian, taught the students about Walmart’s innovative automated-inventory services. Walmart employees use data to create automated inventory services, which ensure the correct number of goods are stocked in stores. Increasing production efficiency enables Walmart to sell goods at lower prices. This allows many Brazilians and individuals around the world to afford to feed their families.
After teaching students about automation services, Paulo divided the students into two groups and gave each group 120 reais, the equivalent of around $32 USD. Each group then had to use that money to buy groceries to feed a Brazilian family of four for one week—a difficult task to accomplish.
“Trying to work out how we could get enough food to feed four people for a week with just 120 reais was really hard and really humbling,” student Tyler Mansfield said of the experience.
The student teams picked out food basics like rice, beans, and fruit. The food students picked was then donated to Brazilian families in need. Learning how applied math individuals afford to feed their families was a priceless experience for many students.
“On the study abroad we would walk through the streets and see these people in need that had so little, which was really difficult. But then we got to go into Walmart and saw how employees use their math abilities to make it possible for others families to afford food. [Applied math] helps people put food on their tables at the end of the day because it allows businesses to increase productivity which helps stabilize the economy on a large scale, which is a really powerful concept,” Mansfield said.
While many STEM students look forward to lucrative careers in STEM, Dorff believes it’s individuals who combine math savvy with a sense of gratitude for the circumstances of their lives who will find the most fulfillment in their careers.
“When you visit places and see people who are less fortunate than yourselves it makes you appreciate what you do have, but also makes you think of ways to help others who are less fortunate than you are,” said Dorff. “There are many big problems that people with STEM backgrounds will be able to solve. You can use math and data to solve pollution problems, to solve hunger problems. You can make energy use more effective and more efficient.”
Problems to be solved
Visiting foreign countries allows students to see just how vast and exciting the opportunities are to apply math in their future careers.
“When I tell people that I’m studying math, they’re like, ‘what will you do with that?’” said student Tyler Mansfield. “What I’ve realized is that so many people have real-world problems that they need math to help them solve. Together, professionals and mathematicians can solve problems in the economy and business that they never would have alone.”
Students also visited the Instituto de Matemática Puras e Aplicadas in Rio de Janeiro, where math and culture intersected as BYU and Brazilian students spent time together.
“We got to sit down with the students there and talk about their lives and how they experience Brazil and their schooling,” said student Gentry Carter. “Learning math changes how everyone views the world, but there is an intersection between culture and math that we shouldn’t ignore. Talking to them about their culture and how they learn math was so cool. They are learning the exact same things we are, but in a different language and applied in different ways.”
At GM, students saw how cars are automated and manufactured. They also met with corporate employees to learn how data analytics help improve production and safety of GM vehicles. Data analytics allow employees to identify production errors in the early stages and to perform cost-performance analysis. Data from consumers also helps employees create future car designs that meet customer needs.
“There are a lot of jobs right now analyzing data,” said Dorff. “If you can get people with different skills in mathematics, computer science, and statistics to work together, their backgrounds will complement each other to help create a better solution to a problem. This is a great opportunity for students to see the interdisciplinary aspects of math. Not everyone that we visited was a math alum—they were engineering, they were computer science, they were finance. Math majors are interacting and solving problems with people of other backgrounds.”
Culture and people
From ancient Inca sites to boisterous soccer stadiums, students enjoyed the food, business tours, and hikes the trip included. According to Dorff, it was by forming relationships with people of different backgrounds that students’ global perspectives changed the most.
“I travel a lot, and people ask me: What’s the best thing you see or the best thing you do when you travel? And it’s meeting the people,” Dorff said. “Whether its Uber drivers or people at restaurants or buses, that’s what’s most important. It’s not about how much money we earn or our belongings, it’s about the people we can learn from and we can help. That happens when you interact with people—you don’t get that in a classroom.”
Friendships spanning cultures flourished throughout the trip, from Uber drivers who shared stories of struggles and diverse circumstances with students to LDS members who reached out to Dr. Dorff about careers in math.
For student McKenna Pitts, experiencing the beauty of new countries granted a new perspective on God’s love for his children and our unique roles in using our talents—whether they be math, music, or science—for good.
“I remember one of the coolest moments for me was at the Christ the Redeemer statue in Rio de Janeiro,” Pitts said. “The statue is ginormous, and you’re at the Savior’s feet and you just feel so, so small, so insignificant when you look out and see all of Rio and all of the ocean. But we know how much Heavenly Father and Jesus Christ really love us. Even though in the grand scheme of things we are absolutely nothing, we mean the world to them. It’s just another testament that God built this earth for us. We are in this huge world and there’s so much you can do because you can make so many important changes, even when you feel small and insignificant.”
Pitts and her fellow students brought home countless memories and photos of hikes, colorful streets, passionate soccer games, and luscious jungles. But what they remember most is the knowledge that wherever they may go in the world, their ability to solve problems can change the lives of others for the better.
As student Tyler Mansfield puts it, “There are so many problems out there that I can help be the solution to.”
Abstract: Height and L-series are two of most important tools in number theory and arithmetic geometry. They were originally invented by Andre Weil in his Ph.D. thesis on Mordell—Weil theorem and his work on Weil conjecture. In this lecture, I will first review original work of Weil, and then survey recent developments.
Date: Tuesday, April 3 Time: 4:00 pm Room: 135 TMCB
Abstract: Many of us are familiar with how to slice a cake ensuring equal sized slices for all. But what about those of us who want an equal amount of frosting as well?! This question is a classic with the problem solvers amongst us. In 1975, Martin Gardner considered a square cake cut into 7 pieces in his Scientific American column. More than a decade earlier, H.S.M. Coxeter posed the problem for a square cake sliced into 9 pieces as an exercise in his book, Introduction to Geometry. Together, we will solve this problem for a square cake cut into 5 pieces, and investigate the other cake shapes for which the same procedure will produce slices with equal cake and frosting.
Bio: Alissa S. Crans has been recognized nationally for her enthusiastic ability to share and communicate mathematics, having been honored by the MAA with the Hasse Prize and Alder Award. Her research lies in the field of higher-dimensional algebra and is currently supported by a Simons Foundation Collaboration Grant. Alissa is known for her active mentoring of women and underrepresented students, as well as of junior faculty as a member of the MAA Project NExT leadership team. When not enticing students with the beauty of mathematics at Loyola Marymount University or sharing her enthusiasm for math in settings ranging from “Nerd Night Los Angeles” to public school classrooms, you can find her rehearsing with the Santa Monica College Wind Ensemble or on her quest to find the spiciest salsa in LA.
Join the Math Department for a special screening of the imitation game March 23rd 6:00PM in 1170 TMCB
In 1939, newly created British intelligence agency MI6 recruits Cambridge mathematics alumnus Alan Turing (Benedict Cumberbatch) to crack Nazi codes, including Enigma — which cryptanalysts had thought unbreakable. Turing’s team, including Joan Clarke (Keira Knightley), analyze Enigma messages while he builds a machine to decipher them. Turing and team finally succeed and become heroes, but in 1952, the quiet genius encounters disgrace when authorities reveal he is gay and send him to prison.
There is a poster from the “Women in Math” club circulating around the internet. The poster displayed the pictures of four faculty members in our department. It was done by a club member with good intentions. It was not meant to demean women or be satirical. We value women in mathematics and their contributions, and work to promote opportunities for women to succeed in mathematics.
The math department chair posted a statement on Facebook with more details about this issue.
Robert Luke Jr. works as a senior e-commerce support specialist at WESCO distribution and loves that he gets to use the problem-solving skills he learned as a math major at BYU to find resolutions to challenging issues at work on a daily basis.
“Sure, I am not doing epsilon-delta proofs every day, but that kind of thinking is what helps me resolve issues all the time,” Robert said.
Robert graduated from BYU in 2013 with a bachelors in Mathematics with an emphasis in cryptography and is now enrolled in the MBA program at Duquesne University. He was recently given the Byrne Award for responsible leadership. He has big plans for the future and once he finishes graduate school he hopes to continue working for WESCO at a higher level and get involved with the video game industry.
Robert’s hobbies include snowboarding, soccer, and playing video games. In fact, he loves games like Final Fantasy and Elder Scrolls so much he once took a part-time job at GameStop just for fun.
Robert currently resides in Pittsburg Pennsylvania with his growing family.