A Florida State College college member is being acknowledged for his analysis to enhance arithmetic schooling for elementary and secondary faculty college students.
The Florida Council of Academics of Arithmetic (FCTM) named Robert Schoen, an affiliate professor on the Studying Techniques Institute (LSI), the Kenneth P. Kidd Arithmetic Educator of the Yr. The award was established in 1976 to acknowledge excellent contributions to arithmetic schooling.
“It is a well-deserved award,” stated LSI Director Rabieh Razzouk. “Dr. Schoen has made main contributions to elementary math and secondary statistics schooling in Florida. His work on Cognitive Guided Instruction and different tasks have straight impacted 1000’s of academics and their college students. We’re happy with his achievements and grateful to FCTM for contemplating and presenting him with this award.”
Schoen is affiliate director of LSI’s Florida Heart for Analysis in STEM (FCR–STEM) and an affiliate professor in Arithmetic Schooling at Florida State. His analysis expertise contains the event of instructional and psychological measurements, in-depth research of pupil mathematical considering, mathematical schooling of academics, and rigorous analysis of the effectiveness of instructional interventions.
“I’ve an excellent respect for FCTM, and I really feel deeply honored to obtain this award,” Schoen stated. “My group and I work so exhausting to assist enhance instructing and studying whereas growing the scientific rigor of schooling analysis. It feels nice to be acknowledged by arithmetic academics for the affect that we’re having on their work.”
The award was introduced at FCTM’s 69th Annual Convention in St. Petersburg, Florida, attended by a whole lot of math schooling professionals. Schoen is the primary Tallahassee-based educator to win the award since 1994 and simply the third ever from Tallahassee to be so honored.
LSI at Florida State College is on the forefront of growing modern options that bridge idea and apply in schooling. For over 50 years, LSI has delivered methods that measurably enhance the educational and efficiency of organizations and people in Florida and globally. Our specialists’ superior analysis offers state-of-the-art strategies and a transparent path for implementation.
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Research led by a Wayne State University Department of Mathematics professor is aiding researchers in Wayne State’s Department of Psychiatry and Behavioral Neurosciences in analyzing fMRI data. fMRI is the preeminent class of signals collected from the brain in vivo and is irreplaceable in the study of brain dysfunction in many medical fields, including psychiatry, neurology and pediatrics.
Andrew Salch, Ph.D., associate professor of mathematics in Wayne State’s College of Liberal Arts and Sciences, is leading the multidisciplinary team that is investigating how concepts of topological data analysis, a subfield of mathematics, can be applied to recovering “hidden” structure in fMRI data.
“We hypothesized that aspects of the fMRI signal are not easily discoverable using many of the standard tools used for fMRI data analysis, which strategically reduce the number of dimensions in the data to be considered. Consequently, these aspects might be uncovered using concepts from the mathematical field of topological data analysis, also called TDA, which is intended for use on high-dimensional data sets,” said Salch. “The high dimensionality that characterizes fMRI data includes the three dimensions of space — that is, where in the brain the signal is being acquired — time — or how the signal varies as brain states change in time — and signal intensity — or how the strength of the fMRI signal changes in response to the task. When related to task-induced changes, the results reflect biologically meaningful aspects of brain function and dysfunction. This is a unique collaborative work focused on the complexities of both TDA and fMRI respectively, show how TDA can be applied to real fMRI data collected, and provide open access computational software we have developed for implementing the analyses.”
The research article, “From mathematics to medicine: A practical primer on topological data analysis and the development of related analytic tools for the functional discovery of latent structure in fMRI data,” appears in the Aug. 12 issue of PLOS ONE.
In it, the team used TDA to discover data structures in the anterior cingulate cortex, a critical control region in the brain. These structures — called non-contractible loops in TDA — appeared in specific conditions of the experiment, and were not identified using conventional techniques for fMRI analyses.
“We expect this work to become a citation classic,” said Vaibhav Diwadkar, Ph.D., professor of psychiatry and behavioral neurosciences and research collaborator. “Instead of merely applying TDA to fMRI, we provide a lucid argument for why medical researchers who use fMRI should consider using TDA, and why topologists should turn their attention to the study of complex fMRI data. Moreover, this important work provides readers with empirical demonstrations of such applications, and we provide potential users with the tools we used so they can in turn apply it to their own data.”
“Our ongoing research utilizing TDA with fMRI will provide a unique and complementary method for assessing brain function, and will give medical researchers greater flexibility in tackling complex properties in their data,” said Salch. “In particular, our work will help fMRI researchers become aware of the significant power of TDA that is designed to address complexity in data, and will enhance the value of using fMRI in neuroscience and medicine.”
In addition to Salch and Diwadkar, co-authors on the paper include Adam Regalski, Wayne State mathematics graduate student; Hassan Abdallah, Wayne State mathematics department alumni and current graduate student at the University of Michigan; and Michael Catanzaro, assistant professor of mathematics at Iowa State University and Wayne State mathematics department alumni.
This work is supported by the National Institutes of Health (MH111177 and MH059299), the Jack Dorsey Endowment, the Cohen Neuroscience Endowment, and the Lycaki-Young Funds from the State of Michigan.
On a cold December night in 1976, a group of mathematicians assembled in a room in Trinity College Dublin for the inaugural meeting of the Irish Mathematical Society (IMS). Most European countries already had such societies, several going back hundreds of years, and it was felt that the establishment of an Irish society to promote the subject, foster research and support teaching of mathematics was timely.
The society has been going strong for the past 45 years. It has organised numerous meetings and conferences and has coordinated activities in a wide range of mathematical fields. The current president is Dr Tom Carroll, who is based in UCC, and there are local representatives at all the centres of higher education. IMS has a keen interest in mathematical education at all levels and a new subcommittee, the Irish Committee for Mathematics Education, has recently been established.
The Society has reciprocity agreements with the Irish Mathematics Teachers Association and with several societies abroad, including the American Mathematical Society, the Deutsche Mathematiker Vereinigung and the London Mathematical Society. IMS is also a member of the European Mathematical Society and is affiliated with the International Mathematical Union (IMU).
Recently, the Royal Irish Academy decided it would no longer fund Ireland’s participation in the IMU. The IMS Committee, feeling that continuing Irish participation in IMU is essential, took over from the Academy the role of Adhering Organisation to the union.
Annual meeting begins today
Each year, IMS organises a scientific meeting, at which mathematicians from all over the country can present new research and discuss mathematical matters. It is a great opportunity to network with colleagues, learn about recent advances and establish new lines of collaboration.
This very day, the 34th Annual IMS “September Meeting” begins, jointly hosted by University College Cork and the newly-formed Munster Technical University. Activities today take place in the Berkeley Library of MTU. Tomorrow, the action moves to the Western Gateway Building of UCC.
The meeting will consist of invited talks and poster presentations on a wide variety of topics of interest to the mathematical community in Ireland. The event will have a hybrid format, with on-site speakers, and delegates able to attend talks virtually if they wish. Students and early career researchers will have a chance to display posters about their research, and a prize will be awarded for the best student poster.
The meeting programme lists 13 speakers. Arcane phrases in the titles indicate some of the specialities: holomorphy in Jordan structures, quantum computation, affine invariant measures and 4-manifold topology. Clearly, this is not a meeting intended for “the interested layperson” but is at an advanced level.
IMS is primarily concerned with professional mathematicians, but there is an opening for an organisation serving the needs of everyone interested in mathematics, focusing on recreational maths and with an emphasis on the beauty, utility and pure delight of the subject. Associations like this are found in many other countries. Perhaps an energetic and enthusiastic reader will seize this opportunity to establish the Irish mathematical association.
A UCD zoom course, on recreational mathematics, AweSums: Marvels and Mysteries of Mathematics, will be presented this Autumn by yours truly. Registration is now open at www.ucd.ie/lifelonglearning
Peter Lynch is emeritus professor at UCD School of Mathematics & Statistics. He blogs at thatsmaths.com
Swiss researchers have spent 108 days calculating pi to a new record accuracy of 62.8tn digits.
Using a computer, their approximation beat the previous world record of 50tn decimal places, and was calculated 3.5 times as quickly. It’s an impressive and time-consuming feat that prompts the question: why?
Pi is, of course, a mathematical constant defined as the ratio between a circle’s circumference and its diameter. The circumference of a circle, we learn at school, is 2πr, where r is the circle’s radius.
It is a transcendental, irrational number: one with an infinite number of decimal places, and one that can’t be expressed as a fraction of two whole numbers.
From ancient Babylonian times, humans have been trying to approximate the constant that begins 3.14159, with varying degrees of success.
The amateur mathematician William Shanks, for example, calculated pi by hand to 707 figures in 1873 and died believing so, but decades later it was discovered he’d made a mistake at the 528th decimal place.
In 1897, the Indiana Pi Bill in the US almost did away with fussy strings of decimals altogether. The bill, whose purpose claimed to be a method to square a circle – a mathematical impossibility – almost enshrined in law that π = 3.2.
What is it good for? Absolutely everything
Jan de Gier, a professor of mathematics and statistics at the University of Melbourne, says being able to approximate pi with some precision is important because the mathematical constant has many different practical applications.
“Knowing pi to some approximation is incredibly important because it appears everywhere, from the general relativity of Einstein to corrections in your GPS to all sorts of engineering problems involving electronics,” de Gier says.
In maths, pi pops up everywhere. “You can’t escape it,” says David Harvey, an associate professor at the University of New South Wales.
For example, the solution to the Basel problem – the sum of the reciprocals of square numbers (1/12 + 1/22 + 1/32 and so on) – is π2/6. The constant appears in Euler’s identity, eiπ + 1 = 0, which has been described as “the single most beautiful equation in history” (and has also featured in a Simpsons episode).
Pi is also crucial to something in mathematics called Fourier transforms, says Harvey. “When you’re playing an MP3 file or watching Blu-ray media, it’s using Fourier transforms all the time to compress the data.”
Fourier analysis is also used in medical imaging technology, and to break down the components of sunlight into spectral lines, de Gier says.
But, says Harvey, there’s a big difference between calculating pi to 10 decimal places and approximating it to 62.8tn digits.
“I can’t imagine any real-life physical application where you would need any more than 15 decimal places,” he says.
Mathematicians have estimated that an approximation of pi to 39 digits is sufficient for most cosmological calculations – accurate enough to calculate the circumference of the observable universe to within the diameter of a single hydrogen atom.
62.8tn digit accuracy – what’s the point?
Given that even calculating pi to 1,000 digits is practical overkill, why bother going to 62.8tn decimal places?
De Gier compares the feat to the athletes at the Olympic Games. “World records: they’re not useful by themselves, but they set a benchmark and they teach us about what we can achieve and they motivate others.
“This is a benchmarking exercise for computational hardware and software,” he says.
Harvey agrees: “It’s a computational challenge – it is a really seriously difficult thing to do and it involves lots of mathematics and these days computer science.
“There’s plenty of other interesting constants in mathematics: if you’re into chaos theory there’s Feigenbaum constants, if you’re into analytic number theory there’s Euler’s gamma constant.
“There’s lots of other numbers you could try to calculate: e, the natural logarithm base, you could calculate the square root of 2. Why do you do pi? You do pi because everyone else has been doing pi,” he says. “That’s the particular mountain everyone’s decided to climb.”
When Noelle Sawyer, a Bahamian mathematician at Southwestern University, came to the U.S. for college, she was taken aback. During the first two years of her undergraduate program, Sawyer, whose research focuses on dynamics and geometry, kept wondering, “Why is no one treating me like I’m good at learning things?”
Marissa Kawehi Loving is a National Science Foundation postdoctoral researcher and a visiting assistant mathematics professor at the Georgia Institute of Technology and co-founder of the Web site Indigenous Mathematicians. When Loving, whose research focuses on low-dimensional topology and geometric group theory, was in graduate school, she says, she “felt like I literally couldn’t win.” If she accomplished something, she adds, either no one acknowledged it or they would say that “I only got that really, really good thing because of my identity and not because of my talent.” Even though Sawyer is now an assistant professor, she says that she still encounters other mathematicians who treat her as if she does not belong. “I hate going to conferences because someone says something hurtful or harmful to me almost every time,” says Sawyer, who, along with Loving and others, co-organized the first Black in Math week on Twitter last year.
Juliette Bruce is an NSF postdoctoral fellow in mathematics at the University of California, Berkley, who works in the field of algebraic geometry. She organized the 2020 Trans Math Day for transgender and nonbinary mathematicians, which she and a co-organizer brought back as a two-day event this year. She is also a board member of Spectra, an association for LGBTQ+ mathematicians. Bruce was harassed at a large mathematics conference. When she was giving a poster presentation, someone “stared at the poster a little long, stood a little bit close and then stared at me for a long time” before making “a very crass comment” on her appearance, she says.
Racism, sexism and other forms of systematic oppression are not unique to mathematics, and they certainly are not new, yet many in the field still deny their existence. “One of the biggest challenges is how hard it can be to start a conversation” about the problem, Sawyer says, “because mathematicians are so convinced that math is the purest of all of the sciences.” Yet statistics on the mathematics profession are difficult to ignore. In 2019 a New York Times profile of Edray Herber Goins, a Black mathematics professor at Pomona College, reported that “fewer than 1 percent of doctorates in math are awarded to African-Americans.” A 2020 NSF survey revealed that out of a total of 2,012 doctorates awarded in mathematics and statistics in the U.S. in 2019, only 585 (29.1 percent) were awarded to women. That percentage is slightly lower than in 2010, when 29.4 percent of doctorates in those areas (467 out of 1,590) were awarded to women. (Because these numbers are grouped based on sex rather than gender, that survey did not report how many of those individuals identify as a gender other than male or female.)
Recently many mathematicians have been pushing to discuss these issues more and force the field to confront the racism, sexism and other harmful bias it sometimes harbors. In response to those who say that such discussions distract collective focus from mathematics research and direct it to social issues, Goins says, “If you think talking about racism is distracting, imagine experiencing it…. Not all of us can just ignore what’s happening to us directly.”
A Human Endeavor
Recently Goins, whose research focuses on number theory and algebraic geometry, has been part of a team working to update the Web site Mathematicians of the African Diaspora, also known as the MAD Pages. It includes a searchable database of more than 700 profiles of researchers in mathematics and related fields. The original version of the Web site was created in 1997 by Scott Williams, then a professor of mathematics at the University at Buffalo, State University of New York, who is now retired. “Mathematics is a human endeavor,” Goins says. “When we prove theorems, when we teach classes, we aren’t an automaton that’s in front of the room, writing abstract symbols on a chalkboard. We really are people that have stories.”
Goins likes to bring attention to the stories of 20th-century mathematicians William Schieffelin Claytor and Vivienne Malone-Mayes, who are both included in the MAD Pages. Claytor was the third Black American to receive a Ph.D. in mathematics and the first Black American to publish mathematics research that was not a thesis. “Here’s someone who started with a very promising career, but because of the forces that be, he gave up,” Goins says. After earning his doctorate from the University of Pennsylvania in 1933, Claytor took a position at West Virginia State College. He applied for one at the Institute for Advanced Study in Princeton, N.J. But others did not want someone “Negro” on the faculty, as Goins puts it. “Even in the town of Princeton, he was not allowed to go to the movie theaters, to even buy clothes,” he says.
When Claytor went on to the University of Michigan for a second postdoctoral position, “because of racist practices, he was not allowed to teach,” Goins says. Furthermore, he notes that at this time “there was a towering figure in topology”—Robert Lee Moore of the University of Texas at Austin—“who was well-known for saying he did not want Blacks in the field, he did not want Jews in the field, he did not want women in the field. And there’s a general feeling that Moore really tried hard to make sure that Claytor did not get his papers published—that behind the scenes, he didn’t really let students of his let Claytor give talks at conferences.”
Malone-Mayes encountered racism and sexism from Moore, but she persevered in the field. When she decided to pursue her doctorate, she wanted to apply to Baylor University, but the school did not allow Black Americans to attend at the time, Goins says. She instead enrolled at the University of Texas at Austin. She had a different adviser, but it was there that she encountered Moore. Last year U.T. Austin announced a decision to remove Moore’s name from one of its buildings, the Dallas Morning News reported. (For more on other instances of problematic naming in mathematics, Sawyer recommends a list posted on the American Mathematical Society’s Graduate Student Blog in July 2020.)
At times, Malone-Mayes “had to sit in a chair in the hallway because she was not allowed to be in the classroom while Moore was teaching,” Goins says. But despite segregation and isolation, Malone-Mayes earned her doctorate in 1966, becoming the fifth Black American woman to do so in mathematics. “And, in an ironic twist of fate, she became the first Black professor at Baylor University,” Goins says.
Too often, the stories of trailblazing mathematicians from marginalized backgrounds have been buried. Alan Turing, the World War II code breaker who has been called “the father of modern computer science,” is often “the one LGBTQ mathematician that most people know,” Bruce notes. “Short of that, I think the list of well-known LGBTQ+ mathematicians becomes pretty, pretty dry.” Looking for additional historical examples “gets into delicate ground of, you know, not everyone wants to be out. And speculating on someone from the past’s gender identity or sexuality can be a minefield,” she adds.
Yet examples of pioneering forerunners are important. Loving, who earned her doctorate in mathematics in 2019, is the first Native Hawaiian woman to do so. When she was in graduate school and faced negative comments and stereotypes, she remembers thinking, “Who is there ahead of me? It’s not the same to be fighting a battle when you sort of can see that you could win it versus when you’re like, ‘Maybe it’s hopeless.’”
Sawyer says that she is “very aware” that she could “just leave academia and leave this all behind.” Ultimately, though, she does not want “math to be a safe corner of science for very bad people,” she says. Every few months, Loving hears about students of color who are leaving math Ph.D. programs. “It’s always these stories of just harassment, abuse and neglect,” she says. Both Sawyer and Loving have clung to opportunities to cultivate math communities that give them support and a sense of belonging. Still, Loving says, “I can’t tell you how many times I’ve had talented students of color, [and] when I talked to their white faculty mentors or when I read the letters from those people, it’s like they can’t see the talent in them. They can’t see themselves in them…. It all comes back to this failure of imagination to think of who could be successful. Who can be a mathematician? Who deserves to be here?”
Goins thinks that it would help if math departments changed their hiring practices to focus more on factors such as whether a prospective faculty member “wants to help build community” and if they “will be good at teaching or perhaps good at encouraging women and minorities as undergraduates to continue in this profession.”
He is lead program director of the African Diaspora Joint Mathematics Workshop (ADJOINT), a year-long program at the Mathematical Sciences Research Institute (MSRI) in which Black faculty form resource communities. The groups meet at MSRI in Berkeley, Calif., for two weeks at the launch of the program and continue meeting throughout the coming academic year, “so they can continue to do research, to foster that community among each other,” Goins says. The research topics vary each year. For 2021, they included “Adventures in Constructive Galois Theory,” “Steinberg Modules of Braid Groups,” “Racial/Ethnic Disparities in Health” and “Using Decision Modeling to Personalize Policy in Complex Human-Centered Problems.”
“I want to ensure minorities are feeling welcomed, that they do have communities that they feel they’re a part of,” Goins says. As the world begins to think about a post-COVID future, new possibilities open up. Mathematics departments, for instance, will have to consider whether to return to “normal” or to deconstruct and rebuild some of the old ways of doing things. Many mathematicians say their field is full of opportunities to reimagine a more inclusive, vibrant future for people of all backgrounds.