Essays

A True Kennedy Legacy: Suzanne Croco and Her Story

posted Apr 14, 2014, 3:17 PM by AWM Editor

2014 AWM Essay Contest
Middle School Level Honorable Mention
by Karen Ge


Coming into the warm Pod from the freezing storm outside feels like going home, as it always does. My school, Kennedy Junior High in Illinois, is organized into various academic teams. The Pod is a separate building that houses my team. Stepping inside, I am greeted by a John F. Kennedy quote, “True happiness is the full use of your powers along lines of excellence in a life affording scope.” I put everything into my locker, except for a pencil and a binder full of scratch paper. Today is our first real MathCounts meeting of the season. Our coach? Mrs. Croco. At exactly 7:00 AM, Mrs. Croco calls for order and distributes a large packet of geometry problems to every student. “On the front are all of the formulas you need,” she says as she starts to write on the board: Stewart’s Theorem, Area Circumradius Formula, Point-Line Distance Formula…, the list goes on. “I want you to work on these with the person sitting next to you. These are homework if you can’t finish.” The classroom immediately begins to buzz. I flip the front page over and stare at the first problem.

……

Sitting there, I am motivated by the desire to succeed, yes, but I am also driven by the teaching philosophy of our coach. Mrs. Croco teaches 8th grade Geometry and Physics. She started the Kennedy MathCounts team in 1996 and has since led it to victory in the state and national levels numerous times. The 2002 National MathCounts Champion, Albert Ni, was an 8th grader of Kennedy. What contributes to Kennedy’s success? Let’s do some casework. In order to stand out in the sea of talented faces in the MathCounts state competition, the contestants and/or the coach must be outstanding. There are elite middle schools in Illinois that participate in MathCounts as well. Surely many parents would rather send their talented students to a prestigious private school or to a magnet public school instead of Kennedy, a part of Naperville School District 203. But Kennedy also has the extra edge of hosting the only middle grade gifted program in the district. So the students from Kennedy and those from other schools are about even, at least in terms of mathematical talent. Therefore the only other factor that could contribute to the Kennedy team’s success must be its coach: Mrs. Croco!
How Mrs. Croco gets here is a story, and the best kind: the story of life. Mrs. Croco grew up in the college town of Penn State, a town surrounded by mountains and teeming with academics. Her teachers gave her insight and inspiration that would guide her down the road to where she is today: a highly regarded math and science educator. Her geometry teacher showed her that a whole body of knowledge could be constructed using only a few axioms and a dash of reason. The axioms of her own teaching philosophy came from her calculus teacher, Mr. Clemson. He would send two or three students up to the board to work on a problem together, an idea that was rather unheard of at the time. The board was supposed to be a place for the teacher to lecture, not for the students to think and solve problems. This student interaction later became a central principle of Mrs. Croco’s teaching style. When she became a teacher herself, she would also have students work together and learn from each other. She would coordinate seating arrangements to allow students the chance to talk about ideas and thoughts.

In addition to teamwork, Mrs. Croco is fond of throwing challenging ideas at her students and letting them wrestle with tough questions. She gives crucial ideas and lets students fill in the gaps in the reasoning. Mrs. Croco is famous for her insanely hard tests. A normal ‘A’ student might wonder: am I supposed to know ALL this stuff? But yes, you are, because you're in Mrs. Croco’s class. Mrs. Croco has a way to make everyone think and thus, she is able to stimulate retention and passion as the two go hand in hand with hard thinking. Like an athlete training for the Olympics, a mathlete needs to wrestle with ideas to the very limit of his/her abilities and then go beyond. “When you struggle through a problem by yourself or with your peers, you learn so much more than what you would learn from the back-of-the-book answer or from your teacher,” says Mrs. Croco. 

Although she is well-known as Coach Suzanne Croco of the Illinois team in the national MathCounts competitions, Mrs. Croco does not coach MathCounts just for the sake of the competition. MathCounts is a great way for students to enter into the real world of mathematics. But it is only a bridge, not the destination. Competition math often involves the ability to do math fast, but perseverance is the key to real success in mathematics. Andrew Wiles, for example, worked hard for several decades before he finally proved Fermat’s Last Theorem. That’s why Mrs. Croco’s advice to young mathematicians is “Be willing to work hard.” She instills work ethic into every corner of her students’ minds and thus promotes perseverance. In her classes, the slackers become diligent and the procrastinators develop good study habits. Her former students told me that Mrs. Croco made them better people.

……

Coming out of the Pod for Spanish, I am greeted by the JKF quote again. “The full use of your powers along lines of excellence,” that’s what Mrs. Croco asks from her students and what she asks from herself. The school which bears John F. Kennedy’s name, my school, has a binding contract of loyalty to its students, ensuring that they have every opportunity to use their powers fully along lines of excellence. Kennedy Junior High serves the gifted in all areas, and the champion of these services is Mrs. Croco. She constantly seeks to uphold her own principles of teamwork and challenge. She trains champions, and is one herself. She is the true meaning of a Kennedy legacy.


About the Student:

Karen Ge is a 7th grader at Kennedy Junior High School in Lisle, Illinois. Her popular study guide Dissecting the New CogAT has helped thousands of students in more than 30 states. She is the concertmaster of Chicago Youth Symphony Orchestras’ Concert Orchestra. She is also an AIME qualifier and the best summer she has ever spent was at MathPath. In her free time, Karen is a regular volunteer in hospitals, rehabilitation centers, and senior residences where she brings music and joy to the infirm and elderly. 

Delving Into Uncertainty Analysis: A Biography of Dr. Laura P. Swiler

posted Apr 14, 2014, 3:15 PM by AWM Editor

2014 AWM Essay Contest
High School Level Honorable Mention
by Simin Liu


Uncertainty is an inescapable part of our lives, a fact which is appalling to the overbearing perfectionist in all of us. Dr. Laura P. Swiler has dedicated her life’s research to the study of uncertainty analysis and to developing methods to treat uncertainty in computational models. Uncertainty analysis has the ability to provide us persuasive data that informs our choices and allows us to make decisions in a more rigorous manner. Swiler’s work has practical applications to a wide range of medical, military, manufacturing and public policy decisions. For example, her research supports risk studies such as the analysis of core meltdowns at nuclear reactors.   We can all derive a little peace of mind from Swiler’s research knowing that we can combat all the terrifying uncertainty in the world and make well-informed decisions through uncertainty analysis.  

Born in Buffalo, New York, Dr. Laura Painton Swiler was the oldest of four children. Her parents were influential to her later success. Her mother, a history teacher, nurtured her love of reading and her voracious appetite for knowledge from an early age: her fondest childhood memories are of afternoons spent with her mother scouring the shelves of the public library. Her father, a vascular surgeon, set high standards for his children and always expected them to accomplish everything to the best of their abilities. “My father’s favorite saying was ‘Being smart and 50 cents will get you a cup of coffee’”, Swiler recalled with a chuckle. “Basically, he tried to impress upon us the idea that success is the combined product of intelligence, hard work and persistence. Possessing solely intelligence is no guarantee of success.” 

Swiler took her father’s words to heart and they served her well: her combined work ethic and determination to succeed allowed her to rank number one in her high school junior class at Williamsville East High School. She was later accepted to Yale University, where her mathematics and physics classes reaffirmed her passion for math and cemented her conviction to pursue it as a career. She also remained an avid reader during her time at Yale and graduated only two English courses short of obtaining a dual degree in Applied Mathematics and English. Though she was discouraged by the paucity of fellow female students in her advanced math and science classes, she refused to allow it to intimidate her. During her senior year at Yale, Swiler was offered a job by Bell Labs (then one of the premier research institutions in the country) that she simply could not refuse. At Bell Labs, she was among a legion of young interns laboring on a large-scale project dubbed ISDN (Integrated Services Digital Network) that aimed to create lines that could host both voice and data and that Bell Labs hoped to implement across the country by the mid-1990’s. Although they did not succeed in doing so, Swiler considers it to be the official starting point of her career and professes that she feels grateful to have taken part in the technology revolution of the 1990’s. 

While working at Bell Labs, Swiler completed a master’s degree at Stanford University in Operations Research, a field which involves using different methods of math modeling and advanced analytical methods to determine the maximum (of profit or yield) or minimum (of risk or cost). After contributing to the Operations Research division at Bell Labs, she decided to pursue a Ph.D. “I wanted to obtain a Ph.D.  so I could be equipped to make the world a better place in whatever little way I could with my math models,” said Swiler. The decision was a pivotal moment in her career. In 1992, Swiler applied to the US Department of Energy Computational Science Graduate Fellowship and received funding for a doctoral fellowship in Engineering and Public Policy at Carnegie Mellon University. Although her parents expressed concerns about the implication of leaving her secure job at Bell Labs, Swiler was convinced beyond a doubt that it was something that she wanted to pursue. “It was an unarguably unique opportunity. Obtaining a PhD is generally the only instance in your professional career that you have the chance to become an expert on a topic,” said Swiler. She did not come to regret her decision. “The process of obtaining a PhD was of inestimable worth because I was focusing like I had never focused before.” 

Swiler then spent the summer of 1993 working at the Sandia National Laboratories in New Mexico, where she decided to stay. In 2006, she obtained a patent for “Method and Tool for Network Vulnerability Analysis”. This innovative approach involves attack graphs, which enable mathematicians to identify the ways in which hackers can attack a network given the particular vulnerabilities on machines and the hacker’s capability to exploit the vulnerabilities. Following Swiler’s pioneering work with attack graphs, the idea rapidly gained popularity in the computer science community. Her current research has been focused on uncertainty quantification of computational simulations. Simulation models (used to model situations like nuclear reactor performance, climate change, shock physics, heat transfer and many more) have specific parameters: one of Swiler’s jobs is to determine which parameters are most influential in governing certain responses. Swiler is also active in the academic community and has mentored many graduate and post-doctorate students. Being a mentor is important to Swiler because she feels grateful for the direction her mentors provided her and wishes to be able to provide that same guidance to other students. “I also learn from the students I am mentoring, often just as much as they learn from me,” said Swiler.  

Swiler is as dedicated to her responsibilities as a wife and mother as she is to her commitment as a mathematician and mentor. For her, having a successful career while raising a family hasn’t been impossible, but has been hard work. In the face of the family/career juggling act, she has found it necessary to maintain a strict, structured schedule in order to be able to work full time and raise her two sons. Although she concedes that having children will inevitably affect a woman’s career, she strongly believes that every woman should be able to pursue a career without fear of discrimination for embracing motherhood. She recalls that in her mother’s generation, it was the tacit rule for women to relinquish their careers after giving birth to their first child. However, Swiler has served as a living testament to the ability of the modern day woman to be both focused in her career and engaged with her children, which is no small feat. Although some academic fields seem stacked against women because the childbearing years coincide with what are usually the years of peak productivity, Swiler has demonstrated that women do not have to choose between their family lives and their careers. 
Swiler’s life story shows us that with perseverance and motivation, it is possible to transcend traditional gender stereotypes and have both a rewarding career and a fulfilling family life. It is apparent that Swiler has never allowed herself to be discouraged by the dearth of women in mathematics. Her profound appreciation of and delight in the power and elegance of mathematics has driven her to pursue her dream of effecting change through mathematics without regard to perceived gender limitations. Though she grapples with uncertainty on a daily basis, one thing there is no uncertainty about is Dr. Laura P. Swiler’s commitment to bettering the world by aiding us in making more informed and appropriate choices.

About the Student:

I am currently a junior at Albuquerque Academy in Albuquerque, New Mexico. I am actively involved in school organizations and my community, including our school newspaper, tennis team, speech and debate team and community service club. I am genuinely fascinated and delighted by mathematics and have eagerly pursued it both through my academic coursework (I am taking AP Calculus BC) and through tutoring younger students in math. To me, math is a splendid way to exercise my problem solving skills (nothing really compares to the satisfaction of finally solving a difficult problem) and has helped me understand that there are usually several different approaches to solving the same problem. In my free time, I enjoy running, drawing and reading (especially National Geographic). I hope to have the opportunity to further pursue my passion for math and science through university and beyond. 

Dr. Kate Stevenson: Adding Value

posted Apr 14, 2014, 3:12 PM by AWM Editor

2014 AWM Essay Contest
High School Level Winner
by Francesca Paris

Katherine F. Stevenson is the daughter of a mathematician and a social worker, and she never imagined she would be either; today, she is both. Growing up, Stevenson had little interest in the latter and only a vague curiosity for math. More than anything, she possessed a penchant for teaching: she used to “line up stuffed animals and pretend to teach them.” Sometimes she included her little sister in the lineup too, finding satisfaction in explaining concepts to others.

Her passion for mathematics blossomed during her undergraduate years at Mount Holyoke. As one of just two thousand students, Stevenson received considerable encouragement, which prompted her interest in further mathematical study. Working on her undergraduate thesis on algebraic geometry, she had a “this is it” moment, and she dove head first into advanced mathematics. 

Before graduate school, Stevenson spent a summer working for a primary dealer in United States government securities, to assure herself that she would not rather bring her education to a close and start working. By the end of the summer, she was sure. The job forced her to be quick where she would rather have been thorough, and the experience left her with the realization that she was “more of a contemplative mathematician.” In many ways, the terrible fit of the job ensured that her education would never end completely.

After earning her PhD at the University of Pennsylvania, Stevenson traveled to Montreal to brave the freezing winters and study Arithmetic Geometry, which falls in between the fields of Algebraic Geometry and Number Theory. By looking at curves defined over abstract fields, she examined the connections between curves and lines.

Her year in Montreal was the penultimate in which she would bear the biting winters of the Northeast, thanks to a chance meeting in Zurich, Switzerland. At a conference, Stevenson ran into a man demanding that someone wash his shirts. She rolled her eyes, and then fell in love with him. Pietro, who became her husband, was so persistent that after their dates in Zurich he continued to pop up in Washington, where Stevenson had just started a tenure track job at University of Maryland, “so that job was doomed from the beginning.”

Indeed, Pietro convinced Stevenson to move to California after just two years at Maryland. Stevenson spent a year at the University of Southern California, then two as a visiting professor at Cal Tech. To earn teaching credibility for her permanent California job search, Stevenson taught for a year at Pomona College. She attributed being hired at California State University, Northridge in part to a recommendation from Pomona College.

Though she always believed she would carry out her love for teaching at a prestigious university, Stevenson has found her calling at the less well known California State University, Northridge. “The job I have now was not the job I imagined for myself. But it has been a perfect job for me.” Stevenson’s “job” is hard to pin down with a single title; it is a balance of teaching, research, and community service. 

Teaching has been her dream since childhood because of the “fantastic reward” of helping somebody truly understand something, and at Northridge, she gets to experience that every day. As a professor of abstract algebra, Stevenson helps her students transform from young men and women who think about math into people “who are mathematicians because they are creating math.” To balance out the exhaustion of “giving up” herself to her students during classes, Stevenson continues her research into algebraic geometry, ring theory, and group theory.

Her research extends past pure mathematics to mathematical pedagogy. Stevenson runs a grant from the Bill and Melinda Gates Foundation for general education math courses across the California State University system. She works to redesign curriculums, secure funding, and coordinate across campuses for the high-failure general education classes that are ignored by many math professors but crucial to the universities. With the grant, she has transformed some entry level pass rates from one-third to three-fourths of students.

Stevenson’s passion for social work, which she attributes to her mother’s genes, extends beyond her grant: she runs the entire remedial math program at Northridge, and she is involved in the implementation of remedial math across the system. With about 3,300 students entering each semester who require remedial math and thirty-five faculty members, Stevenson is the heart of the program. She is responsible for “how they teach, when they teach, and what they teach.” 

Stevenson works with psychologists to determine the challenges remedial math students face, which often extend beyond grasping the concepts to how they think about themselves academically or how they engage with the material. Is a kid failing because he is sitting in the back of the room and texting all of class? Stevenson’s job is to ask why, then use both her research and teaching experience to solve the issue. “What we try to do is make it easy, safe, and desirable for students to engage.” 

Though she loves working in the classroom and researching complicated mathematics, by pouring some of her time into the remedial math program, Stevenson sees that she is making a substantial impact on access to education, a crucial social justice issue. “The social work has turned out to be more important to me than I ever expected.”

At the office, Stevenson creates conceptual, mathematical structures. At home, Stevenson is an avid gardener; among her blossoming flowers and trimmed tomato plants, she creates something tangible. When her two young boys aren’t busy trampling her plants, she introduces them to mathematics through games and logic challenges. Her hope is that they come to the understanding that she did: math is not repeating knowledge back to an instructor, but creating something, and looking for patterns and proving them, “and that’s incredibly fun and rewarding.” In this way, Stevenson does for her children exactly what she does for thousands of students in the California State University system: she holds wide open the door to mathematics, while allowing them to follow their own passions the way that she did.

About the Student:

As a senior at Head-Royce School in Oakland, I am appreciating the warmth before I leave for Massachusetts next year, where I will attend Williams College. At Head-Royce, I serve as the the senior class treasurer and the Editor-in-Chief of the newspaper. Though I have been a year advanced in math since middle school, I have only lately recognized my love for it, in AP Calculus last year and Multivariable Calculus this year. Outside of math and writing, I am interested in international journalism, travel, and perfectly ripe pomegranates. 

No More Excuses

posted Apr 14, 2014, 3:10 PM by AWM Editor

2014 AWM Essay Contest
Undergraduate Level Honorable Mention
by Carolyn Brown

Ever since she was ten years old, Emily Evans wanted to be like Kate Monday the Mathematician from the TV show Square One. Sadly, this profession has a negative reputation and it is unusual for a child to even dream about pursuing it. You mention you even like math and most people will say, “You study math? I don’t know how you can study math, it is so hard. I don’t get it.” But Emily is not like most people: math has always been her passion because she is good at it and she enjoys the satisfaction from solving a challenging problem. “It’s a very creative field; it lets you try new things,” Emily said. “I’ve always loved math because I love patterns, and there’s a beauty in the patterns of math that once you really start to understand the math, then you start to see these patterns repeated over and over again.”

As a mathematics professor at Brigham Young University Emily realizes her path to become the mathematician she is today was not as smooth as other mathematicians’ paths. She graduated from the University of Utah with a degree in Economics and then worked in the industry as a software engineer for eight years. During this time she worked at three software engineer companies including EMC, Lavastorm, and Hewlett-Packard. Though this was a period of time of great growth for Emily, she wasn’t completely satisfied. After marrying David Evans, a fellow lover of math, she decided to pursue what she loved, followed her dreams, and went back to school to become a mathematician. She enrolled in the Worcester Polytechnic Institute in Massachusetts and earned a PhD in Mathematics. Following her graduate studies in domains with fractal boundaries in Massachusetts she moved to Utah with her husband and daughter Eleanor to teach at BYU.  

Through her experiences as a software engineer and in Economics she has gained a broader perspective as a mathematician. She learned important skills to become a better problem-solver. And, as advisor of the Women-in-Math club at BYU, she has inspired many young college women to follow their dreams.
The best piece of advice that Emily said she could give me was to not make excuses for my innate talents. I should be proud of studying math because it is what I am good at and love; it doesn’t matter what others may tell me. She said that as women we are apologetic for our choices and talents. Oftentimes we convince ourselves that our successes are actually not our own; that we couldn’t have accomplished them without the help of others. But in reality, we should not be ashamed of what we do well. We must embrace our talents, and not make excuses in fear of rejection or in fear of going against the social norm.
Emily learned this lesson the hard way; she made excuses not to pursue mathematics and chose a different path. These decisions shaped her into the mathematician she is today who continues to inspire everyone around her. 

Now living her childhood dream as a Mathematician she enjoys working on three research projects that vary from engineering to biology to pure mathematics. She is truly a Renaissance woman in mathematics! Her first project involves computational mechanics and includes doing mathematical analysis of ships and airplane wings. Together with other engineers and computer-aided design programs, Emily helps link different types of engineering to make new discoveries and advancements. And if that is not impressive enough, Emily also works with biologists to improve cell motion. They specialize in a slug-like moving cell called amoeboidal cells. With other biologists, Emily has come up with mathematical models to analyze the movement of these cells. They have had many breakthroughs with their research and continue making contributions to the mathematical/scientific world. Her last (but not least) project deals with her emphasis during graduate school. She researches domains with fractal boundaries, or shapes with bumpy boundaries and how they relate to their surroundings. 

Apart from being a successful mathematician, Emily enjoys spending time with her family, hiking, and reading books. She is living proof that dreams can come to pass despite any detour or challenge you may face.

About the Student:

Carolyn Brown is a senior studying Mathematics at Brigham Young University. She enjoys many aspects of math including combinatorics and complex analysis, two of the classes she is currently taking. She also really enjoys geometry ever since her 8th grade geometry class. In fact, one of her role models is 17th century mathematician Johannes Kepler who said, “Where there is matter, there is geometry.” She is fluent in Spanish and loves hiking, running marathons, and ballroom dancing. 

Nora Moushey: Chief Actuary and Lifelong Learner

posted Apr 14, 2014, 3:07 PM by AWM Editor

2014 AWM Essay Contest
Undergraduate Level Winner
by Tory Fields

Nora Moushey is a remarkable woman. In my own pursuit of becoming an actuary, I had the pleasure of meeting her a year ago in Cincinnati, Ohio at Western & Southern Financial Group where she operates as Chief Actuary. Actuaries, mathematicians who manage risk for insurance companies, have one of the top-ranked professions in the United States, but not everyone realizes the dedication it takes to become one. To become an actuarial fellow, one must pass a series of very difficult exams. The exam process takes years and to complete it is an impressive feat. To become the head of the actuarial department at a company, or a chief actuary, is even more so.  

However, Nora talks very candidly and modestly about her success. I called her during a typical Wednesday morning to ask her some questions about her career. She studied at Miami University of Ohio, where she originally planned to get her PhD in mathematics and teach at the collegiate level. “As I progressed through my undergraduate work, academia became less interesting” she admits. She noticed that there was only one female math professor in the department, and that she taught the lowest level courses. It seemed sexist and political to Nora, so she chose to look into actuarial science. Her father was an actuary and encouraged her to pursue the career. While still in school, she wrote her first exam and passed. She liked that with an actuarial career the exams offered an outside measure of her skill, and no bias could figure into her success. After graduation, Nora began working for Columbus Mutual, a small insurance company. When the company demutualized in 1982, it was acquired by Western and Southern, a larger insurance group, and Nora moved to Cincinnati. Nora says that the jobs were different in nature. At Columbus Mutual, insurance was sold regionally and the company would focus on the agents who sold the policies. At Western and Southern, Nora began working with several different companies, distributions, and target markets. She says she enjoyed different aspects of both jobs. Around 1984, she ascended to the position of chief actuary, becoming a woman with authority in an office that was mostly comprised of men.  

When I asked Nora how it feels to be a woman with authority, she laughed and responded with “It feels good!” When she originally joined the Society of Actuaries, she was curious as to how many of the members were women; she discovered that less than 5% of the Society was female. I wondered about her perspective on being a woman actuary, and she said that when she started her career, being a woman could be used to her advantage. When she was the only female in the room, it made her memorable. However, there were also drawbacks. She explained, “If someone had a project, there was a chance they wouldn’t even think to ask you”. This pushed her to work hard and be noticed, and the work paid off. I inquired about her favorite part of her job, and she identified two aspects of her job that she particularly loves. Nora said that over the years “the company had grown and prospered and I feel like I have contributed to that”. Being part of the big picture and noticing her success has made her rightfully proud, but she also enjoys noticing the success in others. She loves seeing young people learn and pass exams, advancing their own careers as actuaries. 

Hoping to be a successful actuary myself one day, I asked her what advice she might give to young women in the field today. “Some of it is advice I would give to anyone” she explains. She advises young actuaries to do whatever it takes to pass exams. In her experience, she has noticed that the longer it takes for someone to get through the exam process, the less likely it is that he or she will finish. She also believes in lifelong learning. Once someone achieves an FSA, that is the beginning, she says, not the end.  

I believe Nora offers a great deal of wisdom. Her success is something to be admired and emulated. I plan to take her advice as I advance in my own career, remembering that I am extremely fortunate to have the opportunity to become an actuary and to have the support of professionals like Nora along the way.

About the Student:

I am a Junior at Ball State University studying Actuarial Science with minors in Spanish and Foundations of Business. My goal is to become an actuarial analyst. During the summer of 2013, I interned with Great American Insurance Company as an actuarial intern and learned about annuities and financial planning. I will be interning with Nationwide Insurance in their Life/Health division this coming summer. I have written and passed two actuarial exams, P and FM. Along with my interest in actuarial science, I am also president of Omicron Delta Kappa, a leadership fraternity, and currently involved with planning our 2014 All-Campus Leadership Conference. 

"The Road Not Taken"

posted Apr 14, 2014, 3:02 PM by AWM Editor

2014 AWM Essay Contest
High School Level Honorable Mention
by Nathalie Sieh

What makes a person choose Path A over Path B? What makes a person take the road less traveled? 
“My father had a substantial career at the top “Big 8” accounting firm Arthur Andersen, but you could have knocked him over with a feather when I told him I was going to get an MBA and a CPA.  He thought I would be a nice nurse or marry well.”

Mary Judith Gedroiz, a Certified Public Accountant, grew up in a family and in a community where girls were supposed to develop their femininity or their faith - not their academic potential. Mary Judith, however, never saw “being a girl” as something that limited what she could do. And yet, while she never saw it as an excuse, there WAS one obstacle she had to overcome: her dyslexia. “When I was in elementary school, I was labeled a poor speller and somebody who couldn’t read, so I was either sent to the back of the class or off to remedial. I certainly felt like I wasn’t as smart as everyone else.” 

“The beginning of wisdom is calling things by their right name.” - Chinese proverb

Mary Judith is the perfect example of why labels matter. Her teachers labeled her slow and lazy. Her friends used to say, “Poor Mary Judith sitting at the back of the class!” At the time, she did not know she had dyslexia. School eventually got better because she found ways to compensate, not because it became easier or because her dyslexia went away. She would memorize words and how they were spelled. She would count the number of students in front of her, find the section she would be asked to read aloud, and then practice that paragraph over and over until it was her turn. She would create patterns, charts, and tricks to help classify and retain information. She was persistent and worked hard. 

“I believe that learning to develop my compensatory skills played a huge role in my success as a professional because in finance one has to intuit many different things going on at the same time. Perhaps my ability to pull information out of context, concentrating not just on one indicator, but bringing many in laterally, may have been affected by what I learned to do from my struggles with dyslexia.”  Mary Judith never set out to make math her career. “I think I basically focused so much on just getting through school, and not getting labeled and teased, that I wasn’t so much centered on what I wanted to do in the future.” She did not set out to be a trailblazer, though she was the first girl in her family, and, in fact, in her school, to take the “math path.” She simply wanted to get a job, and she knew what she was good at: math. 

“If opportunity doesn’t knock, build a door.” - Milton Berle

Mary Judith first looked for a job as a high school teacher. But there were no jobs. She even looked in the obituaries. She found a dead history teacher in New Hampshire and called the school. “They told me not to send a resume because they already had over a thousand resumes. Well, so much for that!” A neighbor then told her about an MBA in Accounting program at Rutgers University. The program promised an internship, preparation for the CPA exam, and exposure to the “Big 8” accounting firms. “Mathematics,” explained Mary Judith, "made me happy because I felt capable, whereas before I felt good for nothing.” This is why she applied and eventually received an MBA/CPA from Rutgers University, despite discouragement and astonishment from her family. She went on to enjoy a successful early career at Haskins & Sells, now called Deloitte Touche.  After she was married, she partnered with her husband, Paul, in the securities business as a registered principal. She continues to do this today. 

Mary Judith’s ability to see patterns and trends that no one else sees has benefited countless numbers of people. She enjoys her current profession “more than ever” because she loves to help those who are not as adept and knowledgeable in math and in finance. “I believe I do have a gift that other people don’t have, and I will always be compassionate to those who don’t have that gift. I know what it feels like for something not to make sense. I try to share what I can with others, breaking down numbers so they can make sense.”

Nowadays, instead of “slow” or “lazy,” she is often called a role model. She likes this label a lot better. She believes “If you know/have a role model who is, or is perceived as, a superwoman, then people think, ‘Well, that’s not me, I can’t aspire to that.’ Many young girls still have the idea that to excel in math, you have to have Einstein’s brain, funny hair, ugly clothes, thick-rimmed glasses, and be quite boring and serious.” Mary Judith does not fit this stereotype very well. She is beautiful and charming, wears fashionable clothing, and loves having fun! She is an accomplished photographer, devoted wife, loving mother, and great friend. She is exactly what math needs as a spokeswoman for its cause and advancement for young girls. I am proud to say that Mary Judith Gedroiz is my aunt and role model, not just because of the obstacles she overcame, but because she is somebody that one day maybe I could become.

“…Two roads diverged in a wood, 
and I, I took the one less traveled by,
And that has made all the difference…” - Robert Frost


About the Student:

My name is Nathalie Sieh. I am in 7th grade at St. Cecelia Interparochial School in Clearwater, Florida. My whole life, I have been the worst speller in my grade. At first, everyone thought that it was normal because I was so little. As the years passed, it got worse and worse. But, in 5th grade, I got the news that changed my life. I had dyslexia. My life changed so much that I thought it was ruined, only to find out later that it changed for the better. I realized that just because I have trouble with spelling and reading does not mean that I am bad at everything else, too. I am stronger in things that others are not. I love math. This summer I will attend a 3-week program at UC Berkeley called Math Zoom, which is a training program for mathematically gifted students. 

The Special Relativity of a Physics Teacher

posted Apr 18, 2013, 7:04 PM by AWM Editor

2013 AWM Essay Contest
High School Level Honorable Mention
by Alexandria Miskho

On first glance, it looks a tad disorganized. Handmade roller-coasters line the back wall. Papers are dispersed about the room. The board is a canvas of numbers and symbols. Shelves are stocked with crystal-ball-like apparatuses and pressure sensing devices. Seated around the room are students debating equations and questions and problems, while she smiles on.

Jennifer Tillenburg is a unique teacher. She bounces into her classroom every day, ready to take on the challenges of the course. She is the teacher that arrives 45 minutes early every morning and leaves 45 minutes late every afternoon, in the chance that even one student may solicit her help. Jennifer Tillenburg is the young physics teacher at Kamiakin High school, and an inspiration to her students.

As a child, Ms. Tillenburg had but one goal: to be a carpenter. She was raised in a blue-collar family, her mom being a carpenter herself. For years Jennifer wanted to work with her hands, to build bridges and buildings just like her mom. After flaming the fires of this dream for a short while, however, she realized something. To put it simply, she “sucked at it.” In fact, she did not seriously desire to learn any trade or enter into any vocational school. Coming from a working-class family, this idea was novel. However, her mother supported her entirely. She encouraged Jennifer to chase her dreams, to find her place in academia. Initially, Ms. Tillenburg was drawn to the idea of defending the law. As she realized this profession required an extensive knowledge-base in reading and writing, subjects that she didn't particularly care for, she once again vacillated in what her future profession would be. And then, like a shining beacon on a dark stormy night, there was math.

Math was a subject which came easily to Ms. Tillenburg. It made sense. In high school, she was always the student paired with a struggling classmate. Through this tutoring of her fellow classmates, Ms. Tillenburg began to envision a teaching career. From within herself bloomed a motivation to study math and science, to learn the concepts entirely on her own, to share her devotion to math with others, to be practically the first in her family to attend a university.

Upon matriculating at Eastern Washington University, Jennifer enrolled in her first physics class. This subject, this applied mathematics, spoke to her. Previously, she had never taken (or even heard of) physics before. In these introductory courses, Ms. Tillenburg found her niche. However, as she began to take higher level classes, she was surprised at what she saw. In a classroom of ten physics students, there was often only one girl. Her.

Surrounded by a sea of males, professors and students alike, she was the aberration. And what an aberration she was. Ms. Tillenburg became the student her fellow classmates asked questions of; she was the one invited to a multitude of study groups so that she could explain the concepts. Her natural talent at physics surpassed any prejudices that were swirling around her. In fact, she became a physics tutor at college. When meeting the males she tutored, they would look at her surprised, communicating their doubts that “[she] know more than [they] did about physics?” At first, it was difficult to overcome the stereotype that men were more knowledgeable in math and applied mathematics. After her male counterparts were exposed to her desire to learn and her love of mathematics and physics, though, Miss Tillenburg effectively squashed that stereotype, time after time.

As a young, female applied mathematics teacher, Miss Tillenburg is easy to relate to. Spend one moment with her and it is apparent that her devotion to physics transcends all else. Her energy has no place to dissipate into except for the minds of her students. But even as she found herself in a leadership role, stereotypes continued to follow her. Parents, upon realizing that the AP physics teacher was in fact a younger woman, initially looked at her “weirdly.” Similar to Ms. Tillenburg's own college days, in her first year of teaching there was one girl in AP physics. That year, when a fellow teacher asked Ms. Tillenburg which of her students would qualify as a tutor, one male student explained that “it has to be a guy because no guy wants a girl teaching him physics." Sheepishly, he added "except you, Ms. Tillenburg."

It seems as if moments such as these have only propelled Jennifer to advance women in the field of applied mathematics. For example, she purposefully pairs the differing genders in groups in order to encourage girls to engage in meaningful discussions with male classmates. She herself is a constant reminder that women can succeed tremendously in a mathematics field. From teaching mechanics to learning about special relativity, her favorite subject, to taking supplementary calculus courses on the side, she lives every day in a world of equations and formulas.

Leaving Jennifer Tillenburg’s room, a student comes to find that any sense of disorganization is really a vesicle for her work. Having taken her AP physics class myself, I can honestly say that she is the type of woman that doesn’t back down from stereotypes. “Don’t pay attention to them” she advises. Have confidence in your abilities—they are what will help you succeed. As a young woman planning to enter the mathematics and applied science field, I only have to look towards Jennifer Tillenburg to see my future. In her, I found a teacher and an adviser. But I, along with many other people, have found an example to follow as I enter college and my career.

About the Student:

Throughout my high school career I have been actively involved in multiple organizations. I am the student representative to the School Board for the Kennewick school district, president of Key Club, and vice president of National Honor Society. This is my third year in Link Crew Leadership, fourteenth year of playing the piano, and second year of volunteering with my local hospital's Green Team. In school, math has been my favorite subject for the last twelve years. I am currently enrolled in AP Calculus BC as well as math competition. I love all math, from solving a difficult problem with a complex theorem to exercising my mental math skills with my friends. I hope to further immerse myself in math and science upon entering college.


Mary O’ Halloran: “Dear Teacher”

posted Apr 18, 2013, 7:01 PM by AWM Editor   [ updated Apr 19, 2013, 11:34 AM ]

2013 AWM Essay Contest
High School Level Honorable Mention
by Angelique Scheuermann

In Ms. O’ Halloran’s math classes, you are classified as one of two students: you are either a “dear student,” who follows her directions accordingly and respects her authority, or a “VFP,” a “very foolish person,” who talks ubiquitously out of turn and dozes off mentally in class. If classified as a “VFP,” you need not worry, for these statuses are quite flexible, and you may be back in her good graces as soon as the next day. Ms. O’ Halloran tolerates absolutely no nonsense from her students, but her charming Irish accent and her sharp wit creates a lighthearted and enjoyable classroom atmosphere in universally difficult classes: Precalculus and AP Calculus AB. Lakewood High School has been fortunate enough to have such an invaluable teacher as Ms. O’ Halloran, who enthusiastically teaches any and all students who enter her classroom.

Mary O’ Halloran was born and raised in the village of Ballyheigue in County Kerry in southwest Ireland. As the eldest girl in a family of five children, Ms. O’ Halloran “had a taste for being in charge,” and every student who has had Ms. O’ Halloran as a teacher is well aware of this. Mathematics was always one of Ms. O’ Halloran’s interests; in my interview of her, she articulated that in her youth, she “did her math homework first, and would do the rest of the painful stuff after that.” At the all-girls Catholic boarding school that she attended, Ms. O’ Halloran met Sister Peter, her calculus teacher, who taught her to “think outside of the box” and to think more critically, a goal that Ms. O’ Halloran now has for her students. With her innate love for math, she always knew that teaching was the career that she would pursue.

At University College Dublin, Ms. O’ Halloran attained a bachelor’s degree with a major in chemistry, surprisingly, and a minor in math. “I would have majored in math, but I didn’t think I was good enough. In order to major in math, you had math, math physics, and my physics wasn’t strong enough,” she explained in the interview. After college, she went on to teach all levels of math, chemistry, and biology at an all-girls high school in Ireland. The education system in Ireland was vastly different from that of the United States: the only method for determining how a student did in a class was state exams at the end of the year which lasted six hours each; everything in class was just “learning to learn.” After nine years of teaching in Ireland and with a job waiting for her in the United States, Ms. O’ Halloran immigrated to Southern California.

In 1986, Ms. O’ Halloran began teaching the American students at St. Paul High School in Santa Fe, California. From that point on, she decided to cease teaching science and to focus solely on teaching mathematics. In 1990, Ms. O’ Halloran broke through her earlier collegiate hesitations about pursuing mathematics and earned her master’s degree in mathematics at California State University, Fullerton. Within that time frame, she also began her next teaching job at David Starr Jordan High School in Long Beach, CA, where she absolutely loved teaching all levels of mathematics for thirteen years.  More recently, she has taught and been co-chair of the math department at Lakewood High School in Lakewood, CA.

To have Ms. O’ Halloran as a teacher is an absolute pleasure. I am honored to be a student in her AP Calculus AB class this year. Every morning I look forward to calculus class because of Ms. O’ Halloran’s witty remarks and pleasant personality. Her natural gift for teaching and her emanating passion for math transcends the minds of even the most mathematically-contemptuous students. Because of Ms. O’ Halloran, my love of math has grown exponentially, and I have decided to pursue mathematics as a minor in college.

As co-chair of the Lakewood High School math department and a teacher with National Board Certification, Ms. O’ Halloran has no need to prove that she is an accomplished and ambitious woman in her mathematics career. She perpetually enjoys having “a bit of a challenge.” Although earning the National Board Certification was a laborious process, she told me in the interview that she found it “energizing” and was open to the change that came with it. But even with her numerous accomplishments, Ms. O’ Halloran has not lost sight of her initial love of teaching high school students. She loves the daily interaction she has with students my age and derives enjoyment from teaching them novel ways to think about mathematics, rather than having them simply regurgitate formulas. All she desires of her students is that they improve their skills, better their attitudes about mathematics, and “enjoy their years” in high school.

For students who cringe at the utterance of the word “mathematics,” Ms. O’ Halloran is able to make math for them tolerable, and maybe even fun. Ask almost any one of her calculus students about his or her opinion of Ms. O’ Halloran, and he or she will reply with something along the lines of, “she is amazing.” Any future Lakewood High School student will be extremely lucky if he or she begins his or her eye-opening journey through mathematics with the two words Ms. O’ Halloran uses to greet each class: “dear students.”

About the Student:

I am a senior at Lakewood High School in the Merit Scholars program, the most rigorous academic program at LHS. I have served as the president of the California Scholarship Federation Club for the past two years, as treasurer last year and vice-president this year for Key Club, and as the Senior Representative for the Merit Scholars Club this year. Mathematics has always been a passion of mine. I also love Chemistry and Biology, and plan to major in Biochemistry and minor in math in college next year. Running and exercising are my other hobbies, and I completed a triathlon and a 10k run in 2012. I currently tutor two students in algebra II and chemistry.


Destined to count

posted Apr 18, 2013, 6:58 PM by AWM Editor   [ updated Apr 19, 2013, 11:37 AM ]

2013 AWM Essay Contest
Undergraduate Level Winner
by Joy Otobo

In developing nations such as Nigeria, where gender equality and women’s rights are still foreign concepts, female/girl child educational endowment is often relegated to the abyss. It is normal to find few girls in schools and even fewer enrolling for courses such as medicine, law, computer science and the “almighty mathematics” which is feared by even the men. It is therefore a rare sight to see a young female mathematician such as Mrs. Mary-Anne Msuur Shior, who enjoys and derives great pleasure from teaching mathematics.

She was born in the balmy town of Makurdi, the capital of Benue State, on the 24th of March, 1984 to Mr. and Mrs. David Ijuh. The fourth child in a family of five children, she grew up in an average income family where there was just enough of anything to go around and waste wasn’t encouraged. She attended Saint Theresa Primary School, Makurdi, where she grew in strength and wisdom and shone bright in every subject, outdoing both the boys and the girls in her class. She said that mathematics was her favorite subject at the time because of her teacher, Mr. Hakaan, who laid a good foundation and taught with a vigour and steadfastness lacking in most of today’s teachers. After completing her primary school education, she enrolled at Aveco Model School, Makurdi, where she represented and distinguished herself even with limited resources at the Annual Cowbell Mathematics Competition, Junior Category, in her JSS 2. Although she wasn’t the grand prize winner, she brought great honor and recognition to her school as this is the biggest mathematics competition in the country to date. After the completition of her junior secondary education at Aveco Model School, she enrolled at Special Science Senior Secondary School, Makurdi, where she once more represented them at the Annual Cowbell Mathematics Competition, Senior Category.

With all these encounters with mathematics, one would naturally assume that she would choose a career in mathematics, but that wasn’t the case with her: she had set her interest in the medical field and was determined to become a Medical Doctor. She therefore put all her energy into studying and graduated her secondary school the top of her class in the year 2001. Her love for medicine was given impetus by the newly constructed medical school (under the administration of the governor of the state, Mr. George Akume) which came to be known as the Benue State University College of Medicine, but as fate would have it, the commissioning was delayed. This prompted Mrs. Shior to seek remedial admission in the sciences, a program meant to prepare one for a proper degree admission at the same university. While her focus was still medicine, her outstanding performance in mathematics during her remedial earned her placement in the school’s Mathematics Department. Although she was skeptical about the course, parental advice and a zeal to face challenges and make a difference spurred her  into accepting the admission for BSc Mathematics.

According to Mrs. Shior, hard work and perseverance kept her going because there were times when she was overwhelmed by the departmental challenges. Her strongest point and one of the reasons for her success was her unquenchable desire to know more, which prompted her to always ask questions. She remembers attending a lot of tutorials organized by her fellow course mates and asking them to help clarify some confusing formulas. She graduated at the top of her class of thirty five, only five of whom were girls, thereby helping to erase the misconception that girls are not good in mathematics. Immediately after her graduation, she married her fiancé Mr. Shior who coincidentally has a PhD in literature. She laughs when she tells me how he is always trying to make her drop her pen and pick up a novel which she has no interest in reading, preferring instead to unravel the mysteries in mathematical problems, watch inspirational movies or listen to gospel songs in her spare time. They have an adorable girl together. She recalls how she had to wait a year at home after graduation like the rest of her mates but instead of sitting at home idle, she got a job teaching at a community secondary school in Makurdi. It was then that she discovered she had talent and love for teaching as she enjoys seeing that light-bulb come on in the eyes of her students when they finally understand a concept. At the end of that year, the school was inspected by the National Teachers Association of Nigeria and with their recommendation she was awarded the best teacher of the year prize.

She went for her mandatory one-year Youth Service from November 2007 to September 2008, and in November of that year she was offered a lecturing position in the Mathematics Department of her former University due to her excellent performance while a student there. She accepted and became the first Mathematics lecturer at the University. Mrs. Shior did her master’s program in the mathematical modeling of malaria at the University of Agriculture (UA), Makurdi. She chose this because she wanted to do something in mathematics that has practical application to her community. She hopes to do her PhD outside the country but cannot at the moment because this will require her to be away from her family for a long time and she cannot afford the cost of regular visit for her family. She hopes to get a scholarship that will lessen the overall cost. She acknowledges this as one of the many challenges career women face across the globe.

Although the fourth child, and a female one for that matter, she was the first in her family to get a degree. This shows that we can rise above societal limitations and cultural boundaries to be the best that we can be. She advises young girls interested in mathematical careers to be hard working and ambitious. That unlike the humanities, mathematics is straight forward. You can know how well you have done in an exam even before the result is out by your personal evaluation. She enjoys the prestige and recognition she gets when she introduces herself as a Mathematician.

About the Student:

My name is Joy Otobo. I am currently doing a major in psychology at Benue State University, Makurdi, Nigeria. Statistics, a branch of mathematics, is one of my compulsory courses and I enjoy it immensely. When I came across this essay topic, I was excited because it is the perfect opportunity for me to help shine some light on the achievements of this great mathematician whom I admire a lot, Mrs. Mary-Anne Shior.

More than Research: A Day in the Life of a Biomathematician

posted Apr 18, 2013, 6:55 PM by AWM Editor

2013 AWM Essay Contest
Undergraduate Level Honorable Mention
by Anne Talkington

For biomathematics researcher and Duke University Mathematics professor Anita Layton, success comes in many shapes and sizes.  She explains: if you achieve the overall goal you set for a project, that is a big success.  If you make a step towards solving your goal, that is a little success.  If you receive a grant for a project, if a paper gets published, or if a student you mentor graduates and finds a job, you have succeeded.

Layton’s day as a mentor and research supervisor consists of teaching, administrative duties, research, and meetings.  Yet, of the varied aspects of her work, she cannot pick a favorite.  She enjoys it all.

With the full support of her family, Layton (known at the time as Anita Tam) left her native Hong Kong to enroll in Duke University’s undergraduate physics program.  Over time, Layton’s interests shifted from actual experimentation to computer programming, resulting in employment as a computer consultant.  Later, Anita Layton graduated from the University of Toronto with a doctorate in computer science.  Her experience with the mathematical modeling of weather patterns led her to the National Center for Atmospheric Research.  Ultimately, she returned to the Research Triangle and Duke University.

Professor Harold Layton, Anita’s husband, introduced her to research at Duke.  Here, they frequently collaborate on projects together.  The Laytons’ research has incorporated the use of calculus to describe physical and biological processes that are critical to bodily functions. 

Anita Layton’s current research project is a specific example of using mathematical principles to model the biology of everyday life.  It focuses on chemotropisms in yeast, or how yeast cells “know” what is around them.  From data about chemical sensing and cell signaling, Layton models how the yeast responds to its environment.  She is constantly tweaking formulas that relate the strength of specific signals to the path of cell growth.  Each model begins simply, becoming more complex as she adds parameters to better represent reality.  By working with and learning about a specific organism, she finds the potential to expand her ideas to more general modeling, and cell signaling. 

In addition to their work, the Laytons share a happy family life with their two children.  They are careful to prevent their life at work from invading their time at home.  Therefore, the math they do at home is no different from the math other parents do: explaining basic concepts to satisfy their children’s curiosity. 

Despite her busy family life and the multitude of responsibilities at work, Anita Layton has managed to produce nearly 35 papers in the past two years, and has acquired several grants to continue her research.  The scientific papers she writes often take a year to be published in a notable scientific journal, such as the Journal of Computational Physics or the Journal of Mathematical Biology.  While her experiments continue to evolve, Layton publishes her intermediate progress.  Her chemotropism project, already a work of nearly four years, lingers as a research initiative.  Layton presents her discoveries across the United States and abroad, and still manages her schedule of classes among the network of conferences, workshops, and project presentations of her latest findings.

Like her schedule, Anita Layton’s writing is carefully planned.  She likes it to be organized, to “tell a very nice story.”  She views each academic work as a means of communicating an idea to an audience with limited knowledge on the topic.   

Layton loves teaching.  She is serious about her work, but maintains a sense of humor and enthusiasm.  She relates well to students across a variety of majors, from biology, to engineering, to physics.  The diversity in Layton’s classroom resembles the diversity in her laboratory – people with varied interests, coming together to learn and grow.  Each day brings a new topic, and a new mathematical model to explore. 

Anita Layton’s class is discussion-based, a combination of theoretical principles and applications.  Layton challenges her students’ intuition, presents them with scientific concepts, and then encourages them to develop questions of their own to study further.  She promotes a dynamic of academic community within the classroom.  Her students critique one another’s work and the legitimacy and implications of new research.  They learn from each other as well as from their experienced professor.

Anita Layton serves as a mentor for both graduates and undergraduates.  She helps to organize and actively participates in programs such as the Research Experience for Undergraduates (REU) in Mathematical Biology, and serves as Assistant Director of the Research Training Grant at Duke.  Layton, an affiliate of the Association for Women in Mathematics, also supports the Duke University Women’s Mentoring Network.  The predominantly male field does not intimidate her.  “I work just as well with men as I do with women. Really. … As for being a woman mathematician, I don't find it particularly challenging. There are always people against you.  If it is not because of your gender, it will be [because] of something else. I usually don't let such things get to me.”  In the face of adversity, “work hard” is her solution. 

Layton’s parental instincts translate to her mentorship as she sees her students grow up, graduate, and move on.  No two students are exactly the same, so she looks to lead them down the path that will best help them later in life.  She sees each student as an individual with special talents to nurture and specific goals to achieve.  She guides them, as they continue to accomplish great things. 

Regardless of which project Layton is working on, she does not find the conflicting ideas of fellow researchers in the laboratory discouraging.  Layton feels that ideological conflict is a good thing.  It allows people from various backgrounds to share different perspectives.  She knows that collaboration plays a significant role in science.  Although this scientific collaboration could be stressful for many, it is not for Anita Layton.  She thrives on communication, and truly loves what she does.

About the Student:

I am interested in investigating mathematical models with broad biological applications.  My first exposure to mathematical biology was through a research position at the University of North Carolina at Pembroke.  In the biotechnology lab, I developed my own equation for calculating microbial population growth based on the exponential Maclaurin series expansion.  I see complex biological phenomena as a way to test models and use them to refine techniques.  I intend to research patterns that could apply in fields such as molecular biology, ecology, or cancer research, and pursue a doctorate in mathematics.


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