*Constructing Mathematical Thinkers*

Since childhood, Dr. Andrew Clifford seemed to know he would enter the world of Mathematics.

“According to my mom, in kindergarten, the teacher said, ‘what do you want to be when you grow up’ and we had to draw a picture of it.” Clifford reminisced, “I had my paper and drew a line down the middle. On one side I drew a picture of a carpenter and on the other I drew a picture of a mathematician.”

He admitted that at the time he only knew that a mathematician was, as his teacher explained it, “Someone who studies numbers that no one had thought up yet.” This appealed to the young professor. Clifford said, “I was going to either be that or a carpenter because I like saws.”

For undergraduate study, Clifford went to State University of New York (SUNY)–Binghamton for Mathematics. Then in his senior year with the guidance of his advisor, he decided to go to SUNY–Albany for graduate school.

“My interest was in topology, which is kind of like geometry.” Clifford explained, “I liked the low dimensional stuff, but it turned out to understand the low-dimensional topology, you needed algebra. My [current] area is where algebra meets topology.”

Clifford’s area is called combinatorial group theory. “Geometry is shapes. Algebra is the study of operations—addition, subtraction, and multiplication. We are used to doing that on whole numbers; you can make an abstract set on which you can do one operation. That would be a group.” Clifford explained, “It turns out that groups can also describe the symmetry of things, the way you can move things around so it still looks the same. That’s the connection between studying topology and studying groups.”

To explain his interest, Clifford provided a piece of paper as an example of his research in group theory. Imagine a blank piece of paper, which you folded up into different origami shapes. Clifford clarified, “The manipulation is called automorphism.” No matter what origami folds you did, when you unfold it, you would always have that same blank piece of paper. The structure—symmetry—of the paper did not change.

After receiving his Ph.D. in Mathematics from SUNY–Albany in 1994, Clifford embarked into the job market. “I sent out more than 190 applications, and only had two phone interviews,” he said. His first position was as a visiting professor at Western Illinois University for a year. He then taught for another year at the University of Wisconsin–Parkside before getting hired by Trenton State College.

Clifford joked he never has gotten a paycheck from Trenton State College. He explained, “Between the time I was hired and when I started working, they changed the name.” An unforeseen perk of the new job was that he met Dr. Marcia O’Connell, a faculty member in the Biology Department. Within three years, they were married. Their daughter Norah arrived two years later.

“I have to say, it is the students.” Clifford replied when asked about what he liked best about teaching at TCNJ. “They are anxious to do well and want to learn how to get good at this [mathematics].”

Clifford enjoys meeting with his students outside of class. “When they have questions, they are willing to spend the time to come in and wrestle with them.” he said. “Then they go off on their own and wrestle some more.”

Even as I waited outside of his office for an interview, he was having one of those discussions with a student. The math professor’s enthusiasm and availability to discuss various math topics both outside and inside the scope of the course are qualities that his students admire and spark their interest for the subject.

“He entertains my questions and provides just enough insight to spark my curiosity, forcing me (willingly of course) into more research about the topic,” said **Chris Woidill** (‘14), math major and one of Clifford’s senior capstone students.

Clifford’s enthusiasm for the subject is as infectious as his smile, and he is able to help students unravel the mysterious and seemingly complicated topics. This makes him an essential factor of the academic equation that produces inquisitive scholars.

“He knows his subject matter well and has a way of passing his enthusiasm onto the student.” **Michael Muller** (’14), math major, added, “I can certainly say that he’s a very accessible and helpful professor equipped with great skill in elucidating the more difficult parts of the topic.”

Some of the courses Clifford has taught include senior capstone, geometry, and calculus. “I love teaching calculus, where students are just finding out what college math is like and getting beaten up by it a little bit.” Clifford said, “You can imagine not everyone is excited to be in calculus, but our students are. They might hate test day and that kind of stuff, but all in all they want to be engaged in figuring it out. And as you know, I have taught other places, and it is truer here than it was there. So, we [TCNJ] give great students to our faculty.”

“If you ever have a chance,” said Woidill, “observe one of his classes or stop in his office because you have to be there to appreciate his abilities as a professor and a mentor.”

**For more information:**

A summary of the volume is provided below.

*Gene Function Analysis,
Second Edition*

The determination of protein function has been a major goal of molecular biology since the founding of the discipline. However, as we learn more about gene function, we discover that the context within which a gene is expressed controls the specific function of that gene. It has become critical to establish the background in which gene function is determined and to perform experiments in multiple applicable backgrounds. In *Gene Function Analysis, Second Edition*, a number of computational and experimental techniques are presented for identifying not only the function of an individual gene, but also the partners that work with that gene. The theme of data integration runs strongly through the computational techniques, with many focusing on gathering data from different sources and different bimolecular types. Experimental techniques have evolved to determine function in specific tissues and at specific times during development. Written in the successful *Methods in Molecular Biology* series format, chapters include introductions to their respective topics, lists of the necessary materials and reagents, step-by-step, readily reproducible protocols, and notes on troubleshooting and avoiding known pitfalls.

Authoritative and easily accessible, *Gene Function Analysis, Second Edition* seeks to serve both professionals and novices with a growing understanding of the complexity of gene function.

**For More Information:**

In 1991 the Mathematical Association of American instituted Awards for Distinguished College or University Teaching of Mathematics in order to honor college or university teachers who have been widely recognized as extraordinarily successful, and whose teaching effectiveness has been shown to have had influence beyond their own institutions.

The award notes that “Dr. Karen Clark is an extraordinary mathematics teachers and mentor of students. She combines great classroom teaching with a commitment to investing significant time in students outside the classroom. With both high standards and a kind heart, she inspires students in the mathematics classroom and influences their lives outside the classroom.” To read the full Award Citation, please click here.

Congratulations to Professor Clark for this great honor!

Tuesday, April 15, 2014

4:00 – 5:00 pm

SCP-101

*Refreshments will be served

**Abstract**: All behaviors, even those as distinct as breathing and babysitting, depend on functional neural circuits that are established during development. Normal development of these circuits is crucial and is guided by the expression of proteins – growth, survival, and transcription factors – acting at specific points in time. Loss of gene function can lead to abnormalities in neural development, providing a means to explore the role of specific proteins in the production of normal behavior. In this talk, using data generated in my lab from the serotonin-deficient Pet-1 “knockout” mouse, I will discuss how a genetic loss of function approach can provide valuable insight into understanding the requirements for normal breathing and maternal behavior in mammals.

**Abstract**: A long-standing, holy grail of neuroscience is to determine the “wiring diagram” of all neurons in the brain. Only with it in hand, can we even hope to fully understand how the brain works. Within the last few years, major efforts have been underway, utilizing both novel and existing technologies, to tackle this important problem. In this talk, I will describe our work using one method called laser photostimulation to deduce functional connectivity of a large population of neurons.

Four TCNJ Biology majors have been honored by the 2014 Goldwater Scholars Awards Committee. Biology majors **Syndi Barish** and **Andrew Goldfarb** have been selected as * Goldwater Scholars *for 2014, and Biology majors

Goldwater Scholars are chosen as a result of a highly selective national competition which honors exceptional undergraduate students who plan to pursue graduate degrees in science, mathematics, and engineering fields and careers in research. The award is a prestigious one, and the acknowledgment of our students as scholars and honorable mentions is significant.

Congratulations to Syndi and her mentor Dr. Wendy Clement; to Andrew and his mentor Dr. Donald Lovett; to Daniel and his mentor Dr. Nina Peel; and to Dylan and his mentor Dr. KT Elliott.

The Barry Goldwater Scholarship and Excellence in Education Program was established by the U.S. Congress in 1986 to honor Senator Barry Goldwater, who served his country for 56 years as a soldier and statesman, including 30 years of service in the U.S. Senate. The purpose of the Foundation is to provide a continuing source of highly qualified scientists, mathematicians, and engineers by awarding scholarships to college students who intend to pursue research careers in these fields. The Goldwater Scholarship is the premier undergraduate award of its type in these fields.

The 2014 Goldwater Scholars were selected on the basis of academic merit from a field of 1,166 mathematics, science, and engineering students who were nominated by the faculties of colleges and universities nationwide. One hundred seventy-two of the Scholars are men, 111 are women, and virtually all intend to obtain a Ph.D. as their degree objective. Twenty-two Scholars are mathematics majors, 191 are science and related majors, 63 are majoring in engineering, and 7 are computer science majors. Many of the Scholars have dual majors in a variety of mathematics, science, engineering, and computer disciplines. The one- and two-year scholarships will cover the cost of tuition, fees, books, and room and board up to a maximum of $7,500 per year.

April 7, 2014

9:30 – 10:30 am

C-122A

**Abstract: **The talk will cover a range of topics including isotopic enrichment, NMR spectroscopy, and mass spectrometry. Find out where your deuterated solvents and isotopically labeled compounds come from and hear about some exciting applications in chemistry and medicine.

April 1, 2014

11:30 am – 12:30 pm

SCP-229

*Pizza and snacks to be provided

**Abstract: **The Calculus of Variations is the study of finding extremals of functionals. Usually these functionals take the form J(y(x))=\int_{x_1}^{x_2} f(x,y,y’) dx. This talk will discuss some examples which yield exactly this situation,

some of which are the very problems that led to the development of our topic. We will derive the Euler-Lagrange equation and use it to solve these examples. This talk is aimed at students; only a basic knowledge of Calculus is necessary to delve into this subject.

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April 3, 2014

11:30 am – 12:20 pm

SCP-317

**Abstract: **Human beings are remarkably capable at the task of localizing sounds, especially those originating in the horizontal plane. This ability is facilitated by inter-aural time and intensity differences, which our brains have spent a lifetime learning to link to sound source locations. If these difference cues are altered, our ability to localize sound is disrupted, for instance if we enter an environment where the speed of sound is significantly altered. The most common example of this is a diver who attempts to localize sounds while underwater. Compounding this problem is the change in the way sound diffracts around the human head in different environments. In hopes of formulating new ways of allowing divers to localize sound underwater, we will treat the head as a sphere and formulate a theoretical model of inter-aural time and level cues in diverse acoustic environments.