# When Math Comes to Life

It’s summertime, and in the Department of Mathematics, that can only mean one thing: SEE-Math. SEE-Math, which is short for the Summer Educational Enrichment in Math Program, is Texas A&M’s annual two-week day camp for gifted students entering the 6th, 7th or 8th grades to explore their potential in mathematics-related fields and led by professor of mathematics Philip B. Yasskin.

Much of the program’s charm lies in its entertaining and engaging activities that demonstrate the many ways math exists naturally in the world around us. Last week, senior lecturer Mila Mogilevsky had the students try their hand at origami, the Japanese technique of folding paper into elaborate figures. While the students certainly enjoyed the art lesson, they also enjoyed learning about the geometry that makes the beautiful paper creations spring to life.

Here’s a quick video of origami in action:

# Marking Time

Ever wonder what mathematicians do on vacation? In Texas A&M professor Wolfgang Bangerth’s case, he kicked off summer 2015 by hiking through history related to another of his disciplinary specialties: geophysics.

A widely respected expert in computational mathematics and mathematical modeling, Bangerth is the author of the software program ASPECT (Advanced Solver for Problems in Earth’s Convection). His code is helping geodynamics researchers around the world visualize the Earth’s interior and related processes, thanks to funding assistance from a major facility in California at the epicenter of geodynamics research.

Earlier today, Bangerth found himself at the site of one of the worst geological disasters in U.S. history, Mount St. Helens in Washington State. Roughly one month after the 35th anniversary of the historic eruption, Bangerth toured the area, posting these incredible photographs on Facebook and agreeing to share them via the Texas A&M Science blog.

“What a treat,” Bangerth writes, “A seven-hour hike through the devastation area and then halfway up Mount St. Helens. (Additional treat: Total number of people encountered in the first six hours: 1. In fact that equals the total number of mammals encountered during this time.)”

In addition to the photos and captions, Bangerth — ever the educator — offered to expound on the science as follows:

“So here’s the story: Mount St. Helens is one of the chain of Cascade volcanos along the U.S. West Coast that exist because the Pacific (or, more exactly, the Juan De Fuca plate) subducts beneath the North American plate. They take with them millions of years of sediments, entrapped water, etc., and this leads to melting of material when they get to certain depths, and this melt then comes up a couple of 100 miles inland of the subduction zone.

“In 1980, magma rising up bulged out the side of the volcano. After an earthquake, this whole bulge collapsed in a gigantic landslide. Liberated of the pressure of the overlying rock, two enormous explosions then ripped apart most of the mountain within seconds of the landslide. There is a fantastic video of this created from a sequence of 10 or 15 pictures and also another series here.

“What you see in my pictures are the remains of the volcano (1,300 feet shorter than it was before, with its enormous gash on one side) and the valley below the landslide and miles downstream from there — in some places up to 700 feet of debris, ash and the results of several later pyroclastic flows. The deep incisions are streams that have eroded this loose material.

“The landscape is largely barren since it had, of course, not a single living organism left after the 1980 event, and is only slowly re-growing. Along the streams there are man-high trees these days, but elsewhere you only find bare gravel and sand — some covered by hardy mosses and lichens — and in many places lots of miniature bluebonnets and some Indian paintbrushes. There are ants and a few insects, but generally few vertebrates. I did see a small number of birds, including a pair of hummingbirds. By and large, it’s a huge contrast from the densely forested areas around the mountain (and how it looked before the event, as seen in older pictures).”

# Core Competency

As I have mentioned in past blog entries, one of the many perks of my job is having experts at my fingertips. With a simple email, phone call or Facebook message, I can get instant feedback concerning the day’s top headlines, scientific and beyond.

Take for instance last week’s reports celebrating discovery of oceans of water beneath the Earth’s surface. I happened to catch a radio snippet recapping the Huffington Post’s version of the story as I was heading solo to the grocery store on a rare Friday vacation day. (Yeah, I’m as surprised as you are as to what qualifies as vacation for this full-time working mom of three ages 10 and under. But that’s another story with neither experts nor answers!) Intrigued, I first Googled the story to find out where it originated (Northwestern University), then emailed my friend Wolfgang Bangerth, a Texas A&M mathematician and author of a modeling software program, ASPECT, that is designed to develop, among so many other things, clearer pictures of Earth’s interior.

Besides being a computational scientist and modeling genius, Wolfgang is no slouch when it comes to geophysics — or any engineering-related branch of science, in my experience. While I knew this would be right up his alley, I didn’t realize he was in South Korea at the time teaching a weeklong workshop. Distance certainly didn’t affect his ability to advise nor my efforts to produce a press release on the subject with his copious help.

(Here’s an example of Wolfgang’s ASPECT-driven work — convection in a 3D box. Reminds me of those cool optical illusion-type puzzles you got as a kid or the nifty gel-based paperweights you sometimes see in science-types offices!)

For me, curiosity is right up there with a sense of humor and vocabulary prowess in the way of appealing attributes, but I do so love it when others share my enthusiasm for a spur-of-the-moment idea, PR-related and otherwise. Wolfgang certainly went the extra mile (pun intended) to bring this one to fruition, paying me and other communicators what I consider to be the ultimate compliment during a side discussion concerning my use of the formal “Dr.” title with him out of habitual respect:

“It’s a title. I got it by doing my job, not by being particularly brilliant. As for respect, you are doing a fantastic job, too, and I do respect that just as much. At a university, we’re a team. You can’t do your job without us, and we can’t do it without people like you. I see no reason why we shouldn’t treat each other as equals.”

Well said as always, my wise friend. Let the record show (at least in this piece) that I’m recovering nicely.

Thank you, Wolfgang, for the global assist and the team affirmation. Awesome to the core!

Another bonus of being friends with such a world traveler as Wolfgang Bangerth is lots of vicarious adventures, given his love of all things outdoors, nature and related photography. Here are but three picturesque examples: traversing rugged terrain in South Korea’s Seorak Mountains National Park, exploring evolution and iterations of blue at Isla San Cristobal, Galapagos and admiring the jaw-dropping descent and beauty of Victoria Falls, Zambia, South Africa. (Credit: Wolfgang Bangerth)

# You Are Enough

Dear Student,

You almost walked out on a Team Exercise today because you weren’t prepared, and you didn’t want to freeload. I admire that, but I asked you to stay and to learn, because the point of the Team Exercise isn’t the grade; it’s to help the members of the team to better understand the lesson.

At some point we will all walk in unprepared, and have to ask our team to help us out. That’s why some of the hard stuff is Team Stuff, rather than individual. Because I think that having you work together will cause more learning than if I just preach it at you.

I still felt terrible because you did today. And I questioned myself and what I was doing.

I talked to you for while late this afternoon, and there are other things going on in your life. This class isn’t easy for you, and logistics lately have been difficult. I get the feeling there are other things too. You apologized to me, but no apology is necessary. This is my job. I am here to try to help you learn. I know that other things get in the way. I know how they get in the way. I’ve lived that. I just wish you knew it, too. You are worthy of being here. Worthy of my effort. Worthy of the help from your team. Worthy of being taken seriously. Worthy of help. Maybe worthy of better than I am capable of giving you.

I know that you are the type of person who wants to be the one to help others. If another came to you unprepared, or unable to get something, or struggling, you’d be proud to be the person to help them out. You’d treat all their problems with loving kindness. That loving kindness that you’d so easily give to someone else is the loving kindness I want you to give yourself right now.

Just hang in there. Just keep trying. And seeing the high level of frustration and pain I saw in your face today, just in case, I want to say: If there comes a point where you realize or decide that this is not for you, I want you to know that is okay, too. You are still worthy and worthwhile. Sometimes it feels like we are deep in a dark tunnel with no way to climb out. And I can’t even tell you how to get out, except that you have to just keep at it.

I didn’t have the exact right words to say to you. I can only hope that the ones I had were enough to plant this idea, for it to grow and blossom later. You are enough. Just as you are. Deserving of respect and love and help. If you can’t trust yourself to judge that, I hope you can trust me.

Sincerely,

Dr. Linhart

(Credit: Alex Eastman)

# The Name of the Game

Judging from a quick scan of the morning headlines and my Facebook, Twitter and Google+ news feeds, it’s a pretty universal fact that last night’s Super Bowl was a wee bit disappointing. While it’s true the Denver Broncos’ high-octane, option-loaded offense didn’t quite measure up to Seattle’s stifling Legion of Boom nor the pregame billing of an epic battle between league-leading No. 1s on opposite sides of the ball, I was confident from the kickoff, given that we had Aggies on both squads and therefore would emerge victorious. (Yay, 12th Man — the real one!)

But leave it to self-described math geeks to liven up an otherwise lame game with a little game within the game, described here in excerpts from Texas A&M Mathematics’ Amy Austin’s related post last night on Facebook:

* ~ * ~ * ~ * ~ * ~ * ~ * ~ * ~ *

AUSTIN: So me and my geeky friend just calculated how fast that Seahawk player was running when he just scored that most recent touchdown.

14.3 mph.

AUSTIN (admitting a little further into the comments that she was the instigator, if not the geek🙂 Well, it was me that wondered aloud how fast he was running. So the friend I was talking on the phone with is the one that took out her calculator. She’s the geek. Not me. 😉

AUSTIN: Good old distance equals rate times time. And of course we had to convert from yards to miles and seconds to hours.

* ~ * ~ * ~ * ~ * ~ * ~ * ~ * ~ *

Just goes to show that math and science not only are fun but also all around us, if we so choose to recognize and embrace what clearly can be a challenge just as exciting as sports. Possibly even more so on otherwise disappointing nights such as these.

#winning

Yep, now that I actually look, there are the obvious plus, minus and equals signs right there in the laces. What else do you see? (Credit: Torsten Bolten, Wikimedia Commons)

P.S. For those interested in a little 12th Man history, check out this extensive treatise on the subject by the outstandingly enterprising and clever folks at Good Bull Hunting.

# Derivative Bee

Tuesday night was the Math Department’s second annual Derivative Bee, as well as my first visit to the event as a faculty volunteer.

Students participate in two categories. Category U is for students currently taking differential calculus (Math 131, 151 and 171). Category G is for students who have completed differential calculus (Math 152, 172 or higher).

In the first round, students are issued clickers and have 3-5 minutes to choose the correct multiple choice answer to a differentiation question. There wasn’t a lot for the faculty volunteers to do at this point, so I thought I’d play along. I was confident of my advantage; this isn’t the first time I’ve taught calculus. And I have those three magic little letters (Ph.D.) following my name.

It didn’t take long for me to get a little attitude adjustment. Question 1 was to evaluate

$\dfrac{d}{dx}\left[\dfrac{(x+2)(2x+3)}{x}\right]$

Since I don’t like using the quotient rule, I changed it to a product

$\frac{d}{dx}\left[(x+2)(2x+3)x^{-1}\right]$

and promptly made a distribution mistake in the multiple iterations of the product rule required to evaluate the derivative.

What I should have done in the first place was to FOIL out the product and divide through by the x in the denominator

$\frac{d}{dx}\left[\dfrac{2x^2 + 7x + 6}{x}\right] = \frac{d}{dx} \left[2x + 7 + \frac{6}{x}\right] = 2 - \frac{6}{x^2}$

which is just oodles easier.

Another problem I got schooled on: find the derivative of

$\frac{d}{dx}\sqrt{x\sqrt{x\sqrt{x}}}$

Me? I love the chain rule, and the first thing I did was apply it incorrectly, not realizing that all those embedded square roots were also multiplied together and that the product rule is required, too! Fortunately, I caught my mistake and corrected it — with a not insubstantial amount of sweat. I was all proud of myself until one of the other instructors showed us the easy way to do the problem usingthe rules of exponentials.

$\frac{d}{dx}\sqrt{x\sqrt{x\sqrt{x}}} = \frac{d}{dx}(x(x(x)^{\tiny 1/2})^{\tiny 1/2})^{\tiny1/2} = \frac{d}{dx} (x^{\tiny 1/2}x^{\tiny 1/4}x^{\tiny 1/8}) = \frac{d}{dx} (x^{\tiny7/8}) = \frac{7}{8}x^{\tiny -1/8}$

which is an easy problem to solve!

This old dog learned a few tricks tonight. Including renewed respect for my colleagues and students. We have some smart people here at Texas A&M.

# By the Numbers

One of the primary perks of my job involves getting to know many Texas A&M Science faculty, staff and students — several of whom I’m privileged to call friends.

In the wee hours of last Friday morning, one of those friends posted what I considered to be a rather intriguing Facebook status update about having 430 exams to grade — her night’s take from a thrice-per-semester event that’s referred to in the Department of Mathematics as a “common exam.”

Immediately suspecting calculus, I turned to Google and searched “Texas A&M Math 151.” Success with the first option, which took me to a most helpful departmental link that explained a lot:

“The first year of calculus (Math 151/152) is a prerequisite for most math, physics and engineering courses. In fact, the College of Engineering uses the grades in Math 151 and 152 to help determine who is allowed to enroll in upper level engineering courses. Therefore, it is critical that the Mathematics Department have a common standard across all sections of this course. For these reasons, the Department has implemented a system of three common exams in Math 151 and 152. The final exam will not be of common type. …”

However, as both a writer and someone who had her fair share of trouble with mathematics back in the day, I had to know more. I guess I’m still trying in subtle ways to make up for lost time(s) and to figure out what I could have done differently — well, beyond go to class more and, um, have learned it in high school like my exasperated professor back then so often fervently opined and desperately wished. To be fair, I think if I would have realized then there were people who truly wanted to help me (mercifully, they still do) and that they were putting just as much if not more effort into the class as I was, I would have been a lot better off, if not at least more grateful.

Now that my 40-something self has those answers (thanks to my kind friend in the middle of her grading), I can safely vouch to my former-20-something one that what goes on behind this educational scene definitely is not common. More like nothing short of amazing. Consider the following numbers, for which even I can do the math:

• 151 — The course, otherwise known as Math 151: Engineering Mathematics I.
• 68 — Sections offered in Fall 2013 across the Department of Mathematics. My friend is responsible for 12 of those, with between 30-42 students in each.
• ~2,200 — Aggies currently enrolled in what’s more commonly referred to as engineering calculus.
• 13 — Instructors teaching those roughly 2,200 students.
• 23 — Teaching assistants assigned to help those 13 professors and lecturers.
• 15 — Multiple-choice questions on the exam, which is a combination of scantron/show-your-work options.
• 7 — Free-response problems.

Beyond Math 151/152, the department also offers a Math 141/142 Business Mathematics course characterized by “jumbo-sized” sections of roughly 300 students per section, all taught by seven instructors.

Oh, and did I mention they also offer such resources as Week in Review, Supplemental Instruction services, help sessions and even a summer Personalized Precalculus Program — most of which have been created during the past decade and a half to better help all students, regardless of level of experience and secondary preparation?

All in a day’s work and then some within a college responsible for teaching 20 percent of the total class hours (roughly 1 in 5) taught to all 45,000-plus Aggie undergraduates each semester and — by careful and caring design — set up to pass, not fail, each and every one of those students.

Here’s hoping these 20-somethings realize, truly appreciate and take advantage of those efforts for the absolute services they are long before I did.

# Of Forests, Trees and Maroon Roses

Ever find yourself so focused on the little things wrong that you miss the big picture of all that’s right? Easy to do when the day-to-day begins to rule not only the day, but also the week, then the month, then the next month, and so on. Sometimes it takes conscious effort to break this vicious cycle, but thankfully, there’s one routine assignment each year in the late spring/early summer that guarantees I stop and smell the maroon roses (so to speak) representative of Texas A&M Science. And boy, were they particularly fragrant in 2013. Or 2012, I should say.

Each year Texas A&M Science Communications compiles an annual report cataloguing our teaching, research and service efforts across all departments for the previous calendar year. Collectively and per individual tenured/tenure-track faculty member. It’s no small endeavor, with the end result being as weighty as the three-ring binder in which it arrives. One of the first pages within said binder is a foreword from Dean of Science Joe Newton summarizing the highest of the year’s high points — my primary contribution to the larger effort, which mostly involves pinning Dr. Newton down and making him focus on the rear-view mirror even as he’s engrossed in all levels of forward-looking responsibilities as our designated driver. Typically each department head also provides a foreword for each respective unit. All in all, it’s pretty impressive information that definitely goes against the Aggie tradition of humility (arguably the eighth core value!) but speaks volumes about what we value as a college and across the fundamental sciences and professions we represent.

Rather than relegate that summary to the binder for another year, I want to share it here so that you, too, can see it’s been a good year for the roses. Congratulations, Texas A&M Science, but your work here isn’t done. We’ll get more binders ordered…

FOREWORD FROM THE DEAN (2012 Annual Report)

As dean of the College of Science at Texas A&M University, it is my obligation and privilege each fall to take stock of our progress toward our three-part university mission — teaching, research, and service — and to reevaluate our collective commitment to ongoing excellence in all respective phases.

I am pleased to report that the Texas A&M College of Science continues to deliver on its unspoken yet inherent promise to advance discovery and solve real-world problems. In the past year alone, our scientific ingenuity has resulted in hundreds of top-notch graduates and more than $56 million in sponsored research projects that create new knowledge and drive economies around the world. Each year despite all economic indicators to the contrary, those awards steadily continue to increase, both in amount and stature, as testament to the strength of our programs and overall reputation for excellence. Beyond research funding, the past year marked another major milestone in external fundraising — a landmark$20 million legacy gift by George P. Mitchell ’40 and the Cynthia and George Mitchell Foundation toward the George P. and Cynthia Woods Mitchell Institute for Fundamental Physics and Astronomy that followed their $25 million gift (half of which was credited to Texas A&M) to the Giant Magellan Telescope in 2011. Our individual teaching, research, and service highlights in 2012 were many and magnified, highlighted primarily by big discoveries and major research-related awards in each department. Two faculty, physicists Marlan Scully and Alexander Finkelstein, were honored for lifetime research achievement — Scully with the Optical Society’s highest award, the Ives Medal/Quinn Prize, and Finkelstein with a Humboldt Research Award. Chemist Oleg Ozerov was recognized with The Welch Foundation’s Norman Hackerman Award for Chemical Research, while fellow chemist David Russell earned the American Chemical Society’s Field/Franklin Award for Outstanding Achievement in Mass Spectrometry. Three faculty received National Science Foundation CAREER Awards (Helmut Katzgraber, Wenshe Liu, Grigoris Paouris), In other notable accolades, Chemistry’s Sherry Yennello was recognized as a Fellow of the American Association for the Advancement of Science (AAAS), while Karen Wooley was named 2012-14 chair of the Nanotechnology Study Section within the National Institutes of Health Center for Scientific Review. Mathematics celebrated 11 inaugural American Mathematical Society Fellows (Harold Boas, Ronald DeVore, Ronald Douglas, Rostislav Grigorchuk, William Johnson, Peter Kuchment, Gilles Pisier, Frank Sottile, Emil Straube, Clarence Wilkerson, and Guoling Yu, who was named the inaugural holder of the Thomas W. Powell Chair in Mathematics), as well as its first Texas A&M Presidential Professor for Teaching Excellence (Boas). In global research breakthroughs, our high-energy physicists were part of international experiments at the Large Hadron Collider and Fermilab that confirmed preliminary proof for what is believed to be the Higgs boson particle. The Dark Energy Camera, for which astronomer Darren DePoy serves as the project scientist, captured and recorded its first images high atop the Blanco Telescope in Chile. First blast occurred at nearby Las Campanas Peak, marking the beginning of site preparation for the Giant Magellan Telescope, which also celebrated successful completion of its first mirror. Chemist Joe Zhou received his second Department of Energy grant in as many years to develop more efficient natural gas storage tanks for passenger vehicles. Our faculty (Alexander Finkelstein, Christian Hilty, Oleg Ozerov, Jairo Sinova, Clifford Spiegelman, Renyi Zhang) also are involved in six of the eight joint research projects encompassed in a$1.5 million campus-wide collaboration with Israel’s Weizmann Institute of Science.

On a campus achievement front, Physics and Astronomy’s David Lee was selected as a university distinguished professor, Texas A&M’s highest academic honor for faculty. Biologist Michael Benedik was named Dean of Faculties, and a record-tying six faculty received university-level Texas A&M Association of Former Students Distinguished Achievement Awards — Tatiana Erukhimova and Sherry Yennello in Teaching, Kim Dunbar and Nicholas Suntzeff in Research, Marcetta Darensbourg in Graduate Mentoring, and Edward Fry in Administration. Physicists Olga Kocharovskaya and David Toback earned Sigma Xi Distinguished Scientist and Outstanding Science Communicator Awards, respectively. Toback and chemist David Bergbreiter also earned their second University Professorships for Undergraduate Teaching Excellence (UPUTE) appointments. Mathematics’ Sue Geller received the Texas A&M Honors and Undergraduate Research Director’s Award, while chemist Kim Dunbar earned the inaugural Texas A&M Women Former Students’ Network Eminent Scholar Award.

Students shared equally in the accomplishment spotlight, none brighter than Mathematics’ Tanner Wilson, who earned one of two Brown-Rudder Awards presented each year at spring commencement to the top Texas A&M seniors. Allyson Martinez (Biology) and Meng Gao (Physics and Astronomy) earned Phil Gramm Doctoral Fellowships, while Charles Zheng (Mathematics) received an NSF Graduate Research Fellowship. Mathematics major Frances Withrow earned a Pi Mu Epsilon/Society for Industrial and Applied Mathematics (SIAM) Award at MathFest 2012, and physics major Daniel Freeman received the 2012 Outstanding Thesis Award for Undergraduate Research Scholars from Texas A&M Honors. In addition, four graduate students merited Distinguished Graduate Student Awards for their exemplary efforts in research, teaching and mentoring (Michael Grubb and Casey Wade, Chemistry, doctoral research; Wenlong Yang, Physics and Astronomy, master’s research; Scott Crawford, Statistics, doctoral teaching).

One of our most cherished former students and longtime External Advisory & Development Council champions, the late Dr. Robert V. Walker ’45, received a Texas A&M Distinguished Alumnus Award, while Statistics’ Jerry Oglesby ’71 and our own chemist Daniel Romo ’86 were inducted into the college’s Academy of Distinguished Former Students.

From an educational outreach perspective, Chemistry hosted the 25th edition of its award-winning Chemistry Open House and Science Exploration Gallery, while record crowds attended both the Math MiniFair and Physics & Engineering Festival. Dozens of women participated in a three-day, national physics conference hosted by our Educational Outreach and Women’s Programs Office, while the Mitchell Institute unveiled the Physics Enhancement Program (MIPEP) to improve high school physics teaching. The Texas A&M Math Circle also was born to engage and encourage bright middle school students, while Houston-based Halliburton put its name and grant support behind a new “Mathematics All Around Us” outreach program. The Greater Texas Foundation committed $50,000 to round out a$150,000 challenge grant started by another big name in Texas industry, Texas Instruments, to benefit aggieTEACH. Finally our Center for Mathematics and Science Education (CMSE) is helping to lead a new \$10 million science and technology educational outreach program funded by NASA.

Last but certainly not least, longtime Dean’s Office staff member Carolyn Jaros retired in May, capping 30 years of service to Texas A&M and to three different deans in the College of Science. Biology also saw the retirements of three dedicated career staffers: Tonna Harris-Haller (associate director, Freshman Biology Program), Jillaine Maes (assistant head of the department), and Vickie Skrhak (business coordinator).

In 2012 as in years past, I thank each of you, not only for another year of great achievement, but also for the continued distinction you bring to both Texas A&M University and the College of Science in your efforts to deliver the highest quality of science education, scholarly research, and technical expertise and service to benefit the world.

# A Stitch in Time

Even after a decade in the College of Science and going on a (slightly shocking, even to me) combined 24 years as a student and communicator at Texas A&M University, I never cease to be amazed by the absolute care and creativity so many of our professors put into their teaching efforts. Take, for instance, Texas A&M Mathematics’ Jill Zarestky, who each fall since 2009 has taught a first-year seminar course, Arts & Crafts & Maths, that explores the relationship between art, mathematics and a variety of crafting and fiber arts techniques, including knitting, crocheting, needlepoint, embroidery, cross-stitch, weaving and quilting.

Zarestky, who has been knitting and teaching mathematics at Texas A&M since 2007, is active with the Brazos Valley Knitting Guild and regularly teaches knitting workshops and classes. This month, she also is a featured artist with the local Arts Council of the Brazos Valley. If you aren’t able to drop by the ACBV’s College Station headquarters to see some of her knitted works on display as part of the Fiber Arts: All Things Fiber exhibit, then check out her related guest post for their blog describing her insight into the connections between knitting and math.

Jill Zarestky, in front of some of her work at the current Arts Council of the Brazos Valley exhibition.

The human element: It’s alive and well in Texas A&M Science faculty and in the many personal touches, obvious and subtle, they bring to their classrooms. What valuable life lessons for us all.

Bring your A game, folks, but don’t forget to pack your P (personality) one as well.

# Mathematical Modeling in Biology REU

I’m one of of the faculty mentors for the Mathematical Modeling in Biology REU program, which I originally talked about here. Two of our five students are working with me on a project this summer. We are a three-woman dream team!

We are studying mathematical models of how organisms coexist and compete while using the same resources in an ecosystem. There are a variety of ways that organisms use resources. For example, plants need nitrate and phosphate to grow, and without sufficient quantities of both of these nutrients, the plant will die. On the other hand, humans can get energy for daily activities from carbohydrates, protein or fats. If we don’t have carbohydrates, we can substitute some protein or fat and get by; for the sake of providing us with energy, we need any one of these, but we don’t need all. Modeling has been used with multiple organisms using one type of nutrient utilization, but not a lot with multiple organisms having multiple ways of utilizing nutrients. That’s what we are working on.

Mathematical Modeling in Biology REU Group

Thus far, we’ve reproduced some results from existing models with a common type of nutrient utilization; in particular, we’ve shown how one organism can outcompete others for the same resources, and how two organisms can coexist even though they both utilize the same resources. We are working on learning some of the background science of how organisms use resources and the equations and mathematics associated with this. We are performing a literature review to familiarize ourselves with what research has been done in the past and has been published recently. We are learning what types of questions scientists are interested in and have answered in the past, and also figuring out where we can make a novel contribution. And, given that we are a mathematics program, it won’t surprise you to learn that we are developing the equations we need to make the modifications required to the model we have so that we can do something new.

The other three students in our program have interesting problems to work on as well. Two are working on mathematical models for how atherosclerosis (hardening of the arteries) occurs and how diet and exercise might improve arterial health. One student is working on mathematical models for controlling invasive species; personally, I am hoping he will find a way to mitigate the spread of fireants.