About Jean Marie Linhart

I am an assistant professor of mathematics at Central Washington University.

You Are Enough

Posted on February 5, 2014 by Jean Marie Linhart

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)

Derivative Bee

Posted on November 13, 2013 by Jean Marie Linhart

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

TAMU Math Derivative Bee 11/12/2013

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.

Mathematical Modeling in Biology REU

Posted on June 28, 2013 by Jean Marie Linhart

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.

Research Experiences for Undergraduates

Posted on June 24, 2013 by Jean Marie Linhart

It’s summertime in Aggieland, and one thing that means is an influx of students from across the United States participating in Research Experiences for Undergraduates (REU) grants at the university. The Math Department is only one of many National Science Foundation-funded REU sites at Texas A&M. The Math department has been running an REU site every summer since the program was started in 1999. This summer, we have 14 students, 8 women and 6 men, with us for 8 weeks. Five students are participating in the program in Number Theory, five in Mathematical Modeling in Biology, and four in Algorithmic Algebraic Geometry. The Algebraic Geometry group is supplemented by two local undergraduates.

REU students and mentors, summer 2013

Students generally have lectures and homework to deal with for the first two weeks of the program. This familiarizes them with the foundational mathematics they will need for the research problems they’ll be working on. By the middle of the second week, they are given research problems and get started trying to solve them.

This past Friday, the last day of the second week of the program, all the students and mentors in our REU got together for lunch. Students gave short presentations describing their research problems. At the end of the fourth and sixth weeks of the program, we’ll get updates from everyone on their projects. At the end of the eighth week of the program, we have a Minisymposium, where all our REU students present their results.

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