Progress and Struggles of a Math PhD Student

Advice from an Old Friend

by Kamala Diefenthaler on 02/14/13

You are the only person who can write your dissertation.

"Fake it till you make it" is a common catchphrase that means to imitate confidence so that as the confidence produces success. I am gathering information and filling out forms as if I am finishing my degree in December 2012. I have emailed professors about dissertation templates as if I am ready to write and submit my dissertation.

The truth is, I have been focused on my teaching and neglecting my research. There is a long way to go before I can write my dissertation and graduate. However, I have already noticed my confidence growing as I "fake it".

I am going to continue "faking it" as I read renowned author's papers. I have hardly read any papers because of my lack of understanding. My coworker, who has a PhD in one of the sciences, told me that he didn't understand the first 10 papers he read. But by the time he read the 11th paper, he was following along. So that is my plan...read without understanding until I can follow along.

Wish me luck

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Mini Papers

by Kamala Diefenthaler on 01/29/12

I need to gather my work and thoughts into a publishable paper. This is an especially daunting task, because I have never published a paper. Here is my strategy:

Divide the topic into manageable sections.
Write a separate mini paper for each section.
Convince my advisor to review and comment on the mini papers.
Have either me or my advisor combine the papers. Paying special attention to flow and uniform notation.

I am currently writing the mini papers and sending them to my advisor as I finish. I'll post the paper once we have the preprint ready.

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Day 3: Progress

by Kamala Diefenthaler on 01/18/12

Today I reaped the benefits of yesterday's frustration. I had a quick chat with my advisor this morning. Because of all the seemingly worthless articles I read, I knew exactly what he was talking about.

I worked for about 2 hours then took a nap. When I woke up the problem had worked itself out. After about 20 minutes of calculations, I was correct! When my advisor mentioned variational formulation, I immediately thought of a process like 'take the derivative'. However, variational formulation is just a weaker form of a property. Also the discrete inner product I am using is a functional (duh), so the pages of meaningless integrals now relate to my problem. This was HUGE for me. It has been almost a year since I have made any real progress. It was a small step, but very meaningful.

I was in "the dip" and debated quitting. This revelation is my first step out; I truly believe I can finish my PhD while in China. With this momentum I figured out another small piece, and I have one brewing in the back of my mind.

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Day 2: Less Than Impressive

by Kamala Diefenthaler on 01/17/12

Day 2 of no teaching was off to a great start. I got a full 8 hours sleep. Woke up peacefully and read the Bible with my husband. Then immediately Skyped with my advisor. Before 7am rolled around, I was pumped and ready to make today great.

I discussed a fairly routine problem with my advisor, and I wanted to understand his choice of a matrix. Here's the big picture: we are projecting our function to an appropriate subspace then having our approximation equal our function on that space. I get this, but I wasn't clear on the exact technical details. My advisor says the technique is standard and mentioned 3 things: variational formulation (don't know), finite element method (know), and least squares (know).

First task was to understand the technical argument. I go to the internet and search several different combinations variational formulation. This is where my "great" day begins to fall apart. There were no simple Wikipedia articles on variational formulation, no Wolfram definitions. All the hits were papers and books and they focused on solving PDE's, which is not my focus.

I was not getting anywhere. After a couple hours online I had read some interesting and some not interesting pages, but nothing that shed light on my problem. So I packed my stuff up and headed to a local coffee shop. I hoped a change of scenery and some good food would help. I was focused, but still unfruitful.

The graduate AMS blog had an interesting post titled Productive Procrastination: the Importance of Having Several Projects. I am past this point since I must finish writing the paper this month. I can see the benefits of the idea. By having several different tasks, when you are burned out with one you can work on another that requires a different part of your brain.

The big picture is clear to me, so the best thing for me to do is move on and discuss with my advisor tomorrow.

As a side note, I am looking into attending the 2012 International Conference on Applied Mathematics in Hong Kong. If anyone has attended or will be attending, please send me an e-mail.

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No Teaching: Day 1

by Kamala Diefenthaler on 01/16/12

Exams are graded and final grades are submitted. Next up research. It has been a long time sense I have worked on my research, so today I recapped where I was and what I was doing.

Over the past year (or more) I have written a few C++ programs. In my mind, they are separate programs with different applications. However, my advisor views them as branches of the same overarching concept. I need write a paper joining the programs together, yet describing their differences. This has been my task since I moved to China. Now I must tackle it.

I read through what has already been written, reviewed the programs, and made a Skype appointment with my advisor.

When I was distracted today I visited a graduate student blog by AMS (American Mathematics Society) and Terence Tao's webpage. Both of these sites are full of helpful advice, and they refocused me.

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Exposing Yourself to Research

by Kamala Diefenthaler on 12/30/11

I have worked for a few years on my topic, on my program, with my own terminology. I don't know what has been done before in my area, what people are doing currently, or the terms already in use for related topics. This is a big problem when I go to write about my own research.

Here are some suggestions from www.cs.umd.edu:

Make a weekly effort to read at least the abstracts from the premier journals in your field. Choose an article or two to read in depth and critique.
Make a weekly search to find preprints in your field. Read selectively and critique.
Attend a research seminar or colloquium series. Listen and critique.

Two premier journals in my field are Constructive Approximation and Journal of Approximation Theory. A recent paper that I want to read is Processing Terrain Point Cloud Data. I have worked with 3 of the 6 authors. This paper uses the same data that I process, although they use a very different method. The 3rd suggestion will be challenging. I live in Beijing and I am not familiar with any University here researching similar topics. Maybe I can find some seminars or talks on the web.

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Active Listening and Reading

by Kamala Diefenthaler on 12/20/11

Throughout graduate school I learned the importance of giving your full attention in class. I learned to completely understand the homework, not just find an answer. So why do I still struggle with active listening and reading when it comes to research? I can't count the number of times I have slept during a seminar, or read a technical paper without retaining any of it.

I came across this website www.cs.umd.edu/~oleary/ and it had some great advice. When listening to a talk or reading an article ask yourself these questions:

From where did the author seem to draw the ideas?
What exactly was accomplished by this piece of work?
How does it seem to relate to other work in the field?
What would be the reasonable next step to build upon this work?
What ideas from related fields might be brought to bear upon this subject?

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Beginning Again

by Kamala Diefenthaler on 12/19/11

I have been apart of a great research team in the Interdisciplinary Mathematics Institute (IMI) at the University of South Carolina (USC) for the past 5 years. I started as a summer intern in college. Once I got my bachelor's from Coastal Carolina University, I worked at an insurance company for a year. Then the IMI offered me a full time job. I loved this job and the people. They motivated me to start graduate school at USC.

I have completed all the necessary coursework and I have successfully passed both the Qualifying Exam and the Comprehensive Exam. All that remains is the dissertation. I have participated in several research projects over the years, but selecting, researching, and writing for my own dissertation has been a huge struggle. I would love to blame moving across the world to China, but that's not true.

Thoughts of doubt and inferiority plague my mind. Most of the research I previously have done was guided research (i.e. I did as I was told). Now I need to mature in my mathematics and write and research on my own.

Research is protected and may contain sensitive data, so this blog will mostly focus on myself and not the actual research.

"So here I go again on my own..."

If you are working on your PhD and have any suggestions, please send me an email at kdiefenth@gmail.com.

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