By Courtney R. Gibbons, Hamilton College

I’m sure you, like me, have way too much going on.  And I’m sure you, like me, are asked to take on even more.  Some of these projects are fun.  Some of them align with your long-term interests.  Some of them are even better than all of the stuff on your plate put together.  Even if the opportunity is great, you may still want or need to say “No.”  I trust that you have either a good innate sense of when to say no or a mentor who will help you decide.  What I would like to offer you today is a guide to the four things that I put into my no response: Appreciation, No, Explanation, Request.

Here’s a quick example, and then I’ll say a little more about each part.

Dear Courtney,
We would love it if you organized a session for our research program at the Joint Math Meetings.  What do you say?
Sincerely, Research Program Organizer

Dear Research Program Organizer,
Wow! Thanks for thinking of me as a potential organizer.  Unfortunately, I have to say no.  Although it would be fun to do this, when I look at my CV, I realize I should be actively pursuing opportunities to speak in sessions, not organize them.  Here are some people I think would do a great job and might find it valuable for their professional development: (name, name, name).
Best,
Courtney

1. Appreciation
When I read a request, I usually have to get my brain to switch out of cynic mode.  Figuring out how to start off a message with appreciation helps me to do this.  After all, someone asked me — me?! — to do something, and it’s mentally helpful for me to assume it’s because they think I’ll do it well.  I like to start off by recognizing this.

2. No
This part should be easy: say no.  Flavors of “No” that I like range from “Hell no!” to “Not yet” to “Yes, but” — here are some examples.
“That doesn’t align with my goals, so I must decline.”
“It’s tempting, but not yet.”
“I want to do this, but here are some obstacles.”
In my response, these sentences are followed by an explanation, but I try to make it clear right here whether the I want the person sending the request to help me problem solve so that I can say “Yes” instead.

3. Explanation
Here is the most important part of the message based on my experience so far.  As honestly as possible, I give my reasons:
“I have bronchitis.”
“I can’t justify taking on a service role right now without a payoff in terms of compensation, professional development, or work that counts toward tenure.”
I try to make sure that I am honest so that if someone does find a way to respond constructively to my explanation (“But this is instant-tenure, didn’t you know?”), it does change my answer from no to yes.  If you haven’t had the experience of coming up with a great excuse only to have it artfully handled, trust me, it stinks.  Another benefit is that, if your explanation is, “I should be speaking in research sessions,” the person you emailed may try to help you with that!

4. Request
I know it sounds weird to answer a request with a request.  I have found that it’s helpful to give the asker something to do after reading your email.  Do you want to participate, but can’t afford to get to the conference? Ask for help to solve this problem.  Do you not want to do this? If you know of others who would benefit from saying yes to the request, suggest them (I like to ask for permission, first, though). Are you unsure if this is a good career move for you? Suggest that the asker talk to your department chair or someone else who acts as a gatekeeper for your time. Ideally, this gives the asker a next step that isn’t just “get Courtney to say yes.”

So there you have it — that’s how I say no to requests.  I’m happy to trade advice in the comments!

“How should I prepare for the GRE Math Subject Test?” This is a common question asked by students embarking on the math graduate school application process, yet many professors don’t have a great answer. A common part of one’s graduate school application portfolio, the GRE Math Subject Test is notorious as a standardized test that covers fundamentals from courses throughout undergraduate mathematics. Despite being an integral part of one’s application, there aren’t many relevant resources for preparing for this exam. Only a handful of practice exams are available, many of them outdated and irrelevant to the current exams. GRE practice books published by the ETS help with math content review, but do not develop strategies for tackling the seemingly esoteric style of problems on the subject test. In this post, we suggest strategies for helping students prepare specifically for this test.

Creating Content Flow Charts: You might have seen students prepare for the subject test by reviewing specific content and working on practice problems on the chosen content. One of the potential issues with this approach is that problems on the GRE Math Subject test tend to require recall of many different aspects of a subject instead of focus on an isolated topic. An example is the following sample problem I created for a GRE prep program at Harvey Mudd College:
If f(x) is the real-valued function f(x)=x|x|, then which of the following must be true:

I) f is continuous on all of the reals

II) f is differentiable at x=0

III) f is odd

a) II only  b) II and III only  c) I and II and III  d) III only  e) I only

Approaching this problem requires quick recall of different concepts on single variable functions. In order to practice having recall at their fingertips, I highly suggest students make a content flow chart for a subject area. This involves placing definitions, theorems, and implications from a particular subject area all on one large poster. For instance, if a student is reviewing single variable calculus, they might create small boxes with the definitions for continuity, differentiability, and integrability. Then, they can place an arrow from the differentiability box to the continuity box because the former implies the latter. Furthermore, they can write or draw examples of what could go wrong in the other direction. This could include specific counterexamples, and also general properties of functions that are continuous but not differentiable. Content flow charts allow students to see a topic holistically, which is extremely advantageous for quick recall.

Prepare Specifically for the Test Itself:  As mathematicians and educators it is our natural tendency to want to teach the inner workings of a subject area, and spend time motivating the concepts at hand. However, the goal with the GRE Math Subject Test is to answer problems as quickly and accurately as possible, rather than lament over depth. This is one of the biggest struggles I had while holding prep sessions, but it’s a key one to address. To see an example of this, consider the following problem:

Suppose x and y are integers, and 8x-5y is divisible by 7. Which of the following must also be divisible by 7?

a) -6x+2y   b) -6x+3y   c) -5x+3y   d) -5x+3y   e) -5x-2y

As mathematicians, our natural tendency is to explain phenomena that divisibility captures. However, it can be much quicker, as in this problem, to focus on strategies inherent to the test. A quick way to address this problem is to pick a nontrivial pair (x,y) of integers, say for example x=3,y=2, for which 8x-5y is divisible by 7, then check which of the given answers also satisfies the same divisibility property.

Patterns in Old Exams:  Past GRE exams tend to have problems types that are repeated over and over. Knowing how to do such problems quickly saves time on the exam itself. For instance, an analysis of past GRE data shows that multivariable calculus is the subject area with the poorest results, however almost every practice exam has a question on applying Green’s Theorem directly, where doing so simplifies a problem to multiplying the area of a region by some constant.  Knowing this one concept gets students ahead on the exam.

Create a GRE Community:  Along with Dr. Ivan Ventura (now at Cal Poly Pomona), I held GRE practice sessions early fall once a week for 6 weeks, with pizza served. Having practice sessions over food set the tone for a casual study environment. I think this was essential in relieving the stress and anxiety students had.

These are just a few tips that can be very helpful for students studying for the subject test.  I hope you can use them at your institution!

For more practice problems, visit my GRE Math Subject Test YouTube page here:

In December 28, 2016 former President Obama’s Presidential Proclamation declared January National Mentoring Month. In this document he stated:

“Nobody succeeds on their own: each young person’s strength and resilience is fostered by those who have taught them they can do anything they put their mind to. Whether helping mentees study for a test, learn a new skill, or lift their heads up after a setback, mentors provide them the chance they need to move forward and set their sights even higher.” – Mr. Barack Obama

(You may read the proclamation in its entirety here.)

I often ask myself what constitutes mentoring in the mathematical community? Is it teaching our students calculus, how to write proofs, and/or advising their thesis? Or is there more? Even more importantly, how have students (and early career mathematicians) benefitted from mentoring?

I think we’d agree that mentoring can take many forms and teaching is one way to mentor students. Having great teachers in the classroom can make the world of difference for students, both in terms of academic achievement and in building confidence. But my most memorable and life changing mentoring experiences have hardly ever taken place within a classroom setting. They occurred because someone stepped up, with zero regard for how their actions would benefit them, and helped me in some way. From reaching out to make sure I am well, to suggesting conferences to attend, to helping me edit essays for scholarships, or even job materials, my many mentors have never received any benefit other than the joy of seeing me both fall and get back up, and at times succeed.

These mentoring experiences are what I’d like to call our attention to. I want to remind us that small actions can have a large impact on not only our students, but our peers, colleagues, and our community. With this goal I reached out to a selected group of students and faculty friends who contributed the following anecdotal stories of the impact mentoring has had on them and their careers.

Mentoring stories

“When I was a sophomore in high school, taking pre-calculus, my teacher Mr. Huckstep, on a day when we did a review, he came to me and asked me to be on the math academic team. He was the coach for the team and he sat next to me and said `I’m basically going to groom you to be captain over the next couple of years.’ I had been doing well in my math classes since high school started, so it wasn’t like I needed a confidence boost, but I had a shaky relationship with math since I failed Algebra in seventh grade, but this was the end of that. He did exactly what he said. During the season, every Friday, I spent an hour after school, with some of my best friends, being exposed to math in a friendly, stress-free environment. Years later I write this short paragraph, excelling as a math major at Williams College. It may have been possible without him, but it wouldn’t have been so certain, or with as deep a passion and appreciation.” — Anthony Simpson, Math and Computer Science double major at Williams College

Nohemi’s students at Shanti Bhavan

“Shanti Bhavan is truly a haven of peace for the children of southern India. Having been blessed with the opportunity to teach/mentor kids this summer at this nonprofit boarding school allowed me to not only teach my students what I know, but to also learn a lot from them. A very memorable moment with one of my students was seeing the face of my fourth grader, Arasu, lighten up after finishing every math assignment. One day after finishing all of his math problems, he happily said to me, ‘Miss Nohemi, I’m finished! Can you please give me a really challenging math problem?’ Smiling at him, I gladly wrote down on his piece of paper 999 x 99. A few moments later he came back to me with the right answer. I continued to give him more and more challenging problems to work on until we got to 9^8. After showing him an example of how to solve these type of math problems, he continued on to his seat. He came back to me a few times, but had not quite yet gotten the right answer. I offered to help him and I told him that it was fine if he tried to do it up until the fourth power rather than the 8th, but he only looked up at me, smiled, and went right ahead onto his desk. After a few days had passed, on an afternoon when the rest of the students were playing soccer, he approached me with two sheets of paper and many, many numbers. His answer was finally correct! Arasu had not given up on the problem despite the difficulty of it, and neither had he stopped trying despite the amount of times that he continued to redo his work. At that moment not only was I very proud, but I was also so full of joy knowing that Arasu’s perseverance had conquered in the end. Right then and there I saw myself in him since I was the same way when I was his age. I always understood that no matter how many times we fall in the midst of difficulty, in the end all we have left to do is to write down all of those problems on a sheet of paper and start conquering them one by one.” — Nohemi Sepulveda, Mathematics major at Williams College

Dr. Van Nguyen and Professor Susan Geller

“Besides my Ph.D. advisor and many more mentors I have been fortunate to met along my career path, Professor Susan (Sue) Geller (Texas A&M University) is among the first ones that showed me what it means to be a mentor. I have never taken Sue’s class nor been her research advisee, but I had worked with her in coordinating various outreach/seminar events. I knew Sue was very experienced in her career and I reached out to her for help when it came to my first job interview in graduate school. To my surprise, she did not simply reply my email back with an ‘Ok, see you in my office’ appointment but she offered to take me out for lunch; and we had a fruitful conversation in which she provided me with valuable guidance, including interview techniques and career advice. After that, she went far and beyond to arrange several more lunch meetings with the female graduate students and postdocs who were on the job market that year, with a purpose: to ease our job search process. We learned so much from her experience and inspiring stories, especially as a female Mathematician in the early 1970’s. (Sue makes endless efforts to promote opportunities for women and underrepresented minorities in mathematical sciences — another factor that I really admire and look up to). Little did she know, that one initiative lunch had a great impact on me. I benefit not only from her continuous support, but also from the example that she sets out as a mentor/teacher. Her enthusiasm and dedication motivate me to be a better teacher who is willing to take an extra step to reach out to students, and inspires them the way she has inspired me. I would never forget the sight of Sue waiting for me with a bright smile as I walked down the graduation stage; and that warm hug she gave me at my Ph.D. graduation ceremony is the most vivid proof of a proud, caring, and devoted teacher she has been to her students.” — Dr. Van Nguyen, Zelevinsky Research Instructor at Northeastern University

“Throughout my academic life I have been lucky to know really amazing professors, academic advisers, thesis adviser and even administrators, who have helped me advance as a student. However, some of the most meaningful mentoring has come from my peers. As an undergraduate student I found myself in a very difficult personal situation, so I had not seriously considered graduate school. My classmate and friend, Ashley Weatherwax, pushed me to attend conferences. At one of the conferences she took the initiative and introduced me to a professor who later became my PhD adviser. He invited me to visit the school, but I was hesitant. Ashley knew this and tricked me one morning by telling me she wanted to take me to a nearby park for a run, but instead drove me from Dallas to Arlington, TX to meet with the faculty in the graduate program. Ashley saw potential in me and did not take no for an answer. I can honestly say my life would be really different now if she had not believed in me.” — Alicia Prieto Langarica, Associate Professor of Mathematics, Youngstown State University

Mentoring comes full circle

Below is Elise Eckman’s story. Elise is a student of Dr. Alicia Prieto Langarica.

“Starting off my first semester at Youngstown State University was frightening to say the least. The change from the structure of high school to the freedom of college was not an expected change. I was in need of some guidance and thankfully, I was placed into Dr. Prieto’s Calculus 2 class. After proving to be a better than average math student, Dr. Prieto called me into her office to recruit me to pursue a math major, as I was currently a mechanical engineering student. After some deliberation, I left her office planning to obtain a double major. Very soon after we met in her office, Dr. Prieto asked if I would be interested in doing research with her. Of course, I agreed. Since working with her, I have been presented with so many opportunities. For example, I have met other math majors in YSU, other math majors in different colleges, and math professors from all over the United States. I have traveled to places I thought I would never go, and I have been working on a topic in math that is not covered in undergraduate math courses. Without Dr. Prieto, I would not have the future waiting for me that I do now. With her guidance and thoughtful attention, I now have direction and confidence in my studies. I am very thankful that she took me under her wing and believed in my potential.” — Elise Eckman, Mathematics and Mechanical Engineering double major at Youngstown State University

These stories illustrate that there is no one algorithm for mentoring. Mentoring does not have to be a scheduled event, nor a formal process for it to be effective (although these may help!). However, it does require you to care enough and to act in a way that benefits others. It is also timely, it requires you to be available and present when someone needs you.

Among your new year resolutions, I urge you make this year one in which you actively embrace mentoring. This resolution’s benefit may not yield a smaller pant size, but it will have a great impact on the members of our mathematical community.

Opportunities

In hopes of helping you get started, I append a short (and definitely incomplete) list of organizations in math and STEM that provide mentoring opportunities.

• The Math Alliance wants to ensure that every underrepresented or underserved American student with the talent and the ambition has the opportunity to earn a doctoral degree in a mathematical science.
• Association for Women in Mathematics (AWM) Mentor Network matches mentors, both men and women, with girls and women who are interested in mathematics or are pursuing careers in mathematics. Also has applications for mentoring grants to help pre-tenure women work with a research mentor during a summer. 
• The Global STEM Alliance has a variety of mentoring programs, from 1000 Girls, 1000 Futures, to afterschool STEM Mentoring. They are led by The New York Academy of Sciences, and this organization recruits STEM professionals, postdocs and grad students to act as role models and mentors to STEM-interested students in communities around the world. 
• StudentMentor.org an online mentoring program that seeks to increase college completion and career readiness by utilizing its technology platform to connect college students with professionals. 
• Big Brothers Big Sisters of America “seeks to change the lives of children facing adversity for the better, forever.” There are locations all across the United States and their mentors work with children in the community, in their schools, on military bases, and many places in between. 

If you want to find additional mentoring opportunities the Mentoring Connector is a national database of youth mentoring programs vetted for quality standards. The Connector is operated by MENTOR: The National Mentoring Partnership. 

Happy mentoring!

Have a great mentoring story to share or an additional organization to mention? Please share it in the comment section below.

The following is a guest post from Duncan Rocha drocha@g.hmc.edu.

First, allow me to introduce myself. I am Duncan Rocha, a Tejano/Scottish crossbreed from San Francisco, California. I am a little more than two months into my college experience at Harvey Mudd College as a physics major, and so far it has been more than I could possibly ask for.

My father was the record-breaker in his 100% Mexican-American family. Being the first to go to college and eventually earn a masters degree, he conducted research in many branches of physics. Naturally, as a young boy, those were the shoes I wanted to step into. Growing up, though, has made me realize that my interest in physics has not been a string of boyhood fantasies and ideals. It has been a true passion for understanding the universe. As I grew older, I took physics into my own hands, flipping through any material I could find. I learned about research at the LHC, Fermilab, and many other facilities. To me, that was the dream. If I could just make it to Ligo, to the LHC, to an office in a university, I could fill the shoes that a great physicist wears. My childhood dreams, of lab coats and notebooks and complicated mathematical symbols scribbled on a blackboard, would be fulfilled. That is the image I has always painted myself into, but I have never really felt like it was within my reach. Especially as my other dreams faded out of existence, like going to the MLB hall of fame or becoming a star musician, it felt like my dream of being a great physicist was fading too. I never felt like the opportunity might never present itself, and if it were to, it would be years, if not decades, in the future.

I was wrong.

I walked into the SACNAS conference without a clue about what to expect. As I stepped into the exhibit hall, I was simply astounded. The pure vastness of the conference left me a little dazed. I think I managed to mutter a small “whoa” as I wobbled in, eyes wide at the sight. Thousands of people packed corridors upon corridors of booths, each flying different colors of schools, research institutes, or companies. Not only that, but the entire fair was surrounded on three sides by what I estimated was close to a thousand research boards. I began to explore the sea of science and math, but one booth quickly caught my eye. I strolled on over, not really sure what to say or where to begin, because the name of the booth had suddenly opened floodgates in my mind. It was Ligo. All of the stories I read about it, all of the chatter about gravitation waves and the fascination of all the intellectuals and even my own father, all of it came to the forefront of my mind when I approached the booth. This was it! This was an opportunity to step into the shoes of the image of the adult Duncan I had sculpted as a kid, and I was chatting with a man who could give me a chance to fulfill that dream. There is nothing more I could have asked for than to spark that flame, to reignite the hope I had when I was a kid that I would someday become a great physicist. I didn’t even care that a freshman almost certainly couldn’t get an internship at Ligo, I just needed something to reestablish the dream of my future. After that first encounter, I went on to explore the rest of the conference, but those two or three minutes at the Ligo booth were the most impactful for me of any other moment.

I hope, and as a matter of fact I know, that I was not the only young student who had their hopes and dreams reestablished by the SACNAS conference. I know they will continue to inspire young Latino/as and native American minds to aspire to become leaders in their fields.