Do I owe you?


The grad years

You accepted me into a graduate program having just given birth to my daughter 4 months prior. Offered me a fellowship in which I had reduced teaching responsibilities and when I did teach I was left to my own devices — teaching with no prior training other than the single hour when some professors pretended to be students in a classroom and asked me to “teach.” In this way, I learned by doing and I taught many students. Some of these students saw for the first time someone of their same ethnicity reflected back at them from the front of the room.

Throughout I was often made to feel like I owed a debt.

Is this sense of debt and continued expectation for me to be grateful for the opportunities I was provided due to being let into this program because you thought that no one else would accept me? Even with a near perfect GPA? Was the thought that because I started in community college I was going to be unprepared to succeed in any graduate program and so you’d take a chance on me? Was the default to admit me into a Masters program, even though my experience should have placed me in the PhD program? Was this based on preconceived notions of my mathematical abilities based on my ethnicity? On my gender? And when I was left with no supportive mentors and failed examinations did you feel vindicated because you knew I wasn’t ready?

If so, do I now owe you?

The postdoc years

Moving onto that first academic position, that familiar feeling of owing a debt returns. Being told that I should be grateful to have a job, as if I dug at the bottom of a barrel to find an academic position, when I selected this one among over 10 other great offers. Yet simultaneously getting the clear message that these offers only came because I am a Latina woman. Did you hire me because of these reasons? Maybe this is why I am often mistakenly called by the name of the only other person of color in the department… a Black woman. You can’t even tell us apart. Or how about those hallway conversations where you tell her that you met her husband and she corrects you: “I am not married, you met Pam’s husband.” To which he replied: “No I meant your husband… the Black fellow.” Because in your mind, a Latina woman and a Black man together is an unthinkable concept.

Is this why you ask me to mentor women and underrepresented students and tell me it is my job to fix issues of culture within departments in which I am perceived as a constant problem? The expectation that I fix the problems I point out and played no part in creating leads to my exhaustion. So you tire me out. Is this to make room for others whose faces are more reminiscent of those pictured in departmental images of years past? Pictures in which women didn’t appear until my lifetime, and our contributions are constantly erased. So, I should be grateful for the opportunity to be here now.

I ask again, do I owe you?

The tenure track years

Week one on the job a “colleague” told me I never had a real postdoc because it could not possibly compare to their postdoc at Elite University of the Universe. They kindly offer to help as long as they can list me as a mentee on their annual report. Was this because they saw me as a naive fool who they could manipulate to benefit from my work and sheer existence? I later learned that they continually attempted to sabotage my career behind closed doors. Going as far as harassing and intimidating a vocal and supportive advocate whose only mistake was to announce their plan to nominate me for an award. An award I won and for which they congratulated me to my face. All the while my teaching feedback from colleagues includes feedback gems like “today she held a cup of coffee and it made her appear warmer.” To add insult to injury, when I questioned the validity of this feedback, the response was a warning that people will hold grudges when I go up for promotion and tenure. After all, I should be grateful for their mentoring and help in navigating a tenure process that I was surely going to fail.

After years of being under constant surveillance… err mentoring, their narrative changed. My success became theirs, for they “supported” me and that surely helped me thrive. So now my many successes are diluted by those taking ownership of them — after all, what Latina woman could survive without rescue by people who pretend to support her while they pat themselves on the back for feigned caring. That familiar feeling returns — yet again, I am made to feel like I owe a debt.

The tenure process came and went with a positive result. Yet comparing records, we quickly realize the bar was higher — almost insurmountably higher — and yet I should be thankful that with all of the support I received I made it to the other end. Did I thrive because of their support or in spite of it?

So, do I owe you?



Posted in career advancement, General, postdocs, Tenure, Uncategorized, work life balance | 8 Comments


By Alexander Diaz-Lopez, Pamela E. Harris, Vanessa Rivera Quinones, Luis Sordo Vieira, Shelby Wilson, Aris Winger, and Michael Young

In our times of need, we have come together, often behind the scenes, through all mediums and platforms, to make space to discuss the many challenges that we have experienced as underrepresented minorities navigating academic environments within the mathematical sciences. Unfortunately, this work is often unseen, it is personal, and requires long-lasting relationships that are based on mutual trust and a sense of belonging within the mathematical community. Something that can take years to cultivate or even find.

Yet, we are all at a stage in our career where we can look back and without hesitation point to these relationships as a key source of support which helped us complete our graduate degrees and helped us advance professionally. This was not always there for us. In fact, our graduate school years were not only formative, but they were also full of uncertainty. We could not help but wonder:

  1. Am I good enough to do this?
  2. Is it OK to spend time on something I am passionate about that is not school?
  3. Why do I feel so alone in graduate school?
  4. Why am I doing even this?
  5. Why is everyone nodding during this talk?!? I don’t understand a thing these people are saying!

These are questions which many graduate students have, but being underrepresented means we face additional burdens, such as working to quiet an everyday voice telling us that we are not there simply because we checked the right boxes, we must avoid a nonsensical self-imposed pressure in which we represent our entire communities. Also, being the only graduate student of color in a graduate program can be or is an incredibly isolating experience and a huge culture shock.

The fact that there is much work to do to support underrepresented students succeed in completing their graduate programs were leading points of discussion at two meetings of Networks of Mathematicians of Color and Latinx Mathematicians Network, both workshops hosted by the American Institute of Mathematics. As the workshops’ names imply, each of these workshops addressed the need for programs specific to brown people and black people separately. But, as can be expected, there are many commonalities facing underrepresented communities, as a whole. In particular, the need to create spaces and communities where we can flourish together both personally and professionally became a recurring theme. While each AIM group independently brainstormed programs designed to give a survival toolkit for black/brown students, we were inspired and motivated by the EDGE Program which has been successfully mentoring women as they enter and complete graduate programs for over 20 years, and all with excellent results.

Thus we have come together to create and organize Math SWAGGER: Summer Workshop for Achieving Greater Graduate Educational Readiness, a FREE five-week (virtual, due to COVID19, but we hope to be in person in future iterations!) summer program for any underrepresented student who will be enrolled in a mathematical/statistical graduate program in Fall 2020. The goal of the workshop is to provide support, but most of all community, amongst graduate students of color. We hope that students walk out of this as a part of a tiered mentoring network. One where they find community with peers and potential mentors to which they are able to stay connected throughout their careers.

The program will have students and facilitators meet virtually three times per week for 90-minute discussions on predetermined topics centered on the challenges faced by underrepresented students in those programs. We plan to discuss topics such as motivation, which centers the question “Why are you attending a mathematics graduate program?” and how this question is central to success in grad school. We also will not shy away from having difficult conversations, as an example, we will have a session on “Dealing with Whiteness,” where we address the experience that predominant narratives are white narratives, and how we can navigate through such environments while remaining true to ourselves and our identities.

In many ways, for students of color and those from underrepresented backgrounds, the topics we discuss represent only a subset of challenges they will face in their journey to complete their graduate degree. It is because of this that throughout the Math SWAGGER programming, our main effort will be placed on offering participants space and opportunity to connect with other students and faculty that can offer advice, support, and a safe place to have these difficult conversations. Not only do we expect that Math SWAGGER will equip students with tools to navigate their graduate program and be successful, but it will also open the door to a wonderful community among peers, faculty, and mentors.

The importance of getting connected to a community and network of mathematicians, cannot be overemphasized. Having such a network has shaped our own experiences with mathematics and has built a sense of belonging within each of us. Unfortunately, many of us did not feel like we belonged until much later in our careers, and for far too many of us, that sense of community comes too late.

Thus it is our hope that by participating in this program each student will be able to transform their graduate experience in a meaningful way and leave the program having started connections that will have profound impacts on their careers, so that they too can be unapologetically themselves in math.

[Applications to participate in Math SWAGGER are due May 22, 2020, and the application can be found here.]


Posted in career advancement, Changing Graduate Programs, General, Going to graduate school, Graduate School, graduation, Outreach, Uncategorized | Leave a comment

Learning During the Pandemic: What we wish our professors and mentors knew

Student Authors: Mayleen Cortez, Brooke Keene-Gomez, Lucy Martinez, Amaury V. Miniño, Jenna Race, Kelemua Tesfaye, and Stephanie. Blog post compiled by Melissa Gutiérrez González, Pamela E. Harris, and Alicia Prieto Langarica.

In this blog we center the voices of mathematics students as they share their experience with remote learning during the COVID-19 pandemic. 

“What do you wish your professor knew about your current experience with remote learning and living during this pandemic?”

  • How hard it is to focus on school work at home and how anxious I am about finances. 
  • I wish my professors knew that my mental health has not been stable. I am also currently attending online classes in the dining room which is not the best place to focus for my classes. I do not have a designated area in my home to do my homework or to attend my classes. It is difficult to sit at the same spot where you eat and complete homework. Sitting in front of a computer is also exhausting and it has been difficult to focus on each class. 
  • I wish my professors knew how disruptive the move to online courses and social distancing measures have been to my daily and weekly schedule. I spent years learning about myself and how I best function, and all of that feels as though it has been thrown away since I am stuck at home. It is particularly stressful since I am in my last semester, and was in no way prepared for the additional stress and anxiety that has come through the pandemic.
  • One thing I wish my professors knew about my current experience during COVID-19 is that I’m dealing with so much more than just living through this pandemic. My family is currently going through a tough time over something unrelated to COVID-19. My heart feels broken over a certain family member’s situation and I feel helpless. Some of my close friends are stuck at home with emotionally and mentally abusive family members and I feel helpless. Furthermore, so many of my loved ones and friends are undocumented immigrants who are not recieving stimulus checks or unemployment and my heart feels heavy all the time. My people are suffering. Our people are suffering and I feel… helpless. I can’t think of a better word. How can I just sit here and work on an essay or another assignment that feels like “busywork” when people are sick, scared, starving and dying? I’m doing the best I can, but sometimes I wish I could drop my classes and just focus on my family. I want to put my effort into finding ways to help my community… not replying to another discussion post or trying to derive numerical quadrature techniques or writing another essay on whether or not I think numbers actually exist.
  • I don’t have unlimited free time just because we’re quarantined. I live with people who are working from home, my siblings who are also trying to do school online, and my young son, so I don’t have undisturbed time to work.
  • This pandemic has exacerbated the vulnerabilities myself and loved ones hold in society. Those of us operating from communities at high risk are organizing to support one another within the evolving circumstances. Online learning is predicated on students having access to the resources campus offers as well as having the stability and capacity to maintain the workload despite the circumstances. This assumes a privilege of distance from the crisis, as well as a baseline level of wealth, access, and health to navigate the new academic terrain. Students like myself existing at rich intersections are well practiced in resilience and creativity in overcoming structural barriers. Even if this isn’t the dominant narrative at the university, I think it’s vital for institutions to exercise the same creativity we exhibit in support of students. 
  • I wish my professors knew how hard this is. My whole life has changed. Going to class was the highlight of my day. Now I don’t leave the house for days other than to check the mail. I’m above average when it comes to motivation, but lately it’s been a struggle. I’m an extrovert and I get energy from people, especially people who are enthusiastic about their field. Now I watch pre recorded Zoom videos in lieu of lectures. I think perhaps if that was my established expectation, I wouldn’t find it as disappointing. I do hope the professors know they are appreciated, and that everything they do does help. I want them to know that while this is hard, most students realize it’s hard for them too. It’s a transition for everyone.

“What do you need from your mentors during this time?” 

  • I urge my mentors to exercise empathy and organize to challenge structural racism and classism, to combat disposability politics. 
  • I need my mentors to be understanding of the abnormal situation we are in. As I work through my courses, I am less motivated by a desire to learn, and more motivated by a need to establish normalcy. I want to care more about the work that I am doing, but I am scared of what will happen in the coming months and years. One of the best ways my mentors could help is by simply checking in with me, talking with me, and guiding me to ways to ground myself.
  • Advice about future academic goals and less emphasis on exams, more on course material.
  • I need my mentors to motivate me and guide me through this difficult time. I know that this should be a two way ongoing mentorship and guidance because professors are also going through challenges as well. Students and mentors should work together to create a strong and collective participation. Small emails are important for me as a reminder that we are all in this together. Meeting through a form of video call has been essential for me as it keeps up my self-esteem.  
  • To ease up on the workload. Many professors are assigning more work and I don’t have enough time to keep up with it.
  • I need patience and understanding. I just want to be successful. I’m going to ask a lot of questions and ‘blow up your inbox.’ I apologize in advance. Please try and understand this isn’t what I signed up for. I know it’s not what you did either.
  • I need to know that if I don’t end this semester with awesome grades, or if I take a little too long to respond to an email, or if I just haven’t checked in with them in a while, that they understand and aren’t holding it against me… that they still value me and they know I’m trying my very hardest to be positive, productive, healthy and responsible during this pandemic. I just need them to know I’m trying my best… and I need to know that that’s enough.

We hope that these comments inspire faculty and mentors to listen to their own students  and to understand what they are experiencing as they live through this pandemic. May the experiences shared by Mayleen, Brooke, Lucy, Amaury, Kelemua, and Stephanie inspire you to reach out to your students wishing them continued health and safety, and to remind them that they matter, that they are valued, and that they continue to be more than enough.

Posted in career advancement, General, Going to graduate school, graduation, Uncategorized, Undegraduates, work life balance | Leave a comment

A mathematician’s mission statement

By Pamela E. Harris and Julianne Vega

Companies and organizations are driven by their mission statements. These mission statements provide a concrete summary of what they value and what they work to achieve. Take for example the following mission statements:

American Mathematical Society
The AMS, founded in 1888 to further the interests of mathematical research and scholarship, serves the national and international community through its publications, meetings, advocacy and other programs, which

  • promote mathematical research, its communication and uses,
  • encourage and promote the transmission of mathematical understanding and skills,
  • support mathematical education at all levels,
  • advance the status of the profession of mathematics, encouraging and facilitating full participation of all individuals,
  • foster an awareness and appreciation of mathematics and its connections to other disciplines and everyday life.

Mathematical Association of America
The mission of the MAA is to advance the understanding of mathematics and its impact on our world.

Society for the Advancement of Chicanos/Hispanics and Native Americans in Science
SACNAS is an inclusive organization dedicated to fostering the success of Chicanos/Hispanics and Native Americans, from college students to professionals, in attaining advanced degrees, careers, and positions of leadership in STEM.

It appears that the use of mission statements in the mathematical sciences is primarily used by organizations. Yet mission statements provide a strong way for mathematics students (at all levels) and, maybe more importantly, for academics to center their work and their efforts.

Why do we do what we do?

If the “doing” refers to mathematics, we may answer that we love mathematics. Of course, why else would one become a mathematician? But truly there is more a career in mathematics than just mathematics. (Gasp!) For many of us this work involves teaching, mentoring, and building community and opportunities (broadly defined as service). In fact, answering this question is the start of an individual mission statement. Being able to precisely say why we take on certain work and lines of study and how it aligns with what we value helps in a multitude of ways. Let’s look at some of the benefits of having an individual mission statement.

Centering the work you (currently) do
It happens often that we are asked to get involved with some program/project that sounds like a great idea and is valuable. We quickly jump on board, potentially not even taking the time to think about how it aligns with our current and future goals. This seems common within many academic settings, especially as we begin to explore what work we want to achieve in our careers. A mission statement allows us to center the work we do and allows us to concretely state the goals we are working toward.

Connecting with a greater sense of purpose
Think about a typical day. How often do you go home and think, “Wow, I really made a difference today” or “I did meaningful work today”? We would venture that the answer is not often yet that won’t change what a typical day looks or feels like because there is a greater sense of purpose that continues to motivate daily routines. Creating a personal mission statement provides grounding in that sense of purpose. Continually reflecting on and modifying a personal mission statement highlights the greater purpose behind our daily actions.

Clarifying your intentions and goals
There are a handful of mathematicians whose mission statements evidently guide their work. Whether implicitly or explicitly stated, their intentions are clear. For example, Dr. Candice Price has her service mission statement listed on her website, and her many outreach and service activities clearly support her statement:

“My service mission statement is to create and contribute to programs that broaden the participation of underrepresented groups by focusing on strong mentoring and research networks. Thus, I am interested and participate in programs that promote broadening participation in the mathematical sciences and I am on the organizing committee for Underrepresented Students in Topology and Algebra Research Symposium (USTARS).” – Candice Price

Another mathematician who provides his mission statement is Dr. Mohamed Omar, who has dedicated substantial time to disseminating mathematical content via his YouTube channel and more recently via TikTok @profomarmath:

“Dr. Omar’s mission is to change the world from math phobic to math loving, fiercely devoting his life to inclusion in mathematics.” – Mohamed Omar

Another example that comes to mind is Dr. Francis Su, whose mission statement is not explicitly stated but feels ever-present. His recent work with Mathematics for Human Flourishing and “The Lesson of Grace in Teaching” evidences a desire to present mathematics for all and to help others see that math is for them.

All of these mathematicians provide strong examples of the benefits of having a personal mission statement which guides their actions. When you think about their reputation alongside their accomplishments everything aligns towards their personal mission statement. One question still remains:

How do you write a personal mission statement?

When an individual’s mission statement is clear and present in the work that they do, they attract like-minded individuals and begin to build a network that strengthens and supports their own goals. Boiling down your life’s purpose into a few sentences may sound quite overwhelming. And it certainly is overwhelming. Nevertheless, an individual’s experiences, involvements, and personal strengths provide great insight into what their personal mission statement is. Writing a personal mission statement is less about creating it from scratch and more about discovering what it is. One way to discover yours is by thinking about your motivation, your personal strengths and your accomplishments. To get you started think about the following guiding questions:

  • What are you most proud of in your life?
  • What do you enjoy doing?
  • What are your personal strengths?
  • What goes into the decision making for the work you take on?
  • Is there a common theme in your work?

Self-reflection is paramount in creating an individual mission statement. Although the process of creating a personal mission statement requires introspection and time, it will pay dividends for your future endeavors. We hope that this post, along with the sample mission statements presented, inspire you to draft your own mission statement as you reflect and think deeply about the work you are doing, why you are doing it, and how that may change at different points in your career.

If you have a mission statement feel free to add it as a comment below.



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Finding belonging through mentorship

Guest blog by Stephen McKean

On my first day of college, I showed up an hour early to my very first class. The class was Math 2210, multivariable calculus. For some reason, I thought this was the highest math class offered at the university. After a while, the professor and a few older-looking students trickled into the room. The professor clearly knew I was in the wrong place: he looked at me for a moment, wrote “Math 6510: Differentiable Manifolds” on the board, and smiled at the panic on my face. I quickly packed up my things and rushed off to find the right classroom.

Luckily, I also had many math professors who seemed convinced that I was in the right place. They offered me encouragement, advice, and support. When I decided to become a math major in my third year, they told me about graduate school and helped me develop a plan of action. Without these mentors, I never would have been able to become a mathematician.

Becoming a mathematician is difficult. Many days are filled with discouragement, disappointment, and doubt. I have often felt like I did on my first day of college, lost and intimidated by a subject clearly beyond my reach. A mentor can help remind you that you are in the right place — that you belong as a mathematician.

In graduate school, your advisor is a built-in mentor to help you on your journey. As an undergraduate, it can be harder to find a mentor. Many universities have Directed Reading Programs, where undergraduates are paired with graduate student mentors. These graduate-undergraduate pairs work together on a semester-long reading course, and the graduate mentor can help their undergraduate mentee learn more about research and graduate school. Directed Reading Programs also present an excellent way for graduate students to get involved and to improve their mentorship skills. I highly recommend the Directed Reading Program to anyone who is interested.

However, there are many liberal arts colleges, minority-serving institutions, community colleges, and other colleges and universities that do not offer Directed Reading Programs. In response, I am helping organize an online mentoring program called Twoples. Like the Directed Reading Program, Twoples pairs undergraduates with graduate student mentors to work on a semester-long reading project. During the semester, the graduate-undergraduate pair also prepares a final project, such as expository notes or a short recorded presentation. Unlike the Directed Reading Program, these reading projects take place online, so undergraduates from any school can find a mentor.

We will be piloting Twoples during the Fall 2020 semester. If you are interested in being a mentee or mentor, please sign up! We would also love to hear from you if you have any questions, suggestions, or want to get involved. Your participation will help us improve the program for future semesters.

Stephen McKean

Biography: Stephen McKean is a PhD student at Duke. Before Duke, he was a graduate student at Georgia Tech and an undergraduate at the University of Utah. He is interested in questions at the interface of algebraic topology, algebraic geometry, and number theory. Outside of research, Stephen is passionate about making math accessible through teaching, outreach, and advocacy. His non-mathematical interests include hiking, painting, and cooking with his amazing wife.

Posted in General, Going to graduate school, Graduate School, Outreach, Uncategorized, Undegraduates | Leave a comment

Dare To Share

Guest blog by Professor Mohamed Omar

It started as a dare between friends. Would you dare post a video of yourself doing math on YouTube, for the entire world to see? That was the seed of what has become a fulfilling endeavor: creating and building the YouTube channel ProfOmarMath. What I could have never expected was the empowerment this channel has given so many students across the world.

The first video I posted was on a quick method for solving a problem on the GRE Math Subject test. This test is a requirement for entry into many math PhD programs, and is filled with slick problems that are quite non-standard in nature. After posting the first video I realized a few things about the mathematics environment on YouTube:

• There were barely any videos on tips and tricks for the GRE Math Subject Test.
• There were barely any videos on undergraduate mathematics material presented by a person from an underrepresented group.

I was excited to be able to address both of these issues, creating roughly 15 (and now almost 30) videos on tips and tricks for the test. I then essentially abandoned the channel until about 3 months ago.

The revival was something I had planned to do during my sabbatical year when I had more time to devote to it. I expanded the channel to include videos on fun math topics like a combinatorial proof of Fermat’s Little Theorem, clear and empowering solutions to Putnam Mathematics Competition problems, and theorems undergrads don’t usually see like the Gershgorin Circle Theorem.

The impacts of doing this have been astounding. I’ve received many private messages from students across the world who appreciate having access to resources for standardized tests like the GRE Math Subject Test, and supplementary material on random interesting math topics. Students have come up to me at conferences expressing gratitude for the “out of the box” thinking presented in videos, giving them renewed perspectives on familiar topics.

But I think what motivates me the most to continue making these videos is filling the void of underrepresented mathematicians sharing non-standard undergraduate mathematics material on YouTube. Representation is such a critical force in empowering underrepresented students to realize their excellence. In a math culture where underrepresentation is often entangled with a deficit mindset, we need resources that reflect a different narrative. Resources that show underrepresented mathematicians engaging in creative, challenging and interesting mathematics happily.

If you are a student, come join me at ProfOmarMath and have some fun with mathematics. If you are an educator, or anyone interested in sharing your love for math, I highly encourage you to start a YouTube channel. It doesn’t have to be fancy. My first videos were extremely basic in sound quality and production value, but still had an impact to an extent I never could have imagined. Try it! Start today.

Dr. Mohamed Omar

Biography: Dr. Omar’s mission is to change the world from math phobic to math loving, fiercely devoting his life to inclusion in mathematics.  In 2018 he won the Mathematical Association of America’s Henry L. Alder award, the most prestigious early career undergraduate math teaching award in the nation.  He has also been featured online in Forbes and Scientific American.  Dr. Omar is also a fierce advocate for overcoming obstacles of underrepresentation in mathematics.

He is the author of over 20 peer-reviewed articles in internationally recognized journals.  ​Dr. Omar is an associate professor in the Department of Mathematics at Harvey Mudd College after a 2 year award-winning appointment at Caltech.

Posted in General, Going to graduate school, Uncategorized | Leave a comment

A New Type of Learning Community

Setting high standards is expected from all educators. Yet, I think I may have taken this to an extreme in my 2019 spring senior seminar course in algebraic combinatorics. Students walked in to class, got a copy of the syllabus along with a community agreement (sample community can be found here) and saw:

With a pile of 30 or so textbooks on the front desk I pointed out that there was only one undergraduate book on algebraic combinatorics which was published in 2013 — Algebraic Combinatorics by Richard Stanley [1]. It covered classical subjects very well, but what I wanted to do in our class was to get students to a point where they could reach open problems in the field by reading recently published research manuscripts in broad areas of algebraic combinatorics. So to solve this problem we would write our own textbook!

Imagine the students’ surprise to learn of this during the first day of the course. Not to mention the level of work such an undertaking entails, both on the students and on the professor. Fourteen students took on the challenge, and below I discuss the process of building a learning community and how through this community we reached our goal of writing a book.

Sky high expectations

I believe I can do anything if I just try.” — Granville T. Woods

Naturally, some students felt very unprepared to take on the challenge of writing a textbook and decided to wait to take the course in a future semester. And even for those students that remained, they were not convinced that our goal was attainable. After all, it takes mathematicians sometimes decades to complete a book. So how would we be able to accomplish this within the span of a single semester course?

My motto was that we could not know whether this could be done unless we tried. So I set sky high academic standards for students, regardless of whether I or others believed that students were ready for such an academic challenge.

Contingencies and aims

The goal of the class was then clear. But what took more planning was determining the following contingencies:

  • Instructional — how would I support learning activities?
  • Domain — how would I help determine what students should focus on next?
  • Temporal — how would I decide if and when to intervene?

With these questions in mind I set the following aims:

  1. Move students progressively toward stronger understanding and, ultimately, greater independence in the learning process.
  2. Create a scaffolding framework that
    allows students to meaningfully participate in and gain skill at a task that they could not
    complete unaided.
  3. Build a collaborative learning community that promotes critical thinking skills better than competitive/individualistic learning environments.
  4. Learn ways to deal with people that respects and highlights individual group members’ abilities and contributions.

To support the course’s goal of completing a book, I grouped students into pairs who would collaborate on writing a chapter of the book. The research topics were based on student interests, and I provided some initial manuscripts they would explore. The students’ initial job was to understand the material well enough to write about it in detail with the aim of making it accessible to students with calculus or linear algebra background. From this initial content, students then found new resources to further expand their chapter.

As is expected, writing skills would be paramount to completing our class goal of writing a book. Making sure students learned how to read research manuscripts and how to write accessible pieces of mathematics posed the major challenge. Most of our class meetings were spent in small groups working through mathematical arguments and discussing how we should be reading research articles and what constitutes a clear argument with enough detail so not to make huge jumps in logic. After all, what use is there to write another book in which we spend hours dissecting a paragraph? My mantra was “If you cannot explain it simply you don’t know it well enough.”

Logistics and assessments

Hot chocolate helps with editing

Given the goal of the class, a major part of the class assessments was based on chapter drafts. Drafts were due (approximately) every 3 weeks, they were typed in LaTeX, using the online platform overleaf. Given the small size of the class, I focused on giving extremely thorough feedback on students writing. This was the most grading I have ever done in one semester!

Belle at board teaching high school students visiting our course

Throughout the semester, students also gave short presentation describing what their chapter covered. These talks were peer-evaluated and I provided individual feedback based on what students wanted to improve. Also the talks were recorded and students were able to watch them to create a new list of things to improve on for the following presentations.

The last  piece of the course assessment were reflections. I provided students with short writing prompts from which students reflected on the experience of writing and learning math independently/collaboratively.
Reflection prompt included: How does collaboration enhance/hinder the writing and oral presentation of mathematical material? How can you leverage the strengths of each member of the group to create a better chapter and/or have a better presentation? What you think about quantitative evaluation systems like test scores and class rankings, as opposed to qualitative forms of feedback like written comments and conferences. Does one give you a better measure of the knowledge you have gained?

The reflections were key in helping me adapt the course throughout the semester. I also learned so much about the students motivation and how their confidence was growing as the semester progressed. The reflections were our way to communicate deeply and meaningfully about the purpose/value of an education and in fact one student’s reflection developed into a publication, see [2]. Reflections were a refreshing take on an assessment piece, one which I plan to include in all future courses.

Final Product

After a grueling semester we completed the book. There is of course more editing that should take place before any final access to the book is made available, and I hope to teach this course soon so that more students can contribute to it.  Below is the contents along with the authors for each chapter.

A Friendly Introduction to Topics in Algebraic Combinatorics

Chapter 1: Permutations and their peaks by Belle and Ben
Chapter 2: Combinatorics of parking functions by Alex and Maryanne
Chapter 3: Combinatorial representation theory by Franny and Anthony
Chapter 4: Combinatorics and Lucas analogues by Joanne and Francesca
Chapter 5: Chromatic polynomials by David and Katherine
Chapter 6: Combinatorial geometry by Naush and Teresa
Chapter 7: Numerical semigroups by Ben and Aesha

Parting thoughts

I have been asked if I think that more faculty should structure courses in this way. Honestly, I do not know if more people should teach in this particular way. Each institution has different student cultures. What works at a small elite liberal arts college like Williams may not work elsewhere. Moreover, this depth of active teaching is scary even for someone with ample experience. What I do know is that whatever way we structure our courses ought to help students hone their writing and public speaking skills — which will be key for all of their future careers. And we should do so by setting sky-high expectations and building a supportive community in which students can meet those standards.

Pamela and Anthony at is graduation

“This class gave me, or forced me to pick up, the confidence and ability to read a math textbook and genuinely understand the material. Above every lecture based class I’ve ever had, this experience is irreplaceable. Both because it was enjoyable and because it gave me skills that have translated into my life after school.” — Anthony Simpson

[1]. Richard P. Stanley, Algebraic combinatorics, Undergraduate Texts in Mathematics Walks, trees, tableaux, and more. Second edition of [MR3097651], Springer, Cham, 2018.

[2]. Dean, F. “Tired: A Reflection on Asceticism and the Value of Quantitative Assessment,” Journal of Humanistic Mathematics, Volume 10 Issue 1 (January 2020), pages 375-377. DOI: 10.5642/jhummath.202001.19 . Available at:


Posted in career advancement, General, Journals and Publications, Uncategorized, Undegraduates | Leave a comment

Bank of REU/Grad Fair Questions

By Lucy Martinez and Eduardo Torres Davila

We attended the Joint Math Meetings (JMM) conference in Denver to present our research from our work at the Mathematical Sciences Research Institute Undergraduate Program. At JMM, there was a fair of graduate schools and research experiences for undergraduate programs, which was attended by universities from all parts of the nation. At each booth, were university professors and current graduate students who could talk about their PhD program in the mathematical sciences. Selecting a grad school or an REU are critical moments for undergraduates wanting to pursue a PhD in mathematics, and attending this fair provided us with the opportunity of getting to know the schools/programs. Thereby, helping us in making the decision of which schools/programs to apply to. Although, we attended the fair to find out more about the programs offered, there were points in our conversations in which we were unsure what to ask. We quickly realized that if we had a list of questions prior to attending the conference, we could have been more prepared. We talked to Dr. Pamela E. Harris about our situation and she recommended that we go on a scavenger hunt for questions we could have asked! Our goal was to find people at JMM to share questions that students could ask when they attend such a grad/REU fair. We present these questions below, along with some we asked or came up with after this experience. Our hope is that these questions may help other undergraduates in the future.

REU Questions

  • How do collaborations happen?
  • What does the atmosphere at the REU look like? How does the week look like?
  • Are there talks about other topics besides the math?
  • Is there any professional development after the REU?
  • How competitive is your REU?
  • How was the previous REU? How successful was it?
  • What topics are offered in your REU, so that they may best be aligned to my research interests?
  • How is the area/location? What is it like to live there during the summer?
  • How much influence does the student have on the project they are working on?
  • Are the projects assigned or does the student pick their favorite topic?
  • Are the groups assigned or do students choose their group?
  • What kind of projects has your REU worked on?
  • Ask for contact information from professors that are running the REU so that you may send further questions later..
  • Do you have a big emphasis on submitting papers? If so what support is there for the writing?
  • What do you look for in a student for you REU?
  • How is the REU guidance towards the students?
  • Does your REU offer funding to attend math conferences to present the research?
  • Are there fun activities planned for the students during the summer?
  • What is the structure of the REU? Do students meet with faculty every day during the week?
  • How many students are admitted to the program?

Grad School Questions

  • Does your school encourage outside research collaborations? To specify, if someone were to like a professor at a nearby (or not nearby) university would they be encouraged to work with them.
  • Does your school offer funding to attend conferences throughout your grad school career?
  • What is your relationship with the university? To specify, there is not always a professor at a grad fair booth. Sometimes there can be graduate students and other times grad directors so it is important to ask their relationship to the university to know which questions you can ask.
  • How do you resolve problems between graduate students and faculty members?
  • Will there be guaranteed funding for all years of the graduate program?
  • How many years does it take to graduate from your Ph.D. program?
  • Does the university offer any scholarships for minorities?
  • How do students find advisors?
  • What is the grad student community like at your institution? To be more specific, do students work together in doing homework, classwork, or preparing for exams?
  • What is the process that is taken for the qualifying exams? On top of that how many attempts are given to graduate students to pass these exams?
  • What summer support system is provided for students trying to study for the qualifying exams?
  • What kind of research are the professors into?
  • Out of the graduate students who enter how many finish with a math Ph.D.?
  • When a student enters the Ph.D. program how is the funding for the student? Are they going to be a teacher’s assistant? A teacher? Research funding?

The following are questions for current graduate students:

  • What do students do outside of school?
  • Was it easy to find an advisor and did you like them once you were paired up with them?
  • What do you do when you’re not working on math?
  • What helped you to be most successful?
  • What is the social climate at the university? Are the professors approachable?
  • Are professors supportive in a student’s life events? Is there support for both people trying to pursue academia as well as a career in industry?

We thank the following JMM participants who helped us in collecting these questions:
Alex Barrios, Alex Burstein, Natasha Crepeau, Emilie Curl, Daniel Erman, Joshua Flynn, Anant Godbole, Matthew Guhl, Erik Insko, Christian McRoberts, Andrew Miller, Christopher O’Neill, Rebecca Rechkin, Joseph Rennie, Erik Slivken, Sherilyn Tamagawa, and Bianca Viray.

If you have suggestions or other questions to add to this list please comment below!

About the authors


Lucy Martinez: I am currently a junior at Stockton University in New Jersey. My major is Mathematics with a minor in Computer Science. My goal is to pursue a Ph.D. in Pure Mathematics. I plan to influence other minorities to follow their dreams and advocate for more Hispanic women to pursue careers in STEM fields. My other passion besides math is parrots. I think they are amazing animals because some of them have the ability to learn how to talk and imitate humans.



Eduardo Torres Davila: I am currently a senior at San Diego State University. I am an Applied Mathematics major with a minor in Computer Science. I am currently applying to pursue a Ph.D. in Mathematics. Another passion of mine is riding motorcycles. Riding gives me a way to relax and remove all worries from my mind. I also like to do some computer programming on my downtime. My favorite languages are Python and Sage.


Posted in career advancement, Changing Graduate Programs, General, Going to graduate school, Graduate School, Uncategorized, Undegraduates | 1 Comment

Gotta catch ’em all, URM!

By Carrie Diaz Eaton and Pamela E. Harris

We received the same email: Tuesday, Dec 17, 1:37 PM and Tuesday, Dec 17, 1:42 PM. No time to personalize the email. Simply change last names. After all, any one will do, but only if they are underrepresented minorities (URM).

Aren’t underrepresented mathematicians interchangeable?

We have been on search committees, we have chaired searches. We have organized sessions and conferences, we have sent lots of templated letters inviting people to participate in numerous things. Here are some patterns we noticed.

  1. If it is someone we know REALLY well – we can simply ask if they are free to do a thing without the gallantry.
  2. If it is someone we know and respect, but don’t know well enough, we take the time to position why we need their expertise and connect that to the goals, and hopefully they agree that this invitation/request is legitimate and worth their time.
  3. If this is a standard thing to ask of a person, a workshop or dinner for many people, or a standard paper review, then we just write the same templated letter and change the title and name of the person.

These are the unspoken rules in academia. Maybe, we are opening up the black box for those that don’t know. But note that none of those template letters have ever been to invite an underrepresented mathematician to apply an open position for an Associate/Full professor tenured position.

The email read as if it was a personal invitation. As if, this person knew us and it was our track records which helped identify us as the perfect candidate for the job. It clearly states “We are searching for a new colleague with a deep interest in teaching and mentoring undergraduate students and a track record of advancing equity and inclusion in STEM. Our search committee identified you as someone who might be uniquely qualified for our position, and I’m reaching out to invite you to apply.”

The email made us feel needed, valued, but most importantly seen.

We are unique and we have a track record in addressing challenges of being underrepresented within academia and in particular in mathematics. Yet this email was received by the two of us and three others we know. The five of us are coauthors, colleagues, and friends. And it is very likely that many more of our peers received this email. The only requirement was to be a visible person of color.

Like Pokémon – we are interchangeable. It did not matter that some of us are pure mathematicians and others applied mathematicians. What mattered was the box we check: minority mathematician.

This is not a standard way to recruit anyone, let alone minority mathematicians. For example, Carrie’s math-adjacent department is hiring at the Associate/Full rank right now. She has thought a lot about colleagues she knows that might consider this a move up, are committed to anti-racist, decolonizing work, and can teach programming. And if she does not know a particular person really well, she has been shy to reach out. Why? Because as a Latina who has the experience of being actively oppressed by leaders in direct and indirect power over her, she is terrified that she might invite the wrong tenured person into her small department. And yet there are others for which any underrepresented person will do; There is no fear, because they still hold power and privilege. It must be nice.

Pam reached out to a student at the culprit institution and mentioned that we knew others who received the email verbatim. The student is also a URM and disappointment in their voice was clear as they heard how their institution reached out to try and hire diverse mathematicians. Against Pam’s advice they reached out to the author of the email, who said that they “[took] care to personalize the emails to some extent.” Yes, they did. They changed Harris to Eaton (not even Diaz Eaton) within a 5 minute span. Maybe even to other names in between.

But this is not about the particular person or institution. This is about power and privilege. The privilege that comes from not having to think of oneself as representative of a group of people. The privilege that comes from being in a position of power and seeing minority mathematicians as others and not as individuals – as visible and yet invisible.

So what does successful recruiting look like? We can tell you, because Carrie was recruited to Bates College just last year. There are some of the same elements. There might be an identified need to diversify the faculty. There might be a personalized email. But there were relationships built at Bates long before she was asked to interview there. These relationships were made in some ways because she is a URM. But these relationships were made by mutual respect, mentoring, and lifting up of each other’s mathematical work. There was an institutional acknowledgement that there was work to be done to create an inclusive learning environment and a commitment to do the hard work for their underrepresented students. There was also the kind of recognition and compensation for the experience and emotional sweat equity she would bring to the table.

So next time, because we know there will be a next time, before those “personalized” recruitment emails are sent, we ask chairs of departments and of search committees to answer, and discuss with their department, the following questions:

  1. What has the department/institution done to make the environment one in which everyone, specifically underrepresented minorities, can thrive?
  2. What anti-racist, anti-discrimination, implicit bias training has taken place and how long ago was this? What plans are there to continue this work?
  3. Does the demographics of students in the major(s) of the department match the demographics of the student body? If it doesn’t, why is that and what has been done to remedy this? Whose job is it to do address this? The new faculty member you are planning to hire?
  4. What resources are there to address challenges faced within the department by both underrepresented students and faculty?
  5. How will the department value the perspective and lived experience of a person of color within the department?
  6. Does the department’s evaluation process mention how the invisible work of underrepresented faculty will be valued and how it will be weighed at time of promotion and tenure?
  7. Will merit raises take into account this invisible work, or will “research” be the main evidence of academic excellence?
  8. Are you looking everywhere you should be looking, or do you only want a visible URM?
  9. Are you looking for someone to do the work, or look the part?
  10. Will you pay for all that an underrepresented mathematician will do? Whatever invisible labor you think you know of, multiply by 100, and it will still underestimate what marginalized faculty do for students, peers/colleagues, departments, institutions, and our community. Will you pay them adequately and/or give them committed workload reassignment time for all of their labor?

Lastly, to the naysayers. Contrary to what you may believe, minority mathematicians are not just handed academic jobs at the completion of a Ph.D. Nor are they only recruited simply because they are underrepresented. Even when recruited, the research and teaching background are often evaluated against a higher enough bar before anything else is considered. How we get to that initial recruitment stage is the issue here.

Posted in career advancement, General, Leadership, Negotiating faculty / post doc positions, Outreach, postdocs, Tenure, Uncategorized | 2 Comments

Mathematical light shines blindly on us

By William Yslas Vélez
Professor Emeritus
University of Arizona

Bill and Bernice Velez enjoying retirement in Quebec.

“When I go to a Mexican restaurant I would gladly pay the musicians to stop playing.” John (not his real name) did not like the noise level. This statement came up casually as part of a conversation that I was having with a few friends at a mathematics conference in California. John had taught at a Hispanic Serving Institution for years and this was the music of his students. But all that he could say about it was that the music was too loud. I have heard this reaction to this wonderful mariachi music all of my life. In high school a teacher asked me to bring in “Spanish” music and I brought in a mariachi record (see below). The teacher was appalled and had me turn off the music, not even completing a song. She expected something softer, not the wild expression of emotion that is such a part of Mexican music.

Mariachi music is loud. When you have one or two trumpets in a room, full-throated singers accompanied by “gritos” (Yells of joy) from the audience, it is loud. But those “gritos” are an indication that the music and words are connecting with the audience. Going back to the conversation with John, I mentioned a traditional song, “La espiga” (grain, like grain of wheat) and loosely translated the words for him.

Qué poco le importa al sol                         What does the sun care
​que el indio no tenga techo.                      that the Indian has no roof.
Qué poco te importa a ti​​​                            How little you care
​Todo este mal que me has hecho.             all the harm you have done me.

El agua ignora la sed,             ​​​​                   The sea ignores our thirst
​el sol no sabe que alumbra,​​​​                      the sun shines blindly on us,
Y tu no tienes corazón​​​​​                              And you have no soul
​Porque has dejado penumbra​​​​                  Since you have left me in shadows.

John was surprised. He said, “Oh, there’s poetry in that music.” What must have been John’s concept of Mexican music? Was it just to convey noise, to somehow blot out our thoughts? The sentiments expressed in this music deal much with the heartache of love, unrequited, lost, then found, then lost again. And it is sung with such emotion. But also notice how much it alludes to nature.

There is a mathematical culture, and that extends to music. Mathematical culture was not created by Indigenous peoples of the Americas. It was imported. With that came the formalism of mathematics from Europe, and its music. In my career as a mathematician, at mathematical events that I have attended, music is a rarity. But if it does appear it has all of the hallmarks of classical music. Contrast this to a meeting of the Society for the Advancement of Chicanos and Native Americans in Science (SACNAS). In between sessions, music from Latin America, the Caribbean and Native American music loudly fill the halls. A SACNAS conference is a celebration!

How effective can our mentoring be of students when we are so ignorant of their background, of their culture? Our faculties continue to lack minority representation. If faculty think so little of their music and culture, what must faculty think of them? Now add to this that many of these students are first-generation college students and probably also in need of financial aid, further separating them from the life experiences of college faculty.

Our mathematics departments physically sit on lands that belonged to Native American nations. Walk around any mathematics department. Do you see any evidence of that history? Our departments are oftentimes surrounded by a local culture, yet when a local student walks into a mathematics department, it is like going to a foreign land.

The mathematical enterprise has not treated minorities well. Just look at the data on the production of minority Ph.D.s in mathematics and the paucity of minority faculty in our departments. Yet we all know that mathematical training is of absolute necessity for the future. I join with my community when I sing:

The mathematical sea ignores our thirst

Mathematics is brilliant, as are many mathematicians. How is this brilliance impacting the lives of students? It is unfortunate that choirs of humanity sing, in many different languages and dialects:

The mathematical sun blinds us

We live in a very complex and diverse society. We cannot hope to understand all of the different cultures that now grace our mathematics classrooms. But we should not hold any of them in disdain.
What can we do about these matters? I would like to make a few suggestions.

  1. Mathematicians at universities should redouble efforts to increase the number of mathematics majors, especially minority students. We cannot hope to increase the number of minority faculty without having minority undergraduates. The more prestigious the department, the greater its responsibility to increase the number of minorities pursuing mathematical careers.
  2. There is a culture of mathematics which has not been friendly to students. Not all students are capable (or interested in) a Ph.D. in mathematics, but a minor or major in mathematics opens up many opportunities.
  3. Native Americans are invisible in mathematics. This must change. Some Native American culture or symbolism should be present in our departments.
  4. Minority students often form student clubs on campus. Mathematics departments could contact them and establish a dialogue.
  5. Mentoring is a very complex activity. Faculty need guidance on mentoring techniques and how to have conversations with their mentees on course selection and career opportunities. Just as there are weekly colloquia that discuss the latest research, there should also be colloquia to address the serious work of educating and motivating our students to the further study of mathematics.
  6. Smile. It can be contagious.

The music of my youth: Miguel Aceves Mejia singing “La espiga.”

Posted in Changing Graduate Programs, General, Uncategorized | 6 Comments