1. what you have done so far,
2. why this matters,
3. how this defines who you are, and
4. how this sets the foundation of what you are about to become.

In summary, you must justify your existence as a faculty to yourself first and then implicitly to everyone through your tenure documents and personal statement. You have to justify why the university should keep you, and in particular, you must justify why what you bring is unique and extremely valuable to your institution. In order to do this, you need to answer these questions first, so that you may be selective and only include things that serve this purpose. When you have been out of graduate school for a long time, say 9-10 years, like I have, and thus by default have accumulated so much, the process of discriminating what is worth including, and what is not, is extremely difficult especially because we tend to categorize the value of our work or things depending on the time we invested in them, not its impact. We do not realize that some things that we invest our time on are just a means to other bigger things. So, initially everything is important in our eyes.  But we cannot and must not include everything, as this hides or devalues things of impact that you have done and that deserve special attention, for they define who you are and give a glimpse of who you will become. They are not to be mixed with things that might be somewhat important but not of much impact. Discriminating and thinking carefully about the answers to the questions posted above will allow you to put your best tenure case forward.

A peripheral but equally important outcome of this is the opportunity to truly evaluate your life, see the cumulative effect of your work and efforts, and reflect on what you have done and why, as well as ask yourself where you want to be both professionally and personally in the near feature. Reflecting gives you an opportunity to ask yourself Do I want to continue on this path or is it time to use what I have done as leverage to move in a different direction? The course of unraveling the answers to all these questions (including secondary questions that arise) is the source of emotional turmoil that is not spoken of but that some of us go through as we prepare our tenure packet.

In the process of preparing your documents and drafting your personal statement you are forced to look back and evaluate your career and professional trajectory as well as to look forward and project where you are heading and implicitly/explicitly map out the next 10 years or so of your career. You are barely getting used to the idea of being called Dr. or Professor X and you are finally starting to see yourself in this light and now you have to see yourself further than this and in a profound way that shows that you truly understand where you are heading and where you see yourself in the future and most important, that you have a real, coherent, and tangible plan to get there. This is scary- but you have to do it and most important believe it, so that you can write about this and tailor your packet with this in mind. This is like asking a kid not what they want to be when they grow up but if they want to have kids or get married and why. The idea of growing up is still so foreign to them and now we are asking them to expand their concept of growing up to things that they really do not understand, other than very superficially and that they can only see from a very limited lens. This is how I felt as I sat down for the first time to write my statement, for I knew that if I wanted to convince the external and internal reviewers that I indeed have something unique and extremely valuable to offer, I had to discuss my future plan in a very deep way and connect it to my past trajectory (especially things that were in tune with the mission and goals of the university).

While this was daunting at first, the process forced me to connect the dots of my career and take a holistic perspective, highlighting the meaningful things that make my research, teaching, and service a successful blend of the professor I strive to be and that in the my pre-tenured years started to take form to a large degree. Whether this really occurs or not is up to each individual case and the expectations that we set for ourselves. In my case, I still questioned to what degree the latter is true. But regardless of your self-perception and confidence, you have to justify this and to a certain degree be convinced that this is the truth so that your personal statement is strong, positive and convincing to all the individuals sitting in the various stages of the review process.

Inevitably in the development of your statement and packet, you subconsciously end up evaluating your life and asking yourself: How far have I come? What have I done that is significant? Who am I? What do I value? Why do I value this? What is my purpose in life? Why have I sacrificed the things I have to get here? and Where am I going?  The process of answering these questions can take us through a big emotional journey but in the answer to them we gain a perspective that we never had about our role in academia and what matters to us, which together give meaning and define our future goals. We gain an appreciation for the obstacles we have overcome, what we have learned, the price that we have paid to be where we are, and why we would do certain things all over again. It also gives us the opportunity to see resilience and our strengths. Finally, it allows us to see that indeed we have earned our current (and hopefully permanent) place and that it would be very unwise for the university to let us go because someone else would grab us immediately.

It is my opinion that X is doing all the right things.  It has become common in the last few years to do more than one postdoc due to the difficult job market.  I don’t think that this is a negative on her file as long as there is clear progress in research and teaching.  Having said that, there is a rule of thumb out there that a faculty member is expected to be tenured about 8 years after their PhD (an old formula when a 2-year postdoc was the norm). This rule of thumb might be changing more slowly than reality.

The second question is the one I have trouble with. First, I thought that it is a great idea to try to expand one’s activities to become more appealing to a larger pool of potential employers. So, teaching new courses, designing a course, mentoring more students, and other activities that undergraduate institutions want to see should be sought.  Then, I thought that dedicating the required time to these activities will likely reduce the research production. The end result might be that a research institution will perceive a decline in research, which translates into a poor “trajectory” that can place the candidate out of contention for a job at a research university.   What is the best advice? I could say that one should get involved in more activities without affecting the research production, but this is unrealistic.

I was reluctant to give up the time that I had already invested in the Ph.D. program especially since I had passed a qualifying exam.  Ultimately, I chose to finish a Masters Degree at Howard and apply to Statistics programs for the following fall.  Although it meant “starting over,” I was a well-seasoned graduate student and easily hit the ground running compared to many of my peers.

It might also be the case that your current graduate program is not a good fit for you.  Perhaps you haven’t been successful in passing your qualifying exams or you aren’t able to find a thesis advisor whose research you’re passionate about.  If you find yourself in the position where you need to transition to another program, here’s a bit of advice:

1.      Find a professor in your department that you can confide in.  Whether you are leaving to try a different field or because the school isn’t a good fit, you will likely need recommendation letters from your current department.  Reach out to someone that will support and encourage your decision.

2.      Apply to schools that may have initially denied you.  Surprisingly, with a (soon to be) Masters Degree in tow, I looked more attractive to programs that I had gotten rejected from as an undergraduate student.  This was perhaps due to the fact that my transcript clearly showed that I could do graduate level work.

3.      Leave gracefully.  Remember that the graduate students and faculty at your former institution are likely to become your colleagues in the years to come.  Be sure to maintain respectful relationships and not burn bridges should you decide to exit.

By following the advice above, you can make a smooth transition from one graduate program to the next.  Ultimately, my decision to transition to a graduate program in Statistics resulted in me earning my Ph.D. in an area that I am still very passionate about!

I still remember “the dark days” of my years in graduate school. It was 1989-1990, my 4^th-5^th year in the mathematics Ph.D. program at UC Berkeley. I had passed my written and oral exams, had Henry Helson (a world-famous analyst) as my advisor  and was now “doing research” in functional analysis. I use the quotes for emphasis (perhaps sarcasm is a better word), because what I was doing was trying to work on a problem that I’d found myself and was literally getting nowhere. I was learning new mathematics, but was really not making any headway on the unsolved problem that I hoped would bring me the coveted three letters after my name. Yup, each day I would bang my head against the wall for hour after hour, and at the end of the day I would be nowhere closer to solving the problem. I would talk to my advisor on a regular basis, but he also didn’t know how to approach the problem that I was trying to tackle using ideas/techniques that I felt might lead to a solution.

Eventually, Prof. Helson noticed that I had learned some things that could be useful in a different context. He said, “Why don’t you take a look at the thesis of my last doctoral student, G. Choe.” At first, I was somewhat annoyed with his advice. Why should I look at what his last student had done? I wanted to do something original and not look at something that had already been done. But I took his advice, and started looking at Choe’s thesis.

I quickly realized that during the time that I had been cracking my head on the other problem, I had learned techniques that could get a significant improvement on one of the theorems in Choe’s thesis. That was my first breakthrough! I finally had something new that I could call my own. Yes, even though it was a generalization of something already done, I had done it! I had a piece of original mathematics research. This first, very modest result, gave me confidence to look at other problems that I was able to solve. Some of these were different proofs or improvements on recently-proved results, but they were new, i.e., my own.

The lesson of looking at what has been done before, whether on a problem or some other context, is one that I have grown to very much appreciate. For example, now as a faculty member, whenever I teach a class that I haven’t taught before, I ask the colleague who taught it before me to share her/his material with me. I may end up only glancing at it, but it ends up informing my work. Whenever I become interested in a partially solved problem, I’ll try to understand the technique that was used to make headway on it, even though I understand that new techniques likely will be needed to further the work. I guess my point is that originality will most of the time mean variations on what’s been done before, and not a whole “new color.”

When I think about it, this is the norm and not the exception. For example, (in another setting) many of us Angelinos still remember Magic Johnson’s “baby hook” in the 1987 NBA Finals against the Celtics. Was it new? Not totally. It was really a variant of what he’d seen Kareem Abdul Jabbar do on a daily basis for years! What about when we read about the new gotta-eat-there restaurant. We most likely will read a review that says that the “YYY” is a “must-order.” That “YYY” is a dish whose name we will recognize so it really is an improvement on something that already exists. Both of these are examples of improvements, or new variations, on what has been done before.

I’ll end with a story that I believe is relevant to paying attention to what has been done before. I, like many graduate students, wanted to write a thesis that was groundbreaking and would set the mathematical world “on fire.” I didn’t. I wrote a thesis that “got me out.” I wrote a thesis that furthered solutions to problems that had been studied before. I didn’t prove the Riemann hypothesis nor even solved the problem that I racked my brains on for about two years. (BTW, that problem is still unsolved.)

I’m not quite sure if I ever came to grips with this until a few years ago when I had the privilege of meeting Elwyn Berlekamp, a world famous mathematician/computer scientist. In a conversation about being practical about one’s work, especially during graduate school, he said to me (something like this), “A lot of graduate students want to write a thesis that will ‘set the world on fire.’ They fail to realize that the world is a difficult place to burn.”

PAESMEM stands for PRESIDENTIAL AWARDS FOR EXCELLENCE IN SCIENCE, MATHEMATICS & ENGINEERING MENTORING, and it’s widely regarded as the nation’s highest mentoring award. There’s a long list of mathematicians and mathematics programs who have won in the past. They include several MESA programs (New Mexico, University of California, Washington, Maryland and Arizona), mathematics institutes (such as the Mathematical and Theoretical Biology Institute and the Center for Innovation at Stevens Institute), a few departments (including the departments of mathematics at University of Nebraska, Lincoln and University of Iowa) and many well-known mathematicians (including Carlos Castillo-Chavez, Bob Megginson, Peggy Cebe and Phil Kutzko just to name a few).

Winning PAESMEM creates a positive self-reinforcing cycle. The previous awardees were recognized for their success. In turn, successful programs gain significant recognition, spreading the word about these programs and individual mentors, alerting more people to these great mentorship opportunities.

To nominate a program or individual (including yourself!), see the full instructions at
http://nsf.gov/PAESMEM.

The idea seems appealing to most people that are looking for jobs and especially to those who enjoy teaching. It might seem that you get the best of both worlds: you get a postdoc and you get to teach! However, I think it is important to know that a person who accepts a teaching postdoc is instantaneously making a career choice.  The position typically carries a substantial teaching load, like 3 courses per semester.  This is softened slightly by requiring only two preparations each semester (teaching two sections of the same course).  Ambitiously, you might think that there will be some time left to do research, but the reality is that there is not enough time for you to remain competitive for research faculty positions later.  Yes, there will be some exceptional people that can manage both sides of this equation, but that is not the norm.  You should recognize that you have put all your eggs in the teaching basket and you will be competitive only in the teaching school market.

If this is what you want as a career, the teaching postdoc can offer several benefits. For instance:

1. you get to teach a variety of undergraduate courses and build experience teaching at all undergraduate levels.  This is very important when you interview for tenure-track jobs and you can say that you have experience teaching freshmen through seniors.
2. you get opportunities to learn and implement new instructional techniques and develop curriculum. In a good environment, you can learn new teaching techniques from more advanced postdocs and faculty.
3. your postdoc supervisor should visit your classes and provide valuable feedback. This is part of the mentoring that should be available to you.

I have to stress that it is up to you to make these happen.  I know teaching postdocs that have not been visited in class or have been visited but received no valuable feedback.  When this happens, talk to the department Chair and ask for someone else to visit your classes. Think of the fact that you will need excellent teaching recommendations when you leave and so you need faculty who know first-hand how you teach.  The danger of teaching postdocs is that, without proper mentoring, they can degenerate into an instructor-like position without guidance and without much feedback. Ironically, this is especially true if you are a decent teacher and the department receives no complaints from your students. Teaching postdocs are often departmental postdocs and it can happen that no particular faculty member is designated as your supervisor.

It is up to you to make sure it is clear who your faculty supervisor is and that he or she will write a letter of recommendation for you later.  Make sure some type of helpful evaluation takes place at least annually and that opportunities for you to grow as a teacher are available to you.

First, background on the conference itself. On February 9, 2013 HMC hosted the first annual AfterMath Conference: Preparing for Careers in the Mathematical Sciences. This conference was co-organized by Alissa Crans, Talithia Williams, Robin Wilson and myself. Our goals included (1) working to broaden participation in mathematics by engaging a diverse cohort of students from Southern California, (2) encouraging applications to graduate school from local undergraduate students and (3) providing information and resources surrounding mathematically oriented careers outside of academics. The conference homepage is here: http://www.math.hmc.edu/AfterMath/.

The AfterMath Conference took place on a single Saturday, and included a keynote talk, two panels and two workshops. The keynote address was given by Phil Kutzko (co-Director of the National Alliance for Doctoral Studies in the Mathematical Sciences–http://www.mathalliance.org/), who spoke about the cultural history of mathematics and how it has shaped the discipline and its practitioners.

The structure of each panel was simple: panelists introduced themselves and provided important background information. Then the floor opened up for discussion, and the audience and panel engaged in questions and answers and discussion for the duration.

The first panel centered on Graduate School, and panelists included America Chambers, Alberto Soto, and Karen Wood of UC Irvine, Jackie Lang of UCLA and Syvillia Averett of Central State University. The panelists ranged from earlier graduate students to new Professors, and were able to answer audience questions ranging from qualifying exam tips, to choosing an advisor, to finding a peer group.

The second panel focused on Industrial Mathematics, with panelists Gary Green of Aerospace Corporation, Enrique Schultz of Mercer and Susan Martonosi in Operations Research at Harvey Mudd College. Discussions ranged from networking advice, to specific sub-disciplines worthy of focus for industrial applications, to general career advice, to degree requirements in various industries.

In addition, two workshops allowed for active participation among conference attendees. First, students brainstormed their graduate school Statements of Purpose and wrote rough drafts and outlines. The collective results of this graduate school application workshop are collected at http://bit.ly/GradEssayTips. (Thanks to Rachel Levy for running this workshop and preparing the Grad Essay Tips!) Next, students engaged in a workshop on choosing the right PhD program, complete with an application timeline and checklist.

Finally, the day ended with a graduate school fair, with schools (and representatives) including USC (Francis Bonahon), University of Arizona (Tom Kennedy), UC Riverside (Julie Bergner) and University of Iowa (Colleen Mitchell).

We conducted follow up evaluations with students; here are a few reflections on the conference and its evaluations.

(1) With a modest budget (generously provided by the National Alliance, with local support from the HMC Department of Mathematics), we were able to attract over 100 students from greater Los Angeles, on a Saturday. Students came from as far north as UC Santa Cruz, as far south as Biola University, as far west as Loyola Marymount University
and as far east as Cal State San Bernardino. Aside from the content of the conference, their only reward was a free lunch. In particular, students drove themselves without compensation.

(2) There is a thirst for career advice in mathematics, both in and out of academics. This was made clear time and again throughout the conference and in evaluations.

(3) There is a strong desire from many PhD programs in mathematics to connect with a diverse group of undergraduate students. (And many such programs are willing to fund the travel of representatives for recruitment purposes.)

(4) Many students left before the last afternoon session was over. To encourage students to give up their entire Saturday, and stay for the duration of the conference, additional incentives are required. (For instance, I know of other conferences that feature raffles and so forth towards the end of the day.) Next time, I’ll try to find funding to give away an iPad or something.

(5) Hosting a regional mathematics conference builds community, and is a way to gather like-minded faculty, students and industrial mathematicians who may be from disparate institutions, but from the same geographic region.

The National Alliance hosts a big annual Field of Dreams conference. However there are many mathematically talented students who haven’t yet had the opportunity to attend FoD (or don’t know about it, or have yet to realize that math is an option). Regional alliances and conferences are additional tools to support students (and professors!) in mathematics. I hope this model (for a regional Alliance conference) will be easily replicable at other institutions.

Students, please consider attending the 2013 Field of Dreams conference, the SACNAS National Conference, or any other mentorship related conference. (SACNAS is a magical and important organization, and will be the subject of many future posts.) Faculty, let’s organize more regional conferences centered on mentoring future mathematicians, for the benefit of us all!

Your salary is always negotiable. In public (and many private) institutions, salary information on faculty is available and reviewing this will give you an idea of the typical range at your institution. Also useful is knowing national averages, which is published annually in the AMS Notices. This report from the AMS contains the most recent publication.  Make sure you are aware of your institution’s group when reading this report and note that these graphs represent information from only those departments that responded to the survey. Remember your benefits are also tied to your salary, so there is a compounding effect on your retirement plan.

Another negotiable aspect is the teaching load or the structure of your teaching load. Some departments are able to offer a lower initial teaching load. Others have no problem shifting the load, say from a 2-2 to a 1-3. Again, it is very helpful to find out what is currently done at the institution via the department’s website or by simply contacting the faculty you met on your on-campus interview.

Startup packages are important to discuss. It is important to know what the department provides and what you will eventually have to maintain on your own. Anticipate the specific needs of your profession: office space, office furniture, desktop/laptop/printer/hardware/software and their eventual replacements/updates, office supplies, travel / conference funds, relocation, funds to bring collaborators/speakers, summer teaching, etc… You should also distinguish between what you need (minimal requirements) and what you want (ideal situation). Note that every compromise requires a give and take from both parties and it helps to be thorough yet flexible. Do your homework: (1) find out the costs of others’ packages and what they included, (2) have a general idea of the costs for the items you are requesting.

Do not forget: your future chair / colleague is mediating your negotiation with the Dean. So, when you receive an offer, respond.  Non-responsiveness can burn some bridges, whether intentionally or not. If you need more time, respond saying that.  For those with a “two-body” problem, you should definitely discuss this issue during the negotiation period. The sooner you disclose this information during the negotiation, the greater the possibility the department has to adjust and assist your situation.  Be honest with your needs and truthful about competing offers — the mathematical community is a small world. Be consistent about what you ask for and with whom you negotiate. It simplifies this already complex experience.

Do NOT ask vague questions like: Are graduate students happy here?  Do students have funding for the entire time? or Are graduate students given professional support when they need it?  The answers to all questions will be ‘yes’ but you will not find out about the student who are no longer in the program; you won’t find out what type of funding students have (maybe they work off campus!); and you won’t know if the support they receive is adequate.  You must ask specific questions.

Ask professors (e.g. the graduate coordinator) How many students have been admitted to the PhD program in the last 3 years and how many students have received their PhDs in the last 3 years? The answer are hard numbers and you will be able to deduce the percentage of students that drop out of the PhD program.

Ask professors: What percentage of students failed the written exams each of the last 3 times they were offered? Again, this requires a specific answer that cannot disguise the reality.  Regarding student academic support, you can ask professors and current graduate students: What activities do they have in place to ensure as much as possible that their students will successfully complete their PhD?  You should expect an answer that include workshops for preparing for the written exams; departmental funding for students to attend conferences; professional development workshops on writing papers, collaborations, etc.; and teaching opportunities.

If you have been offered 5 years of funding, you don’t have to worry.  However, if you have been offered funding for only 1 or 2 years, ask professors about the sources of funding that they currently offer their older students.  Ask the graduate coordinator how many 4th and 5th year students do not have funding from the department. The goal is to find out whether students have to find their own funding in later years or if the department or their advisors find funding for them.

Ask 1st and 2nd year graduate students if they currently work in groups in their Analysis, Algebra, and Applied Math courses.  This will give you an idea of the environment of the department: Is it one of cooperation or competition? Ask the older students how they went about choosing their advisor and selecting their dissertation topic.  Some advisors provide thesis problems to their students and others are open to letting the students choose a topic according to their interests.

There are other important questions that one can ask, but at this point, you get the idea.  Ask questions that require objective and quantitative answers so that you can get an accurate picture of the type of program it is and the environment (supportive or sink-or-swim) it provides. Readers that have additional ideas or questions, please post here as comments!

If you’re a student, I’d suggest reading through one of the following books for problems. Richard Guy of the University of Calgary has a compilation of hundreds of wonderful problems in his text Unsolved Problems in Number Theory. The book has dozens of sections with self-contained explanations of the history and current knowledge of the problems. I’ve even written a paper based on one of the problems! Actually, this book is one in a series by Springer Publishers entitled Problem Books in Mathematics. Other books in the series are Problems in Probability by Albert Shiryaev; A Problem Book in Real Analysis by Asuman Aksoy and Mohamed Khamsi; and Problems in Geometry by Berger, Pansu, Berry, and Saint-Raymond. There are 43 different books in this series to choose from!

If you’re a faculty member looking for projects, I’d suggest looking into being a part of a summer workshop geared for such faculty to work with students. Let me discuss a couple of examples which I have been a part of myself.

The Park City Mathematics Institute (PCMI), an entity run by Princeton’s Institute for Advanced Study, will run just such a summer workshop during 2012, 2013, and 2014. Steve Cox of Rice University and Dennis Davenport of Howard University will run a one-week workshop designed to guide and develop faculty mentors of minority students who will offer REU programs primarily for these students. For more information, visit the web site http://pcmi.ias.edu/REUWorkshop/2013.

The American Institute of Mathematics (AIM), located in Palo Alto, California, has hosted a series of such workshops over the past five years or so. Organized by Leslie Hogben of Iowa State University, Roselyn Williams of Florida A&M, and Ulrica Wilson of Morehouse College, the Research Experiences for Undergraduate Faculty (REUF) bring together leading research mathematicians with faculty at undergraduate institutions who are interested in involving their students in areas of active research. Such workshops were run in 2008, 2009, 2011, and 2012. For more information, contact Brianna Dolandson, Director of Special Workshops at AIM, at brianna@aimath.org.

Whether you are a student or a faculty member, there are many opportunities to conduct research!