On My First Semester of Math Grad School

On August 22nd, 2016 at around 7:45 A.M, my mom dropped me off at the Southwest Airlines terminal in Tampa International Airport. A short six hours later I exited The Eastern Iowa Airport with nothin’ but a marked plane ticket and a Linear Algebra Done Right textbook in my hand.

Not really. I had about 200 dollars in cash and several suitcases.

Nonetheless, that day I became an Iowan. Iowan. I had never been anything but a New Yorker. Even though I spent four years of undergrad in Providence, Rhode Island (where my little heart will forever be anchored), I always knew deep down that it wouldn’t last. I was a Friar for life but I was never a Rhode Islander, and I knew I would never be one. Throughout my undergraduate career, I had struggled to figure out where my place would be post-graduation. I thought it would be pretty cool to go back to New York–but obviously only if I were living in the New York that is far too often romanticized by upper east-siders and delusional Long Islanders. I also thought that it would be cool to try out another big city. Like Chicago. I even had my sights set on something huge: California. I believed that regardless of where I ended up, it would be a booming metropolis of some sort. Every clothing store, restaurant, and night club would be within walking distance of my new home, and my New York City lifestyle would adapt to the likes of a new yet similar city very quickly.

They say that if you want to make God laugh, then tell him your plans. I told God my plans. And on August 22nd, 2016, with nothin’ but a marked plane ticket and a Linear Algebra Done Right book in my hand, I moved to Iowa City, Iowa.


 

Theorem. Finite point sets in a Hausdorff space are closed. 

You know when something really sucks and you didn’t expect it to suck so much and you start to wonder, why didn’t anyone tell me it would suck this much? Well that’s not what happened to me at all. Literally everyone tells you that graduate school is going to be hard. That it truly is going to suck (the life out of you). That you’re going to be challenged in ways in which you’ve never been challenged before. Even before you start to begin to initiate possibly contemplating the idea of applying to graduate school, current victims as well as survivors pop their heads out of dark alleys telling you that it is going to be the most exhausting 5 (if you’re lucky) to 8 (if you’re masochistic enough to endure that kind of pain) years of your life. That you will be humbled immediately by the amount of material that will be catapulted at you in combination with your inability to comprehend it all at once (or ever). That you will devote every second of your life to studying–even if it means not showering or not cleaning your apartment for a questionable amount of time. They said that you will mostly likely wake up one day and find yourself drowning in feelings of inadequacy, anxiety, and the all too common depression.

And I believed them wholeheartedly. I believed every ounce of every caveat that was given to me. I saw it in the weight that pulled the bags under their eyes closer and closer to the bones of their cheeks. I saw it in the grey hairs that entangled themselves between the red or blonde or brown ones. I thought that believing them would have prepared me mentally and emotionally for the exhaustion that was bound to hit me and that would continue to hit me throughout the next five or six years. It did not.


 

Theorem. Let G be a group of order . Then G is abelian. 

On the University of Iowa

Upon my acceptance into the Mathematics PhD Program at UIowa, I was awarded two fellowships: The GAANN Fellowship and the Sloan Fellowship. I won’t go into too much detail regarding the benefits of each fellowship, but just know that the combination of the two awards made UIowa’s offer one that I would be an idiot to turn down. Also know that as a fellow, I don’t begin any TA duties until (if I choose to go so far) my 3rd year of grad school. And by then I (ideally) will have passed all three of my qual exams, have found a research advisor, and have began researching and working towards completing my doctoral thesis. Irrevocably, the university has been more than kind to me. By awarding me these fellowships, the university has given me hours of time (which I would not have at my expense if I were a TA) to devote to my studies. Because I don’t have to devote any hours of the day towards teaching, tutoring, or grading (or all three God Bless your souls, TAs), I have what on the surface seems like all of the time in the world to study and do math. And while it hardly feels like I have all the time in the world, I am utterly grateful to the university for giving me something so precious: time. They’ve given me time in an environment that makes you long for ‘just one more day to study, just one more week to finish that assignment, just one more year to understand’.


Theorem. Let f be absolutely continuous on R and let g be absolutely continuous and strictly monotone on [a,b]. Then the composition g o f is absolutely continuous on [a,b]. 

The People I’ve Met, My Cohort

I’ve always found that wherever life takes me, whether it be the Upper East Side of New York City, Providence, Hilo or Camarillo, there will always be good people nearby. People I can trust. People I can love. People who are inherently good and kind-hearted. And by the grace of God, Iowa has been no different.

One of my biggest concerns entering graduate school was the possibility of not finding a solid cohort of people to share my aspirations with, people who would give and receive emotional support and people to ask stupid questions to without fear of judgment.

Not only have I found an amazing cohort of friends, but I am also part of a program that is filled with amazing people in general. Throughout the semester, I’ve come to find that even those who aren’t necessarily in my cohort are exceptionally approachable and helpful at all times. Besides a very small (and by very small I mean epsilon small) group of people, essentially all of the first-year graduate students enjoy working collaboratively and genuinely enjoy extending help to anyone who needs it–whether it’s a small push in the right direction or complete catapulting towards the answer. Now, don’t get me wrong–not everyone is the same kind of helpful. If you want a very small hint to get you thinking, you go to this one person. If you want a turn-on-my-light-bulb-please kind of hint, you go to this other person. And if you’re absolutely fed up and it’s 1 A.M. and you’ve decided to throw in the towel and just really want the fuckin answer, you go to this other person. And honestly, I think that’s pretty great.

I’ve also found that many people within my program defy several graduate student stereotypes. For example, one common stereotype is: Math graduate students, especially male students, just find solutions online and then claim them as their own. While I’m sure this is the case with many graduate students, a lot of student at Iowa are honest about the source of their homework solutions–especially the men. I often hear people admit: Oh, yeah I found this one online and rewrote it in my own words, or: Yeah, I had no idea how to do it, so I had to model an online solution, or even the occasional: I gave up and just copied the solutions straight from the internet. Overall, the people in my program are remarkably honest when it comes to their strengths and flaws. It seems as though we are all kind enough to offer help but also humble enough to admit when we’ve received help. And I think that’s pretty great.

Now, within my small cohort there exists a pretty interesting dynamic. About half of us are Pure math students while the other “half” are Applied. Diversity. And about half of us are women while the other half are men. More diversity. And to top it all off, we are from different parts of the world: the continental U.S., Puerto Rico, Mexico, Kenya, Nepal–you name it. And honestly, I think that’s pretty great.

While pairs of us work on homework/study together virtually all of the time, we’ve never really studied together as a whole. I mean, we’ve all done work at the same table, in the same room, maybe even on the same subject at once, but we’ve never really collaborated all at once. And honestly, I think that’s pretty great. Why is that great? Because we avoid inflicting a potentially competitive and unhealthy environment upon our cohort. Because you never have to make yourself vulnerable (by asking a stupid question or confirming your stupid answer) to all of your friends all at once. And because it shouts that we are not just “math friends” but friends. And let me tell you: people will go on and on about how in graduate school, you’d better find you lots of “math friends”, but I will tell you right now that a huge part of what’s kept me going and what has pushed me forward these past few months was

A warm hug from a friend after finding me in the office, crying from sheer anxiety.

A friend who spends hours teaching me topology, hoping to cheer me up. I have no knowledge to offer in return–he helps me anyways.

A beautiful carrot cake on my birthday, baked by a friend–a gesture I loved.

A drunken “This is Why You Kickass (Inductively)” speech from a friend in a bar after a long week of classes.

A weekly invitation to go grocery shopping from a friend who knows I’m a loser who can’t drive (working on it).

A culturally relevant meme from a friend who reminds me that a sense of humor is important, too.

A “Hey! gym?” text from a friend–who knows you love to work out and who knows your mind could use a break, too.

When Dr. Candice Price and Dr. Heather Russell (both Iowa alumnus/kick-ass topologists) told me that the best part of being at Iowa was the cohort that they had formed, I was skeptical of how big a role a cohort could possibly have on ones perception of graduate school. But after a long semester filled with challenges of all sorts, their common reflection has never seemed more appropriate. While excellent professors and engaging lectures build your attraction towards a PhD program, it is the people you meet, the support system that you yourself build that makes you stay.

3 A.M. trips on the NiteRide. Movie nights at Aspire. Spontaneous group volleyball at the Rec. Center: these are the things that have made me love Iowa. These are the things that not only make me a Hawkeye but that make it okay to call myself an Iowan.


Theorem. Let F be a field and E be a finite subgroup of the multiplicative group of F. Then G is cyclic.  

Inadequacy, Anxiety, and Depression

In my freshman year of high school, my mother, grandfather, and I got into a car accident. The light had just turned green for us, so my mother drove forward, and a taxi driver ran a red light and hit us from the right, making our car spin around 3 whole times in the counterclockwise direction. My neck hurt a little, but I was fine. My mom was fine. But that accident cost my grandfather two head surgeries, my mother a frivolous lawsuit, and me my inner peace for the next year.

That was the year I experienced depression for the very first time. After the car accident, I was moody on all levels. I lashed out at my best friends whenever they complained about anything I found trivial–like bad hair days and fuckboy problems. I felt like a cloak of darkness weighed down on me everywhere I went, and I didn’t know why. My grandfather and my mother were alive–healing but alive. And I was alive. So I did not understand why I could not rid myself of that cloak, why I couldn’t just take it off. I convinced myself that no one knew what I was feeling and I let that idea cultivate into a habitual way of thinking. I put on the cloak. As a freshman in high school, depression looked like a dark cloak.

This time around, depression looks like inadequacy. It looks like anxiety. It looks like confusion. It looks like–It does not look like anything. It does not have a face.

When you’re in high school and even in undergrad, sitting in a classroom in utter confusion is a norm, maybe even comical at times. But when it happens everyday in nearly every class with increasing severity, it’s no longer funny. And you know damn well it’s not the norm when your peers (who might say they are as lost as you are) ask seas of questions that you can not even begin to understand. Do you see? You’re so lost that you don’t even understand the nature of the question. And why is that so bad? Why does something like that affect me and thousands of other graduate students around the world?

Maybe it’s because I am oozing with pride. How can someone who graduated Magna Cum Laude, who was the “go-to” person in her math classes, who lied in the top fifteen percent of her graduating class possibly find herself in such a severe state of confusion? Or maybe it’s because throughout this semester, I kept my spirits up by expecting a light at the end of the tunnel. I thought that one day I would sit through an entire lecture with a clear and intuitive understanding of the material or that one day it would take just one sentence, one added line on the chalkboard, one think of it this way to clear up the confusion that had lingered in my brain throughout the past 45 minutes (and perhaps throughout the entire semester). That would be the day that I had found my calling, my research topic, my area of interest, the reason I decided to choose math over writing; whatever it was, it would be mine to call mine because it would be the one thing that made sense. The one thing that made my decision worth it. That day would be the day that one thing would make sense. That day never came.

Before graduate school, me and mathematics were very much in a honeymoon phase. I loved math, and as far as I knew it, it loved me back. If I paid attention in class, I would understand the material (and occasionally even use the word beautiful to describe it). If I asked questions in class and read the textbook afterwards, I would get through the homework in 1-2 days. And if I stayed curious about the material and if with every new concept I asked myself what does this really mean?, then my enthusiasm for logic and problem solving would flourish–and transitively, so would my mathematical prowess. Surely I enjoyed some math classes more than others, but with the right attitude, I believed I could harvest a healthy and productive appreciation for math of all sorts.

Now I kind of hate everything. Nothing is beautiful, and that makes me sad.

Before graduate school, I would go days and sometimes even weeks without doing anything besides math. No writing. No dancing. No singing. And when I received 90s and above on my tests, it was all worth it. Then with a mind free of stress I, unbothered and buoyant, could retreat to writing, dancing, and singing–at least until the next test.

Now I go months without doing anything besides math. No writing. No dancing. No singing. And when I receive low test scores and even lower homework grades, I wonder if it was all worth it. Was it worth drinking four cups of coffee within a 24-hour time span to stay focused? Was it worth only getting four hours of sleep so that I could read a paragraph over and over again and still not get it? Was it worth neglecting to call Maya back when she had weeks of life, love, and sophomore undergrad experiences to update me on? With a wounded spirit (and ego) and a mind inundated with stress, I could not retreat back to writing, dancing, or singing, but once again to my studies–vowing to push myself even harder because the next test is always nearby.

That’s the thing. I was used to giving up everything else temporarily so that I could excel in mathematics; and with that came an abundance of confidence in my mathematical ability, my ability to learn, and most of all in my capability of achieving what ever I set my mind to. There’s a subtle beauty in devoting your time and energy to one thing and having all of that time and energy spent pay off in the end. You’ve given up pieces of you for a moment, but in return you find that a different piece has grown bigger and stronger. But now I give up nearly all my pieces and for much longer than a moment only to still fail. Then I’m left with a lingering sense of (you guessed it) inadequacy. I am no longer a writer. I am no longer a dancer. I am no longer a singer. And I am bad at math. Just like that, I have grown smaller. Growing smaller is dangerous for tons of reasons, one of which being that the inevitable perpetuation of your smallness eventually is no longer exclusive to you. I feel smaller, so I let others treat me like I am smaller. I find myself accepting bad friendship, bad intentions, backhanded compliments, and even second-class citizenship in the hearts of people who call themselves your friends. I watch as others categorize me. They tell me who I am and listen. They decide how good I can be and I hope I can be half as good. They put me in a box, and I let them. What is good about me?

While this sense of inadequacy has only been made more severe by graduate school and all of its challenges, I can’t help but think that there are other factors in my life that have made this semester my worst semester thus far. Sometimes I think I’m sad because of other things. Pre-graduate school things. And perhaps because of these things, I haven’t been able to tackle graduate school in a positive and healthy manner. Now you might me wondering: Why are you sharing this, you weirdo? I think it’s important. I think it’s important to realize which problems graduate school has caused and which problems graduate school has worsened. There is a stark difference between the two; I truly believe that awareness of where that difference lies will be helpful in my journey towards recovering of my self-esteem. (I hope that if you’re reading this, identifying with any of sentiments, that you, too, try to make this distinction)

So maybe I’m sad also because Providence College is the best place on earth, and two hours after receiving my diploma, I drove away from it knowing that I would probably never go back.

Or Maybe it’s also because I was here in Iowa while my family said their last goodbyes to the house that built me in the Bronx, NY.

Or maybe it’s also because I let a boy kiss me for the very first time two weeks before graduation and it wasn’t what I had waited twenty-one years for.

Or Maybe it’s also because I had always yelled at Alexa for trying to hold my hand everywhere we went and now I wish more than ever to be holding her hand in mine when I’m on the bus, when I’m in the office until 2:30 A.M., when I’m in the bathroom stall bawling my eyes out after getting back my topology exam.

My point is that maybe I can’t blame graduate school entirely for the wave of sadness that has hit me this past semester. Maybe there are other wounds that needed to heal before making such a drastic change in my life and taking on such a challenging task.

I am not depressed. I do not know what depression looks like, but I know what my depression looks like, and I haven’t seen it since high school. But if I continue to allow feelings of inadequacy and anxiety impose themselves on my life and if I allow them to redefine the person that I am, then depression will make a comeback in my life–a grand one at that. If I continue to accept others’ perceptions of me and if I continue to view my value as a person as a reflection of the numerical values of my test scores, then depression is inevitable. And even if I somehow were to get through grad school in a state of depression, I nonetheless would be failing myself. I’d be failing the God that tells me that I am worthy of so much more. I’d be failing my mother, who taught me that happiness should always be a priority. I’d also be failing myself. I would fail myself as a mathematician by marking my mathematical career by passionless efforts. And I would fail myself as a writer by choosing mathematics over writing only to suffer my way to mathematical accomplishment.

So while it is so easy to put myself down for not understanding and for not excelling, the only way I can get through this without putting on that cloak is by giving myself permission to grow. Not smaller, but bigger–right? Because that’s only the way in which the word grow makes any sense, right? I must grow bigger with faith. Bigger with love. Bigger with compassion for others and for self. Bigger with patience. Bigger with passion. Bigger with as much knowledge as I can possibly fit inside of me.


 

Theorem. Let X be a topological space. Then X is Hausdorff if and if only the set D = {(x,x)| x ∈ X} is closed in X. 

On Being Underrepresented in My Field

At the University of Iowa, there’s technically two sectors of the Math department. There’s the Applied Mathematics/Computer Science Department (the enemy) and the Pure Mathematics Department a.k.a my department. There is a total of twenty-five first-year Math graduate students. There is one student in the Master’s program. Nine students are in the Applied program, three of which are women, three of which are minorities, one of which is both. On the other hand, there are seventeen students in the Pure program, three of which are women, nine of which are minorities, two of which are both. I am one out of two students who is a minority in two resects: I am a woman and I am a Black Latina.

Now, being underrepresented in my field is nothing new to me. At Providence, I was often one of a handful of women in my classes and more often than not, the only minority in many of my math classes. However, for some reason that fact never really affected my daily classroom experiences. Occasionally I would look around and remember that no one in the classroom looked like me. I’d take a moment to reflect on that, think to myself, Why is that? and then I’d quickly respond with a Oh yeah–because mathematics has been negatively stigmatized within the Black and Latino communities. Then I’d go back to my work and not really think about that kind of stuff until the next time it would unexpectedly hit me.

At Iowa, it’s a little different. Because there are only four fellows among the first-year students, everyone knows you’re a fellow, so everyone knows about your privileges and benefits. In addition, our fellowships are exclusive to ethnic-minorities, i.e., all of us are African-American, Black, Latino, or both. So because there are only four of us, I often feel as though the word “FELLOW” is stamped across my forehead, and below it is another stamp which reads “MINORITY”. Therefore, I am constantly reminded that not many people in the math community look like me, and I am constantly reminded that my being here goes against a very strong statistic. While being a Black Latina from the Bronx enrolled in a Mathematics PhD program is something that I am very proud of, as many people from my neighborhood were unable to make it to college, I would be a fool if I didn’t admit that such an honor comes with immense responsibility and pressure.

Pressure to defy the odds, which say that I will drop out before even completing enough credits for a Masters. Pressure to maintain a positive outlook towards math so that I don’t perpetuate the stereotype that minorities are poor at/abhor the sciences. And mostly, I constantly face the pressure to excel in order to defend my fellowship status. I constantly fear that if I don’t excel or if I don’t excel by my own doing, then everyone will see me for the impostor that I am. I fear that people will look at me and start to wonder why I got this fellowship, and then soon enough their questions will be answered by one sheer fact: I am a minority.

This way of thinking is not only nonsensical, but it is extremely harmful to my self-esteem. Somehow I need to give myself permission to enjoy being a fellow. Rather than wondering what people think of me as a fellow, I must own the title of GAANN Fellow and Sloan Fellow. Because I worked my ass off in undergrad.

I may not have come out of it knowing an abundance of mathematics (in comparison to my peers at Iowa), but I made sure to learn every ounce of mathematics that was presented to me. I participated in REUs as long as I qualified to participate in them. I presented at conferences whenever funding was available to me, and when funding was not available to me, I searched for it and found it. By doing so, I traveled to Texas and California and Alabama, networking and immersing myself into the realm of math so that I, one day, could become a part of that realm. I may not (by a landslide) be the smartest, most brilliant, most impressive student, but I’ve worked hard academically my entire life. Not for allowances. Neither for celebratory gifts nor for sentiments of pride from others. But so that I could continuously perfect my skill.

Yes, I am a minority.

I am a Black Latina.

But I am a dedicated, hard-working, driven Black Latina who, throughout her whole life, has had statistics, racism, and crude stereotypes telling her that the odds of success are not in her favor. I am a Black Latina who has continued to pursue success despite those odds. A Black Latina who has sat as the only Black Latina in all of her mathematics classes. I am a Black Latina who has yet to meet a mathematician who is also a Black Latina, who has yet to be presented with some kind of proof that this dream is, in fact, attainable. So if my university wants to commend me for that and celebrate me for that with a fellowship, then that is totally fine with me–and it should be totally fine with you, too.

You see, because my fellowships do not allow me to sit back and relax while others work hard. My fellowships do not allow me to perform mediocrely for the sake of increasing diversity within the program. Instead my fellowships offer me a helping hand. They are a reflection of the time and energy I’ve put into my studies and they are indication that someone, the University of Iowa namely, believes in the power and of the work ethic I’ve maintained my entire life. This is something to be proud of. I will learn to embrace the words written across my forehead.


Theorem. Let X be a metric space. Then X is complete if and only if whenever there exists a countably infinite, contracting sequence of nonempty closed sets, there is a point x ∈  X for which the intersection of all such closed sets is the singleton set {x}. 


Where Do I Go From Here?

If there’s only one part of this blog that you decide to read, I hope it is this:

While I arguably may be the weak link of my PhD program, I can proudly admit to you that I know a lot more mathematics than I’ve ever known in my life thus far. I finally understand why the Fundamental Theorem of Finitely Generated Abelian groups is actually pretty important. I finally know that a set is not a door, so being open and being closed are not mutually exclusive. And while it is more than likely the case that I only understand about thirty-percent of the topology I’ve learned this semester, that is thirty-percent more than I’ve ever known before. And even if that understanding is shallow and green, it is undeniable that I have expanded my knowledge in mathematics in some way within the topics of group and ring theory, measure theory, and point-set topology.

While the thought of dropping out has been crossing (and perhaps even ran through) my mind ever since graduate orientation, I’ve decided that it isn’t time for me to call it quits. If I do decide to drop out, I can only pray that it will be purely because I belong elsewhere; that is, my vocation lies in one of my other talents or something else that I am passionate about. If I do decide to drop out, it will not be because I have been defeated. Because if that is the case, then I’ve given up. And let me tell you, my friends: I may be soft-spoken and I may be timid and I may be easygoing, but I. don’t. give. up. If I want something, I chase it. I’m not be a fighter like you, but I’m a fighter like me. It may take me some time and I may need to overcome fears and cross bridges I’ve never even imagined having to cross, but I always do what it takes to achieve something that my heart yearns for. So if somewhere along the way I decide that I really want to go through with this thing and if I find that even after all of the strife and exhaustion that I still have enough passion and respect for mathematics, then I am confident that I have enough faith in God and I will learn to have enough faith in myself to push forward. Besides–I’m from the Bronx. In the Bronx we don’t run: we run shit (sorry Lil Kim but I had to change it up–Brooklyn is cool too though)

Throughout the semester and up until this very moment, I’ve mentally compiled a list of things I’ve learned as well as things that I can improve on and the ways in which I can go about such improvement. This is quite possibly the most important part of this post–because it’s meant for you. Whether you’ve completed graduate school already or you are thinking about applying to graduate school, I hope you read this. I truly believe that if I take the following advice then I will not only survive graduate school but I will excel. And if your graduate experience or the graduate experience of someone you know can in any way be made better by this advice, then I’ve succeeded in the art of blog writing. In the art of mentorship. In camaraderie.

(1) Ask Questions

If you sit in on any of my lectures on any given day, you will leave the classroom fifty minutes later noticing at least one thing: all questions were asked by men. Now, I’m not sure why this is the case. Whatever the reason is, though, I think it is personal and is different for each woman. Maybe the women in my classes feel comfortable enough with the material that they don’t need to ask questions. That is not the case with me. Maybe the women in my classes feel outnumbered by the inundation of male voices in the classroom. That might be the case with me.

While it’s always the men in the class who ask all of the questions, I’ve never felt like any of them intend to scare off or intimidate the women in the classroom. Don’t get me wrong–there have been plenty of douche-bag non-questions that disguise themselves as questions but in nature are acts of self-aggrandizement, BUT I haven’t found any instances of such egotism as being specifically directed towards making the female voice, the female presence grow small in the classroom. (Note: the absence of outward sexism within my program does not mean that there is a lack of it in general. Many women can tell you that sexism has a very blatant presence within their departments.)

All in all, I vow to ask questions this upcoming semester. Even my stupid ones. Smallness is fed by this particular kind of silence. My personal refusal to ask questions in class stems from a once subconscious belief that either my questions are not important enough to ask or that I am not important enough to be asking them. I vow to break the habit of turning to the closest male in sight, leaning in, expecting him to be the source of all knowledge–feeding a machista rationale that is the very reason why I’m too afraid to ask questions in the first place.

(2) Figure out Your Speed. Embrace It. 

One of my professors compared graduate school to riding a bus. He’s driving the bus. We students are the passengers and we get on and off at different times, at different places. We all enter math graduate school with at least a Bachelor of Arts/Science in math, but that means different things for different schools. For Providence College, that means having taken Calculus I,II, and III, Linear Algebra, Foundations of Mathematics, Abstract Algebra I, Real Analysis II, and four other classes. At La Universidad de Guanajuato, at Simpson College, at Wiley College, at Princeton it can mean something completely different.

I came into graduate school with a very weak background compared to other students. While I only took 3 elective math courses in undergrad, other students had taken over 10. Others had taken a full year of Combinatorics, Partial Differential Equations, and Fluid Dynamics. I didn’t even know what those words meant when you put them all together like that. There are students who came in knowing exactly which field in Analysis they wanted to do research in, exactly which area of Topology they wanted to work in. I didn’t even know what topology meant.

What I’m saying is that my professor is right. Graduate school is like riding a bus. Who cares if that guy’s getting off at Intervale Avenue? You need to get off at Prospect Avenue! You can’t try to keep up with the rest of the crowd and expect success. We all learn things at a different rate and in a different way, and that is something that is beyond difficult to understand, but trust me–it is so important to understand. This is something that I continue to struggle accepting each and everyday. It’s especially challenging because it truly is a daily trial; everyday you will sit in class and take note of how many people seem to understand the material better than you do; and while you may not do this in a competitive manner, but rather to know whether or not you can keep up with your peers, it is so harmful and painful for your self-esteem and overall detrimental to your mental health. Trust me. I know.

If I continue to compare my thirty-percent knowledge of topology with someone else’s seventy-five percent, inadequacy and defeat will continue to follow me. I will become so focused on what I lack that I overlook what I gain. I will become so distraught about what I do poorly that I might miss what I shine in, what I am meant for.

So I vow to take my time. To accept the state of not knowing what to write or how to think–I will not get comfortable there. I will not make a home there. But I will accept it enough to love myself. I will work hard to understand what I don’t understand, keeping in mind that (even if it takes a whole semester) once I do understand something, once I truly and intuitively comprehend a concept and how it works, I can run with it.

(3) Remember Who The Fuck You Are

I’ve already explained to you the ways in which I’ve lost myself this semester, so with that in mind I urge you to avoid doing the same. For every seemingly negative trait you have, you can always find a positive one. For every failure, a success. If you fail your algebra test, accept it, move on, and commend yourself for scoring a few points higher on your topology homework this time around, for getting up early enough to put in your hair extensions, for finally making time to call your father, even if it was only a 10-minute phone call.

People will always tell you that in graduate school it is important to celebrate even your smallest academic victories, but I’m going to go one step further and suggest that you celebrate any small victory–academic or not. Because graduate school makes life in general very hard; you become so busy with academic duties that it becomes nearly impossible to keep in touch with the outside world. You’ll find yourself out of touch with your best friends for nearly a month. You’ll find that your mother texted you every day throughout the past week and it took you that whole seven days to realize that you had responded not even once. You’ll find that Donald Trump is your president and you have no idea how the fuck that happened.

As a friend of mine put it, graduate school makes you wish the world around you would stop. So when you are occasionally successful at balancing graduate school with a world that refuses to stop or even slow down for you, celebrate that. 

Graduate school is hard. There’s no lie in that. It’s ripped me to pieces and now I have to put them back together again. My Step 1 is writing this blog. I started writing because it gave me life, so when I stopped writing this semester, I lost a piece of my happiness and life felt off in all sorts. So I’ll write because it gives me life, it gives me a voice–and those are two things you should never have to lose in order to gain something else. It’s that simple. 

I am Meghan Brigantty Malachi. I am a writer. I am an aspiring mathematician who is learning how to love math again. I believe in God. I believe in winged eyeliner. I believe in family. I believe in the bench press. I believe in banana granola crunch pancakes. I believe in fashion. I believe in short sentences with heavy words. I believe in short fingernails. I believe in Toni Morrison. I believe in airplanes, buses, and trains. I believe that zero is a natural number. I believe in having a positive body image. I believe in Afro-Latinidad. I believe in open hearts and open minds. I believe in selfies. I believe in the power of silence. I believe in hair. I believe you only fall in love once. I believe in Kerry Washington. I believe in this.

This is a snippet from one of my most recent poetry pieces. This style of “I believe”-writing is called a creed poem, where the speaker simply expresses his or her beliefs. As is the case with all forms of creative writing, the layout or the structure of a creed poem is determined by writer. You could simply state what it is you believe in, you could express your beliefs in a more ominous and less straightforward way, or you could do a combination of both. I learned about creed poetry in my Creating Writing: Poetry seminar during my last semester of undergrad; I really enjoy this style of poetry for a number of reasons.

First of all, it’s the quintessential “non-poet’s poem”, i.e., you don’t need to identify as a poet or even like poetry to write a creed poem; you can write in a very prose-like fashion if you’d like or you can just throw together a bunch of facts about yourself and that’s totally fine. It’s a very personal kind of project.

Second of all, it can be very therapeutic. I found that in writing this poem (which in its entirety is a little over two pages long), I started to remember a lot of subtle yet powerful things about myself–including my love for Toni Morrison as a voice for Black Americans in literature or the excessive amount of pancakes I can eat in one sitting. I started to remember that it is the tiny details, the subtle intricacies of your thoughts and predilections that distinguish you from all the other people who also enjoy mathematics, Kerry Washington, and winged eyeliner.So if you’re reading this, I urge you to give this whole creed poetry thing a shot. It doesn’t need to be long or complicated. It doesn’t even have to feel like a poem. Just try to record the little things you believe in or the big things you believe in, and see where it takes you.


Theorem. Let f be continuous on an open set U, and suppose that f has a primitive g, i.e., that g is holomorphic and g’ = f. Let a, b be two points of U, and let p be a path in U that joins a to b. 

Then the integral of f over the path p is equal to g(b)-g(a). 

In particular, this integral only depends on the beginning and end point of the path. It is independent of the path itself. 


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10 thoughts on “On My First Semester of Math Grad School

  1. Omg! You made me cry …… I’m so proud of you and I know that your future will be brighter than you could ever phantom! Remember the climb is always difficult and scary but once you reach the peak the view will be more than you could have ever expected. I love you 😘

    Liked by 1 person

  2. I thought your post was incredibly well written and I’m glad I got around to finishing it. I think as a first semester math graduate student I came to many similar conclusions as you did. For example, I also learned to celebrate every little thing I could do a little better. The truth is the first semester is all about learning to accept a little bit of failure as a learning experience. I found it interesting how you integrated your position as a minority into the piece but I can tell you, as someone who is not the least bit a minority (white male), that I still felt just as small and the “weak link” of my Phd program, as well as many of the other things you did. I also was afraid to speak up in class, not because I was a minority, but because I didn’t have an idea what was going on a lot of the time. You should never feel like you can’t relate as well to people in your program just because they aren’t minorities. If the men in your program act like they have it together all the time, I’m sure they’re just exhibiting a facade to protect themselves (it’s just what men do). Good Luck with your second semester and remember you’re not alone in feeling overwhelmed in this type of program!

    Liked by 1 person

    1. Thank you so much for reading! After writing this post and hearing feedback from a lot of different people, I’ve found that many of them related to my struggles as well–including white males. So I am definitely starting to believe more and more that all kinds of students from all kinds of backgrounds struggle in graduate school. I guess a lot of people just don’t share their feelings about it and like you said, many put on a facade. I think this next semester I will feel less embarrassed and ashamed about my struggles now that I know I’m certainly not alone in this. Thank you for your well wishes!

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