
If you would like a recommendation from me either for colleges, internships, scholarships, whatever, these are what I need from you:
 An email request with information about due dates and then emailed reminders along the way.
 The answer to the following prompt: What impact have taking my courses had on you? I'm not looking for a flattery letter. I ultimately only get to see a small portion of who you are as a person by interacting with you in classes or in extracurriculars. You are a complex person made up of more than the grade you acheive and whether you answer questions in class. Each letter I write is unique and this information helps me to create that for you. There are sample answers to this prompt below.
 What are some of the achievements academic or otherwise that you are proud of? A resume can do for this, but a description of some of the unique things in your resume would be appreciated.
 A sampling of your college essays. I know these are probably in a draft stage when you are asking me. I can take drafts. Again, these give me more insight about you as a person.
The further in advance you provide me with these things, the better your recommendation will be. I spend a lot of time on each recommendation and try to really represent you as a whole both based on my own observations of you and on the information you provide to me as well.
Sample Essays below
Sample 1
You've known me ever since I was a freshman wannabe (I couldn't think of any better word to describe my freshman self lol), since I struggled to break 100 on UIL mathematics exams, when I inched my way up the mathematical ladder in my freshman year to win 2nd place at TMSCA State in Mathematics, and when I became a member of our school's math team of four.Since then, through math and science team, Mu Alpha Theta, and in my own time, I've worked to develop not only my problemsolving abilities but also my leadership skills. After two years of managing lunch and after school meetings and working with/teaching students myself, I've developed a passion for education and mentorship. I've enjoyed leading these clubs because it's allowed me to step out of my comfort zone and lead with confidence. As an introvert by nature, it takes a lot out of me. But over the years, I've done my best to establish relationships with my team members, my peers, and my teachers. I aspire to continue growing as a person, as a student, and as a leader at a vibrant, innovative university. Your strong recommendation letter has a momentous influence on the strength of my application, so I am forever thankful for your willingness to write on my behalf.___________________________________________________________________________________________________________________________________________Why did I take the courses?Mathematics wasn't always one of my "strong suits." As a middle schooler, robotics was my forte and my passion. Math was just a banal, purely abstract, waste of time that countered my innate pragmatism. I had a desire to apply my knowledge towards a tangible goal at the time, there was no goal more tangible than building and programming a robot that could transport cubes or climb steep ramps.It was only in high school when I began to perceive mathematics as a toolkit in the vast web of disciplines, ripe for application. I was a novice to the wondrous world of math, and found ways to work my way upwards. At the beginning of the year, I figured that math would only be an ancillary hobby, secondinline to robotics. I just thought, if I was going to wait for my parents to pick me up after school, might as well stay and learn some math. As I attended more meetings, more UIL invitationals, I was inspired by the upperclassman to improve iteratively. In the process, I took practice tests regularly, each time recording the questions I got wrong. It was like doing test corrections, except without the 'points back'; but over time, the points would add up in each new exam, each new problem, and each new competition. I even made my own UIL program on my TI84 (this was before I even knew the Nspire was a thing), that had a variety of useful functions for each question type. I used it as a way to reconcile my passion for programming with my growing love for mathematics, thereby giving me a unique advantage as a competitor.I have always been the type of student who actively seeks the most challenging consortium of classes. As an active member and leader of the math team, I especially sought the challenging math classes. Thus, PreCal BC and Calculus BC were natural choices. I chose to take PostCalculus as a junior for a similar reason a pure desire to take the next step forward in my mathematical progression. It was the next rung on a ladder that I wanted to climb. I wanted to 'be ahead of the curve' it always appealed to me to learn 'advanced' topics, concepts that students my age typically don't have the opportunity to study. Most of all, I was ecstatic to take the class because of its application in AI. The PostCalculus curriculum would formally cover topics like linear algebra and partial differentiation that were required to develop a deep understanding of machine learning.What impact did your classes have on me?I'm glad that you've been my math teacher for my last three math classes (PreCal BC, AP Calculus BC, PostCalculus). I hope that in each class, I've demonstrated an authentic desire to not only perform well on tests but to absorb each new tidbit of information and use it in competitions and personal projects.Precalculus BC was the first time I deliberately studied for math exams. It was the first time where I can say that my math class challenged me. I'm not sure if you remember, but for each quest or test, I would compile a list of topics that we learned within that unit, and made sure I understood the heck out of them before the day of the exam. As a result, my overall understanding of math improved... tremendously.Moreover, both PreCal BC and Calculus BC have given me a strong mathematical foundation that I have used in competition and research. I enjoyed both classes, using each new lesson to reinforce my understanding of topics that I thought I 'knew' before the class, but always discovered that there was some nuance that I never encountered before. By using your own challenge problems in lectures and exams, my mathematical scope has widened significantly. Using a machine learning analogy: you've given us a variety of challenging data sets, each augmented to improve our ability to generalize to problems that we haven't seen before. So now, when solving problems, I have a habit of thinking in terms of calculus.A perfect example of this was this past summer. I was accepted to the biomedical research program at the UT Medical Branch. I was assigned to the ophthalmology laboratory that specializes in image processing. I was able to convince my mentors to allow me to do a project that involved deep learning! I spent eight weeks developing an algorithm to segment retinal layers in OCT images and quantify pathology. When approaching the quantification problem, the concepts of calculus were the first to permeate my thoughts. It was a volume calculation given 3D BScans. It was the perfect application for the classic "divide and conquer" that's characteristic of calc. Break the volume down into its constituents (pixels), then sum the number of pixels within the algorithm's segmentation. It was a realworld application of integration!PostCalculus was the ultimate kicker. Your lessons on linear algebra and multivariable calculus are the cornerstones of the math behind AI. Before the class, I had to make use of my understanding of derivatives and integrals to decipher the mysteries of partial differentiation, stochastic gradient descent, and convolution. It was only after postcalculus that I was able to synthesize my newfound understanding of eigenvalues and eigenvectors in addition to multivariable optimization to the specific AI topics that used these mathematical principles. In other words, I expanded not only the scope of my mathematical knowledge, but also my understanding of artificial intelligence. After the first semester, I delved into the reputable "Deep Learning" book that is known for scaring people off with the first few chapters, all of which contained math. It turns out that the first semester of postcalculus was enough to get me through the pages of pure Latex (I was still a struggle, but with the postcal foundation, it was much easier).As a result, your classes have made me an 'outlier'. Due to your initiative to create a personalized postcal curriculum, I was able to take one momentous step forward in deep learning, a field that I enjoy, and a field that I believe will be a major part of my problemsolving career. Thank you for opening it up to juniors!! It had a huge impact on my summer research, from being able to understand the math in research papers to being able to apply the math in an actual algorithm. I will continue to carry the content with me to college, and (hopefully) into an interdisciplinary career where I can do what I enjoy doing applying math to solve realworld problems.Sample 2When I was in middle school, I hated math with a passion. Every math class I went into drained the life out of me. In fact, when I was in 7^{th} grade, I was part of a math class that was so bad we got extra time with the math teacher just because we were dumb enough to need it. Everything in math involved memorizing a specific way to show your process and point taken off for even the slightest difference from the teacher’s process. My work is generally very freeform and messy, so I hated having to confine myself to a specific way of learning math in order to get an answer. On top of that, every class I was in was just boring. Every middle school teacher of math that I had made it into a boring class, where we just sat and listened to them talk while trying not to go mad.
In spite of my failures, I realized that some kids thrived in my middle school’s math system. The students who were good at math were the top intellects in the entire school, and were respected, if not necessarily liked, by everyone else. I came to associate being good at math with being smart, and wanted desperately to be good at math so that I could be smart and respectable, instead of being a dumbass barely getting through the class.
Needless to say, when I went into high school at Carnegie, I thought that the pattern was going to continue. From the moment I walked into the school, almost everybody I met was going to be taking Geometry or above, while I was merely in Algebra I. I saw Algebra I at 2^{nd} period on my schedule and was ready to begin to hate the class. And then I walked into Mr. Cantu’s Algebra I class, sat through the first class, and walked out with a realization: I actually enjoyed the class. And as I continued to go through his class, another thing became apparent: I was really good at it. Where there had previously been low 70s and even failing grades, there were now high 90s and even 100s. And the momentum was carried through my entire freshman year. I ended the class one of my Algebra I teacher’s favorite students and the recipient of an award for my performance in the class.
In spite of this, I still felt terrible at math. After all, I was only in Algebra I, the lowest level math class. Surely the people who did the same as I did in other classes were far superior in intellect to me. I believed at the time that while I had had 1 good year, the next year would bring the same struggles as I advanced through math. It was to the point where, when I was congratulated by Ekin for receiving the Algebra 1 award, I couldn’t really take it seriously, though I did my best not to show it to him. I mean, he was the best student in Algebra II and one of the premier students of my year. His intelligence was far greater than mine. And he seriously considered my meager achievement worth congratulating? It was almost to ridiculous to bear.
In spite of this, I decided to double up on Algebra II and Geometry. While my years rather poor academic ability made the administration reluctant to let me do so, they were far more willing once they saw my Algebra I grades. In order to quell my fears, I studied Geometry over the summer. It still didn’t seem incredibly difficult, but I was prepared for the worst. But once I got to both classes, some interesting things happened. Algebra II wasn’t terribly difficult, and I really liked the new Algebra II teacher when I had him, in spite of his quirks and flaws. [...]
Geometry, on the other hand, was arguably my best math class ever. I easily learned everything he taught me in class, and got grades well over 100 on every quiz and test he gave me due to copious amounts of extra credit. He also offered “Hard problems” on the whiteboard for every week, and I did a few of them when I could, but I didn’t really care at the time as I was too caught up in the euphoria of being good at math.
Then in the 2^{nd} semester, a few things came crashing down. I got rejected by a girl in theatre that I really liked and felt like absolute shit about myself. The feelings I’d had since middle school started to resurface and I didn’t know what to do. One day, my Geometry teacher told the whole class a proverb he learned when he was young, roughly translated into English as “There is a beauty in the book. There is a big house in the book.” In other words, study super hard and you will get what you want. Now, the big house wasn’t of concern to me at the moment, but the whole “beauty in the book” part sounded really good to a hormoneaddled, lovesick, depressed teenage boy. Ergo, I started solving as many hard problems as I could, partially to alleviate my own feelings of inferiority and partially out a delusional hope that the girl I liked would like me back once she saw how smart I was (This worked about as well as you’d expect, but I grew up a lot from the experience, so it was worth doing). I wasn’t able to fulfill the 2^{nd} objective and only slightly helped the first, but I soon became famous in his Geometry class for solving the most “hard problems” of any student he had at the time. I solved everything even the smart kids wouldn’t solve out of a desperate attempt to feel like the smartest person in the room, and because they helped me develop a lot of skills I wasn’t developing in the normal classes. And at the end of the year, I was awarded a reward for solving the most “hard problems” out of anyone in his class.
Around the middle of the 2^{nd} semester, the PreCal BC entrance exam came up. I was at UIL for the first day of its administration, so I didn’t take it with everyone else. I was really determined to be in the class, because in my mind, if I made it into PreCal BC, then I would’ve truly surpassed my middle school self and would be on even ground with the intellectuals of my year. So I emailed you asking if I could take it in your class, and you didn’t respond (in retrospect, probably bc you had a million other things to do). After about a week or so of waiting, I walked timidly into your classroom and asked if I could take it, expecting to be rejected with the knowledge that I missed my chance. Instead, you told me that it would be fine if I just took it in your classroom. So I took the test over two days. It was, at the time, the hardest math test I had ever taken, and I left the classroom certain that I hadn’t made it into PreCal BC. Imagine my surprise when I got a letter of acceptance into the class one day in Algebra II, completing my dreams of ascending to the intellectuals’ level.
Then I went into PreCal BC junior year, and a lot of things changed. First off, I started struggling in the class, bc I hadn’t adapted to your level of difficulty at first, though it got better as I was in the class for longer. Secondly, I realized that a lot of the ideas that had been driving me to be good at math before were really stupid, such as the idea of the magical mileswide gap in intelligence between me and other students who were good at math and the idea that I could never be on their level of intelligence if I wasn’t good at math (people have a whole range of talents, I now realize). In response to the second one, I started enjoying math more for math’s own sake, rather than as an egobooster, and this helped me enjoy your class and start watching more math channels so that I could learn more. I also continued to do more of Mr. Li’s hard problems, since they were fun little challenges of my basic fundamental skills (except the Holy Roman Empire one. That’s a bunch of guess and check and I’d rather eat a giant bag of potatoes than sit through it). These changes ultimately helped me develop into a student who genuinely enjoyed math, even if he was lazy with his homework (as you well know). PreCal BC became one of my favorite classes as the year went on, and it pushed me to love math to a degree that I hadn’t really considered possible before. And at the end of the year, I applied the Mu Alpha Theta, expecting to be rejected bc of my homework “difficulties”, and was, to my surprise, accepted. And now I’m a senior, following the same path that I began to follow in my junior year.
Sample 3
I honestly feel that taking your classes during my time at Carnegie/in high school has taught me how to truly think independently and figure things out for myself. (and to not give up!)
It’s probably not a surprise to hear this, but I literally breezed through all of my math classes up until PreCalc BC. In middle school, nothing was ever actually difficult; I never had to worry about having less than a 95, and I could usually figure out the answer after staring at the problem for a little bit.
Now, don’t get me wrong. Mr. Cantu and Mr. Li are great teachers, I adore them, but their classes were also really easy to get through. The only time I felt really challenged by anything was on the first day of school  I accidentally walked into Mr. Cantu’s room before I had him and immediately saw “QUIZ” on the board. (I took both Geometry and Algebra 2 my freshman year, and I literally texted my dad freaking out about the possibility of geometry being on that quiz; it was not).
So, as you can imagine, PreCalc BC was like an entirely different beast, but it turned into a class that I thoroughly enjoyed. You might have heard / seen me, Akhil, Serena, Ekin (maybe not Ekin), or Quynh saying “BIG BRAIN” or making *mindblown* gestures while you were lecturing, but that’s honestly what taking your class felt like. Every day, we were learning something really interesting and new, and most importantly, you could always explain things extremely well and very thoroughly. It wasn’t like  oh here’s a theorem, remember it, proof why is above your level. You always led us through where that law or theorem came from, no matter how daunting or crazy it looked. Learning new things in your classes therefore always felt like we were making new discoveries by ourselves, and that made everything we learned that much more fascinating, interesting, and “big brain.” And, it actually meant that I understood something from all aspects, not just the example way to approach a problem.
Overall, your classes really just opened my eyes to how truly diverse math is. I thought vector optimization (planes, rafts, etc.) was absolutely relevant and fascinating, although tricky at times, trig integrals were a pain but amazing when I solved them, and the dimensiondefining properties of eigenvectors and eigenvalues are so so so interesting. I really have you and your classes to thank for expanding my view of math.
Okay, the struggle part. PreCalc BC and Calc BC were most definitely not smooth sailing  I definitely panicked on a good number of tests before I would eventually figure out how to do the struggle problems. However, the fact that I could no longer immediately see the answer after just staring at the problem taught me important principles and practices to have. First, to “trust the process.” Sounds cliche, but that is the first thing I learned in your class. No matter how hairy and nasty something looks, it is always solvable! And, solvable using methods that I already know  it’s just not a twostep problem, so don’t panic and brain fart. That mindset has helped me many times (and still does) on quizzes, quests, and tests.
Having no more corrections in the second semester of Calc BC was definitely a scary moment, but that was when I really learned that I needed to think for myself, and that I was in charge of what was going to happen to me (or in this case my semester average).
PostCal so far is a lot of fun (and big brain moments). I am really enjoying it, and it’s kind of refreshing to learn things that aren’t dictated by the school district or College Board. I am also looking forward to many more hands on projects where I can actually experience things for myself.
This has been a long and rambly response, so I will wrap it up here. Taking your classes has expanded my view and understanding of math, but also of myself (wow) in that I have learned to become more selfsufficient and selfconfident. Truly, when I think back on all the things I’ve learned and skills I’ve gained in your classes, I’m amazed. I cannot thank you enough :)
Sample 4
The Importance of Chen Classes Through the Lens of The (Truncated) Precalculus BC Syllabus
Course Overview:
Algebra 2 review:
The first three words to go in my PreCalculus BC notebook were “What is symmetry?” By all means, this should have been a simple question. This was a topic we were covering on the first day of school, and it was a question that every student that had matriculated Carnegie’s Algebra II class should know the answer to. As such, I was thrown when, in this firstday review topic, something new was added into the mix. Even and odd functions. I didn’t believe I had ever heard those terms before. Scribbling the terms down madly, I was puzzled. Symmetry was a simple topic; I thought this would be a laidback review of something I still knew and remembered.
That first impression set a tone for every Chen math class I took throughout the rest of my three years. I found that there was always something new to be expected even when rehashing a familiar topic. In fact, because of that experience, I developed a curiosity for math that I hadn’t had before because, previously, I took it for granted that if I knew a topic, I comprehended it fully (or at least enough to satisfy me). This “review” revealed to me that I did not. I was starting to realize that, when it came to math, there could always be more: new facets to be discovered, nuances to be explored, a new lens through which to investigate an old topic.
Polar Coordinates:
This idea was only further emphasized with polar coordinates—albeit in a slightly different way. Forcing us to consider plotting points onto a plane that had traded in the neat box grid of Cartesian for the odd concentric rings that was a polar coordinate grid, we were challenged to take an old skill (graphing) and reapply it in new ways (polars).
This concept made me more flexible in how I considered mathematics. Prior to this, I felt very much like a computational robot (Editing note: I’m realizing I could’ve just said computer or calculator here). Given a question, I would answer it; on a test, similar question, same method, just plug, chug, and done. Polars were a whole different playing field (or should I say…“plane” field). I initially struggled a bit, trying to adapt my very much Cartesianminded self to wrap my mind around doing things I was quite used to doing in this new landscape.
Additionally, this challenge wasn’t one unique to polars. I felt that several of the tests, across all three levels of Chen classes I’ve taken (Precal BC, Calc BC, and Postcal) incorporated these sort of “reframing your mind” sort of questions. Rather than letting me solve without understanding, I was forced, by these tests, to really grasp the concept so that it could be applied in ways we hadn’t explicitly covered in class. This wasn’t always easy; I had to relearn my method of studying mathematics (going from a quick skim of notes to more interactive methods of study like reworking practice problems), and, even then, there were still times I would just stare at the questions hoping that an answer would hit me because I wasn’t even sure how to begin to approach it. Nevertheless, I gradually became more acclimated to that simple demand—understand what I’m doing and its reasoning—and slowly I improved on those questions, less daunted by having to find new ways to interpret the same concept.
Application of Derivatives:
That leads us from reapplication to application. Not to sound ~derivative~ here, but this section was another that changed my perspective on higherlevel mathematics. Prior to sections of mathematics that emphasized application (like application of derivatives or the projects completed in precalculus, calculus, and postcal), I didn’t really think math to be super relevant to the real world, except for basic elementary mathematics (so one can do the basic operations like addition and subtraction) and Algebra I (because sometimes one needs to run basic equations like linear functions). This section reinforced the idea that, no, every single level of math will likely be useful, reigniting an appreciation for the concepts we learned. For example, one application described in this unit was using derivatives to optimize (minimums and maximums). Optimization is a technique that would benefit a wide range of industries, and that versatility and functionality of a calculus concept was significant because it drove me to be more openminded when coming across concepts that may not initially seem to have practical uses because there oftentimes were ways to connect these seemingly random concepts into ideas that have real world implications.
Extra Credit:
In spite of everything mentioned previously, this class wasn’t only significant to my life in the lessons I learned about mathematics (and their nonmathematical implications on my skillset and mindset). It also impacted my extracurriculars, namely with UIL Academics. While I had joined UIL Academics in ninth grade, I didn’t feel all that invested in it. I joined as a freshman really only because it was something familiar (I had competed in UIL Academics in elementary and middle school, as well.) Offered as extra credit, UIL Academics became a larger part of my life than I originally intended. I ended up finding new events in order to secure those few extra points for precalculus and calculus. This led me to discovering (and regularly competing in) two niche (but fun) journalism events: headline writing and copy editing. Although I considered them, fun, filler events; they have actually had quite an impact on some of my future decisions. When I first toyed with the idea of going into business, my immediate thoughts were 1) business administration and 2) finance. However, because of my involvement with these journalism events, I found that I tend to lean in favor of activities that incorporate a sense of creativity and some (though minimal) writing, resulting in a penchant for activities like advertising and marketing. As such, those challenging Chen classes not only had an effect on the way I approached math but a part in my future.