This is a summary of topics that I have tutored, or am capable of tutoring. This shouldn't be considered exhaustive: I like to be challenged. I have had a number of students requesting tutoring in a topic that I was not completely familiar with. We agreed to them providing me their materials (textbook, etc), I kept at least a week ahead of their schedule, and I would provide them my insights and help them with any problems. I find these students quite fun to engage with, but I also understand people who want more expertise than this implies.

First, I will discuss my expertise in topics that I "specialize" in. Technically, I think I should start with a list of topics I don't tutor, but psychology says one should first focus on one's strengths.

Specialities

Mathematics

I have tutored mathematics at all age levels. I have taught first graders the number system, elementary schoolers the basic field operations, middle schoolers pre-algebra and basic geometry, high schoolers all of algebra and geometry, as well as calculus to people of many ages. I have taught the math needed for many different standardized tests, including high school entrance exams, ACT, SAT, ASVAB, NCLEX, GRE, MCT, GMAT, and the GRE math subject test. I have additionally taught mathematics beyond the calculus level, where my specialities would be in algebraic geometry and algebraic topology. Basically, if you have a math topic that you need tutoring for, feel free to contact me and I'm quite sure we can work something out.

It is my opinion that mathematics education in the United States is sorely lacking. This is somewhat caused by the large classroom environment and the way that mathematics topics are frequently layered on top of each other. For example, if a student did not fully understand fractions, they will struggle with all further mathematics topics (covered in a standard education through high school). In fact, I quite frequently find myself having to start with a review of fraction operations, quite independent of the age of my student.

Due to this observation and my extensive experience in tutoring, I have grown quite accustomed to teaching students who believe they hate mathematics. I am well-versed in looking for the root of misunderstandings, and providing different, novel approaches to problems. My methods never advocate for a particular solution method, but rather stress that the answer is what is most important: Creativity in getting to the answer is, if anything, encouraged. In short, if you have found yourself frustrated in mathematics courses, I can, perhaps, find a better approach to suit your needs.

Dually, if one is instead an advanced student in mathematics, I have the requisite knowledge and experience to challenge the student and provide the groundwork for whatever future one desires. I have studied a wide variety of undergraduate and graduate topics in mathematics, and have also helped students prepare for various mathematics competitions. Thus, if one is instead bored in mathematics courses and is searching for a path to new topics, I can provide a way forward.

If a student is going to be a long-term student, my approach focuses on immediately laying the groundwork for mathematics not inherently as a computational discipline, but always with an eye forward to advanced topics. I have tutored elementary school students to be able to prove basic facts of numbers (e.g., that there are infinitely many primes, or that the square root of two is irrational).

Of course, most of my students are instead looking for a faster approach with a specific end-goal in mind. This could be test preparation, or simply to pass the current course. I have extensive experience in test preparation, dating all the way back to my own time in high school (where I tutored fellow students in the ACT mathematics section). I myself have taken a wide variety of standardized tests in mathematics; if you are preparing for one that I haven't heard of, I am sure I can find enough information about it to prepare you adequately for the exam. (There might be an exception for particular graduate school exams: If you need tutoring in a graduate-level mathematics topic, please contact me and we can find out if I can provide any help.) I have helped students through all of the classically challenging courses, including geometry, precalculus, calculus, multivariable calclus, and so on.

To summarize, there is very little that I cannot tutor in mathematics (at least at or below the undergraduate level), and I also enjoy tutoring mathematics (be it integer arithmetic to an eight-year old, fractions to a 40 year old, calculus to a teenager, or GRE prep work for a 30 year old). I have experience in it all, and would be happy to discuss your needs.

My experience itself comes from my bachelor's and master's degree in mathematics. I have also taught precalculus and calculus at university; TA-ed for abstract algebra, applied linear algebra, and numerical analysis; held sessions for test preparation in ACT, SAT, GRE, and the GRE mathematics subject test; and ran seminars in highly specialized topics of advanced mathematics. I have tutored mathematics for over a decade.

Please, if you have a problem, I would like to try to help.

Writing

I claim writing as a specialty in spite of not having a formal education in writing. In fact, the last course that I have taken in writing was back in high school, where I took AP Language and Composition.

Instead, my experience comes simply from the fact that I have four college degrees. I wrote papers for all of these degrees, and have thus written many, many, many papers. Throughout this experience, I have gained a passion for writing. Given my analytical nature from my mathematics side, I am very good at analyzing writing and telling people what they lack.

This led to me, throughout my undergraduate career, critiquing people's work. Friends who discovered my ability would have me read through important papers. I'd return the draft covered in red marks filled with errors and suggestions. As a fun anecdote, I was in a course with a friend where we had to provide feedback on a random classmate's paper, anonymously. I got my friend's paper by chance. He guessed it was me providing feedback because I found an error consisting of a mismatch between an in-text citation and the references at the end of the paper: I had no idea which was correct, only that they did not agree.

Due to this intense level of scrutiny, I have provided feedback to professors on publications, students on theses, and other important papers. When I picked up tutoring, I would have many younger students who needed general tutoring across both mathematics and English. I quickly realized that I could imbue my understandings of writing to younger students as well, providing a good focal point. This especially agreed with the fact that writing education in the United States is rather...lackluster. Nobody really enjoys reading a five paragraph essay, but I think they are for some reason still taught now. If your writing isn't enjoyable to someone, then why are you writing it? (If your retort is that what I am writing right now isn't enjoyable to anyone, my reply is that I myself am finding this quite enjoyable to write.)

I, of course, have also used my knowledge of tricks and shortcuts to help high schoolers with their many exams. I took a large number of AP tests back when I was in high school, and have thus picked up many ways to write "good" essays quickly for standardized tests. This would also apply to the GRE, which I believe has a more fun writing section.

If you would like help with a writing project you are working on, I would like to hear about it. Note I haven't helped with anything longer than an about 70 page thesis, but I would be open to trying to help on a longer project. If you instead want generic help with getting better at writing, I can also provide assistance. Highly opinionated assistance, of course, but everybody has opinions.

Chemistry

I list chemistry as another topic in part to emphasize that I have background in scientific topics, in part because it is a subject many people struggle with, in part because I find chemistry quite enjoyable, and in part because I have a degree in chemistry.

My focus in chemistry is the mathematical side, of course. I took many courses in physical chemistry, at the undergraduate and graduate level. What this means is that my method for understanding chemistry is not memorization: Anyone can give you a set of flash cards and tell you to memorize it. I, instead, focus on understanding a few key underlying concepts, and trying to generalize from here. The upside of my method is it can get you 95% on an organic chemistry test without having to memorize hundreds of flashcards; the downside is it cannot get you the last 5% at all. Some of any science is necessarily memorization.

Chemistry is not nearly as demanded of a topic, so I have less experience in tutoring it. I am always looking for more students, since I enjoy chemistry and like talking about it. I have tutored general chemistry, organic chemistry, analytical chemistry, some specific sessions on NMR, and very few sessions on further topics of physical chemistry like quantum mechanics.

Although I have a degree in chemistry, I would not claim to be nearly as well-versed in the topic as I am in mathematics. I find chemistry fun, but I live and breathe math. That being said, I would be happy to try to help you with any chemistry problems you are having.

Test Preparation

Test preparation would be how I began tutoring, all the way back in high school (although I guess I also tutored some calculus back then as well). I have tutored for many exams. I probably cannot list them all. A partial list would be: High-school entrance exams, PSAT, ACT, SAT, various SAT II subject tests that I won't list since I think they have been deprecated, ASVAB, GRE, GRE mathematics subject test, MCAT, LSAT, GMAT, NCLEX, AP United States History, AP Microeconomis, AP Macroeconomis, AP Language and Composition, AP Physics B and C (which I think have changed names), AP Calculus, AP Chemistry...this list is definitely incomplete.

Due to my extensive experience in taking tests, I have developed a philosophy and strategies for the exams. I have raised student scores on exams by a significant margin (at least if they adhere to the program I outline). A particular example would be an ACT student: She came to me with a score of 18. After months (a year?) of work, she took the exam and excitedly told me she got a 31. My response was, "Were you nervous? You did better in session."

These exams are imperfect and unfair. This also means that one can prepare for them and significantly increase their score. How long this takes depends upon how well one knows the base material, so I can't provide a generalized program.

In some sense, test preparation is one of my least favorite topics to tutor. However, it also gives me a good background to stand on my soapbox and rant, which I always enjoy. I am also good at it, and it is unfortunately necessary: I have yet to hear of a different plan for a capitalistic society that allows for adequate comparison across disparate backgrounds.

If you are preparing for an exam, feel free to contact me. We can figure out what your best plan of attack is. If it is an exam I haven't heard of, that'll be fun for me.

Topics I Can't Tutor

The exact reverse of the previous section, I should state topics that I can't tutor. (Or more accurately shouldn't tutor: Hopefully one can find a more appropriate tutor. If you've tried and can't, then we can discuss your options.) Note that all of these subjects have qualms: Every single one I have tutored before. These are simply my weaknesses, that I need a severe amount of preparation for (or can only tutor specific aspects of).

Foreign Languages

I cannot speak (conversationally) any foreign language.

I have extensively studied Spanish, and modestly studied Arabic. I can read Spanish at an undergraduate level, and Arabic at maybe an elementary school level (the abjad aspect of it never agreed with me: I need my vowels evidently). I can understand both when they are spoken to me (although Arabic I have to really concentrate).

For other foreign languages, I can read French and German well enough to understand mathematics papers. I can also modestly read Russian, but would need extensive external support. Any romance languages with a high familiarity with Spanish I will be able to understand to some degree, of course, like Portuguese.

I also have an interest in linguistics, but have never formally studied it.

I have before had students who I tutored in multiple topics, and who took Spanish. They would occasionally ask me for help with their Spanish work. When they had questions on the grammar, I could provide fairly good advice; much else, I am not who one should ask.

Computer Science

I am completely self-taught in computer science. I can program in Fortran, C++, and Python, with external support. I have experience with spreadsheets and their ilk, database management, and other such things. I am currently making this website (although since I prefer a simple design, this is fairly easy). Additionally, due to my mathematics background, I am quite well-versed in Latex. Additionally, my mathematics background helps with theoretical computer science, algorithms, and similar such nonsense.

However, I should not be the one to teach computer science. I do not have the requisite experience, and I am also not at all enmeshed in the environment. My perspectives on programming, for example, are entirely different than anyone who has had even a modest amount of formal education. My programs look vastly different than anything else that one would see. They work (and if I cared to optimize them, which I rarely do, they work fast), but they do not respect the higher-level organization that "computer scientists" want to see.

That being said, I have had computer science students before. For example, I helped a student with an undergraduate course in database management. They were not a computer science "major": This was simply a required course for their work (which, if I recall correctly, was nursing). They provided me with the syllabus, textbook, and any assignments. I stayed at least a week ahead. I helped her through any assignments, and answered at least my thoughts on her questions. She passed the course easily, and I picked up some basic database management skills (which I then applied to my own database I was setting up).

However, this is not for everybody. For example, a computer science major should definitely not accept such an arrangement: Maybe a computer science major could learn algorithms and computational complexity theory from me.

In short, I would hope you could find somebody better suited than me for such topics. If you can't, though, I would enjoy the challenge.

Literature

I dislike classical literature. Thus, I can't easily tutor it.

I, of course, regularly teach English to elementary, middle, and high schoolers. This necessitates a program for reading. I simply choose from books I actually enjoy (or let the student pick).

My dislike, though, means I shouldn't teach to what other people desire to read: What I teach will be highly skewed to the negative.

I am making this sound more dramatic than it actually is. I can, of course, tutor standard high school reading courses. I may not like the book being read, but I can provide accurate and detailed analyses of the concepts therein. What I should not tutor is things like AP Literature and Composition, and undergraduate literature courses. I took the AP test, and did well, but I did not enjoy it at all.

It is always better to have a tutor who enjoys the topic they are teaching you.

Now, of course, if you are a negative person, you yourself hate the course, or you think a negative perspective on classical literature would be a refreshing outlook, then you are welcome to seek me out: I won't turn away literature students. I am simply providing a warning. Also, I have most likely not read whatever classical literature you may need help with: Since I had such negative experiences, I haven't read most of it. I see no reason to, when it is extremely easy to find books you actually like.

History

I have no head for history. I am bad with dates and names and all of it. It is "just" memorization: Create some flash cards and learn it.

That being said, I took AP European History and AP United States History. I did very well on both exams. The reason I did well is the essay portion: I created well-written essays, with an intriguing thesis. This means that I have had students who I "taught" AP US History (and maybe also World or European). However, I did not teach them any of the actual "history" aspects: As far as I'm concerned, they were writing students.

Topics I'm Working On

Here, I will list topics that I am trying to get better at, or is at least on my to-do list.

Biology and MCAT

I am not a biologist. In my opinion, it is too much memorization. I have taken biology courses in undergrad, so I am familiar with the basic concepts.

One may have also observed that I have listed the MCAT before as a topic that I have tutored. Any time I tutored for the MCAT so far, it was with the explicit understanding of the student that I was not an expert on the biology aspect of the exam. For those who don't know, the MCAT is a very long test, due to a somewhat recent change. It covers Biology, Biochemistry, Organic Chemistry, General Chemistry, Physics, Math, Behavioral Sciences, and "Critical Analysis and Reasoning" or something similar. I regularly tutor Chemistry, Physics, and Math; I have a degree in Psychology which covers a lot of Behavioral Sciences (I have also taken courses in Anthropology, Sociology, and Political Science, which covers a lot more; my wife is also a nurse, which has allowed me to pick up even more).

One day, I noted that the increased length of the exam made me almost extremely qualified to tutor the exam. There are also regular requests for tutoring the exam, and not many tutors can handle it (given the extreme diversity of topics). In order to handle the entire exam, all I have to do is review Biology so that I am convinced I have adequate knowledge. I have textbooks (underneath this very computer I am typing on); I must simply find the time to review them. My plan is to study the material, and then actually go sit for the MCAT and see how I do. Currently, it is hard to validate the time and expense; if I get further requests for MCAT students, I will have to do so.

One way to make me learn it would be to have a student. So if you want to be such a trial student, we could negotiate a discounted price.

A (not) full list

Here I provide a list, which I will try (and fail) to make exhaustive. First, topics that I have formally studied, at least at the undergraduate level or standardized exams. Note this is from memory, so is definitely missing topics. Finally, a list of topics that I have tutored before. Again, this is from memory. Topics Tutored