Tips

This list is currently in the middle of being heavily revised.

I've thought a lot about how to be productive, both for classes and for work in general. Here are some of my personal thoughts on the matter. A couple things of note:

1. These are my personal thoughts and opinions. What works for me definitely won't work for everyone.
2. Living according to these tips is a practice that takes time and discipline. In particular, even I don't follow all of these rules perfectly all the time.

Tips for Class

• If your professor has a list of tips for doing well in class, you should probably at least skim over that list.
• Read ahead.
  • If you know you're going to cover chapter X in your next lecture, spend 15 minutes before the lecture reading through chapter X on your own to get a feel for the definitions and techniques used there.
  • If you don't do this and your professor introduces a new definition at the beginning of class, you'll be too busy digesting the definition to absorb much of the content beyond that.
• The only thing worse than not studying is tricking yourself into thinking you're studying when you actually aren't.
• If you're studying properly, it should be hard. If you're simply passively re-reading your notes or posted solutions over and over again without trying to solve problems on your own, you're not actually absorbing the information.
• Without looking at your notes, try and summarize the things you've covered in class. Try and restate important definitions and prove important results (again without looking at your notes). Only look back at your notes when you're stuck.
• Attending a discussion section is only useful if you're actively engaged with it. Again, don't trick yourself into thinking sitting for an hour in a room and not engaging with the material counts as studying.
• As much as possible, try to mix up the type of problems you solve when studying (e.g. do a problem from chapter 4, then one from chapter 2, etc.). While harder, this makes you better at identifying the techniques you need to solve problems.
• On taking exams.
• Do not try and solve problem 1, then problem 2, and so on. Read problem 1. If you immediately know what to do, write out the solution. If you don't immediately know what to do, go onto the next problem. Once you've read through all the problems, go to the problem which seems to be the easiest to solve.
• By using this technique, you (hopefully) won't waste a huge amount of your time on a hard problem and miss out on easy problems that appear later on in the exam.
• Also with this technique, you won't end up sepending half your time on the first problem which has a typo and is impossible to solve (which happened in one of the classes I took!).
• Use office hours sparingly for homework questions, but freely use them for questions about concepts (especially those that are unrelated to the course).
  • Especially for upper level courses, homework problems are meant to challenge you (to a reasonable extent). E.g. In the first class I ever took in the area that I ended up getting my PhD in, I would be thrilled when I could solve a problem in less than 3 hours.
  • This being said, if you fundamentally don't understand part of the question, or if you've genuinely thought long and hard about a problem, you should consult your professor for clarification/hints.
  • This being said, when you ask about a problem, you should demonstrate to the professor that you have genuinely thought about the problem to some extent. For example, if a question asks you to prove a map is surjective, you should be able to answer the professor when he asks you for the definition of "surjective". If the problem is that you don't know what surjective means, then the first thing you should ask the professor is "what does surjective mean", and not "how do I solve question 4?".
  • Similarly, you should briefly mention what you have tried so far to solve the problem, as this demonstrates to the professor that you've actually worked on things and aren't just trying to get easy access to solutions. Pro tip: if you ask me about a homework question, I will always start by asking you "what have you tried so far?", and if you can give me an answer to this (especially if you can do this before I even ask the question), I will be very happy to help!
  • Most professors actually like the subject area they're teaching in. Thus if you come to office hours and show a genuine interest in the subject by talking about something that isn't immediately going to help you on your next homework assignment/test, they will be more than happy to chat with you about it.
• Talk in class (when the professor asks you to).
  • There are few things professors hate more than asking a question and no one in the class responding.
  • Personally, I'd much rather have someone say something wrong so that I can figure out where the gap in your knowledge is than to be met with silence.
  • If a professor asks a question which has two possible answers, and literally no one is responding for a few moments, just guess something. Half the time you'll seem like you know what you're doing, and the other half of the time no one cares that you're wrong.
  • This all being said, if you find yourself being one of the few people in class who say anything, try and pause a moment before answering to give other students the chance to participate.
  • For more tips related to this, see "Pretend to be Confident" below.
• Sit in the front of the classroom.
• This makes it harder to get distracted by people in front of you, makes the teacher recognize your face more (useful if you want a letter of recommendation), and pressures you to focus more.
• This is not the easy option, and that's precisely why it is useful/worth doing.
• If you can avoid it, don't take notes (e.g. if the professor has notes online or if he's effectively going through the textbook). With this you can actually pay attention to what the professor is saying instead of desperately trying to write down every word he says.
• You (sometimes) don't have to go to lecture.
• If you're not getting much out of lecture (and if your teacher doesn't require you to be there), you'd be better off spending the time teaching yourself the material (and learning how to learn is a good skill to develop).
• Especially for a standard course like calculus, there are tons and tons of high quality resources freely available online from people who have dedicated their lives to teaching (and the professor for your course may not be one of these people).
• There are many flaws with this system, and in particular it requires a lot of self-discipline to actually learn the material on your own. This definitely is NOT for everyone, but there are certainly some classes and students that would benefit from this.
• "While grades attempt to measure what you have learned, they do not measure your dignity as an individual," Francis Su.
  • To reiterate, your grade in my class (or anyone else's) is not an evaluation of you as a human being.
  • In particular, I will not think less of you regardless of how you're doing in my class, especially if you're trying to do the best you can given your current circumstances.

Concrete Resources

• Calculus
  • https://www.calc1.org/ is a very nice site for calculus videos and exercises.
  • Calculus.org has a ton of resources, and in particular a lot of practice problems and exams with solutions.
  • Some step by step solutions to solving basically any kind of problem you'll see in a calculus course.
• For (algebraic) combinatorics, Federico Ardilla has a number of nice lecture series on his YouTube account.

Tips for Working

• Read the books "Deep Work" and "Getting Things Done."
  • I owe almost all of my productivity skills from these two books. I will warn that the latter book is less approachable than the former, but it's definitely worth trying out if you have the time (and perhaps all the more if you don't have the time!).
• Dedicate time to not doing work.
  • E.g. don't do any work after 5pm, or don't do any work on Saturdays.
  • If you're working so much that you're just rereading the same sentence over and over again, all you're doing is tricking yourself into thinking your studying while not giving your brain the chance to rest and recover.
  • If you're really strict with this rule, you'll find that you're a lot more productive during the working day (since you know you have to finish up your work before your down time), and you can guilt-free enjoy yourself when it's time to stop working.
  • Personally I don't like the "take a day off" strategy since I feel like I'm not warmed up for the next day, but really you should just do whatever works best for you.
• You're not really working if you're distracted.
  • Don't work with your phone on (or at least turn it on airplane mode), and ideally don't even have it physically on you (e.g. put it in a backpack or leave it at home).
  • It takes time to get into a focused mindset, and the moment your phone gets a notification you lose all your progress towards this goal.
  • Similarly, don't check your email, and ideally don't study with friends if they aren't also focused on studying the same thing you are.
• Have an ordered todo list of actionable items.
  • The hardest thing about doing things is starting, and the hardest part of this is deciding what to start with.
  • To avoid these issues, have a todo list, and each night reorder the list. Then the next day, start with the first thing on your list, then the second, and so on.
  • Of course things will come up so that doing item 1 becomes impossible, or maybe item 7 now has to be done much sooner than expected. You can adjust your list as the day goes on, but the point is that all else being equal, you have pre-decided that you will at least try to start with item 1.
  • It is very important that each item on your todo list is actionable. The task "study for test" is not very actionable, but "make flashcards" or "redo homework 5" is. Again this makes it much easier to actually start the task.
  • This rule is also useful for non-work settings. E.g. I have an ordered list of "to read" books which I just go through from top to bottom regardless of what kind of book the next one is.
• Track how much time you actually spend working.
  • If you are like most humans, you work a lot less than you think you do.
  • To rigorously track yourself, I personally recommend Toggl (which is free).
  • Be sure to only track hours where you're really working. E.g. if you get distracted, cut off the timer; and ideally don't even start the timer if your phone is on (or at least not on airplane mode).
  • It is an interesting experiment to track every facet of your life using this, but as someone who has gone down this rabbit hole I don't recommend doing it much longer than a week or two.

Tips for Life

• Do the best you can with what you've got.
  • I have some fairly bad insomnia. If I've only gotten three hours of sleep for the past three nights in a row, I'm not going to be solving any hard math problems anytime soon. However, I can still try and start some small things that have been sitting on my todo list, try to do some exercise, and ultimately try to live the day as best I can.
  • Conversely, if I've had a few great nights of sleep, I need to focus on doing the hard things on my todo list, otherwise I don't know when I'll be able to do them in the future.
  • Another critical thing is to not beat yourself up over not being able to do the things you want to do. Even if your current situation is partially your fault, you just need to accept things as they are and proceed from there. This is much easier said than done, and it is something I struggle with quite a bit.
• "In any situation in life, you only have three options. You can change it, you can accept it, or you can leave it," Naval Ravikant.
  • "What is not a good option is to sit around wishing you would change it but not changing it, wishing you would leave it but not leaving it, and not accepting it."
  • E.g. if you're doing poorly in a class, you can either drop the class, do something to try and improve your situation (talk to the teacher, change your habits), or accept the situation as is (and ideally not complain about it).
  • In this example (and in general), none of these three options are strictly better than the others; the best choice will depend on your exact circumstances.
  • The important thing is to decide which of these things you're going to do, and to go on from there.
• Pretend to be confident.
  • Confidence is a skill, and one that you can develop by doing things that make you feel mildly uncomfortable/that you think a confident person would do.
  • Some particular things I've done to improve my confidence include: deciding to always answer questions in class (after a brief pause to let other people talk), doing pushups/exercise in airports, asking for 10% discounts at stores (for no reason), asking random people sitting alone in the dining hall if I can join them for lunch (I made a lot of my friends in undergrad this way).
  • In general, if the only reason I can think of to not do a thing is that it makes me feel mildly uncomfortable, then I always try and do that thing.
  • As you do these things, the main thing you'll realize is that people are too busy thinking about themselves to really care about what you're doing.
  • This all being said, don't train this skill by doing things that harms/bothers other people or yourself. E.g. don't start doing pushups in the middle of a lecture since that serves as a distraction to everyone else.
• You aren't "smart" (and neither is anyone else).
• I choose to believe that no one is "talented", and that the only thing that measures how proficient someone is in a skill is (roughly) how many hours someone has invested into said skill.
• Admittedly, I don't think this is entirely true (e.g. Gauss and Euler exist), but I find it more useful to believe in this than to believe that I can never be as good as someone else in some skill.
• The quality of hours matters a lot here, e.g. an hour spent studying in the morning with your phone off is a lot different than an hour spent "studying" at 4am with your phone on while stressed about an upcoming exam.
• Prioritize your physical health, namely your sleep, diet, and exercise.
  • For sleep, an easy thing to do is to download the program "flux" which dims the blue light on your computer around nighttime.
  • For diet, there is a lot of conflicting information out there, and ultimately you should just follow whatever dietary philosophy makes sense to you/that you're able to mostly follow. Personally I'm a fan of the philosophy offered in the book "In Defense of Food", which can be summarized as "eat food, not too much, mostly plants."
  • For an easy exercise routine, I recommend "the 7 minute workout."
• The situation may not be your fault, but it is always your responsibility.
  • If you don't like something about the current situation, it's on you to do something about it (even if it's not your job to do so).
• You're already "good enough."
  • At one point I thought I would have made it after I got into a good grad school. Then I thought I'd have made it after I got my first publication. Then I thought I'd have made it when I got my first citation. And so on, and so on.
  • These things were all nice for a brief moment, but overall they didn't make me any happier (and if anything, achieving them made me feel more hollow inside).
  • It is perfectly fine to strive for further success, but it's important to remember (1) it won't really make you happier and (2) it won't make you feel like you're "good enough" if you don't already feel that way now.
  • Related, imposter syndrome is something that I've struggled with a lot in my life, and there's a reasonable chance this is true for you as well. Unfortunately I haven't figured out how to significantly reduce these feelings. The best I can hope to offer you is the fact that you're definitely not the only one who feels this way.

  Minor Life Advice

  • Only consume media that is great from start to finish.
    • No matter how much or little time you have invested in a piece of media, it is the job of the media to convince you to keep consuming it.
    • As much as possible I try and stop reading books whenever they aren't so good that I have to keep reading them. Because of this I often end up dropping books that start off decently within 5-10 minutes of reading.
    • The main argument against this philosophy is that you'll miss out on things that end up being really good later on. My first counter to this is that I prefer my media to be great from start to finish.
    • My second counter is that without this rule, you'll also be missing out on great things. For example, the book "The Way of Kings" is a 40 hour long audiobook and is part 1 of what plans to be a 10 part series. Upon seeing this, I was quite reluctant to start such a colossal series, and if I didn't have this rule I probably wouldn't have. But because I knew that I could drop the book whenever I wanted to, I could safely start it, and very quickly the book ended up becoming one of my all time favorites.
  • Read (audio)books.
    • I love reading, but even I find it difficult to read physical books. It wasn't until I discovered audiobooks that I really got into reading again; and you too may find it much easier to read in this format.
    • For those interested in things to read (especially in audio format), some of my favorite books can be found here.
    • Podcasts are also a great (usually free) alternative to audibooks, though I do think it's hard to replicate a really well written book with a podcast.
  • Take cold showers.
    • There are a variety of health benefits, and it's a good way to train your willpower.
    • This is of course easier said than done, and I often fall out of practice with this. One tactic I find useful is to pick some energetic song that you like and to play it whenever you do a cold shower. This makes it easier to take the shower, and it may accidently conditioned yourself to want to take a cold shower whenever you hear that song (this ended up happening for me!).
  • Archive your emails.
    • I personally get a great calm from having literally nothing present in my inbox. However, if you're one of those people that has 1000 unread emails in their inbox, I don't think this tip is for you.
  • Make your technology less distracting.
    • Your phone becomes a lot less exciting if you set it to be monochromatic.
    • Kill News Feed is a good way to make facebook less appealing.
    • DF Tube, and in particular its ability to turn off recommended videos, makes it a lot harder to get lost in a mindless YouTube binge.
  Finally, here's the last piece of advice I remind myself of every week (and which is so easy to forget):

  You'll be fine.