How to Study Math

Studying math ain’t easy. Whether you’re in college in-person, online, or the rare person who self-studies, math presents a unique challenge. I’ve taken a number of courses towards my major, and want to share some techniques that have worked for me. Hopefully you’ll get some use out of them as well.

  1. Read the textbook, work examples.
    This may seem obvious at first, but during my first few courses I would read the textbook, wait for a flash of understanding, then go to town on the homework assignment. This method does not work. A better way is to read the chapter with a pencil and paper in hand, attempting to work example problems as you go. After you’ve finished do NOT start on the homework assignment. Look at the exercises in the text, and work those before you do the homework. You won’t ‘get’ math until you actually do it, and in the process of doing it, you will make mistakes. It’s far better to make those mistakes while reading the text itself than on the graded assignment. Yes it takes longer, but you will have a far greater understanding of the content.
  2. Buy (cheap) supplementary textbooks.
    In my experience, electronic resources open the door to digital distractions. The solution? Read a paper textbook. The great thing about math is that the core subjects haven’t changed much in hundreds of years. As a result, used copies of textbooks are cheap, like less than $10 cheap, and provide a wealth of resources that are unmatched by digital alternatives (for me anyways). I personally used this method for every math class I have taken, and have found that a second perspective on material can make all the difference. I recommend Dover publishing for cheap math books, as well as buying used, older editions of textbooks. Anything you can get in the $5–$10 range will prove helpful.
  3. Start early.
    Mathematical concepts often take awhile to sink in, no matter how many times you read and reread a theorem, sometimes it just won’t make sense. In these cases, the answer is often to step away for awhile, whether that be 20 minute walk or a full nights sleep will depend on the severity of the problem. In any circumstance, rushing is your enemy. You need to give yourself time to work through concepts without the stress of deadlines. I’m bad about this, but I’ve found in weeks where I start assignments early, I understand more with less stress.
  4. Find a quiet spot.
    This is more of a general study habit, but it applies well to math. Find a quiet place to buckle down and study. Having a dedicated study area where you can sit down with a book and paper (no electronics if possible) to focus is essential. For me this is the public library, but any place that works well for you is fair game.

Since my classes are asynchronous, I often feel like I am self-studying a math degree. I suspect however, that the self-teaching mindset is beneficial to anyone studying math, whether in school or just as a hobby. So to summarize: Work example problems and exercises before doing your assignment, buy supplementary textbooks, start early to allow concepts to sink in, and find a quiet study place to do the work.

Thank you for reading, and good luck in your studies,

Simon

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