To learn effectively, it’s more important to have good study habits than good study skills. Study skills include activities like taking notes, reading with comprehension, and preparing for exams. Study habits cover topics like time management, focus, and prioritization. Skills and habits are both important. But even with the best skills, it’s hard to overcome poor habits. You can be a champion speed reader with the ability to write every word of a lecture in real-time. But if you start studying an hour before an exam and have YouTube videos blaring in the background, you won’t get great results. In contrast, if you consistently plan what you need to get done in the coming week, follow your schedule diligently, and cultivate the ability to concentrate exclusively on the task at hand, you will succeed even without fancy study techniques.

Good study habits don’t happen on their own, especially given the incentives of the online attention economy. You have to develop them. For a practical habit handbook, it’s hard to do better than James Clear’s Atomic Habits. This week, I’ll cover a summary of key ideas in the book. Next week, I’ll suggest ways to apply these lessons to studying technical subjects.

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Learning math is often about learning specific math topics. But it can also be useful to step back and take a higher-level view of math learning. Keith Devlin, professor of mathematics at Stanford University and creator of the popular Introduction to Mathematical Thinking course on Coursera, says modern students of math have to master two types of thinking:

• In K-12, the goal is to develop strong number sense.
• In college, those who continue their studies in STEM need to learn mathematical thinking.

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Back in the day, textbooks and classes were the way to learn math. Today, we have abundant online options. I wrote earlier this year about the benefits of practicing on Khan Academy, even if you’re not in its target audience. A similar online offering is Brilliant, which like Khan Academy has online math problems, but which uses a different philosophy of learning.

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I’m working this year on a specific area of math, but it can also be helpful to browse around and see what math ideas are out there. Last week, I wrote about the kinds of answers that pop up on Quora’s general math topic. Another math destination is Mathematics Stack Exchange. That site works a bit differently.

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If you’re studying a high school or undergraduate college math topic and you have a question, the answer is probably somewhere online. Finding it is just a matter of coming up with the right search terms. Or if searching doesn’t work out, you can always ask on Quora. But another way to use Quora is for an overview of what math concepts are available to study.

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Math problems on standardized tests have short, simple answers that fit in a multiple-choice format. But college-level math problems require more detailed explanations. In How to Write a Math Solution, Richard Rusczyk and Mathew Crawford of Art of Problem Solving present a detailed checklist for ensuring that your proofs and solutions communicate your thinking as clearly as possible. Here’s some advice from the article that I found especially useful.

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Last week, I considered what we can learn from the standardized test approach to studying math. This week, I’m continuing that line of thinking with some advice from another PrepScholar article.

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One way to find out how well you know math fundamentals is to take a timed math test. In the U.S., over two million students per year take the SAT (which includes a math portion) as part of the college admissions process. A multitude of online resources, including Khan Academy, are available to help with SAT preparation. One resource that caught my eye is a blog post by Allen Cheng, founder of an SAT prep company called PrepScholar. Although the post targets SAT preparation, I found parts of it useful for my current math project.

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When you’re studying a topic, a course acts as a filter for the material: Rather than having to consider every reference on a subject, you get a nicely curated subset that the instructor believes fulfills the goals of the course. Rather than having to read an entire textbook, you get a list of sections, or maybe just notes and lectures. Rather than having to solve every problem in the book, you get a list of suggested problems, or a standalone problem set.

But a textbook without a course is also a filter. Rather than having to read through all the original research papers on a topic, you get an expert’s distillation of the important results, combined with a set of problems to help you learn and understand the topic. Since I’m using the textbook approach rather than the course approach, here are some ideas about how to select problems from a textbook.

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When you’re studying math on your own, a question you must continually ask yourself is how much time to spend on the problem you’re working on. That question also comes up when you’re taking a traditional class, though your options are more limited in that case because of the fixed class schedule. I wrote about this topic last year in the context of competitive programming problems, but there are some special considerations for math problems.

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