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If you were starting to study math today, what advice would you like to know about it?

11 Answers

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Build sustainable study habits. Sometimes, I’ll get super excited to study, study a whole lot in a short period of time, and burn myself out. Space out your studying, and set goals that are easily reachable. I tell myself: “I am going to study 25 minutes a day.” This way, if I reach that bare minimum, I can be done. However, I usually end up studying more. This extra study time, since it is unplanned, is done because I want to, not because I have too. This helps a lot with motivation for me.

Edit: also, watch Professor Leonard lol
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Start or join a study group. This helped me immensely with calculus and beyond.  Just talking through a problem with someone is sometimes enough to make it click. I also made a few friends that i still keep in contact with and got hooked up with some job interviews after I graduated.
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Understand the definitions and rules.

Completely.

Not partially.
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Draw a picture. Sure, not every problem will really make it a practical approach, but after a certain comfort level with algebra and geometry, training yourself how to visualize a problem, and clearly list out what you know and what you are trying to find will take you really far — at least through the major calculus topics.
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Think of learning math as learning a language. Both are used to express something, at first the power of the language is gated behind learning the basic rules and the exercises may seem pointless. But once you've got the basics down it opens up. You'll have a lot of "eureka" moments.

Learning it requires a good understanding of the basics and practice, lots and lots of practice. Don't expect to understand how it all connects right away, and give yourself time to absorb it all. Be sure to take breaks, getting some distance from heavy material can help a lot.

Visualization can be extremely valuable to understanding what the mathematics is trying to tell you, as it can bring order to what seems like chaos.

And remember to try to have fun with it. Instead of only focusing on working through exercises, try to find something unrelated and interesting to calculate. This could be interesting subjects in physics, game mechanics etc. anything that involves math.
If you only feel frustrated every time you sit down with mathematics, you're very likely to get burned out.
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stress plays a huge role in being able to properly retain and process information
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Understand all basic building blocks. And i mean really basics.
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Definitions, definitions, definitions. So much frustration can be prevented by making sure you understand the definition properly. I can't begin to count the number of times I've struggled with a problem only to find out the answer was living within the definition all along!
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Ask yourself 'why' at every step. Really helped me understand the basics.
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The absolute value of x is just the distance from x to 0. Similarly the absolute value of x-y is just the distance from x to y.

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