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Let someone has completed a Bachelor degree. For some reason, he needs to take a graduate course in something hard and unrelated to his Bachelors; how should he approach studying the subject?

For example, Quantum Physics for an arts student. Or, Chinese/Japanse-language for an English speaker.

Assume he didn't study even the basics of physics/Chinese in his entire life and time is very limited, like only one trimester.

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Is quantum physics just an example or the specific subject being asked about. I expect that someone with no background in science trying to jump right into a graduate course on quantum physics simple isn't going to be able to succeed. There is simply too much background material that will be critical to understanding the course that they don't know yet. I'd recommend lookup up the course prerequisites and becoming fluent in those first. – Adam Wuerl May 25 '14 at 21:31

I came from an engineering background and moved into comp science and I found Information Theory quite easy and interesting.

It was not so much that I was more talented than everyone else, but because it used mathematics that I was already familiar with at the time. I had a natural 'feel' for information theory because I knew how it functioned.

For mathematics, I find the easiest way is to drill it. Just keep doing math problems. That's why they teach it separately and need it as a requirement. Think of it like your ABCs in school... you had to memorize letters before learning to read and write. Much like learning to read, it will click intuitively after a while.

Memorization of formulas is a poor method, because you will forget it, especially when you are stressed and have little sleep. Drilling it, by repeating and reusing the formulas dozens of times works.

If you have more time and willpower, derive equations. It is a technique used by and taught to elite students because it requires a lot more hard work, but it will quickly deepen your understanding.

You will need to grasp a solid foundation of these principles first before using them in more complex applications. If you don't know half the letters of the alphabet, reading will be a struggle to say the least. Mathematical formulas are much like words, except with one symbol representing a sentence.

If you don't have time to master the basics, print out the notes, and write the formulas as sentences. For example,

p is probability of something happening
1-p is probability of something *not* happening
p(x) is probability of x happening
Σ with the x ∈ X under it, means the sum of everything in X

and so on. Have this cheat sheet/glossary in your notes somewhere and use it to 'translate' weird mathematical things. That way, you only have to look it up once and not flip through a thick math book every line.

Also, learn how something works as you learn what it does. Almost every good textbook teaches this for good reason. The ones that don't assume you already know how all the components go together. As with math, you can learn how it works a few years after you learn what it is, and there's no real hard guideline to this.

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I'm a big fan of Tony Buzan when it comes to studying, have a look at Buzan's Study Skills: Mind Maps, Memory Techniques, Speed Reading and More! for a short and sweet introduction to his approach.

I also recommend Tim Ferriss who breaks down learning into a skill that you can master: How to learn fast and Accelerated learning are both good to read.

It is important not to over do things, try not to spend more than 45 minutes studying something. After that take a break and do something else, best if you can do something totally unrelated. This gives your brain a chance to focus on something else and process the information you've given it. If you can get up and go for a walk, or do some push ups or make some tea and have a quiet 10 minutes.

When you come back to your subject start with some revision of the previous 45 minutes. If you like Tony Buzan's mind maps then that could be a good way to jot down what you remember, making the associations will also help you lock the information into your mind. The more 'hooks' you can hang ideas on the easier remembering becomes.

When the subject is abstract, as in the case of formulas and equations, then it is harder to find mnemonics and the approach of 'making up a funny story' wherein you place your items to remember is less applicable. But if you can make parts of your equation tell a story or relate them to other equations then you begin to build up a mental map of related functions.

Derren Brown has good advice on memorising things as well; a nice summary can be found at How to remember things, how he memorises decks of cards translates nicely to remembering formulas and equations because the subject (playing cards) is also abstract enough that there aren't many places in normal life that we encounter H3, S9 etc.

Lots of links and reading, but I hope some of it helps.

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Well, that would change from person to person. Different people learn differently. For me, I need to have a clear understanding of the topic and it's basics or fundamentals to learn it. Good analogues, or real world examples help. Also, applying the knowledge helps. In 11th grade we had programming, and I had coded a bunch of equations from the Physics book - I didn't forget those equations for a long time, without ever having to revise them or memorize them again. Usually I have a very hard time remembering equations, unless I understand the relationship between the variables. Then I can derive the equation on my own without having to memorize it. In fact, one of the most brilliant students I've known, used to derive basic equations on the back of his answer sheet at the beginning of an exam, instead of trying memorizing them. Understand the basics of how things work, and how they are related, things will fall into place themselves.

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If you have a feeling that you are studying, revising, trying to memorize and got no effect it can mean you need to change the way. Something what you do, become too much routinized. There can be a flow somewhere and you don't see it.

You can find a friend who does worst than you and offer him/her your help. Set up some meeting with clear goals. For example, today we going through "integration by parts" or some other chunk of the material you study. Try to explain to your friend what you already know and how the expressions work.

Very soon you will find it as a very powerful technique. Your friend will start to ask you questions which point material not well explained. The reason of course is that you not always entirely confident with it. That way you achieve a few things:

  1. reformulate your knowledge
  2. find weak points in your knowledge
  3. learn to express what you know (very helpful on exams)
  4. say mathematical expression in words (good for better memorization)
  5. find analogies
  6. find "hidden" connection between theories
  7. and last but not least you can make a better friendship

After you start working with someone, it will be much easier to work throughout big sections of material and also easier to spot mistakes in each other works.

Good luck with it.

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+1 for teaching someone else. Though don't ever do it right before an exam, whenever I did that, I ended up forgetting the topic I taught and it would always be on the paper. – elssar Feb 11 '13 at 10:32

Consider the study by Dale (1969). You will learn more if you write a summary of the stuff yourself, rather than just reading it in a textbook. For best results, you should explain the stuff to others, possibly in a presentation. This also applies to learning stuff with a lot of mathematical notation.

What I hear, I forget; What I see, I remember; What I do, I understand.

Old Chinese proverb, sometimes attributed to Confucius

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