When making Maths self study notes... (1 Viewer)

[yellowhighlighterr]

Is it necessary to include each formula's proof? Like for the quotient and product rule how they were derived? As well as where they were used in life?
Thanks,
yellowhighlighterr

 

[yellowhighlighterr]

No not all, you don't need to know about the derivation of a formula, it will never be tested - just make notes about the formula and how it works (ie use it in some examples)

tyyyyy

 

[cossine]

Is it necessary to include each formula's proof? Like for the quotient and product rule how they were derived? As well as where they were used in life?
Thanks,
yellowhighlighterr

The proof is not important. What is important that you are able to understand the steps of the proof because the techniques used they are part of the syllabus. Not understanding a step could mean a potential weakness in your knowledge/skills.

That being said some proofs are well outside the syllabus.

E.g., proof of d/dx sin(x) = cos(x)

For these situations you will need accept the theorem(theorem is a statement that is true and can be proven)

To further add there many theorems. Since there are so many theorems in mathematics you cannot be except to memorise the proof theorems or even the theorems themselves. However you should aim to know important/fundamental theorems

 

[Drongoski]

You make study notes for your own needs. Different students should have different study notes, tailored to the needs of each. I suggest you prepare your notes by topics. For each, write down materials/items that are likely to be important to the course; include solutions of special relevance. But leave out items/points you are already very familiar with, that are at the top of your head: there is no point including them as they will needlessly clutter your notes. You want a, say, 10-page summary of all those relevant material you cannot readily recall, rather than a 30-page summary that include material you are already very familiar with. For example, if you already know that sin^2x + cos^2x = 1, there's no point putting it in. You don't have the time in your final revision to go over a lengthy document. With the passage of time, as you become very well-versed in some of the material you have written down in your notes, you can delete these (or simply cross a single line over them). Remember, an overly lengthy set of notes may overwhelm you during your last panicky pressed-for-time revision.


One more thing: hand write your notes, rather than typing out. In writing out, you somehow "connect" the material with your memory; that's what I think, anyway.