MHB Mathematics Study: How to Master the Theory

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Studying mathematics effectively often hinges on the balance between theory and practice. When faced with a book that contains only theoretical content, individuals emphasize the importance of actively engaging with the material by deriving concepts and working through examples independently. Many learners find that understanding math topics is significantly enhanced by completing exercises, which reinforce theoretical knowledge. In the absence of exercises in a theory book, it is recommended to supplement study with an exercise book to facilitate practice. The discussion also notes that as mathematical topics advance, the complexity of problems increases, and there is an expectation of prior knowledge that aids in understanding. Additionally, it is mentioned that some publishers focus solely on theory without exercises, which can limit practical application.
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Hi!

I'm wondering how do we study mathematics. If the book has exercises, after reading (maybe several times) the theory, you can go and do the exercises. If the book is only theory and no exercises, how do you check your understanding on the subject?
 
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Ruun said:
Hi!

I'm wondering how do we study mathematics. If the book has exercises, after reading (maybe several times) the theory, you can go and do the exercises. If the book is only theory and no exercises, how do you check your understanding on the subject?

You read maths books with a pad and pen and derive things yourself as you go.

CB
 
Ruun said:
If the book is only theory and no exercises, how do you check your understanding on the subject?

I learn maths by doing the exercises.

If your book is only theory and no exercises, maybe you should get an "exercise book". (Out of curiosity, which is this "theory book"?)
 
Alexmahone said:
I learn maths by doing the exercises.

If your book is only theory and no exercises, maybe you should get an "exercise book". (Out of curiosity, which is this "theory book"?)
I agree. I don't remember ever understanding a maths topic without doing a large number of problems.
 
Sherlock said:
I agree. I don't remember ever understanding a maths topic without doing a large number of problems.

Fair comment, you'll find through your journey of Math education that there is less empathsis on this.

The two reasons are 1) as the topics become more advanced the amount of work required to solve problems also increases and 2) there is an assumption on prior learning that will always be there to help you.
 
Sherlock said:
I agree. I don't remember ever understanding a maths topic without doing a large number of problems.
I have worked in a book publisher which makes theory books and one of the rules is no exercises, just examples.
 
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