Mathematics Study: How to Master the Theory

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    Mathematics Study
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Discussion Overview

The discussion revolves around strategies for studying mathematics, particularly focusing on the challenges of understanding theoretical concepts when a textbook lacks exercises. Participants explore methods for self-assessment and comprehension in the absence of practice problems.

Discussion Character

  • Exploratory, Conceptual clarification, Debate/contested

Main Points Raised

  • Some participants suggest that reading mathematics books with a pad and pen to derive concepts can aid understanding, especially when exercises are absent.
  • Others emphasize the importance of doing exercises to grasp mathematical topics, arguing that practical application is essential for comprehension.
  • A participant proposes that if a book contains only theory, obtaining an "exercise book" could be beneficial for reinforcing understanding.
  • Some participants note that as mathematical topics advance, the complexity of problems increases, which may affect the learning process.
  • One participant mentions their experience in a publishing context, indicating that some theory books are intentionally designed without exercises, focusing instead on examples.

Areas of Agreement / Disagreement

Participants generally agree on the necessity of exercises for understanding mathematics, but there is no consensus on how to effectively study when exercises are not available. Multiple views on the best approaches remain present.

Contextual Notes

Participants express varying assumptions about prior knowledge and the role of exercises in learning, which may influence their perspectives on studying mathematics.

Advent
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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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