How to Speak Mathematics: Subjects & Recommended Books

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Discussion Overview

The discussion revolves around the subjects and resources recommended for learning mathematics effectively, with a focus on achieving a deeper understanding of mathematical concepts and language. Participants explore various approaches, including books, courses, and foundational topics in mathematics.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant inquires about subjects to study for superior mathematical communication and seeks book recommendations.
  • Another suggests using Wikipedia for definitions but is uncertain about specific book recommendations.
  • A participant expresses a desire for a deeper core understanding of mathematics, emphasizing the importance of solving problems and grasping concepts.
  • It is proposed that learning from books and attending courses with in-person support is beneficial for understanding mathematics.
  • Questions arise regarding a mathematical subject analogous to Assembly Language in Computer Science, with a participant sharing their experience of progressing from Perl to C and then to Assembly.
  • One participant suggests that logic and set theory serve as foundational topics for a low-level understanding of mathematics, recommending Enderton's "A Mathematical Introduction to Logic."
  • There is a caution expressed about starting with the complexities of mathematical logic, with some agreeing that it may not be the best entry point for beginners.

Areas of Agreement / Disagreement

Participants express differing views on the best starting points for learning mathematics, particularly regarding the role of mathematical logic. There is no consensus on specific subjects or books, and multiple competing perspectives are present.

Contextual Notes

Some discussions hinge on the definitions of foundational topics and the varying interpretations of what constitutes a "low-level" understanding of mathematics. The effectiveness of different learning resources remains subjective and context-dependent.

arevolutionist
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Which subjects should I study to speak mathematics in a superior form? Also, which books do you recommend?
 
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You could try going on wikipedia the online encyclopedia, to search for definitions of mathematical terms, but I am not sure what book would help you learn the language of math. Hope this helps!
 
I wish to obtain a deeper core understanding of mathematics. Solving problems of course helps. I wish to have more pure understanding of the concepts. I am not sure if I am describing this clearly.
 
Books and school/university courses. there's no better way to learn something than with an actual person physically there to ask for help from.
 
Is there a subject of mathematics that is similar to ASM in Computer Science? For example, when I first studied programming, I learned Perl. I wanted a deeper understanding of the computer, so I studied C then I mastered Assembly.
 
arevolutionist said:
Is there a subject of mathematics that is similar to ASM in Computer Science? For example, when I first studied programming, I learned Perl. I wanted a deeper understanding of the computer, so I studied C then I mastered Assembly.

Logic and set theory are the underpinnings of modern mathmatics, so if you want an 'assembly'-style low-level understanding I'd start there. I used and enjoyed Enderton's A Mathematical Introduction to Logic.
 
"Common sense logic" takes you deep into maths, to study the subtilities of mathematical logic is not, perhaps, the best starting point.
 
arildno said:
the subtilities of mathematical logic is not, perhaps, the best starting point.

I agree that mathematical logic is deep and not a good place to begin. However, if you're looking for ASM, that's where it is.
 

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