What main branches of mathematics are there?

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Discussion Overview

The discussion revolves around the main branches of mathematics, exploring various fields and topics within the discipline. Participants seek to identify and categorize different areas of mathematics, while also expressing a need for resources and textbooks that include practice problems.

Discussion Character

  • Exploratory
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant lists several areas of mathematics, including trigonometry, calculus, differential equations, linear algebra, and discrete mathematics, and requests a comprehensive list.
  • Another participant categorizes mathematics into "applied" and "pure" fields and suggests looking at college prospectuses for further division.
  • There is a repeated request for textbooks that include practice problems, emphasizing the importance of practice in retaining mathematical knowledge.
  • Discussion arises regarding the terminology used, with some participants noting the difference between "math" and "maths," depending on regional usage.
  • A participant proposes that algebra and geometry are the two main branches of mathematics, with analysis being an overlap of the two.
  • A quote from David Hilbert is shared, reflecting on the nature of mathematics, although it is noted as off-topic.

Areas of Agreement / Disagreement

Participants express varying opinions on the classification of mathematical branches, with some proposing different categorizations. There is no consensus on a definitive list of branches or the best resources for learning.

Contextual Notes

Participants emphasize the need for specificity when discussing textbooks, indicating that the broad nature of mathematics requires targeted recommendations.

Mathmanman
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Besides trigonometry, calculus, differential equations, linear algebra, and discrete mathematics.
Can you give me a list? And maybe links to where I can learn them?
 
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The main fields in maths are called "applied" and "pure".
"Trigonometry, calculus, differential equations, linear algebra, and discrete mathematics..." are examples of topics in mathematics.

To get a good idea of how maths gets divided up, instead, have a look at your local college's prospectus and the titles of the higher-level papers.

However, it is a common enough request: did you have a look online?
http://en.wikipedia.org/wiki/Areas_of_mathematics
http://en.wikipedia.org/wiki/Lists_of_mathematics_topics
... which should give you a starting place.
 
Ok, so what textbooks are there? I need the ones that also give me problems to practice. Without practice problems, I would forget it fast. I thought it was math, not maths.
 
People of the UK persuasion call it 'maths'. In the US and Canada I think it is just 'math'.
 
Ok, so what textbooks are there? I need the ones that also give me problems to practice. Without practice problems, I would forget it fast.
https://www.physicsforums.com/showthread.php?p=4758465#post4758465

I thought it was math, not maths.
Technically, it's "mathematics" - a kind of pseudo-plural of "mathematic" - hence the s on the end of the abbreviation.
http://en.wikipedia.org/wiki/Mathematics#Etymology

Aside:
Him: You do the math!
Me: Maths.
Him: Same thing.
Me: No. Mine has five letters and yours has four.
Him: What's the difference?
Me: One.
 
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In a rough sense there are two main branches of mathematics: algebra and geometry. Analysis comprises the overlap of those two.
 
Not on topic but interesting nevertheless:

David Hilbert
" Mathematics is a game played according to a few simple rules with meaningless marks on paper."
 
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Mathmanman said:
Ok, so what textbooks are there? I need the ones that also give me problems to practice. Without practice problems, I would forget it fast. I thought it was math, not maths.
What textbooks for what kind of math? With so broad a subject as math, you must be more specific.

Have you heard of Amazon.com? You can find all sorts of math textbooks there.
 

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