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October 10th, 2012, 09:42 AM   #1
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Beginner Book Suggestions?

Hi! It's my first time posting here. I'm a social sciences/humanities guy who hasn't had to use mathematics even semi-regularly for a decade, with most of my life's numerical need suitably accounted for with arithmetic. Math has withered on my mindvine.

However, I'm finding that any kind of half-decent philosophy is, if not directly built upon a math-heavy philosopher's works like Wittgenstein or Leibniz, at least referential of the math geniuses in human history in a casual way that my non-comprehending ass always has to look up. I'm inspired to learn math and dive into the deep end of it, but I've got to get out the kiddie pool first. I don't want to dive into the psychedelic non-Euclidian gymnastics of mathematical gods until I've found purchase on the cliff of algebra at least (to say nothing of calculus or trig). If that makes sense to anyone, what would you recommend? I've already had someone recommend Euclid's Elements, A Course of Pure Mathematics and How To Solve It.
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October 10th, 2012, 10:27 AM   #2
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Re: Beginner Book Suggestions?

Quote:
Originally Posted by davethebrave
Hi! It's my first time posting here. I'm a social sciences/humanities guy who hasn't had to use mathematics even semi-regularly for a decade, with most of my life's numerical need suitably accounted for with arithmetic. Math has withered on my mindvine.

However, I'm finding that any kind of half-decent philosophy is, if not directly built upon a math-heavy philosopher's works like Wittgenstein or Leibniz, at least referential of the math geniuses in human history in a casual way that my non-comprehending ass always has to look up. I'm inspired to learn math and dive into the deep end of it, but I've got to get out the kiddie pool first.
A commendable goal.

Quote:
Originally Posted by davethebrave
I don't want to dive into the psychedelic non-Euclidian gymnastics of mathematical gods until I've found purchase on the cliff of algebra at least (to say nothing of calculus or trig).
Non-Euclidean geometry is so much fun! I hope you get to this, I think you'll really enjoy it.

Quote:
Originally Posted by davethebrave
I've already had someone recommend Euclid's Elements, A Course of Pure Mathematics and How To Solve It.
Three extremely different books.

Elements is good but perhaps a bit tough to follow. It covers what is now high-school geometry.

A Course of Pure Mathematics is a challenging book at the college level (so at a much higher level than Elements). You won't be able to understand it until you take calculus.

How to Solve It is a simple read, I think. I might call it paramathematics: it's really about the process of doing math rather than math itself.
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October 11th, 2012, 05:46 AM   #3
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Re: Beginner Book Suggestions?

Yeah, I think I remember one of the books being recommended to me as something I'd get mileage on once I was on a roll, which was probably A Course of Pure Mathematics.

Do you have any ideas for good books on algebra and calculus for beginners?
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October 11th, 2012, 06:34 AM   #4
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Re: Beginner Book Suggestions?

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Originally Posted by davethebrave
Do you have any ideas for good books on algebra and calculus for beginners?
Actually I don't. I would be happy to help with the next level of recommendations once you get to a higher level, but I don't know much about the elementary stuff.
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December 21st, 2012, 04:36 PM   #5
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Re: Beginner Book Suggestions?

Seeing your philosophical concerns, I think you will be interested with my work on the foundations of mathematics, that especially aims to encompass much of the philosophical aspects of mathematics : the meaning of Russell's paradox, the Completeness and Incompleteness theorems, nonstandard models of arithmetic, the consistency of ZF set theory, and the paradoxical properties of quantum states and measurements. But sorry I did not include calculus. I just started writing about algebra and I intend to continue later (there is already an introduction to tensors but I'll have to add things before that part).
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December 21st, 2012, 05:33 PM   #6
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Re: Beginner Book Suggestions?

Hey, thanks! This is some great stuff!
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December 18th, 2013, 08:11 PM   #7
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Re: Beginner Book Suggestions?

Quote:
Originally Posted by CRGreathouse
Quote:
Originally Posted by davethebrave
Hi! It's my first time posting here. I'm a social sciences/humanities guy who hasn't had to use mathematics even semi-regularly for a decade, with most of my life's numerical need suitably accounted for with arithmetic. Math has withered on my mindvine.

However, I'm finding that any kind of half-decent philosophy is, if not directly built upon a math-heavy philosopher's works like Wittgenstein or Leibniz, at least referential of the math geniuses in human history in a casual way that my non-comprehending ass always has to look up. I'm inspired to learn math and dive into the deep end of it, but I've got to get out the kiddie pool first.
A commendable goal.

Quote:
Originally Posted by davethebrave
I don't want to dive into the psychedelic non-Euclidian gymnastics of mathematical gods until I've found purchase on the cliff of algebra at least (to say nothing of calculus or trig).
Non-Euclidean geometry is so much fun! I hope you get to this, I think you'll really enjoy it.

Quote:
Originally Posted by davethebrave
I've already had someone recommend Euclid's Elements, A Course of Pure Mathematics and How To Solve It.
Three extremely different books.

Elements is good but perhaps a bit tough to follow. It covers what is now high-school geometry.

A Course of Pure Mathematics is a challenging book at the college level (so at a much higher level than Elements). You won't be able to understand it until you take calculus.

How to Solve It is a simple read, I think. I might call it paramathematics: it's really about the process of doing math rather than math itself.

Some saying Geometry is such a boring subject, but if you will do deeply and understand the philosophy of this subject you will enjoy dealing with your Geometry.
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