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A Gentle Introduction to the Art of Mathematics

giam.southernct.edu

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Re: A Gentle Introduction to the Art of Mathematics

#41

Post by yboris »

auggierose wrote: post #4

At the very start of the book: > It has been said that “God invented the integers, all else is the work of Man.” This is a mistranslation. The term “integers” should actually be “whole numbers.” The concepts of zero and negative values seem (to many people) to be unnatural constructs. It is not a mistranslation. In German "ganze zahlen" actually means "integers". It is just if you translate it word for word, "ganze"…

I find that philosophically, "all math is discovered" is a better way to think of mathematics.

E.g - it's always been true, that given a set of axioms A, B, and C, the claim X is true. Humans discover these conclusions when they explore implications of taking different assumptions to be true.

Re: A Gentle Introduction to the Art of Mathematics

#42

Post by UncleOxidant »

thewanderer1983 wrote: post #11

Fearless Symmetry and Elliptic Tales are fascinating, accessible and fun introductions to the art of mathematics.

> Fearless Symmetry

I happened to pick up a copy of Fearless Symmetry at a garage sale recently. Was wondering if it was worthwhile (kind of hard to go wrong for $1), thanks for the recommendation.

Re: A Gentle Introduction to the Art of Mathematics

#43

Post by mindcrime »

drBonkers wrote: post #29

Are there prints for sale?

GIAM is now available in hardcopy as a printed-on-demand paperback from CreateSpace. Please rest assured that GIAM will remain available for free download from this site.

https://www.amazon.com/Gentle-Introduction-Art-Mathematics-v...

Re: A Gentle Introduction to the Art of Mathematics

#45

Post by dotancohen »

lupire wrote: post #30
auggierose wrote: post #4

At the very start of the book: > It has been said that “God invented the integers, all else is the work of Man.” This is a mistranslation. The term “integers” should actually be “whole numbers.” The concepts of zero and negative values seem (to many people) to be unnatural constructs. It is not a mistranslation. In German "ganze zahlen" actually means "integers". It is just if you translate it word for word, "ganze"…

Mistranslation or not, conceptually "natural numbers Z+" or "whole numbers Z*" are a more fitting claim. Peano would go further: God invented 0 and +1, and all the rest are the work of people.

In software development it is often said that there are only three relevant numbers: 0, 1 and infinity. Everything else is contrived.

Certainly, nature follows a very similar pattern. For limited values of infinity ))

Re: A Gentle Introduction to the Art of Mathematics

#46

Post by nyrikki »

nicf wrote: post #28
xk_id wrote: post #8

Would be nice if we could see experienced mathematicians endorse this, please. It would help to decide whether to put time into it. At first glance it looks really nice.

I'm a mathematician, currently working as a private tutor for adults who want to learn proof-based math. I had a quick glance through this book and it seems to me like a pretty nice version of this "intro to proofs" sort of book. This is a topic that's done well in a lot of different books, though, so if you really want to dig into this topic I'd maybe recommend looking at a couple different ones and finding the one…

As someone who tutors adults, can you suggest a more digestible book for abstract algebra?

While I was motivated, I used one of the typical college books. For me Abstract Algebra is what opened a lot of doors for me... but I am simply using applied math.

That moving away from proofs being magical across sub-topics is what I would like to share with some co-workers who are unwilling to buy a textbook and answer key.

As I didn't even mind Spivik for calc, my radar is way off for making suggestions to most people.

Re: A Gentle Introduction to the Art of Mathematics

#47

Post by wyager »

ChainOfFools wrote: post #40
danielvaughn wrote: post #37

I was prepared to hate this book as much as I've hated any other "introduction" to math, since I've found that mathematicians generally suck at introducing or explaining things. But the first little section that breaks down set notation into plain english was fantastic. That's exactly the kind of thing I need personally, as notation is extremely off-putting and confusing for me.

> I've found that mathematicians generally suck at introducing or explaining things. and then there's Grant Sanderson

I don't think it's much of an exaggeration to describe Sanderson as a contemporary Feynman, at least from the pedagogy side of things.

Re: A Gentle Introduction to the Art of Mathematics

#48

Post by mcguire »

xk_id wrote: post #8

Would be nice if we could see experienced mathematicians endorse this, please. It would help to decide whether to put time into it. At first glance it looks really nice.

Putting on my Computer Scientist hat (and getting all of the tentacles out of my face so I can see), GIAM seems to be a good, if a little verbose[1], introduction to formal logic and basic set theory. Those are fundamental to CS and this is a heck of a lot better than many of the intros to those topics that I have seen in curricula without a dedicated class.

Re: A Gentle Introduction to the Art of Mathematics

#50

Post by __rito__ »

Keegs wrote: post #2

The quality of writing in this book is fantastic. If you're studying math or have a recreational interest I really recommend it.

What other resources would you recommended for learning Math that is a bit more advanced?

It needs to be suitable for someone studying alone.

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