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Anyone know of a good book on mathematics as a language? What I mean is a book that spends most of its time simply introducing the notation and the concepts tha

by api 16y ago

Anyone know of a good book on mathematics as a language? What I mean is a book that spends most of its time simply introducing the notation and the concepts that it refers to rather than dealing excessively with the mechanics of doing math. IMHO math as a language should be taught first.

timwiseman 16y ago
I do not know if it is exactly what you want, but Chapter Zero ( http://www.amazon.com/Chapter-Zero-Fundamental-Abstract-Mathematics/dp/0201437244/ref=sr_1_1?ie=UTF8&s=books&qid=1281034245&sr=8-1 http://www.amazon.com/Chapter-Zero-Fundamental-Abstract-Math... )comes close. It talks about a lot of the foundational mathematics that and symbolism that is often never taught to non-math majors, but it does so in an easily understood way. Proofs and Refutations by Lakatos also touches on this topic, though it is not the primary or sole discussion there.
eru 16y ago
Related: I know of a book that deals with history as mathematics. You may be interested in it. "The Pleasure of Counting" by Tom W. Körner. See a review at http://plus.maths.org/content/pleasures-counting http://plus.maths.org/content/pleasures-counting and another one here http://www.maa.org/reviews/counting.html http://www.maa.org/reviews/counting.html Quote from the second review: >> Körner says, in his preface, that this book is "meant, first of all, for able school children of 14 and over and first-year undergraduates who are interested in mathematics and would like to learn something of what it looks like at a higher level." I don't know about English school children; there won't be many American 14-year-olds who will read this book. But that doesn't matter: for those who do read it (and I hope many potential math majors do read it), it offers a unique look at what mathematics, especially applied mathematics, is like. >> Rather than attempt a book on "mathematics for poets", Körner explains that he decided to talk as if he were speaking to another mathematician. Almost all of his topics involve only elementary mathematics (though here and there an occasional remark or exercise goes quite a bit deeper than that), but the attitude is quite sophisticated. As he says in the preface, this means that most of the book's intended readers will find at least a few points where they are in over their heads. Körner urges them to skip over such parts or, even better, to find some professor willing to discuss them. Read this way, Körner's The Pleasures of Counting is really a pleasure, and may well attract many students to mathematics. It strikes me, in many ways, as the ideal book for independent reading or for a first-year seminar.

by api 16y ago

timwiseman 16y ago

I do not know if it is exactly what you want, but Chapter Zero ( http://www.amazon.com/Chapter-Zero-Fundamental-Abstract-Mathematics/dp/0201437244/ref=sr_1_1?ie=UTF8&s=books&qid=1281034245&sr=8-1 http://www.amazon.com/Chapter-Zero-Fundamental-Abstract-Math... )comes close. It talks about a lot of the foundational mathematics that and symbolism that is often never taught to non-math majors, but it does so in an easily understood way. Proofs and Refutations by Lakatos also touches on this topic, though it is not the primary or sole discussion there.

eru 16y ago

Related: I know of a book that deals with history as mathematics. You may be interested in it. "The Pleasure of Counting" by Tom W. Körner. See a review at http://plus.maths.org/content/pleasures-counting http://plus.maths.org/content/pleasures-counting and another one here http://www.maa.org/reviews/counting.html http://www.maa.org/reviews/counting.html Quote from the second review: >> Körner says, in his preface, that this book is "meant, first of all, for able school children of 14 and over and first-year undergraduates who are interested in mathematics and would like to learn something of what it looks like at a higher level." I don't know about English school children; there won't be many American 14-year-olds who will read this book. But that doesn't matter: for those who do read it (and I hope many potential math majors do read it), it offers a unique look at what mathematics, especially applied mathematics, is like. >> Rather than attempt a book on "mathematics for poets", Körner explains that he decided to talk as if he were speaking to another mathematician. Almost all of his topics involve only elementary mathematics (though here and there an occasional remark or exercise goes quite a bit deeper than that), but the attitude is quite sophisticated. As he says in the preface, this means that most of the book's intended readers will find at least a few points where they are in over their heads. Körner urges them to skip over such parts or, even better, to find some professor willing to discuss them. Read this way, Körner's The Pleasures of Counting is really a pleasure, and may well attract many students to mathematics. It strikes me, in many ways, as the ideal book for independent reading or for a first-year seminar.