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eBook The Four Pillars of Geometry (Undergraduate Texts in Mathematics) download

by John Stillwell

eBook The Four Pillars of Geometry (Undergraduate Texts in Mathematics) download ISBN: 1441920633
Author: John Stillwell
Publisher: Springer; 2005 edition (December 1, 2010)
Language: English
Pages: 244
ePub: 1304 kb
Fb2: 1195 kb
Rating: 4.9
Other formats: txt lrf docx azw
Category: Math Sciences
Subcategory: Mathematics

John Stillwell is Professor of Mathematics at the University of San Francisco.

John Stillwell is Professor of Mathematics at the University of San Francisco. The book is extremely interesting, but there is a major problem with the book binding. Initial copy received missing text on dozens of pages scattered throughout the book-i. Returned first copy asking for a replacement, second copy promptly shipped, but received with the same problem. Second book returned asking for full refund.

This is a fine book for learning Euclidean and non-Euclidean geometry. I wish it had more examples.

Undergraduate Texts in Mathematics (UTM) is a series of undergraduate-level . Stillwell, John (2005). The Four Pillars of Geometry

Undergraduate Texts in Mathematics (UTM) is a series of undergraduate-level textbooks in mathematics published by Springer-Verlag. The books in this series tend to be written at a more elementary level than the similar Graduate Texts in Mathematics series, although there is a fair amount of overlap between the two series in terms of material covered and difficulty level. The Four Pillars of Geometry.

PROFESSOR HadiSulaiman. TAGS Geometry, Euclidean geometry, Isometry, isometries, M. J. HOPKINS.

MR 2163427 (2006e:51001) Department of Mathematics, Harvard University, Cambridge, MA 02138 E-mail address :. TERM Fall '12. PROFESSOR HadiSulaiman.

In this book, I wish to show that geometry can be developed in four fundamentally different ways, and that all should be used if the subject is to be shown in all its splendor. Euclid-style construction and axiomatics seem the best way to start, but linear algebra smooths the later stages by replacing some tortuous arguments by simple calculations. And how can one avoid projective geometry? It not only explains why objects look the way they do; it also explains why geometry is entangled with algebra.

Undergraduate Texts in Mathematics. Any new mathematics textbook by John Stillwell is worth a serious look. Stillwell is the prolific author of more than half a dozen textbooks. Autoren: Stillwell, John. Stillwell is the prolific author of more than half a dozen textbook. .

Undergraduate Texts in Mathematics Abbott: Understanding Analysis. The full story is beyond the scope of this book, but we say more about it below

Undergraduate Texts in Mathematics Abbott: Understanding Analysis. Anglin: Mathematics: A Concise History and Philosophy. Readings in Mathematics. John Stillwell Department of Mathematics University of San Francisco San Francisco, CA 94117-1080 USA. The full story is beyond the scope of this book, but we say more about it below.

Поиск книг BookFi BookSee - Download books for free. The Four Pillars of Geometry (Undergraduate Texts in Mathematics). Категория: M Mathematics, MA Algebra, MAt Algebra textbooks. Категория: Математика, Геометрия и топология.

This book is unique in that it looks at geometry from 4 different viewpoints - Euclid-style axioms, linear algebra, projective geometry, and groups and their invariants

Approach makes the subject accessible to readers of all mathematical tastes, from the visual to the algebraic

Abundantly supplemented with figures and exercises

Comments: (7)
Onetarieva
Usually I find math books, especially geometry, to be nothing short of terrible. I've purchased this for a class and it's actually very well written. Includes diagrams and a good set of problems, though I'm only a few chapters in at the time of writing. It seems clear enough without spending pages and pages describing one concept. Except to reread paragraphs if you're not well versed in geometry already. It's a fairly small book, easy to toss in a bag and take with you.
Tinavio
The book is extremely interesting, but there is a major problem with the book binding. Initial copy received missing text on dozens of pages scattered throughout the book--i.e. blank pages. Returned first copy asking for a replacement, second copy promptly shipped, but received with the same problem. Second book returned asking for full refund.
Todal
He takes you through Euclidian geometry, analytic geometry, projective, vectors, all the way up to transformations, fields, abstract stuff like that. If you are just reading for fun, you can read it over a long weekend. But it could be a survey course, too.
Jelar
I was surprised at how much I liked this book.
Akta
Fast shipping. Great book!
Cala
People learn differently. I prefer a book that clearly outlines the theorems and assumptions, and provides plenty of precise examples and problems. This is not one of those books. I would compare it more to a novel; read a few chapters, look at the problems, keep going. Questions make implicit assumptions when asking you to prove things, very annoying. If you're just looking for a geometry book to read for pleasure, this may be for you. If you actually wanted to learn specific theorems and be able to pass tests, I would say look for another.
Whitemaster
Great introduction to geometry.
Around 1900, David Hilbert published his "Foundation of Geometry." It was the first book to really make Euclid's Elements obsolete. Humans had developed mathematics for thousands of years - from bone markings to the Summerian/Babylonian algebra. They certainly left some record of their mathematical activities. But, for one, their mathematics was arbitrary; it kind of worked. Only with the Greek discovery of deductive reasoning(as far as everybody can tell) did mathematics become firmly established. It's a subtle point. But, a major point is that with Hippocrates of Chios(not the guy from cos who did the Hippocratic oath) discovery of axiomatics which was an advance beyond Thales and Pythagoras's deductive reasoning discovery(not to be systematized till hundreds of years later with Aristotle; Aristotle's only real lasting contribution), and eventually Euclid's effort at axiomatisation, all that knowledge before and Greek mathematical knowledge was systematized, put in a bottle figuratively speaking, and sent out to the world(most people back then never heard of it or saw a copy). Euclid's "Elements", the works of Archimedes, and Appolloniuses Conics were the only real systematic deductive mathematics all the way up to David Hilbert's work.

That last part isn't strictly true. There was some beginning efforts to axiomatise algebra in the 1800s. There's also Ptolemy's work; i'm really not sure how much of an axiomatic effort that book is. The point is that David Hilbert's "Foundations of Geometry" was the first axiomatic effort of geometry to make Euclid's Elements more or less obsolete(see Thomas Heath's translation of Euclid's Elements; in it, Thomas Heath shows the mathematical, and historical significance of just about every theorem in there.

But, this book is more of a easier version. John Stillwell tries to make an easier approach by relating advanced with ancient mathematics. The truth is that advanced mathematics solves problems the ancient or previous mathematics couldn't solve or did so in a less elegant way. Still, John finds modern fresh versions of those ancient theorems like Pythagoras and Thales. As with new deductive theories that are suppose to be able to derive the old theories and deduce new theorems the old couldn't, one certainly should try to make connections between old and new. One must realize that John Stillwell can only fit so much in one book(even with his putting extra stuff sometimes more advanced stuff as exercises). As far as I can tell, nowhere does John Stillwell feel the need to show Archimedes theorems about pie, and all the great Greek mathematics involved and relations to the new modern mathematics. This is just one example. See Thomas Heath "History of Greek Mathematics" not to mention his translation of Euclid's Elements, and Van Der Waerden's "Science Awakening for a proper technical history of Mathematics(certainly more about ancient mathematics).

I'd like to note that John Stillwell does some things in Geometry that I never got into in two geometry courses(one in High school, and then when I went to college after the Navy, they made me take it again). In those two geometry courses, I never proved the Pythagorean theorem once, much less delt with transformations. Transformations overcome a famous logical bottleneck of Euclid's Elements. So yes, John Stillwell's book is like the geometry class you never got to have.

I wouldn't worry about figuring everything out. I'd worry if you can't figure your way through the main text though.

A big point is that John Stillwell tries to show some great connections between ancient mathematics and modern. He tries to show what little one can understand of advanced mathematics. The stress is on geometry of course, but if you read his other books which do similar things, you'll see that his point is that one shouldn't disregard geometry. So, in some ways this book is a good place to start. He has other geometry books, but I wouldn't get into them till you get through the number theory/abstract algebra, and at least one semester of calculus. Overall, John Stillwell has succeeded in showing people that they too can learn mathematics. I would read the majority of these books before reading his "Mathematics and its History" as well. He's able to show some more stuff there, but his accounts of abstract algebra and number theory are even sketchier there.