Geometry for College Students

ISBN-10: 0821847945
ISBN-13: 9780821847947
Edition: 2009
Authors: I. Martin Isaacs
List price: $66.00
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Description: One of the challenges many mathematics students face occurs after they complete their study of basic calculus and linear algebra, and they start taking courses where they are expected to write proofs. Historically, students have been learning to  More...

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Book details

List price: $66.00
Copyright year: 2009
Publisher: American Mathematical Society
Publication date: 3/10/2009
Binding: Hardcover
Pages: 222
Size: 7.00" wide x 10.00" long x 0.75" tall
Weight: 1.540
Language: English

One of the challenges many mathematics students face occurs after they complete their study of basic calculus and linear algebra, and they start taking courses where they are expected to write proofs. Historically, students have been learning to think mathematically and to write proofs by studying Euclidean geometry. In the author's opinion, geometry is still the best way to make the transition from elementary to advanced mathematics. The book begins with a thorough review of high school geometry, then goes on to discuss special points associated with triangles, circles and certain associated lines, Ceva's theorem, vector techniques of proof, and compass-and-straightedge constructions. There is also some emphasis on proving numerical formulas like the laws of sines, cosines, and tangents, Stewart's theorem, Ptolemy's theorem, and the area formula of Heron. An important difference of this book from the majority of modern college geometry texts is that it avoids axiomatics. The students using this book have had very little experience with formal mathematics. Instead, the focus of the course and the book is on interesting theorems and on the techniques that can be used to prove them. This makes the book suitable to second- or third-year mathematics majors and also to secondary mathematics education majors, allowing the students to learn how to write proofs of mathematical results and, at the end, showing them what mathematics is really all about.

The basics
Triangles Circles and lines
Ceva's theorem and its relatives
Vector methods of proof
Geometric constructions
Some further reading
Index

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