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Geometry for College Students

I. Martin Isaacs University of Wisconsin, Madison, WI
Available Formats:
Hardcover ISBN: 978-0-8218-4794-7
Product Code: AMSTEXT/8
List Price: $70.00 MAA Member Price:$63.00
AMS Member Price: $56.00 Electronic ISBN: 978-1-4704-1121-3 Product Code: AMSTEXT/8.E List Price:$66.00
MAA Member Price: $59.40 AMS Member Price:$52.80
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $105.00 MAA Member Price:$94.50
AMS Member Price: $84.00 Click above image for expanded view Geometry for College Students I. Martin Isaacs University of Wisconsin, Madison, WI Available Formats:  Hardcover ISBN: 978-0-8218-4794-7 Product Code: AMSTEXT/8  List Price:$70.00 MAA Member Price: $63.00 AMS Member Price:$56.00
 Electronic ISBN: 978-1-4704-1121-3 Product Code: AMSTEXT/8.E
 List Price: $66.00 MAA Member Price:$59.40 AMS Member Price: $52.80 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$105.00 MAA Member Price: $94.50 AMS Member Price:$84.00
• Book Details

Pure and Applied Undergraduate Texts
Volume: 82001; 222 pp
MSC: Primary 51;

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.

Undergraduate students interested in Euclidean geometry.

• Cover
• Title page
• Dedication
• Preface
• Contents
• Chapter 1. The Basics
• Chapter 2. Triangles
• Chapter 3. Circles and lines
• Chapter 4. Ceva’s theorem and its relatives
• Chapter 5. Vector methods of proof
• Chapter 6. Geometric constructions
• Some further reading
• Index
• Back Cover

• Reviews

• Thanks to his ability to identify and describe interesting problems, and his skills at motivating proofs, and communicating results, Isaacs more than delivers on his promise to show readers some of the spectacular theorems of plane geometry. This book is a textbook, but I venture to say it shouldn.t be just for students. Professional mathematicians, especially those who haven.t thought much about Euclidean geometry since their own course in high school, will certainly benefit from reading this book.

MAA Reviews
• Requests

Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 82001; 222 pp
MSC: Primary 51;

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.

Undergraduate students interested in Euclidean geometry.

• Cover
• Title page
• Dedication
• Preface
• Contents
• Chapter 1. The Basics
• Chapter 2. Triangles
• Chapter 3. Circles and lines
• Chapter 4. Ceva’s theorem and its relatives
• Chapter 5. Vector methods of proof
• Chapter 6. Geometric constructions
• Some further reading
• Index
• Back Cover
• Thanks to his ability to identify and describe interesting problems, and his skills at motivating proofs, and communicating results, Isaacs more than delivers on his promise to show readers some of the spectacular theorems of plane geometry. This book is a textbook, but I venture to say it shouldn.t be just for students. Professional mathematicians, especially those who haven.t thought much about Euclidean geometry since their own course in high school, will certainly benefit from reading this book.

MAA Reviews
Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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