Useful references for MATH 5200/7200

Elementary geometry and trigonometry

Theory and Problems of Geometry, third edition, by Barnett Rich, Schaum's Outline Series, McGraw Hill, 1999.
This book gives a good review of Euclidean plane geometry. Though the axioms and logical structure are not emphasized, all of the key theorems are here, with lots of examples. (The first and second editions are also very good.)

Famous Problems of Geometry and How to Solve Them, by Benjamin Bold, Dover Publications, 1982.
This little book is a complete treatment of the classical construction problems of Greek geometry, and the modern proofs of impossibility. All you need to understand this book is high school algebra and analytic geometry!

Taxicab Geometry, An Adventure in Non-Euclidean Geometry, by Eugene Krause, Dover 1986.
This introduction to taxicab geometry is suitable for use in middle school or high school.

Discovering Geometry, An Inductive Approach, second edition, by Michael Serra, Key Curriculum Press, Emeryville, California, 1997.
This innovative high school textbook emphasizes visualization, experimentation, writing, and cooperative problem solving.

Schaum's Outline of Trigonometry, third edition, by Frank Ayres and Robert E. Moyer, McGraw-Hill 1998.
This is a good basic review of trigonometry, with numerous worked problems.

Trigonometric Delights, by Eli Maor, Princeton 1998.
This book contains lots of interesting history, and a very wide range of applications of trigonometry to the rest of mathematics. If you think trig is boring, this book may change your mind!

Geometry at Work: Papers in Applied Geometry, edited by Catherine A. Gorini, Mathematical Association of America 2000.
Areas of application include architecture, history, engineering, and science.

Advanced geometry

Geometry: A Metric Approach with Models, second edition, by Richard Millman and George Parker, Springer-Verlag 1991.
This rigorous approach to geometry contains a very careful treatment of the relation of coordinate (analytic) geometry to axiomatic (synthetic) geometry.

Geometry: Euclid and Beyond, by Robin Hartshorne, Springer-Verlag 2000.
This book gives a twentieth century perspective on axiomatic geometry, taking Euclid's Elements as the starting point. The relations between geometry and abstract algebra are explored at length.

Proofs and writing

How To Solve It, by George Polya, Princeton University Press, 1957.
This is the world's most famous book on "heuristic." How do mathematicians come up with proofs? Polya's answer: experience and common sense! His examples are taken from high school mathematics, and a large part of the book is about teaching and learning.

Writing to Learn, by William Zinsser, Harper and Row, 1988.
This book takes a fresh look at the uses of writing in teaching and learning. Chapter 9, Writing Mathematics, is based on an interview with a pioneering high school math teacher.

Writing Math Research Papers, by Robert Gerver, Key Curriculum Press, 1997.
This is a very helpful discussion of how to use writing in undergraduate math classes. You can use it as a guide on how to write up homework and term projects in our course.

Writing in the Teaching and Learning of Mathematics, by John Meier and Thomas Rishel, Mathematical Association of America 1998.
This book is for teachers of mathematics who want to incorporate writing assignments into their courses.

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