REVISED – More exercises have been added throughout.
REVISED – Material has been refined and rewritten as needed to bring in line with current standards.
Implementation of "The Mathematical Education of Teachers (MET)" and the Common Core State Standards for Mathematics (CCSM) achieves the goals of MET and CCSM within the context of a traditional axiomatic approach to geometry. Students are prepared to teach high school geometry by making connections that enable a deeper understanding of the subject.
Comprehensive coverage of most of Euclid's Elements includes almost all of the material in the first six books of that work.
Careful statements of the axioms encourage students to understand how the theorems of geometry are built on the axioms.
Coverage of transformations and the transformational approach to the foundations contains a complete classification of rigid motions of the plane and an explanation of how the Reflection Postulate can substitute for the Side-Angle-Side Postulate. This helps students understand the transformational perspective and how it can be incorporated into the axioms.
A complete construction of the traditional models for Hyperbolic Geometry provides a model that helps students understand the relationships spelled out in the axioms.
A study of geometry in the real world examines some non-traditional models and curved spaces, helping students arrive at answers to questions that arise naturally about the relationship between non-Euclidean geometry and the geometry of the real world.
Careful attention to the historical development of geometry discusses certain cultural and philosophical issues, and demonstrates the changes that the foundations of geometry have gone through over time.
An introduction to proof acts as a bridge between lower-level courses (in which technique is emphasized) to upper-level courses (in which proof and the understanding of concepts are emphasized). This enables students to experience the axiomatic method and study careful proofs that characterize more advanced mathematics.
Emphasis on how to write proofs provides many model proofs as well as commentary on key proofs.
- Provides students with an excellent introductory chapter on how to write proofs, and provides more advanced techniques as they progress through the course.
- Includes many proofs that are exercises, with hints given so that students know roughly how the proof should be structured.
- Enables students to concentrate on how to organize and communicate the proof.

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Foundations of Geometry, 3rd edition

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