
Thinking Geometrically: A Survey of Geometries
Thomas Q. Sibley
Thinking Geometrically: A Survey of Geometries is a well written and comprehensive survey of college geometry that would serve a wide variety of courses for both mathematics majors and mathematics education majors. Great care and attention is spent on developing visual insights and geometric intuition while stressing the logical structure, historical development, and deep interconnectedness of the ideas.
Students with less mathematical preparation than upperdivision mathematics majors can successfully study the topics needed for the preparation of high school teachers. There is a multitude of exercises and projects in those chapters developing all aspects of geometric thinking for these students as well as for more advanced students. These chapters include Euclidean Geometry, Axiomatic Systems and Models, Analytic Geometry, Transformational Geometry, and Symmetry. Topics in the other chapters, including NonEuclidean Geometry, Projective Geometry, Finite Geometry, Differential Geometry, and Discrete Geometry, provide a broader view of geometry. The different chapters are as independent as possible, while the text still manages to highlight the many connections between topics.
The text is selfcontained, including appendices with the material in Euclid’s first book and a high school axiomatic system as well as Hilbert’s axioms. Appendices give brief summaries of the parts of linear algebra and multivariable calculus needed for certain chapters. While some chapters use the language of groups, no prior experience with abstract algebra is presumed. The text will support an approach emphasizing dynamical geometry software without being tied to any particular software.

The Continued Adventures of the Parrot
Gary Brown
Fritz, better known as the Parrot, solves cases using mathematical reasoning and metaphors from modern game theory. In The Case of the Missing Heroine, Fritz is enticed by a seductive voice to find two characters that appear in a recurring dream. All he is given is an old photo and a client that has a missing childhood. In the process of his investigation he encounters the stories of three famous heroines and a possible connection to the characters in the dream. He tries to build game theoretical models using ideas from Heisenberg and Von Neumann that give some sort of measure of randomness and information. In the end, is he successful in finding a quantitative method for determining the truth from a collection of four similar stories?

The Adventures of the Parrot
Gary Brown
Fritz, better known as the Parrot, solves cases using mathematical reasoning and metaphors from modern game theory.

The Foundations of Mathematics
Thomas Q. Sibley
Finally there's an easytofollow book that will help readers succeed in the art of proving theorems. Sibley not only conveys the spirit of mathematics but also uncovers the skills required to succeed. Key definitions are introduced while readers are encouraged to develop an intuition about these concepts and practice using them in problems.
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