This is a self-contained, comprehensive survey of college geometry that can serve a wide variety of courses for students of both mathematics and mathematics education. The text develops visual insights and geometric intuition while stressing the logical structure, historical development, and deep interconnectedness of the ideas. Chapter topics include Euclidean geometry, axiomatic systems and models, analytic geometry, transformational geometry, symmetry, non-Euclidean geometry, projective geometry, finite geometry, differential geometry, and discrete geometry. The different chapters are as independent as possible, while the text still manages to highlight the many connections between topics. Appendices include material from Euclid's first book, as well as Hilbert's axioms, and provide brief summaries of the parts of linear algebra and multivariable calculus needed for certain chapters.
Sibley
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Preface; 1. Euclidean geometry; 2. Axiomatic systems; 3. Analytic geometry; 4. Non-Euclidean geometries; 5. Transformational geometry; 6. Symmetry; 7. Projective geometry; 8. Finite geometries; 9. Differential geometry; 10. Discrete geometry; 11. Epilogue; Appendix A. Definitions, postulates, common notions, and propositions from Book I of Euclid's Elements; Appendix B. SMSG axioms for Euclidean geometry; Appendix C. Hilbert's axioms for Euclidean plane geometry; Appendix D. Linear algebra summary; Appendix E. Multivariable calculus summary; Appendix F. Elements of proofs; Answers to selected exercises; Acknowledgements; Index.
Sibley, Thomas Q.
Thomas Q. Sibley is a Professor of Mathematics at Saint John's University, Minnesota. He has taught mathematics in the Democratic Republic of the Congo and Liberia as well as in the USA, and has received several teaching awards, including the Distinguished Teaching Award from the MAA, North Central Section (2003). He is a member of the American Mathematical Society, the Association for Women in Mathematics, the Society for Mathematical Biology, and the Council for Undergraduate Research.
