This two-volume set collects and presents many fundamentals of mathematics in an enjoyable and elaborating fashion. The idea behind the two books is to provide substantials for assessing more modern developments in mathematics and to present impressions which indicate that mathematics is a fascinating subject with many ties between the diverse mathematical disciplines. The present volume examines many of the most important basic results in geometry and discrete mathematics, along with their proofs, and also their history. ContentsGeometry and geometric ideasIsometries in Euclidean vector spaces and their classification in ℝnThe conic sections in the Euclidean planeSpecial groups of planar isometriesGraph theory and platonic solidsLinear fractional transformation and planar hyperbolic geometryCombinatorics and combinatorial problemsFinite probability theory and Bayesian analysisBoolean lattices, Boolean algebras and Stone’s theorem

• Preface 6
• Contents 10
• 1. Geometry and geometric ideas 14
• 2. Isometries in Euclidean vector spaces and their classification in ℝⁿ 30
• 3. The conic sections in the Euclidean plane 64
• 4. Special groups of planar isometries 80
• 5. Graph theory and platonic solids 114
• 6. Linear fractional transformation and planar hyperbolic geometry 148
• 7. Combinatorics and combinatorial problems 174
• 8. Finite probability theory and Bayesian analysis 226
• 9. Boolean lattices, Boolean algebras and Stone’s theorem 258
• Bibliography 292
• Index 294