Preface1. Pure MathematicsIntroduction; Euclidean Geometry as Pure Mathematics; Games; Why Study Pure Mathematics?; What's Coming; Suggested Reading2. GraphsIntroduction; Sets; Paradox; Graphs; Graph diagrams; Cautions; Common Graphs; Discovery; Complements and Subgraphs; Isomorphism; Recognizing Isomorphic Graphs; SemanticsThe Number of Graphs Having a Given nu; Exercises; Suggested Reading3. Planar GraphsIntroduction; UG, K subscript 5, and the Jordan Curve Theorem; Are there More Nonplanar Graphs?; Expansions;Kuratowski's Theorem; Determining Whether a Graph is Planar or Nonplanar; Exercises; Suggested Reading4. Euler's FormulaIntroduction; Mathematical Induction; Proof of Euler's Formula; Some Consequences of Euler's Formula; Algebraic Topology; Exercises; Suggested Reading5. Platonic GraphsIntroduction; Proof of the Theorem; History; Exercises; Suggested Reading6. ColoringChromatic Number; Coloring Planar Graphs; Proof of the Five Color Theorem; Coloring Maps; Exercises; Suggested Reading7. The Genus of a GraphIntroduction; The Genus of a Graph; Euler's Second Formula; Some Consequences; Estimating the Genus of a Connected Graph; g-Platonic Graphs; The Heawood Coloring Theorem; Exercises; Suggested Reading8. Euler Walks and Hamilton WalksIntroduction; Euler Walks; Hamilton Walks; Multigraphs; The Königsberg Bridge Problem; Exercises; Suggested Reading Afterword Solutions to Selected Exercises Index Special symbols