Distilling Ideas cover -- copyright page -- title page -- Contents -- Preface -- Introduction -- Proof and Mathematical Inquiry -- Graphs -- The Königsberg Bridge Problem -- Connections -- Taking a Walk -- Trees -- Planarity -- Euler Characteristic -- Symmetries -- Colorability -- Completing the Walk around Graph Theory -- Groups -- Examples Lead to Concepts -- Clock-Inspired Groups -- Symmetry Groups of Regular Polygons -- Subgroups, Generators, and Cyclic Groups -- Sizes of Subgroups and Orders of Elements -- Products of Groups -- Symmetric Groups -- Maps between Groups -- Normal Subgroups and Quotient Groups -- More Examples* -- Groups in Action* -- The Man Behind the Curtain -- Calculus -- Perfect Picture -- Convergence -- Existence of Limits -- Continuity -- Zeno's Paradox™ -- Derivatives -- Speedometer Movie and Position -- Applications of the Definite Integral -- Fundamental Theorem of Calculus -- From Vague to Precise -- Conclusion -- Distilling Ideas -- Annotated Index -- List of Symbols -- About the Authors.