Geometry for Americans
The new edition of Paul Zeitz's "The Art and Craft of Problem-Solving," aimed at college math majors, adds a chapter titled "'Geometry for Americans' instead of 'Geometry for Dummies' so as not to offend. The sad truth is that most mathematically inclined Americans know very little geometry, in contrast to their luckier peers in Eastern Europe and Asia. . . We call Sections 8.2-8.3 'survival geometry' because they contain a lean but adequate stock of facts and techniques that will allow you to get started on most problems. If you master the facts and lemmas and fearlessly employ the problem-solving ideas presented in the next two sections, you will be able to tackle an impressive variety of challenging questions." Zeitz has been active with many problem-solving competitions, both as a competitor and as a coach; he emphasizes the fun and exhiliration of challenging problems (as opposed to "exercises").
The Art and Craft of Pproblem Solving, by Paul Zeitz. 2nd ed. Hoboken, NJ: John Wiley, 2007. Mathematics Library QA63 .Z45 2007 Link to MnCat Record