MARC Record from harvard_bibliographic_metadata

LEADER: 03482cam a2200469 i 4500
001 013732268-2
005 20131206190502.0
008 121211t20132013riua b 001 0 eng
010 $a 2012043438
020 $a9780821884782 (alk. paper)
020 $a0821884786 (alk. paper)
024 8 $a40022448983
035 $a(PromptCat)99954440454
035 0 $aocn821066968
040 $aDLC$beng$erda$cDLC$dOCLCO$dYDXCP$dBWX$dOCLCQ$dMUU$dYUS$dOCLCF$dCDX
042 $apcc
050 00 $aQA481$b.L44 2013
082 00 $a516$223
084 $a51-01$a51M05$a51M10$2msc
100 1 $aLee, John M.,$d1950-
245 10 $aAxiomatic geometry /$cJohn M. Lee.
264 1 $aProvidence, Rhode Island :$bAmerican Mathematical Society,$c[2013]
264 4 $c©2013
300 $axvii, 469 pages :$billustrations ;$c26 cm.
336 $atext$btxt$2rdacontent
337 $aunmediated$bn$2rdamedia
338 $avolume$bnc$2rdacarrier
490 1 $aPure and applied undergraduate texts ;$v21
504 $aIncludes bibliographical references (pages 451-453) and index.
505 0 $a1. Euclid -- 2. Incidence geometry -- 3. Axioms for plane geometry -- 4. Angles -- 5. Triangles -- 6. Models of neutral geometry -- 7. Perpendicular and parallel lines -- 8. Polygons -- 9. Quadrilaterals -- 10. The Euclidean parallel postulate -- 11. Area -- 12. Similarity -- 13. Right triangles -- 14. Circles -- 15. Circumference and circular area -- 16. Compass and straightedge constructions -- 17. The parallel postulate revisited -- 18. Introduction to hyperbolic geometry -- 19. Parallel lines in Hyperbolic geometry -- 20. Epilogue: Where do we go from here? -- Appendices.
520 $aThe story of geometry is the story of mathematics itself: Euclidean geometry was the first branch of mathematics to be systematically studied and placed on a firm logical foundation, and it is the prototype for the axiomatic method that lies at the foundation of modern mathematics. It has been taught to students for more than two millennia as a mode of logical thought. This book tells the story of how the axiomatic method has progressed from Euclid's time to ours, as a way of understanding what mathematics is, how we read and evaluate mathematical arguments, and why mathematics has achieved the level of certainty it has. It is designed primarily for advanced undergraduates who plan to teach secondary school geometry, but it should also provide something of interest to anyone who wishes to understand geometry and the axiomatic method better. It introduces a modern, rigorous, axiomatic treatment of Euclidean and (to a lesser extent) non-Euclidean geometries, offering students ample opportunities to practice reading and writing proofs while at the same time developing most of the concrete geometric relationships that secondary teachers will need to know in the classroom. -- P. [4] of cover.
650 7 $aGeometry.$2fast$0(OCoLC)fst00940864.
650 7 $aAxioms.$2fast$0(OCoLC)fst00824492.
650 0 $aAxioms.
650 0 $aGeometry.
650 7 $aGeometry$xInstructional exposition (textbooks, tutorial papers, etc.)$2msc
650 7 $aGeometry$xReal and complex geometry$xEuclidean geometries (general) and generalizations.$2msc
650 7 $aGeometry$xReal and complex geometry$xHyperbolic and elliptic geometries (general) and generalizations.$2msc
830 0 $aPure and applied undergraduate texts ;$v21.
899 $a415_565004
988 $a20130718
906 $0DLC