MARC Record from harvard_bibliographic_metadata

LEADER: 02799nam a22004215a 4500
001 014157661-8
005 20141003190132.0
008 130508s2000 xxu| o ||0| 0|eng d
020 $a9780387226767
020 $a9781441931450 (ebk.)
020 $a9780387226767
020 $a9781441931450
024 7 $a10.1007/978-0-387-22676-7$2doi
035 $a(Springer)9780387226767
040 $aSpringer
050 4 $aQA440-699
072 7 $aMAT012000$2bisacsh
072 7 $aPBM$2bicssc
082 04 $a516$223
100 1 $aHartshorne, Robin,$eauthor.
245 10 $aGeometry: Euclid and Beyond /$cby Robin Hartshorne.
264 1 $aNew York, NY :$bSpringer New York :$bSpringer,$c2000.
300 $aXI, 528 p.$bonline resource.
336 $atext$btxt$2rdacontent
337 $acomputer$bc$2rdamedia
338 $aonline resource$bcr$2rdacarrier
347 $atext file$bPDF$2rda
490 1 $aUndergraduate Texts in Mathematics,$x0172-6056
505 0 $a1. Euclid’s Geometry -- 2. Hilbert’s Axioms -- 3. Geometry over Fields -- 4. Segment Arithmetic -- 5. Area -- 6. Construction Problems and Field Extensions -- 7. Non-Euclidean Geometry -- 8. Polyhedra -- Appendix: Brief Euclid -- Notes -- References -- List of Axioms -- Index of Euclid’s Propositions.
520 $aIn recent years, I have been teaching a junior-senior-level course on the classi­ cal geometries. This book has grown out of that teaching experience. I assume only high-school geometry and some abstract algebra. The course begins in Chapter 1 with a critical examination of Euclid's Elements. Students are expected to read concurrently Books I-IV of Euclid's text, which must be obtained sepa­ rately. The remainder of the book is an exploration of questions that arise natu­ rally from this reading, together with their modern answers. To shore up the foundations we use Hilbert's axioms. The Cartesian plane over a field provides an analytic model of the theory, and conversely, we see that one can introduce coordinates into an abstract geometry. The theory of area is analyzed by cutting figures into triangles. The algebra of field extensions provides a method for deciding which geometrical constructions are possible. The investigation of the parallel postulate leads to the various non-Euclidean geometries. And in the last chapter we provide what is missing from Euclid's treatment of the five Platonic solids in Book XIII of the Elements. For a one-semester course such as I teach, Chapters 1 and 2 form the core material, which takes six to eight weeks.
650 20 $aGeometry.
650 10 $aMathematics.
650 0 $aGeometry.
650 0 $aMathematics.
776 08 $iPrinted edition:$z9781441931450
830 0 $aUndergraduate Texts in Mathematics.
988 $a20140910
906 $0VEN