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LEADER: 02583fam a2200373 a 4500
001 1530597
005 20220608182509.0
008 940308t19941994nyua b 001 0 eng
010 $a 94010085
020 $a0387942904 (New York : acid-free paper)
020 $a3540942904 (Berlin : acid-free paper) :$cDM69.90
035 $a(OCoLC)30071354
035 $a(OCoLC)ocm30071354
035 $9AJZ5368CU
035 $a(NNC)1530597
035 $a1530597
040 $aDLC$cDLC$dDLC
050 00 $aQA155$b.S75 1994
082 00 $a512/.02$220
100 1 $aStillwell, John.$0http://id.loc.gov/authorities/names/n80047987
245 10 $aElements of algebra :$bgeometry, numbers, equations /$cJohn Stillwell.
260 $aNew York :$bSpringer-Verlag,$c[1994], ©1994.
300 $axi, 181 pages :$billustrations ;$c25 cm.
336 $atext$btxt$2rdacontent
337 $aunmediated$bn$2rdamedia
490 1 $aUndergraduate texts in mathematics
504 $aIncludes bibliographical references (p. [162]-169) and index.
505 0 $aCh. 1. Algebra and Geometry -- Ch. 2. The Rational Numbers -- Ch. 3. Numbers in General -- Ch. 4. Polynomials -- Ch. 5. Fields -- Ch. 6. Isomorphisms -- Ch. 7. Groups -- Ch. 8. Galois Theory of Unsolvability -- Ch. 9. Galois Theory of Solvability.
520 $aThis book is a concise, self-contained introduction to abstract algebra that stresses its unifying role in geometry and number theory. Classical results in these fields, such as the straightedge-and-compass constructions and their relation to Fermat primes, are used to motivate and illustrate algebraic techniques. Classical algebra itself is used to motivate the problem of solvability by radicals and its solution via Galois theory.
520 8 $aThis historical approach has at least two advantages: On the one hand it shows that abstract concepts have concrete roots, and on the other it demonstrates the power of new concepts to solve old problems.
520 8 $aAlgebra has a pedigree stretching back at least as far as Euclid, but today its connections with other parts of mathematics are often neglected or forgotten. By developing algebra out of classical number theory and geometry and reviving these connections, the author has made this book useful to beginners and experts alike. The lively style and clear exposition make it a pleasure to read and to learn from.
650 0 $aAlgebra.$0http://id.loc.gov/authorities/subjects/sh85003425
830 0 $aUndergraduate texts in mathematics.$0http://id.loc.gov/authorities/names/n42025566
852 00 $bmat$hQA155$i.S75 1994