On Gauss's first proof of the fundamental theorem of algebra
Authors:
S. M. Gersten and John R. Stallings
Journal:
Proc. Amer. Math. Soc. 103 (1988), 331332
MSC:
Primary 20E05; Secondary 1201
MathSciNet review:
938691
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Abstract: Gauss's first proof of the Fundamental Theorem of Algebra is shown to be related to basic properties of free groups.
 [1]
C. F. Gauss, Werke, vol. 3, Georg Olms Verlag, Hildesheim and New York, 1973.
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Richard
Z. Goldstein and Edward
C. Turner, Applications of topological graph theory to group
theory, Math. Z. 165 (1979), no. 1, 1–10.
MR 521516
(80g:20050), http://dx.doi.org/10.1007/BF01175125
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Steve
Smale, The fundamental theorem of algebra and
complexity theory, Bull. Amer. Math. Soc.
(N.S.) 4 (1981), no. 1, 1–36. MR 590817
(83i:65044), http://dx.doi.org/10.1090/S027309791981148588
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Shlomo
Sternberg, Lectures on differential geometry, PrenticeHall,
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(33 #1797)
 [5]
A source book in mathematics, 1200–1800, Edited by D. J.
Struik, Harvard University Press, Cambridge, Mass., 1969. MR 0238647
(39 #11)
 [1]
 C. F. Gauss, Werke, vol. 3, Georg Olms Verlag, Hildesheim and New York, 1973.
 [2]
 R. Z. Goldstein and E. C. Turner, Applications of topological graph theory to group theory, Math. Z. 165 (1979), 110. MR 521516 (80g:20050)
 [3]
 S. Smale, The Fundamental Theorem of Algebra and complexity theory, Bull. Amer. Math. Soc. (N.S.) 4 (1981), 136. MR 590817 (83i:65044)
 [4]
 S. Sternberg, Lectures on differential geometry, PrenticeHall, 1964. MR 0193578 (33:1797)
 [5]
 D. J. Struik, A source book in mathematics 12001800, Harvard Univ. Press, 1969. MR 0238647 (39:11)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939198809386913
PII:
S 00029939(1988)09386913
Keywords:
Free group,
polynomial
Article copyright:
© Copyright 1988
American Mathematical Society
