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The Mathematical Intelligencer

, Volume 33, Issue 2, pp 1–2 | Cite as

The Fundamental Theorem of Algebra: An Elementary and Direct Proof

  • Oswaldo Rio Branco de Oliveira
Note

Keywords

Complex Number Mathematical Note Positive Real Number Abstract Analysis Direct Proof 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. [1]
    Argand, J. R., “Philosophie mathématique. Réflexions sur la nouvelle théorie des imaginaires, suivies d’une application à la démonstration d’un théorème d’analyse,” Annales de Mathématiques Pures et Appliquées, tome 5 (1814-1815), 197-209.Google Scholar
  2. [2]
    Burckel, R. B., “Fubinito (Immediately) Implies FTA”, American Mathematical Monthly 113 (2006), 344-347.zbMATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    Cauchy, A. L., Cours d’analyse, Vol VII, Première Partie, Chapitre X, Editrice CLUEB, Bologna (1990).Google Scholar
  4. [4]
    Chrystal, G., Algebra, An Elementary Text-book, Part I, Sixth edition. Chelsea Publishing Company, New York, 1952.Google Scholar
  5. [5]
    Estermann, T., “On the Fundamental Theorem of Algebra”. J. London Mathematical Society 31 (1956), 238-240.zbMATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    Fefferman, C., “An Easy Proof of the Fundamental Theorem of Algebra,” American Mathematical Monthly 74 (1967), 854- 855.zbMATHCrossRefMathSciNetGoogle Scholar
  7. [7]
    Fine, B., and Rosenberger, G., “The Fundamental Theorem of Algebra,” Springer-Verlag, New York, 1997.zbMATHGoogle Scholar
  8. [8]
    Körner, T. W., “On the Fundamental Theorem of Algebra,” American Mathematical Monthly 113 (2006), 347-348.zbMATHCrossRefMathSciNetGoogle Scholar
  9. [9]
    Littlewood, J. E., “Mathematical Notes (14): Every Polynomial has a Root,” J. London Mathematical Society 16 (1941), 95-98.CrossRefMathSciNetGoogle Scholar
  10. [10]
    Redheffer, R. M., “What! Another Note Just on the Fundamental Theorem of Algebra?,” American Mathematical Monthly 71 (1964), 180-185.zbMATHCrossRefMathSciNetGoogle Scholar
  11. [11]
    Remmert, R., “The Fundamental Theorem of Algebra”. In H.-D. Ebbinghaus et al., Numbers, Graduate Texts in Mathematics, no. 123, Springer-Verlag, New York, 1991. Chapters 3 and 4.Google Scholar
  12. [12]
    Rudin, W., Principles of Mathematical Analysis, McGraw-Hill, Tokyo, 1963.Google Scholar
  13. [13]
    Searcóid, M. O., Elements of Abstract Analysis, Springer-Verlag, London, 2003.Google Scholar
  14. [14]
    Stillwell, J., Mathematics and its History, Springer-Verlag, New York, 1989, pp. 266-275.zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Mathematics-IMEUniversity of São PauloSão Paulo-SPBrazil

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