Bibliography for the Fundamental Theorem of Algebra

unabridged

 

  1. The fundamental theorem of algebra and linear algebra.  
    Derksen, Harm
    Amer. Math. Monthly  110  (2003),  no. 7, 620--623, MathSciNet.  
  2. Green's Theorem and the Fundamental Theorem of Algebra
    Loya, P.
    American Mathematical Monthly, 2003, vol. 110, no. 10, pp. 944-946, Ingenta.  
  3. Teach Gauss's 1799 Proof of the Fundamental Theorem of Algebra
    Hecht, L.
    21St Century Science and Technology, 2002, vol. 15, no. 1, pp. 2, Ingenta.  
  4. Gauss's Declaration of Independence: The Fundamental Theorem of Algebra
    Director, B.
    21St Century Science and Technology, 2002, vol. 15, no. 1, pp. 66-69, Ingenta.  
  5. A Constructive Proof of the Fundamental Theorem of Algebra without Using the Rationals
    Geuvers, H.; Wiedijk, F.; Zwanenburg, J.
    Lecture Notes in Computer Science, 2002, no. 2277, pp. 96-111, Ingenta.  
  6. Another topological proof of the fundamental theorem of algebra.
    Almira, J. M.; Jiménez, M.; Del Toro, N.
    Elem. Math. 57 (2002), no. 1, 32--37, MathSciNet.  
  7. On the Fundamental Theorem of Algebra
    Mays J.
    Lithuanian Mathematical Journal, October 2002, vol. 42, no. 4, pp. 364-372(9), Ingenta.   
  8. Polynomial interpolation and a multivariate analog of the fundamental theorem of algebra.
    Hakopian, H. A.; Tonoyan, M. G.
    East J. Approx. 8 (2002), no. 3, 355--379, MathSciNet.  
  9. On the fundamental theorem of algebra.
    Mera, Severina; Mera, Nicolae
    Proof based on topology. Acta Univ. Apulensis Math. Inform. No. 4 (2002), 135--138, MathSciNet.  
  10. On the fundamental theorem of algebra. (Russian)  
    Machis, Yu.
    Liet. Mat. Rink.  42  (2002),  no. 4, 459--469;  translation in  Lithuanian Math. J.  42  (2002),  no. 4, 364--372, MathSciNet.  
  11. Une démonstration élémentaire du théorème fondamental d'algèbre. (French) [An elementary proof of the fundamental theorem of algebra]
    Nakaoka, Akira
    Mem. Fac. Engrg. Design Kyoto Inst. Tech. Ser. Sci. Tech. 50 (2001), 9--12 (2002), MathSciNet.  
  12. A graphical approach to understanding the fundamental theorem of algebra  
    Sudhir Kumar Goel, Denise T. Reid.
    Mathematics Teacher Dec 2001 v94 i9 p749(1), Expanded Academic.
  13. The Fundamental Theorem of Algebra Revisited
    von Sohsten de Medeiros, A.
    American Mathematical Monthly, 2001, vol. 108, no. 8, pp. 759, Ingenta.
  14. Une démonstration élémentaire du théorème fondamental d'algèbre. (French) [An elementary proof of the fundamental theorem of algebra]
    Nakaoka, Akira
    Mem. Fac. Engrg. Design Kyoto Inst. Tech. Ser. Sci. Tech. 50 (2001), 9--12 (2002), MathSciNet.  
  15. Fundamental theorem of albegra - yet another proof  
    Anindya Sen  
    The American Mathematical Monthly Nov 2000 v107 i9 p842(2), Expanded Academic.  
  16. On a kind of function equations and the fundamental theorem of algebra  
    Won Sok Yoo  
    Bull. Korean Math. Soc. 37 (2000), no. 4, 669--674, MathSciNet.   
  17. A forgotten paper on the fundamental theorem of algebra  
    Frank Smithies  
    Notes and Records Roy. Soc. London 54 (2000), no. 3, 333--341, MathSciNet.   
  18. The fundamental theorem of algebra: a constructive development without choice  
    Fred Richman  
    Pacific J. Math. 196 (2000), no. 1, 213--230, MathSciNet.   
  19. An elementary proof of the fundamental theorem of algebra  
    Martin Kochol  
    Internat. J. Math. Ed. Sci. Tech. 30 (1999), no. 4, 614--615, MathSciNet.   
  20. A simple proof of the fundamental theorem of algebra  
    John Byl  
    Internat. J. Math. Ed. Sci. Tech. 30 (1999), no. 4, 602--603, MathSciNet.   
  21. The Fundamental Theorem of Algebra  
    Michael D. Hirschhorn  
    College Math Journal: Volume 29, Number 4, (1998), Pages: 276-277.   
  22. Errata to: "On the fundamental theorem of algebra"  [Colloq. Math. 73 (1997), no. 2, 193--194; MR 97m:30003].
    Diego Vaggione  
    Colloq. Math. 77 (1998), no. 2, 321, MathSciNet.   
  23. Another Proof of the Fundamental Theorem of Algebra (in Notes)  
    Daniel J. Velleman  
    Mathematics Magazine, Vol. 70, No. 3. (Jun., 1997), pp. 216-217, Jstor.  
  24. A Proof That Polynomials Have Roots  
    Uwe F. Mayer  
    College Math Journal: Volume 28, Number 1, (1997), Pages: 58.   
  25. On the fundamental theorem of algebra  
    Diego Vaggione  
    Colloq. Math. 73 (1997), no. 2, 193--194, MathSciNet.   
  26. An explicit proof of the fundamental theorem of algebra in the elementary theory of real numbers  
    Judit Robu  
    Modern applied analysis (Ilieni, 1997). Pure Math. Appl. 9 (1998), no. 1-2, 171--179, MathSciNet.   
  27. A theorem equivalent to Picard's Little theorem and a derivation of the fundamental theorem of algebra  
    Paula Kemp; Alexander Abian  
    Far East J. Math. Sci. 5 (1997), no. 4, 623--626, MathSciNet.   
  28. The fundamental theorem of algebra  
    Benjamin Fine; Gerhard Rosenberger  
    Undergraduate Texts in Mathematics. Springer-Verlag, New York, 1997. xii+208 pp. ISBN: 0-387-94657-8, MathSciNet.   
  29. Why Polynomials Have Roots  
    Javier Gomez-Calderon; David M. Wells  
    The College Mathematics Journal, Vol. 27, No. 2. (Mar., 1996), pp. 90-94, Jstor.  
  30. Supersymmetry, vacuum statistics, and the fundamental theorem of algebra  
    Donald Spector  
    Comm. Math. Phys. 177 (1996), no. 1, 13--25, MathSciNet.   
  31. On the `Fundamental theorem of Algebra'
    Leung, T. W.
    International Journal of Modern Physics A, v 10, n 8, 1995, p 83, Compendex
  32. A probabilistic proof of the fundamental theorem of algebra and a generalization  (Chinese)  
    Shun Long Luo  
    Math. Appl. 8 (1995), no. 4, 487--489, MathSciNet.   
  33. Facilitating an Intuitive Basis for the Fundamental Theorem of Algebra Through Graphical Technologies.
    Movshovitz-Hadar, Nitsa; Shmukler, Alla; Zaslavsky, Orit
    The Journal of computers in mathematics and science teaching, 1994, vol. 13, no. 3, pp. 339, Ingenta.  
  34. Vom Fundamentalsatz der Algebra zum Satz von Gelfand-Mazur," (German) [From the fundamental theorem of algebra to the theorem of Gelfand-Mazur]  
    Reinhold Vom Remmert  
    Math. Semesterber. 40 (1993), no. 1, 63--71, MathSciNet.   
  35. The fundamental theorem of algebra before Carl Friedrich Gauss  
    Josep Carrera  
    Publ. Mat. 36 (1992), no. 2B, 879--911 (1993), MathSciNet.   
  36. Euler and the Fundamental Theorem of Algebra  
    William Dunham  
    The College Mathematics Journal, Vol. 22, No. 4. (Sep., 1991), pp. 282-293, Jstor.  
  37. Plane Curves, Polar Coordinates and Winding Numbers  
    John A. Baker  
    Mathematics Magazine, Vol. 64, No. 2. (Apr., 1991), pp. 75-91, Jstor.  
  38. Sur l'histoire du théorème fondamental de l'algèbre: théorie des équations et calcul intégral," (French) [On the history of the fundamental theorem of algebra: the theory of equations and integral calculus]
    Christian Gilain  
    Arch. Hist. Exact Sci. 42 (1991), no. 2, 91--136, MathSciNet.   
  39. Discovering the Fundamental Theorem of Calculus Using Computer Algebra Systems.
    Gordon, Sheldon P.
    Mathematics and computer education, 1991, vol. 25, no. 1, pp. 6, Ingenta.
  40. A theorem equivalent to the fundamental theorem of algebra  
    Alexander Abian; James A. Wilson  
    Nieuw Arch. Wisk. (4) 8 (1990), no. 1, 47--48, MathSciNet.   
  41. Gauss' first proof of the fundamental theorem of algebra  
    A. Fryant; V. L. N. Sarma  
    Math. Student 52 (1984), no. 1-4, 101--105 (1990), MathSciNet.   
  42. Finding Rational Roots of Polynomials (in Classroom Capsules)  
    Don Redmond  
    The College Mathematics Journal, Vol. 20, No. 2. (Mar., 1989), pp. 139-141, Jstor.  
  43. Graphing the Complex Zeros of Polynomials Using Modulus Surfaces  
    Cliff Long; Thomas Hern  
    The College Mathematics Journal, Vol. 20, No. 2. (Mar., 1989), pp. 98-105, Jstor.  
  44. Using Computer Algebra Systems To Teach The Fundamental Theorem Of Calculus.
    Mathews, John H.
    Mathematics and computer education, 1989, vol. 23, no. 3, pp. 199, Ingenta.
  45. Shorter Notes: On Gauss's First Proof of the Fundamental Theorem of Algebra  
    S. M. Gersten; John R. Stallings  
    Proceedings of the American Mathematical Society, Vol. 103, No. 1. (May, 1988), pp. 331-332, Jstor.  
  46. Beweis des Fundamentalsatzes der Algebra als Anwendung des Spernerschen Lemmas," (German) [Proof of the fundamental theorem of algebra as application of Sperner's lemma]  
    Hermann Hering  
    Math. Semesterber. 34 (1987), no. 1, 65--70, MathSciNet.   
  47. A new proof of the fundamental theorem of algebra  
    A. Abian  
    Caribbean J. Math. 5 (1986), no. 1, 9--12, MathSciNet.   
  48. On the impossibility of a fixed point proof of the fundamental theorem of algebra  
    Alexandru Aleman  
    Seminar on mathematical analysis (Cluj-Napoca, 1985), 157--161, Preprint, 85-7, Univ. "Babecs-Bolyai", Cluj-Napoca, 1985, MathSciNet.   
  49. On fundamental theorem of algebra  
    S. Ghosh  
    Bull. Calcutta Math. Soc. 76 (1984), no. 6, 349--350, MathSciNet.   
  50. Zum Fundamentalsatz der Algebra (German) [On the fundamental theorem of algebra]  
    Hermann Hering  
    Elem. Math. 39 (1984), no. 2, 38--42, MathSciNet.   
  51. A Brouwer type coincidence theorem and the fundamental theorem of algebra  
    M. M. Dodson  
    Canad. Math. Bull. 27 (1984), no. 4, 478--480, MathSciNet.   
  52. Roots of Polynomials and Loci  
    Ali R. Amir-Moez  
    The Two-Year College Mathematics Journal, Vol. 14, No. 4. (Sep., 1983), pp. 313-317, Jstor.  
  53. A multivariable form of the fundamental theorem of algebra.  
    Salzberg, Pablo M.
    Canad. Math. Bull. 26 (1983), no. 3, 271--272, MathSciNet.  
  54. Zum Fundamentalsatz der Algebra (German) [On the fundamental theorem of algebra]
    Hans-Joachim Kowalsky  
    Abh. Braunschweig. Wiss. Ges. 35 (1983), 111--120, MathSciNet.   
  55. An Advanced Calculus Proof of the Fundamental Theorem of Algebra (in Classroom Notes)  
    Frank Forelli  
    American Mathematical Monthly, Vol. 88, No. 5. (May, 1981), pp. 347-348, Jstor.  
  56. Proof of the Fundamental Theorem of Algebra  
    J. L. Brenner; R. C. Lyndon  
    American Mathematical Monthly, Vol. 88, No. 4. (Apr., 1981), pp. 253-256, Jstor.  
  57. The fundamental theorem of algebra and complexity theory  
    Steve Smale  
    Bull. Amer. Math. Soc. (N.S.) 4 (1981), no. 1, 1--36, MathSciNet.   
  58. Herausragende Einzelleistungen im Zusammenhang mit der Kreisteilungsgleichung, dem Fundamentalsatz der Algebra und der Reihenkonvergenz. (German)
    [Notable individual accomplishments in connection with the cyclotomic equation, the fundamental theorem of algebra, and series convergence]
    Schneider, Ivo
    Carl Friedrich Gauß (1777--1855), pp. 37--63, Wissenschaftsgeschichte, Minerva, Munich, 1981, MathSciNet.  
  59. Counterexamples from the Algebra of Polynomials over a Nonfield (in Mathematical)  
    Janet B. Pomeranz  
    The Two-Year College Mathematics Journal, Vol. 8, No. 1. (Jan., 1977), pp. 11-14, Jstor.  
  60. A proof of the fundamental theorem of algebra (Spanish)
    José Manuel Bayod  
    Gac. Mat. (Madrid) (1) 29 (1977), no. 5-6, 107--110, MathSciNet.   
  61. Gauss and the fundamental theorem of algebra  (Dutch)
    R. C. F. Kooistra
    Nieuw Tijdschr. Wisk. 64 (1976/77), no. 4, 173--175, MathSciNet.   
  62. The Fundamental Theorem of Algebra (in Classroom Notes)  
    Frode Terkelsen  
    American Mathematical Monthly, Vol. 83, No. 8. (Oct., 1976), p. 647, Jstor.  
  63. A new proof of the fundamental theorem of algebra Pivoting and extensions.  
    H. W. Kuhn  
    Math. Programming Stud. No. 1 (1974), 148--158, MathSciNet.   
  64. From the history of the analytic proofs of the fundamental theorem of algebra," (Russian)
    S. S. Petrova
    History and methodology of the natural sciences, No. XIV: Mathematics, mechanics (Russian), pp. 167--172. Izdat. Moskov. Univ., Moscow, 1973, MathSciNet.   
  65. A Note on the Geometry of Zeros of Polynomials  
    C. A. Long  
    Mathematics Magazine, Vol. 44, No. 3. (May, 1971), pp. 157-159, Jstor.  
  66. Open Mappings and the Fundamental Theorem of Algebra  
    R. L. Thompson  
    Mathematics Magazine, Vol. 43, No. 1. (Jan., 1970), pp. 39-40, Jstor.  
  67. The first proof of the fundamental theorem of algebra," (Bulgarian)
    Svetlana S. Petrova
    Fiz.-Mat. Spis. Bcdprime lgar. Akad. Nauk. 13(46) (1970), 205--210, MathSciNet.   
  68. The Fundamental Theorem of Algebra  
    Paul J. Campbell  
    Pi Mu Epsilon J., (1967), V. 4, No. 6, pp. 243-247.   
  69. An Easy Proof of the Fundamental Theorem of Algebra (in Classroom Notes)  
    Charles Fefferman  
    American Mathematical Monthly, Vol. 74, No. 7. (Aug. - Sep., 1967), pp. 854-855, Jstor.  
  70. Proof of the Fundamental Theorem of Algebra (in Classroom Notes)  
    S. Wolfenstein  
    American Mathematical Monthly, Vol. 74, No. 7. (Aug. - Sep., 1967), pp. 853-854, Jstor.  
  71. On the Fundamental Theorem of Algebra  
    Hans Zassenhaus  
    American Mathematical Monthly, Vol. 74, No. 5. (May, 1967), pp. 485-497, Jstor.  
  72. A constructive form of the second Gauss proof of the fundamental theorem of algebra  
    R. L. Goodstein  
    1969 Constructive Aspects of the Fundamental Theorem of Algebra (Proc. Sympos., Zürich-Rüschlikon, 1967) pp. 69--76 Wiley-Interscience, New York, MathSciNet.   
  73. Constructive aspects of the fundamental theorem of algebra  
    Bruno Dejon; Peter Henrici, Editors  
    Proceedings of a Symposium Conducted at the IBM Research Laboratory, Zürich-Rüschlikon, June 5-7, 1967. Wiley-Interscience A Division of John Wiley & Sons, Ltd., London-New York-Sydney 1969 vii+337 pp., MathSciNet.   
  74. The fundamental theorem of algebra in recursive analysis.
    Specker, E.
    1969 Constructive Aspects of the Fundamental Theorem of Algebra (Proc. Sympos., Zürich-Rüschlikon, 1967) pp. 321--329 Wiley-Interscience, New York, MathSciNet.  
  75. The fundamental theorem of algebra for polyanalytic polynomials (Russian)
    M. B. Balk  
    Litovsk. Mat. Sb. 8 1968 401--404, MathSciNet.   
  76. A proof of the "Fundamental theorem of algebra" by means of Galois theory and 2-Sylow groups  
    L. Horowitz  
    Nieuw Arch. Wisk. (3) 14 1966 95--96, MathSciNet.   
  77. What! Another Note Just on the Fundamental Theorem of Algebra? (in Classroom Notes)  
    R. M. Redheffer  
    American Mathematical Monthly, Vol. 71, No. 2. (Feb., 1964), pp. 180-185, Jstor.  
  78. Yet Another Proof of the Fundamental Theorem of Algebra (in Mathematical Notes)  
    R. P. Boas, Jr.  
    American Mathematical Monthly, Vol. 71, No. 2. (Feb., 1964), p. 180, Jstor.  
  79. The Fundamental Theorem of Algebra (in Classroom Notes)  
    J. E. Eaton  
    American Mathematical Monthly, Vol. 67, No. 6. (Jun. - Jul., 1960), pp. 578-579, Jstor.  
  80. Generalizations of the Fundamental Theorem of Algebra  
    M. Reichbach  
    Bull. Res. Council Israel Sect. F 7F 1958 155--164 (1958), MathSciNet.   
  81. The Fundamental Theorem of Algebra (in Mathematical Notes)  
    Raymond Redheffer  
    American Mathematical Monthly, Vol. 64, No. 8. (Oct., 1957), pp. 582-585, Jstor.  
  82. A new proof of the fundamental theorem of algebra (Chinese)
    Heng-san Kao  
    Advancement in Math. 3 1957 608--611, MathSciNet.   
  83. On the fundamental theorem of algebra  
    T. Estermann  
    J. London Math. Soc. 31 (1956), 238--240, MathSciNet.   
  84. The Fundamental Theorem of Algebra (in Mathematical Notes)  
    S. Stein  
    American Mathematical Monthly, Vol. 61, No. 2. (Feb., 1954), p. 109, Jstor.  
  85. On the fundamental theorem of algebra  
    Kanesiroo Iseki  
    J. Math. Soc. Japan 6, (1954). 129--130, MathSciNet.   
  86. A Matric Proof of the Fundamental Theorem of Algebra for Real Quaternions (in Mathematical Notes)  
    Mark Leum; M. F. Smiley  
    American Mathematical Monthly, Vol. 60, No. 2. (Feb., 1953), pp. 99-100, Jstor.  
  87. Group Invariant Integration and the Fundamental Theorem of Algebra  
    Herbert Scarf  
    Proceedings of the National Academy of Sciences of the United States of America, Vol. 38, No. 5. (May 15, 1952), pp. 439-440, Jstor.  
  88. A Correction A Topological Proof of the Fundamental Theorem of Algebra (in Mathematical Notes)  
    B. H. Arnold; Ivan Niven
    American Mathematical Monthly, Vol. 58, No. 2. (Feb., 1951), p. 104, Jstor.  
  89. Extension of a Topological Proof of the Fundamental Theorem of Algebra (in Mathematical Notes)  
    Ivan Niven  
    American Mathematical Monthly, Vol. 57, No. 4. (Apr., 1950), pp. 246-248, Jstor.  
  90. A Topological Proof of the Fundamental Theorem of Algebra (in Mathematical Notes)  
    B. H. Arnold  
    American Mathematical Monthly, Vol. 56, No. 7. (Aug. - Sep., 1949), pp. 465-466, Jstor.  
  91. On the fundamental theorem of algebra III.
    J. G. van der Corput  
    Nederl. Akad. Wetensch., Proc. 49, (1946) 985--994 = Indagationes Math. 8, 605--614 (1946), MathSciNet.   
  92. On the fundamental theorem of algebra I, II.
    J. G. van der Corput
    Nederl. Akad. Wetensch., Proc. 49, (1946) 722--732, 878--886 =Indagationes Math. 8, 430--440, 549--557 (1946), MathSciNet.   
  93. One More Proof of the Fundamental Theorem of Algebra (in Mathematical Notes)  
    N. C. Ankeny  
    American Mathematical Monthly, Vol. 54, No. 8. (Oct., 1947), p. 464, Jstor.  
  94. An Elementary Constructive Proof of the Fundamental Theorem of Algebra  
    P. C. Rosenbloom  
    American Mathematical Monthly, Vol. 52, No. 10. (Dec., 1945), pp. 562-570, Jstor.  
  95. The "fundamental theorem of algebra" for quaternions"
    Samuel Eilenberg; Ivan Niven  
    Bull. Amer. Math. Soc. 50, (1944). 246--248, MathSciNet.   
  96. Exercise on the fundamental theorem of algebra (Norwegian)  
    Carl Størmer  
    Norsk Mat. Tidsskr. 24, (1942). 33--42, MathSciNet.   
  97. A comment on the essay "The fundamental theorem of algebra and intuitionism"
    D. van Dalen
    Math. Z. 46 (1940), 287--302, MathSciNet.   
  98. A Proof of the Fundamental Theorem of Algebra (in Questions, Discussions, and Notes)  
    R. P. Boas, Jr.  
    American Mathematical Monthly, Vol. 42, No. 8. (Oct., 1935), pp. 501-502, Jstor.  
  99. On the Fundamental Theorem of Algebra  
    W. Paul Webber  
    Mathematics News Letter, Vol. 7, No. 5. (Feb., 1933), pp. 9-13, Jstor.  
  100. On Certain Proofs of the Fundamental Theorem of Algebra  
    Robert E. Moritz  
    American Mathematical Monthly, Vol. 10, No. 6/7. (Jun. - Jul., 1903), pp. 159-161, Jstor.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004