Bibliography for Complex Roots of Polynomials

short

 

  1. The simultaneous approximation of polynomial roots.
    Niell, A. M.
    Comput. Math. Appl. 41 (2001), no. 1-2, 1--14, MathSciNet.  
  2. 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.
  3. Fundamental theorem of albegra - yet another proof  
    Anindya Sen  
    The American Mathematical Monthly Nov 2000 v107 i9 p842(2), Expanded Academic.  
  4. Algebraic geometry and computer vision: Polynomial systems, real and complex roots
    Petitjean, S.
    Journal of Mathematical Imaging and Vision, v 10, n 3, 1999, p 191-220, Engineering Village.
  5. The Newton and Halley methods for complex roots  
    Yau, Lily; Ben-Israel, Adi  
    Amer. Math. Monthly 105 (1998), no. 9, 806--818, MathSciNet.  
  6. The Fundamental Theorem of Algebra  
    Michael D. Hirschhorn  
    College Math Journal: Volume 29, Number 4, (1998), Pages: 276-277.   
  7. Bounding the Roots of Polynomials (in Classroom Capsules)  
    Holly P. Hirst; Wade T. Macey  
    The College Mathematics Journal, Vol. 28, No. 4. (Sep., 1997), pp. 292-295, Jstor.  
  8. Solving a Polynomial Equation: Some History and Recent Progress  
    Victor Y. Pan  
    SIAM Review, Vol. 39, No. 2. (Jun., 1997), pp. 187-220, Jstor.  
  9. A Proof That Polynomials Have Roots  
    Uwe F. Mayer  
    College Math Journal: Volume 28, Number 1, (1997), Pages: 58.   
  10. Why Polynomials Have Roots  
    Javier Gomez-Calderon; David M. Wells  
    The College Mathematics Journal, Vol. 27, No. 2. (Mar., 1996), pp. 90-94, Jstor.  
  11. A Geometric Interpretation of the Solution of the General Quartic Polynomial  
    William M. Faucette  
    American Mathematical Monthly, Vol. 103, No. 1. (Jan., 1996), pp. 51-57, Jstor.  
  12. Polynomial roots: the ultimate answer?
    Brugnano, L.; Trigiante, D.
    Linear Algebra Appl. 225 (1995), 207--219, MathSciNet.  
  13. Cubic Equations, or Where Did the Examination Question Come From    
    H. B. Griffiths; A. E. Hirst  
    American Mathematical Monthly, Vol. 101, No. 2. (Feb., 1994), pp. 151-161, Jstor.  
  14. Polynomial Root Dragging (in Notes)  
    Bruce Anderson  
    American Mathematical Monthly, Vol. 100, No. 9. (Nov., 1993), pp. 864-866, Jstor.  
  15. Root distribution of a polynomial in subregions of the complex plane
    Tsai, Jason S.H.; Chen, Shyan S.
    IEEE Transactions on Automatic Control, v 38, n 1, Jan, 1993, p 173-178, Engineering Village.
  16. The pth Root of an Analytic Function (in Notes)  
    Lawrence J. Wallen  
    Mathematics Magazine, Vol. 65, No. 4. (Oct., 1992), pp. 260-261, Jstor.  
  17. Infinitely Many Different Quartic Polynomial Curves  
    Nitsa Movshovitz-Hadar; Alla Shmukler  
    The College Mathematics Journal, Vol. 23, No. 3. (May, 1992), pp. 186-195, Jstor.  
  18. Cubics with a Rational Root (in Notes)  
    William C. Schulz  
    Mathematics Magazine, Vol. 64, No. 3. (Jun., 1991), pp. 172-175, Jstor.  
  19. Inclusion of multiple polynomial roots in complex rectangular arithmetic.
    Petkovi'c, M. S.; Herzberger, J.
    Computer arithmetic, scientific computation and mathematical modelling (Albena, 1990), 367--375, IMACS Ann. Comput. Appl. Math., 12, Baltzer, Basel, 1991, MathSciNet.  
  20. Determining Roots of Complex Functions with Computer Graphics  
    Kowalski, Robert; Helen Skala  
    Coll. Micro., (1990), V. VIII, No.1, pp. 51-54.
  21. Finding Rational Roots of Polynomials (in Classroom Capsules)  
    Don Redmond  
    The College Mathematics Journal, Vol. 20, No. 2. (Mar., 1989), pp. 139-141, Jstor.  
  22. 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.  
  23. Graphical Representation of Complex Function  
    Renka, Robert J. and Floyd Vest  
    Math. and Comp. Ed., (1988), V. 22, No. 1, pp. 33-45.  
  24. Graphing the Complex Roots of a Quadratic Equation  
    Floyd Vest  
    The College Mathematics Journal, Vol. 16, No. 4. (Sep., 1985), pp. 257-261, Jstor.  
  25. Picturing Functions of a Complex Variable (in Computer Corner)  
    Bart Braden  
    The College Mathematics Journal, Vol. 16, No. 1. (Jan., 1985), pp. 63-72, Jstor.  
  26. Roots of unity revisited  
    Denton, Brian  
    The Math. Gazette, (1985), V. 69, No. 447, pp. 17-20.
  27. Complex Roots Made Visible (in Classroom Capsules)  
    Alec Norton; Benjamin Lotto  
    The College Mathematics Journal, Vol. 15, No. 3. (Jun., 1984), pp. 248-249, Jstor.  
  28. Using an Interactive Computer Program in the Calculus Classroom to Find Complex Roots of Polynomial Equations  
    Sorkin, Sylvia  
    Math. and Comp. Ed., (1984), V. 18, No. 2, pp. 93-99.
  29. 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.  
  30. Measuring Complex Roots  
    Farnsworth, David  
    Math. and Comp. Ed., (1983), V. 17, No. 3, pp. 191-194.
  31. Those elusive imaginary zeros  
    Kim, David;  Robert Travers  
    The Math. Teach., (1982), V. 75, pp. 62-64.
  32. Computers and the Multiplicity of Polynomial Roots  
    John J. Wavrik  
    American Mathematical Monthly, Vol. 89, No. 1. (Jan., 1982), pp. 34-36+45-56, Jstor.  
  33. 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.  
  34. 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.  
  35. Luddhar's Method of Solving a Cubic Equation with a Rational Root  
    R. S. Luthar  
    The Two-Year College Mathematics Journal, Vol. 11, No. 2. (Mar., 1980), pp. 107-110, Jstor.  
  36. A proof of the fundamental theorem of algebra (Spanish)
    José Manuel Bayod  
    Gac. Mat. (Madrid) (1) 29 (1977), no. 5-6, 107--110, MathSciNet.   
  37. The Fundamental Theorem of Algebra (in Classroom Notes)  
    Frode Terkelsen  
    American Mathematical Monthly, Vol. 83, No. 8. (Oct., 1976), p. 647, Jstor.  
  38. The Influence of Practical Arithmetics on the Algebra of Rafael Bombelli (in Documents & Translations)  
    S. A. Jayawardene; Di Rafael Bombelli  
    Isis, Vol. 64, No. 4. (Dec., 1973), pp. 510-523, Jstor.  
  39. The Solution of a Certain Quartic Equation  
    B. Fisher  
    Mathematics Magazine, Vol. 45, No. 2. (Mar., 1972), pp. 97-98, Jstor.  
  40. The Quadratic Polynomial and Its Zeros (in First- or Second-Year Transfer)  
    C. A. Long  
    The Two-Year College Mathematics Journal, Vol. 3, No. 1. (Spring, 1972), pp. 23-29, Jstor.  
  41. A Note on the Geometry of Zeros of Polynomials  
    C. A. Long  
    Mathematics Magazine, Vol. 44, No. 3. (May, 1971), pp. 157-159, Jstor.  
  42. The Fundamental Theorem of Algebra  
    Paul J. Campbell  
    Pi Mu Epsilon J., (1967), V. 4, No. 6, pp. 243-247.   
  43. 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.  
  44. 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.  
  45. On the Fundamental Theorem of Algebra  
    Hans Zassenhaus  
    American Mathematical Monthly, Vol. 74, No. 5. (May, 1967), pp. 485-497, Jstor.  
  46. A Numerical Method for Locating the Zeros of an Analytic Function  
    L. M. Delves; J. N. Lyness  
    Mathematics of Computation, Vol. 21, No. 100. (Oct., 1967), pp. 543-560, Jstor.  
  47. 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.  
  48. 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.  
  49. A Method for the Real and Complex Roots of a Polynomial  
    Van A. McAuley  
    Journal of the Society for Industrial and Applied Mathematics, Vol. 10, No. 4. (Dec., 1962), pp. 657-667, Jstor.  
  50. On the Utility of Newton's Method for Computing Complex Roots of Equations (in Technical Notes and Short Papers)  
    I. M. Longman  
    Mathematics of Computation, Vol. 14, No. 70. (Apr., 1960), pp. 187-189, Jstor.  
  51. 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.  
  52. Complex Roots of Real Polynomials (in Classroom Notes)  
    J. P. Ballantine  
    American Mathematical Monthly, Vol. 66, No. 5. (May, 1959), pp. 411-414, Jstor.  
  53. The Probability That the Roots of a Real Quadratic Equation Lie Inside or on the Circumference of the Unit Circle in the Complex Plane  
    Joseph W. Andrushkiw  
    Mathematics Magazine, Vol. 32, No. 3. (Jan. - Feb., 1959), pp. 123-128, Jstor.  
  54. The Fundamental Theorem of Algebra (in Mathematical Notes)  
    Raymond Redheffer  
    American Mathematical Monthly, Vol. 64, No. 8. (Oct., 1957), pp. 582-585, Jstor.  
  55. Polynomial Root Solving on the Electronic Differential Analyser (A Technique for Finding the Real and Complex Roots of a Polynomial Using an Electronic Differential Analyser)  
    Cyril Atkinson  
    Mathematical Tables and Other Aids to Computation, Vol. 9, No. 52. (Oct., 1955), pp. 139-143, Jstor.  
  56. Complex Roots of an Integral Rational Equation (in Classroom Notes)  
    D. Trifan  
    American Mathematical Monthly, Vol. 61, No. 9. (Nov., 1954), pp. 640-641, Jstor.  
  57. The Fundamental Theorem of Algebra (in Mathematical Notes)  
    S. Stein  
    American Mathematical Monthly, Vol. 61, No. 2. (Feb., 1954), p. 109, Jstor.  
  58. 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.  
  59. Deduction of Cardano's Formula by Conformal Mapping (in Mathematical Notes)  
    C. F. Moppert  
    American Mathematical Monthly, Vol. 59, No. 5. (May, 1952), pp. 310-314.
  60. 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.  
  61. 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.  
  62. The Determination of the Complex Zeros of A Polynomial  
    G. C. Best  
    American Mathematical Monthly, Vol. 54, No. 5. (May, 1947), pp. 269-273, Jstor.  
  63. 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.  
  64. Graphical Solutions for Complex Roots of Quadratics, Cubics and Quartics  
    George A. Yanosik  
    National Mathematics Magazine, Vol. 17, No. 4. (Jan., 1943), pp. 147-150, Jstor.  
  65. Graphical determination of real and complex roots of cubic equations. (Spanish)
    Babini, J.
    An. Soc. Ci. Argentina 134, (1942), MathSciNet.  
  66. Complex Roots of a Polynomial Equation  
    H. M. Gehman  
    American Mathematical Monthly, Vol. 48, No. 4. (Apr., 1941), pp. 237-239, Jstor.  
  67. A comparison of methods for evaluating the complex roots of quartic equations.
    Sharp, Henry S.
    J. Math. Phys. Mass. Inst. Tech. 20, (1941). 243--258, MathSciNet.  
  68. Sidelights on the Cardan-Tartaglia Controversy (in Humanism and History of Mathematics)  
    Martin A. Nordgaard  
    National Mathematics Magazine, Vol. 12, No. 7. (Apr., 1938), pp. 327-346, Jstor.  
  69. A Graphical Solution of the Cubic  
    H. B. Curtis  
    National Mathematics Magazine, Vol. 12, No. 7. (Apr., 1938), pp. 325-326, Jstor.  
  70. Graphical Representation of Complex Roots  
    James A. Ward  
    National Mathematics Magazine, Vol. 11, No. 7. (Apr., 1937), pp. 297-303, Jstor.  
  71. Graeffe's Method and Complex Roots (in Questions, Discussions, and Notes)  
    B. A. Hausmann  
    American Mathematical Monthly, Vol. 43, No. 4. (Apr., 1936), pp. 225-229, Jstor.  
  72. A Graphical Solution for the Complex Roots of a Cubic  
    George A. Yanosik  
    National Mathematics Magazine, Vol. 10, No. 4. (Jan., 1936), pp. 139-140, Jstor.  
  73. The Graphical Interpretation of the Complex Roots of Cubic Equations (in Questions, Discussions, and Notes)  
    Garcia Henriquez  
    American Mathematical Monthly, Vol. 42, No. 6. (Jun. - Jul., 1935), pp. 383-384, Jstor.  
  74. 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.  
  75. On the Fundamental Theorem of Algebra  
    W. Paul Webber  
    Mathematics News Letter, Vol. 7, No. 5. (Feb., 1933), pp. 9-13, Jstor.  
  76. On the Nature of the Roots of a Quartic Equation  
    Raymond Garver  
    Mathematics News Letter, Vol. 7, No. 4. (Jan., 1933), pp. 6-8, Jstor.  
  77. Enrique Cruchaga's Solution of the Quartic Equation (in Questions and Discussions)  
    Raymond Garver  
    American Mathematical Monthly, Vol. 37, No. 6. (Jun. - Jul., 1930), pp. 303-304, Jstor.  
  78. A Short Account of the History of Symmetric Functions of Roots of Equations  
    H. Gray Funkhouser  
    American Mathematical Monthly, Vol. 37, No. 7. (Aug. - Sep., 1930), pp. 357-365, Jstor.  
  79. The History of the Solution of the Cubic Equation  
    Lucye Guilbeau  
    Mathematics News Letter, Vol. 5, No. 4. (Dec., 1930), pp. 8-12, Jstor.  
  80. On the Numerical Solution of Equations with Complex Roots  
    R. A. Frazer; W. J. Duncan  
    Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, Vol. 125, No. 796. (Aug. 1, 1929), pp. 68-82, Jstor.  
  81. Discussions: A Solution of the Quartic Equation (in Questions and Discussions)  
    Raymond Garver  
    American Mathematical Monthly, Vol. 35, No. 10. (Dec., 1928), pp. 558-560, Jstor.  
  82. Discussions: A Criterion that a Cubic Equation has an Integral Root (in Questions and Discussions)  
    H. S. Vandiver  
    American Mathematical Monthly, Vol. 33, No. 2. (Feb., 1926), pp. 94-95, Jstor.  
  83. A Contribution of Leibniz to the History of Complex Numbers  
    R. B. McClenon  
    American Mathematical Monthly, Vol. 30, No. 7. (Nov., 1923), pp. 369-374, Jstor.  
  84. Graphical Discussion of the Roots of a Quartic Equation  
    E. L. Rees  
    American Mathematical Monthly, Vol. 29, No. 2. (Feb., 1922), pp. 51-55, Jstor.  
  85. Discussions: Resolution of a Certain Quintic Equation and a Geometrical Construction for its Roots (in Questions and Discussions)  
    C. B. Haldeman  
    American Mathematical Monthly, Vol. 27, No. 6. (Jun., 1920), pp. 257-258, Jstor.  
  86. Discussions: Relating to the Graph of a Cubic Equation Having Complex Roots (in Questions and Discussions)  
    Edwin S. Crawley  
    American Mathematical Monthly, Vol. 25, No. 6. (Jun., 1918), pp. 268-269, Jstor.  
  87. A Simple Method for Graphically Obtaining the Complex Roots of a Cubic Equation  
    Rutherford E. Gleason  
    The Annals of Mathematics, 2nd Ser., Vol. 11, No. 3. (Apr., 1910), pp. 95-96, Jstor.  
  88. On the Reciprocal Quartic Equation  
    R. L. Berger  
    American Mathematical Monthly, Vol. 15, No. 4. (Apr., 1908), pp. 85-87, Jstor.  
  89. Condition in Terms of the Invariants of the Quartic that its Four Distinct Root-Points be Concyclic  
    T. E. McKinney  
    American Mathematical Monthly, Vol. 14, No. 2. (Feb., 1907), p. 23, Jstor.  
  90. Approximation of the Greatest Root of a Cubic Equation with Three Real Roots  
    Charles Gilpin, Jr.  
    American Mathematical Monthly, Vol. 13, No. 6/7. (Jun. - Jul., 1906), pp. 140-141, Jstor.  
  91. 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.  
  92. On the Complex Roots of Numerical Equations of the Third and Fourth Degree  
    A. C. Burnham  
    American Mathematical Monthly, Vol. 4, No. 8/9. (Aug. - Sep., 1897), pp. 201-204, Jstor.  
  93. On the Solution of Cubic and Biquadratic Equations  
    G. W. Hill  
    The Analyst, Vol. 2, No. 1. (Jan., 1875), pp. 4-8, Jstor.  
  94. Solution of the Quartic Equation, x^4 + Ax + B = 0  
    A. M. Sawin  
    The Annals of Mathematics, Vol. 1, No. 1. (Mar., 1884), pp. 14-15, Jstor.  
  95. The Deduction of Final Formulas for the Algebraic Solution of the Quartic Equation  
    Mansfield Merriman  
    American Journal of Mathematics, Vol. 14, No. 3. (Jul., 1892), pp. 237-245, Jstor.  
  96. On a Soluble Quintic Equation  
    Prof. Cayley  
    American Journal of Mathematics, Vol. 13, No. 1. (Oct., 1890), pp. 53-58, Jstor.  

 

 

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