Change of email address:

My old and standard email address alias: dummit at math “dot” uvm “dot” edu, is being discontinued. Please contact me at the address: david “dot” dummit at uvm “dot” edu instead.

Errata File for textbook “Abstract Algebra” by Dummit and Foote, 3rd edition

The version of the errata here is a backup and may not be the most recent version; the most recent errata files for the textbook are maintained by Richard Foote and can be found at https://site “dot” uvm “dot” edu /rfoote/

Files Related to Quintics

Description: Quintics.nb is a Mathematica notebook containing data from “Solving Solvable Quintics” (Math. Comp. 57 (July 1991) and Supplement in 59 (1992)).

Notebook includes definitions of all parameters from the paper in terms of coefficients p,q,r,s of a quintic (whose x4 term is 0). At the end of the notebook is some code to explicitly solve for the roots of the quintic numerically (and the code can be modified easily to produce the exact algebraic values of the roots in terms of radicals).

Description: This is an Adobe PDF file containing the solution of Ramanujan’s quintics (problem 699) explicitly in terms of radicals.

Description: This is an Adobe PDF file containing the paper “Solving Solvable Quintics”, Math. Comp. 57 (no. 195), 1991, pp. 387-401.

Errata: (April 25, 2021) In the second example (on page 399), the coefficient of x^3 in the resolvent sextic should be -20000, not +20000. (With thanks to Saim UYANIK for pointing out this error).

Errata: (October 27, 2021) In the third example (on page 400), the constant term in the resolvent sextic should be -360260685644469671875 [one digit longer, with three consecutive 4’s, not two]. (With thanks to David BROSH for pointing out this error).

Note the Appendix mentioned in the paper appeared as a Corrigendum (on microfiche) in a later issue of the journal and appears below.

Description: This is an Adobe PDF file containing the content of an email from Robin Chapman (dated Wednesday, January 22, 1992) that corrects a gap in the proof of Theorem 1 of “Solving Solvable Quintics”. In Theorem 1 of the paper, it is stated that a polynomial (whose roots are the θi for i = 2,3,…,6) is irreducible because the Galois group acts transitively on the roots. This is correct unless all of the θi for i = 2,3,…,6 are equal. This note proves that this cannot happen for the choice of θi in the paper.

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