UPDATED MARCH 11, 2015
Freshman Seminar-WINTER 2015-EVOLUTION ALGEBRA
Tuesday 11:00-11:50 AM 1420 Donald Bren Hall (DBH1420) 11:00-11:50 AM
(syllabus}
NOTES for January 6, 2015, covering DICKSON, pp. 1-6 and REED, pp.107-108 (pdffile)
(References follow)
L.E.Dickson, "Linear Algebras", Cambridge Tracts in Mathematics and Mathematical Physics, No. 16, 1914.
(73pp---only pages 1-6 were scanned) (pdffile)
Mary Lynn Reed, "Algebraic Structure of Genetic Inheritance", Bulletin of the American Mathematical Society, Volume 34, 1997, pp. 107-130
(pdffile)
For more background in genetics (if you want it), see the next three files (which can also be safely ignored).
(The History of Genetics) chapter 1 of Barbara Wexler, "Genetics and Genetic Engineering" 2009 (pdffile)
(Understanding Genetics) chapter 2 of Barbara Wexler, "Genetics and Genetic Engineering" 2009 (pdffile)
"Cliff Notes" (for the previous file)
(Understanding Genetics) chapter 2 (pdffile)
NOTES for January 13, 2015, Review of DICKSON, pp. 1-6 and REED, pp.107-108; new material: REED, pp. 109-110
(References follow) (pdffile)
"Cliff Notes"
for the beginning of the following two books: Hartl-Clark and Ayala-Kiger (available in the Ayala Science Library when I return them!---There are many similar books on the same shelf)
(pdffile)
Principles of Population Genetics, 1997, by Daniel L. Hartl and Andrew G. Clark, Third Edition (Ayala Science Library)
Modern Genetics, 1980, by Francisco J. Ayala and John A. Kriger
(Ayala Science Library)
NOTES for January 20, 2015, Gametic and Zygotic Algebras (Etherington 1939,1941) and Derivations (Russo Transfer Seminar 2012)
(References follow) (pdffile)
I. M. H. Etherington, "Genetic Algebras" Proc. Royal Soc. Edinburgh, volume 59, 1939, pp.242-258
(pdffile-for viewing)
I. M. H. Etherington, "Genetic Algebras" Proc. Royal Soc. Edinburgh, volume 59, 1939, pp.242-258
(pdffile-for printing)
I. M. H. Etherington, "Non-associative algebra and the symbolism of genetics" Proc. Royal Soc. Edinburgh, volume 61, 1941, pp.24-42
(pdffile)
Bernard Russo, ``Playing havoc with the product rule'', Transfer Seminar Fall 2012
(pdffile)
NOTES for January 27, 2015, Review of Derivations; new material: bracket product, axiomatic approach, Lie algebras (skip circle product and Jordan algebras)
(No new references) (pdffile)
NOTES for February 3, 2015, Evolution Algebras, TIAN parts of chapters 2,3,5
(References follow) (pdffile)
Evolution Algebras and their Applications, 2008, by Jianjun Paul Tian, Lecture Notes in Mathematics No. 1921 (Ayala Science Library)
TIAN Chapter 2
(pdffile)
TIAN Chapter 3
(pdffile)
TIAN Chapter 5
(pdffile)
TIAN References
(pdffile)
SOME RESOURCES FOR TERM ESSAYS
Books on genetics from the Ayala Science Library (Ayala Science Library)
Evolution Algebras and Markov Chains (TIAN Chapter 4)
(pdffile)
Derivations on Jordan and Lie algebras (The Fullerton Lectures)
(pdffile)
Mathematical Research Papers on Genetic Algebras (From Tian's Lecture Notes)
(here)
Mathematical Research Papers on Genetic Algebras and Evolution Algebras (not cited in, or appearing after, Tian's Lecture Notes)
(here)
NOTES for February 10, 2015, Algebras with Genetic Realization REED Section 3, pp.111-114, Discussion of term-essay resources
(pdffile)
NOTES for February 17, 2015, Bernstein Algebras, REED Section 3, pp.118-120 (references follow); More discussion of term-paper resources.
(pdffile)
[2] S. Bernstein, Demonstration mathematique de la loi d'heredite de Mendel
Comptes Rendus Acad. Sci. Paris 177 528-531 1923
(article)
[3] S. Bernstein, Principe de stationarite et generalization de la loi de Mendel
Comptes Rendus Acad. Sci. Paris 177 581-584 1923
(article)
[4] S. Bernstein, Solution of a mathematical problem connected with the theory of heredity
Ann. Sci. de l'Ukraine 1924 (translated from Russian) 9pp.
(article)
[25] Holgate, P. Genetic algebras satisfying Bernstein's stationarity principle
Journal of London Math. Soc (2) 9: 613-623
(article)
(REVIEW)
[21] I.R. Hentzel, L.A. Peresi, and P. Holgate,
On k-th order Bernstein algebras and stability at the k+1 generation in polyploids, IMA J. of Math. Appl. in Med. and Biology 7 33-40 1990
(article)
(REVIEW)
NOTES for February 24, 2015, Derivations on Genetic Algebras (references follow)
(pdffile)
Mathematical Research Papers on Derivations of Genetic Algebras
(here)
Bingham, N. H. Obituary: Philip Holgate (1934-1993). Bull. London Math. Soc. 32 (2000), no. 4, 484-492
(article)
NOTES for March 3, 2015, Derivations on Bernstein Algebras (references follow)
(pdffile)
TERM PAPER OPTIONS AND SUGGESTIONS
(here)
Mathematical Research Papers on Bernstein algebras
(here)
Mathematical Research Papers on Derivations on Bernstein Algebras
(here)
Miscellaneous Mathematical Research Papers on Genetic Algebras
(here)
Mathematical Papers on Genetic Algebras, from "Nonassociative algebra and its applications" University of Sao Paulo, Brazil 1998
(here)
Mathematical Papers on Genetic Algebras, from "Nonassociative algebra and its applications" University of Oviedo, Spain 1994
(here)
Mathematical Papers from "Colloque de Montpellier July 7-11, 1989" ALGEBRES GENETIQUES; and other longer papers in French
(here)
NOTES for March 10, 2015, Three proofs of earlier statements
(pdffile)