• 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)