Integer Sequences (Math 19, Fall 2019)

Instructor: Igor Pak
pak@math.ucla (add .edu at the end, see more on the bottom of this page)

Class schedule: Thu 10:00 - 10:50 pm, MS 6221

Office Hours: Thu 11-11:50, MS 6125

CCLE site: here. (includes class description and reading)

Weekly seminars:

• Week 1: The story of OEIS (see also Wikipedia article). Reading:
  • NJA Sloane's article, Sections 1-6 (first 5 pages).
  • J. Borwein and K. Devlin book, Chapter 1 (pages 7-24)

• Week 2: Inverse Symbolic Calculator. Fibonacci numbers (OEIS A45, Wikipedia). Reading:
  • J. Borwein and K. Devlin book, pages 40-45, 132-135.
  • A. Posamentier and I. Lehmann, "The fabulous Fibonacci numbers", pages 17-20, 25-32.
    (download Chapter 1 from CCLE website, Week 2).
• Week 3: Catalan numbers (OEIS A108, Wikipedia). Reading:
  • M. Gardner, Catalan Numbers, Scientific American (June 1976).
  • I. Pak, History of Catalan numbers, an appendix to Richard Stanley, Catalan Numbers, Cambridge Univ. Press, 2015, 177-189.
• Week 4: No reading.

• Week 5: Partition numbers (OEIS A41, Wikipedia). Reading:
  • L. Debnath A brief history of partitions of numbers, partition functions and their modern applications, Sec. 2 (pp. 337-339)
  • G.H. Hardy, Ramanujan. Twelve lectures on subjects suggested by his life and work, pages 1-7; see CCLE website.

• Week 6: No new reading.

• Week 7: Somos sequence (OEIS A6720, Wikipedia). Reading:
  • D. Gale, The Strange and Surprising Saga of the Somos Sequences.

• Week 8: Lozenge tilings of a hexagon and solid partitions (OEIS A8793, OEIS A5130, Wikipedia articles on plane partitions and on ASMs). Reading:
  • F. Ardila and R. Stanley, Tilings, pp. 32-36 (middle of right column), and bottom of 39, left 40.
  • D. Keating and A. Sridhar, Random tilings with the GPU, Sections I, II and V.

Grading:

This is a P/NP seminar. The grading is based on attendance and participation.

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Last updated 11/29/2019.