Syllabus for 640:338

To be updated during semester

  1. Tue 18 Jan: basic terminology from genetics, as needed from chapter 1; Section 3.2: allele and gene frequencies, random mating
  2. Thu 20 Jan: Section 3.3, one gene/two allele models; basic iterations, Hardy-Weinberg
  3. Tue 25 Jan: continued H-W; autosomal and sex-linked chromosome cases
  4. Thu 27 Jan: continued sex-linked chromosome case (pp 23-24), but with matrix approach (see also two additional sets of notes on difference equations)
  5. Tue 1 Feb: 3.3.5 mutations; 3.3.7 Wright-Fisher, introducing Markov Chains (see Maple example worked out)
  6. Thu 3 Feb: continuation
  7. Tue 8 Feb: Moran model (page 33)
  8. Thu 10 Feb: 3.4.2/3 model with selection (later we come back to 3.4.1 cobwebbing); derivation of model. Quiz 1: frequencies, monecious and diecious populations, X chromosome case
  9. Tue 15 Feb: analysis by cobwebing of model with selection
  10. Thu 17 Feb: 3.4.4 mean fitness increase for model with selection. Chapter 4: coverage in shotgun sequencing, Clarke-Carbon
  11. Tue 22 Feb: continue coverage in shotgun sequencing. Quiz2/3 (double quiz): matrix solutions of for linear difference equations, mutations, Wright-Fisher (using Markov chains) and Moran, model with selection, cobwebbing.
  12. Thu 24 Feb: estimate number of contigs; stochastic model for lengths Li in sequencing.
  13. Tue 1 Mar: finish stochastic model for lengths Li in sequencing; start restriction enzymes
  14. Thu 3 Mar: Continue restriction enzymes. Poisson approximation of binomial.
  15. Tue 8 Mar: Class officially cancelled because of snow (university closure).
  16. Thu 10 Mar: Exam 1.
    Tue 15 Mar: Spring Break
    Thu 17 Mar: Spring Break
  17. Tue 22 Mar: Poisson model of number of cuts. Exponential lengths. Thining. Partial and double digests.
  18. Thu 24 Mar: Residual and current life. Coverage probabilities for digest libraries.
  19. Tue 29 Mar: Characterization of Poisson processes (extra notes). Start Markov chains.
  20. Thu 31 Mar: Markov chains and graphs. Path probabilities.
  21. Tue 5 Apr: Multi-step transitions using powers of transition matrix. Start equilibrium distributions.
  22. Thu 7 Apr: Continue equilibrium distributions. Jukes-Cantor model for DNA evolution based on Markov chains. (Scanned section from a textbook.)
  23. Tue 12 Apr: (Class taught by Prof Ocone.) Chapter 6. The idea of a statistical hypothesis. The likelihood function, maximum likelihood estimates. (Illustrated with IID model for coin tossing and IID sites model for DNA.)
  24. Thu 14 Apr: Finish Jukes-Cantor, and mention Kimura model (from scan). Hypothesis testing.
  25. Tue 19 Apr: Likelihood ratio, chi-squared distribution.
  26. Thu 21 Apr: Testing for independence vs Markov. Scoring sequence alignments. 1/2 hour test (Poisson models for restriction enzymes, partial and double digests, Markov Chains)
  27. Tue 26 Apr: Continue scoring sequence alignments; start intro to dynamic programming, and applications to alignment.
  28. Thu 28 Apr: Continue dynamic programming and applications to alignment. 1/2 hour test (Markov chains, max likelihood estimation, hypothesis testing)
  29. Wed 11 May, 4:00PM to 7:00PM: final exam (tentative) VERY PROBABLY A TAKE-HOME.