For a copy of the course syllabus, click here

Homework 1 (To be turned in Monday, September 8).

• Page 20-22, #12, 18, 20.

• Page 30, #34.

• Page 39-40, #44, 56.

• Page 57-59, #12, 18, 24.

• Page 65-66, #30, 34, 36, 38.

• Click for a note on uses of Bayes's theorem to testing (medical, drug, etc.).

• Here is an article appearing in the Telegraph newspaper about ``false positives''. It will make you think twice about testing results! Click here for a link to a Nature article on this.

Homework 2 (to be turned in Monday, September 22).

• Page 74-75, #46, 50, 52, 56, 60.

• Page 80, #70, 72, 74, 76, 78.

• Page 89-90, #1, 4, 8.

• Page 98-99, #12, 14, 18, 20.

• Page 106-107, #30, 32, 34, 36, 38.

• Click for a copy of notes on Bayesian spam filtering (in the note the set Sigma is the set of events).

• **** I have scheduled your first exam for Monday, Sept. 15. **** It will cover all material up to and including section 3.2 (which we have yet to get to). Click for an old Math 3225 exam, a few of the questions from which would be appropriate for your first exam. Click for a copy of another 3225 exam (don't worry if the questions look too hard -- I will post a study sheet at the level of Math 3770 soon.). And, here is another.

• Click for an old note I wrote (for an honors version of our class) on the ``birthday paradox''. In this note, Sigma denotes the set of events -- it is the set of subsets of the sample space S.

• Click for a fascinating article on the misuse of math in criminal cases (unjustified independence assumptions and the prosecutor fallacy), written by Keith Devlin, mathematician and regular on NPR's Weedkend Edition.

• Click for a link to Simpson's paradox and baseball scores (the Derek Jeter and David Justice example from class today).

• Remember the random triangle example from the beginning of class on Monday, Sept. 8? Click for a webpage about it.

• Click here for a copy of some selected solutions to the homework you just turned in.

• Click for an article by AICPA (American Institute of Certified Public Accountants) on how accountants can use Benford's Law (the leading digit law from class today) to detect fraud.

• Info about your exam: There will be 5 questions. One will be a definition question (you will be asked to define 5 terms). One will be a proof (you will be asked to verify a simple probability identity). One will be a tricky combinatorial problem about drawing marbles from a bag. One will be a tricky Bayes's theorem question. And one will be a problem on statistics. I will let this info, and the info presented in class today, stand in for a ``study sheet'' for your exam.

• Click for a note on Zipf's Law from class today -- the empirical law about the ranking of English words.

Homework 3 (due Monday, Oct. 6).

• Page 113-114, #46, 48, 50, 52, 54.

• Page 120-121, #68, 70, 72, 74.

• Page 125-126, #80, 82, 86, 92.

• Page 135-136, #1, 2, 3, 4, 10.

• Page 143-144, #12, 14, 22.

• Click for a note on the ``Feigenbaum constant'' from class today. Click for another webpage about ``bifurcation diagrams'' that come up in determining the Feigenbaum constant.

• Click for a link to the Google Tech talk given by our own Vijay Vazirani.

• here for an article about ``the wisdom of crowds'' from class today. Here is another webpage about it.

• Here is a Youtube video of fireflies in Sync. Here is a link to a webpage about Steven Strogatz's work. Here is an article about Kirkwood gaps.

• Click for an article about Marian Rejewski from class today.

• Click for a copy of the solutions to exam 1.

• Click for a link about Jonathan Farley's work on catching terrorists using mathematics (i.e. probability theory).

• Click for a note on how to solve the ``two slips of paper'' problem from the beginning of class today.

• Click for a lecture note on Poisson random variables. Basically, it contains material I presented in class that is not covered in your book.

• Click for the ``two portfolios'' problem from the beginning of class today.

Homework 4 (Monday, October 20).

• Page 154-155, #28, 36.

• Page 162-163, #60, 62, 64, 68.

• Page 194-196, #2, 4, 15.

• Page 201-202, #24, 26, 28.

• For a link about the Google Pagerank Algorithm, and a discussion of the probability theory it uses, click here .

• Click for a copy of some notes I typed up on the chi-squared random variable. Much of the material is not in your book.

• Click for a survey article on using Hidden Markov Models (a particularly common type of statistical model) to do speech recognition. Although the article is quite old (written in 1989), it is a classic and gives a good introduction to the subject. Click here for an article on uses of HMM's in biology.

• Click for an article on statistics, prime numbers, and energy levels of atoms. Click here for another note on this.

• Click for an article on John Scott Russell and solitions. Click here for an amazing video of a Falaco Soliton (a type of topological soliton) in a swimming pool. Go here for an article about a solition found in the upper atmosphere.

• Click for a nice Wikipedia article on the counterintuitive Banach-Tarski Paradox (one small correction to the Wikipedia article: The five sets in the sphere decomposition can be chosen so that they are each ``connected sets'', not mere ``infinite scatterings of points''. This was shown by deGroot and Dekker way back in 1956.).

• Click for a rather technical Wikipedia article on the Black-Scholes model, a very useful statistical model to price options. Click here for an article titled ``Don't blame the quants'', which concerns recent economic troubles and quants' role in them. Click here for an MIT Technology Review article on the subprime crisis and quants (registration required). Here is another link to this article which may work without registration.

Homework 5 (due Wednesday, November 5).

• Page 218, #46, 48.

• Page 240, #2, 4.

• Page 251-252, #20, 22, 29.

• Click for an article about a statistical model that predicts why some traffic jams form for no apparent reason. Click here for the article I mentioned in class about the Biham-Middleton-Levine Traffic Model. It concerns how interesting patterns emerge as traffic exceeds a certain critical threshold of around 32 to 34 percent full.

• Click for an article on the clouds of Saturn distributed as a hexagon. Click here for an article about strange Earth hurricane eyewall shapes, in particular hurricane Isabel. Click here for a fascinating article on the Great Red Spot of Jupiter by James Gleick, author of the book Chaos: The Making of a New Science. Click here for a link about the upcoming Nova episode about fractal geometry.

• I have finished writing up the lecture note on moment generating functions, which is a topic not covered in your book. Click here for a copy of these notes.

• I have also written up a lecture note on applications of the central limit theorem, including the hypothesis testing example from class about smokers (taking into account Benjamin Davis's comments). This note also has some material on Maximum Liklihood Estimates, which we haven't yet gotten to. Click here for a copy of this lecture note.

• I will be speaking this weekend (Saturday Oct. 25) at a math conference on somewhat recent research of mine (and A. Granville, R. Pemantle, and P. Tetali) on rigorous analysis of ``integer factoring algorithms'' (which are used to break certain cryptosystems). Since this is probability-related, I will mention it in class today. Here is a copy of our paper on this. It is a bit technical, but perhaps you will be able to read the introduction.

• I have scheduled your second exam for Monday, Nov. 10 . I have decided to allow you to bring a non-scientific calculator to the exam. Also, I have decided to make at least one of your exam questions the same as one of your homeworks, verbatim; and maybe I will take two of the questions from HWs -- I haven't decided yet. One of your questions will be a definition, and one will be an easy proof. The remaining question(s) will be calculations. I hope that the median score will be much higher for this exam than it was for the first one.

• Click for a copy of the Geman and Geman article on using a ``Gibbs Sampler'' to do image reconstruction. Click here for a link to Gary Miller's work on image segmentation. Click here for a copy of the paper by Miller and Tolliver.

• Click here for an interesting Youtube video about the a mathematics child prodigy, who happens to also be the son of the former Georgia Tech math grad student Mark Ladue (who studied under Bill Green).

• Michael Barnsley was once a professor of math at Georgia Tech, and was a pioneer in the use of randomness and fractals to do image compression (he founded the company Iterated Systems Incorporated). Click here for a Wikipedia entry related to his work. Click here for Barnsley's homepage (at Australian National University).

• Click for a copy of the study sheet for the exam.

• Click for a link about the Rhind Papyrus that I spoke about on Halloween -- basically, one of the oldest math ``textbooks'' at the time of its discovery, copied by the Scribe Ahmes. The scribes studied language and mathematics, and worhiped the god Thoth, click here for info.

• While looking through the TED foundation website the other day, I came across an interesting online video about the use of statistics in genetics and in court cases (basically, the things we discussed early in the course). Click here for this fascinating video. (And here is one of my favorite non-math TED talks.)

• Here are three articles on Daniel Bernoulli's work on the epidemiology of smallpox: 1. 2. 3.

Homework 6 (due Friday, Nov. 21).

• Page 262, #2, 3.

• Page 269, #14.

• Page 276-277, #28, 32, 34, 36.

• Page 293, #2, 4.

• Page 304, #16, 18.

• Page 310, #36.

• Page 317, #46.

• Page 465, #12.

• Click for a note on one of the early ``branching processes'', called the Galton-Watson process, which concerns the loss of noble surnames through time (it was worked out in the late 19th century). Click here for some applications to nuclear physics.

• Click for a paper on some applications of probability theory to a certain inventory problem in systems engineering. Here is a paper with a few algorithms (not as mathematical as the first one).

• Most people I have talked with have said that they think the exam today was quite a bit more difficult than the first one. I certainly tried to make it easier than the first exam (the questions on this one are more standard and basic), though maybe because there was so much material to study, and because you didn't have enough time, you didn't perform as well as you would have otherwise. If it is the case that the median score is lower than 80, then I will curve the exam by adding enough points to everyone's score to bring the median up to 80.

Homework 7 (turn it in with the final exam).

• Page 475, #30.

• Page 492, #58.

• Page 483, #44.

I have decided to make the final exam optional for everyone; HOWEVER, you will not be allowed to keep the 27.5 curve on the second exam. If you wish to avoid taking the final, you must use a curve of 18 points; and, your grade if you skip the final will be computed as follows: Final grade = (2/7)(Exam1 + Exam2 + 18) + (3/7)(Homework grade). So, if you got a 60 on the first exam, and 65 on the second (pre-curve), and a grade of 90 on the HW, the grade you would get if you didn't take the final is (2/7)(60 + 65 + 18) + (3/7)(90) = 79.429, which is a C. Of course, if you DO take the final, then you get to use the curve of 27.5 points.

*** Your final exam is scheduled for Wednesday, Dec. 10 from 11:30 - 2:20 ***

I came across an interesting article by the CS titan Edsger Dykstra, which you can view here .

Click here for a copy of the final exam.