3225_syllabus_2010 - variance distributions law of large...

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Syllabus for Math 3225, Honors Probability and Statistics, Fall 2010 August 24, 2010 Instructor: Ernie Croot Ofce: 103 Skiles Ofce Hours: TBA Place and Date oF Classroom: MWF, 1:05 - 1:55 in Skiles 271. Book: Probability and Random Processes, 3rd Edition , by Grimmet and Stirzaker. Grade: You grade will be based on 20% for each of two midterms, 30% homework, and 30% for the ±nal exam. Homeworks will be collected about once every two weeks. Material: Though you have a required text for this class, I will mostly be using my own notes, which I will post on the website occasionally. The book should be seen as a place to ±nd more elementary explanations of some of the ideas – to consult when you don’t understand something from the lecture, study for exams, or to complete some of the homeworks. In this course we will work through the foundations of probability the- ory, such as set theory, measure theory, conditional probability, expectation,
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Unformatted text preview: variance, distributions, law of large numbers, central limit theorem, and so on. You will be required to understand and develop proofs as part of your homework. We will also work through some interesting, exciting applications of the theory, such as applications to number theory, Bayesian spam ±ltering, sta-tistical sampling and inference, Bayesian Networks and their application to arti±cial intelligence, and perhaps Hidden Markov Models with applications to gambling and speech recognition. 1 Puzzles and Paradoxes will also be discussed occasionally. Probability theory is full of them – it is interesting just how often our intution can lead us astray! I also plan to talk about the history behind some of the ideas. For exam-ple, who some of the people were, what contexts they operated in, and what impact their ideas have had on the ±eld. 2...
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3225_syllabus_2010 - variance distributions law of large...

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