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ESE 520 – Probability and Stochastic Processes – Fall 2015Tu, Th 4:00 – 5:30 revised classroom:Mc Donnell, rm 162Instructor: Heinz Sch¨attler,Bryan, rm 229,extension 5-6019e-mail: [email protected] Hours: Tu Th, 3:00-4:0 0, and by appointmentPrerequisites:1. familiarity with calculus (series, integrals, change of variables, . . .);2. familiarity with mat rix calculations and fundamental results about positive semi-definite matrices (covariance matrices);3. a standard undergraduate course on probability, e.g., ESE 326 or any similar cal-culus based undergraduate course; we shall redo much of this material, but in amathematically more sophisticated and abstract way, and at a (really) fast pace.If you want to understand all the proo fs (but this is no t really necessary to do well inthe course), familiarity with the more fundamental concepts from “advanced” calculus isrequired, such as topological notions like open and closed sets in Rn, compactness, etc.Grading:There will be two exams given on Thursday, October 8 and Thursday, December 3.The second date is the last day of classes for this course and cannot be moved. Bothexams are during the class period in the classroom. Exams will be closed book, but youwill be allowed to bring in a cheat-sheet. Classroom notes or use of the textbook will notbe a llowed.Your grade will be based to 40% each on these exams and to 20% on graded solutionsto homework problems that will be assigned on a biweekly basis throughout the semester.I am planning to attend an out-of-town workshop in November and this would causeme to miss two classes, on Thursday November 19 and on Tuesday, November 24 (thisis during the Thanksgiving week). We shall need to make up for the missed class timeand thus need to schedule two additional class meetings and I would like to take careof this ASAP. Based on previous experiences, I expect that these may need to be onFriday afternoons. There will be exactly o ne week of classes left after the Thanksgivingbreak with lectures on Tuesday, December 1 a nd on Thursday, December 3. I will use theDecember 1 lecture for a general review and then give the final exam on December 3.Web page:There is a mini web page for this course accessible through my old homepage (which istotally out-dated, but still under my own control) atwww.ese.wustl.edu/~heinz/Fall15ese520.htmlI will only post handouts and other pertinent information such a s homework assignmentsthere and make a n effort to keep the info r ma tion up-to-da t e.e-mail:Please keep e-mails to essential communications. If you want to discuss course materialor have questions about class, please see me. Any time I am in is fine.Textbook: Probability and Random Processes f or Electrical and Computer Engineersby John A. Gubner,Syllabus and Other References:The first half of the course gives a (graduate course style) intro duction to probabilitytheory, the second part introduces fundamental concepts from stochastic processes. Sta-tistical methods are not covered in this course. For this we have a separate course, ESE524, that will be offered in the spring.Throughout the course the emphasis is on introducing concepts and ideas that areimportant to engineers (e.g., covariance functions, spectral density, white noise, etc.), butalso with some of the necessary mathematical rigor. The textbook contains much morematerial than can be covered in a one-semester course and, naturally, I will make selectionsand I also prefer to rearrange the material according to my taste. A detailed syllabuswhere I mar k sections of the textbook that relate to these topics is given separately.Essentially, everything we do in the course is also covered in the textbook. I highlyrecommend the wealth of worked out examples that I simply cannot cover in class for lackof time.Finally, the course has a theoretical flavor, but all the material we discuss is inher-ently related to real world practical applications, e.g., spectral densities and white noiserepresentations play a big ro le in your cell pho nes, Poisson processes have a lot to do withmedical imaging techniques. But this is a n introductory course and it would lead us toofar astray to get into those directions. I will try to mention some of these connections, butthese topics would only be developed in depth in more advanced and specialized


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