M362M: Introduction to Stochastic Processes First-day Handout Fall - - PDF document

M362M first-day handout Page 1 of 5 DEPARTMENT OF MATHEMATICS UNIVERSITY OF TEXAS AT AUSTIN

M362M: Introduction to Stochastic Processes

First-day Handout Fall 2019 Caveat: This syllabus is subject to change; students who miss class are responsible for learning about any changes to the syllabus.

• I. COURSE-SPECIFIC INFORMATION

Welcome to M362M. Here is some information and some ground rules. Read carefully and let me know if there is anything unclear. Course number: M362M (53095) Class meets: RLM 5.104, MWF 10:00am - 11:00pm Flags: QR (quantitative reasoning) Instructor: Gordan ˇ Zitkovi´ c Instructor’s Office Hours: Mon, Wed, 1:00pm-2:00pm Instructor’s Office: RLM 11.132 Instructor’s E-mail: gordanz@math.utexas.edu (Please do not use e-mail for mathematical questions, those are reserved for office hours and are very difficult to answer through a typed message anyway. Also, you should not expect to have your e-mail replied to in fewer then 48-72 hours. Finally, as a rule, I will not answer any questions about the material the night before the exam.) Course Description/Learning Objectives: M362M is an undergraduate course on stochastic processes and

• applications. We focus on several classes of elementary stochastic processes which are often used in various

applications: random walks, branching processes, discrete Markov chains and, time permitting, the Poisson process and Brownian motion. The student will get acquainted with mathematical tools and techniques, as well as the probabilistic intuition necessary for understanding and successful use of stochastic models in a variety of applications within mathematics and in science, engineering, economics, etc. He/she will also learn how to build new models, in yet-unencountered situations and novel frameworks. Prerequisites: The formal prerequisite is the grade C- or better in M362K. Students are assumed to be at home with the basics of probability as presented in, e.g., Ross’s “First Course in Probability” or Pitman’s

M362M first-day handout Page 2 of 5 “Probability”; there will be a brief review. Also, a good working knowledge of calculus and linear algebra is assumed; no review will be given. To make sure you have a minimal amount of preparation, a diagnostic quiz focusing on discrete probability as well as basic mathematics will be administered before the 12th day of class. Textbook: There is no required textbook. Lecture notes written by the instructor will be posted on Canvas. The students in need of an additional source of problems (or explanation) are referred to the following books:

• 1. Essentials of Stochastic Processes by Rick Durrett (free, for now, at http://www.math.duke.edu/~rtd/

EOSP/EOSP2E.pdf),

• 2. Adventures in Stochastic Processes by Sidney I. Resnick
• 3. Introduction to Probability Models by Sheldon Ross.

Course webpage: The course-management system Canvas will be used in this course. Homework: A weekly or bi-weekly homework will be assigned (with the assignments posted on Canvas). The submission will be electronic, through Canvas. No paper submissions will be accepted. Your submission does not have to be typed - you can scan your hand-written work if you want. However, you need to upload your file in the pdf format. Submit well before the deadline - the system has been known to get “overwhelmed” close to it. If everything else fails, send your pdf file directly to the instructor (before the dealine!) with a detailed explanation of the problem. Late hw will not be accepted.

• 1. You are expected to write down the solutions and carefully explain your reasoning. Numerical answers,

without proper justification, will not be accepted. For computational problems, do not include your code. Do explain what methods/software you used and exactly what mathematical problem they were used to

• solve. For example, do not write

I used Mathematica to get the value 0.34 for the absorption probability. Instead, write something to the effect of By (statement from class) absorption probability is the entry (3, 4) in the fundamental matrix of the Markov chain X. The fundamental matrix itself is given by F = (I − Q)−1, where Q is . . . I used Mathematica to compute the matrix I − Q = . . . and then to invert it to get F = . . . The entry at position (3, 4) turns out to be 0.34.

• 2. You are allowed (and, in fact, encouraged) to work in groups and to submit a single document per group.

Do not forget to include the names of all group members. Special features:

• The lowest hw score (if there are ≤ 5 assignments) or the lowest 2 hw scores (if there are > 5 assignments)

will be dropped. Attendance: Attendance is not mandatory. It is, however, strongly recommended. Moreover, you are responsible for the material covered during your absence (and for informing yourself, presumably from your fellow students,

• f what that material is).

M362M first-day handout Page 3 of 5 Exams: There will be four exams/quizzes altogether.

• 1. A 50-min diagnostic quiz on prerequisites, and
• 2. Three 50-min in-term exams.
• 3. There will be NO FINAL EXAM!

The diagnostic quiz and the three in-terms will take place during regular class times and in the regular class auditorium (see p. 5 of this handout for the exact schedule). Even though the final exam date/time/place will be published by the university, simply disregard it. There will be no final exam. If you miss an in-term for a documented reason (illness, approved and previously announced religious holiday,

• r some other extraordinary circumstance), make-up arrangements will be made on a case-by-case basis.

The diagnostic quiz will contain basic mathematical skills and prerequisite knowledge. The in-terms will focus on the material covered since the last exam and will not be cumulative. What is allowed, and what is not: You are not permitted to use the lecture notes, any textbook, your notes

• r any other written material during any exam. Calculators are are not outlawed but the exams will be designed

in such a way that you will not need them. Grading: Your final grade is composed as follows: Diagnostic Quiz 10% Homework 30% In-term exams 60% (20% each) There is no curve in this class and the letter grades are assigned according to the following table: A B+ B B- C+ C C- D+ D D- F 90 - 100 86 - 90 83 - 86 80 - 83 75 - 80 70 - 75 65 - 70 60 - 65 55 - 60 50 - 55 0 - 50

• II. GENERAL, UNIVERSITY- or STATE-MANDATED INFORMATION

Drop Dates: The procedure/consequences are different, depending on whether you drop before or after the 12th day of classes (09/13), and then, before or after the Q-drop date (10/31). (See https://ugs.utexas.edu/ vick/academic/adddrop for details) Academic (dis)Honesty: Students who violate University rules on academic dishonesty are subject to disciplinary penalties, including the possibility of failure in the course and/or dismissal from the University. Since such dishonesty harms the individual, all students, and the integrity of the University, policies on academic dishonesty will be strictly enforced. For further information, please visit the Student Conduct and Academic Integrity website at: http://deanofstudents.utexas.edu/conduct Students with Disabilities: The University of Texas at Austin provides upon request appropriate academic accommodations for qualified students with disabilities. If you have a documented disability and you need special treatment as a result of your disability, please let me know as soon as possible, but definitely within the first 3 weeks of class. For more information, contact the Office of the Dean of Students at 471-6259, 471-4641 (TTY), 1-866-329- 3986 (video phone) or go to http://ddce.utexas.edu/disability/

M362M first-day handout Page 4 of 5 Religious Holy Days: Religious holy days sometimes conflict with class and examination schedules. Sections 51.911 and 51.925 of the Texas Education Code relate to absences by students and instructors for observance of religious holy days. Section 51.911 states that a student who misses an examination, work assignment, or other project due to the observance of a religious holy day must be given an opportunity to complete the work missed within a reasonable time after the absence, provided that he or she has properly notified each instructor. It is the policy of The University of Texas at Austin that the student must notify each instructor at least fourteen days prior to the classes scheduled on dates he or she will be absent to observe a religious holy day. For religious holidays that fall within the first two weeks of the semester, the notice should be given on the first day of the semester. The student may not be penalized for these excused absences but the instructor may appropriately respond if the student fails to complete satisfactorily the missed assignment or examination within a reasonable time after the excused absence. Counseling/Mental Health: Counseling and other mental-health services are available from Counseling and Mental Health Center, Student Services Bldg (SSB), 5th Floor. (hours: M–F 8am–5pm. phone: 512 471 3515, web: http://www.cmhc.utexas.edu) Sanger Learning Center: All students are welcome to take advantage of Sanger Center’s classes and workshops, private learning specialist appointments, peer academic coaching, and tutoring for more than 70 courses in 15 different subject areas. For more information, please visit http://www.utexas.edu/ugs/slc or call 512-471-3614 (JES A332). Important Safety Information: If you have concerns about the safety or behavior of fellow students, TAs or Professors, call BCAL (the Behavior Concerns Advice Line): 512-232-5050. Your call can be anonymous. Occupants of buildings on The University of Texas at Austin campus are required to evacuate buildings when a fire alarm is activated. Alarm activation or announcement requires exiting and assembling outside.

• Familiarize yourself with all exit doors of each classroom and building you may occupy. Remember that

the nearest exit door may not be the one you used when entering the building.

• Students requiring assistance in evacuation shall inform their instructor in writing during the first week of

class.

• In the event of an evacuation, follow the instruction of faculty or class instructors. Do not re-enter a

building unless given instructions by the following: Austin Fire Department, The University of Texas at Austin Police Department, or Fire Prevention Services office.

• Link to information regarding emergency evacuation routes and emergency procedures can be found at:

http://www.utexas.edu/emergency

• Further information about campus safety and security can be obtained from the Office of Campus Safety

and Security, 512-471-5767, http://www.utexas.edu/safety/

Schedule on the next page. − →

M362M first-day handout Page 5 of 5

• III. The SCHEDULE of CLASSES and EXAMS

Date Weekday Topic Note 1 Aug 28 Wed Introduction, probability review 2 Aug 30 Fri Probability review Sep 02 Mon no class 3 Sep 04 Wed ” 4 Sep 06 Fri “Diagnostic” quiz 5 Sep 09 Mon Random Walks 6 Sep 11 Wed ” 7 Sep 13 Fri ” 8 Sep 16 Mon ” 9 Sep 18 Wed ” 10 Sep 20 Fri " 11 Sep 23 Mon ” 12 Sep 25 Wed ” 13 Sep 27 Fri ” 14 Sep 30 Mon In-term exam I 15 Oct 02 Wed Branching Processes 16 Oct 04 Fri ” 17 Oct 07 Mon ” 18 Oct 09 Wed ” 19 Oct 11 Fri ” 20 Oct 14 Mon ” 21 Oct 16 Wed ” 22 Oct 18 Fri Markov Chains 23 Oct 21 Mon ” 24 Oct 23 Wed ” 25 Oct 25 Fri ” 26 Oct 28 Mon ” 27 Oct 30 Wed ” 28 Nov 01 Fri In-term exam II 29 Nov 04 Mon ” 30 Nov 06 Wed ” 31 Nov 08 Fri ” 32 Nov 11 Mon ” 33 Nov 13 Wed ” 34 Nov 15 Fri ” 35 Nov 18 Mon ” 36 Nov 20 Wed ” 37 Nov 22 Fri ” 38 Nov 25 Mon ” Nov 27 Wed ” no class Nov 29 Fri ” no class 39 Dec 02 Mon ” 40 Dec 04 Wed ” 41 Dec 06 Fri ” 42 Dec 09 Mon In-term exam III