Math 180C

Spring 2020, Lecture A00/B00

Introduction to Stochastic Processes II

Announcements
Calendar
Syllabus
Piazza
Gradescope
Homeworks

Announcements

June 5: Instructions for the final (to be updated):
- Update: Important. Have your student ID with you during the oral part of the exam.
- Update: If you want to change your exam time (to one of other two available options), send an email before Wednesday.
- Update: The solutions to the exam problems that you upload to Gradescope must be handwritten.
- Structure of the exam:
  - The problems for the final exams will be published on the Canvas page of this course and will become available at scheduled times.
  - The solutions to the final exam should be written separately and submitted through Gradescope before the submission deadline.
  - The written part will be followed by a Zoom conversation with instructors.
- Written part:
  - The problems for the final exams will be published on the Canvas page of this course and will become available at scheduled times.
  - You will have 90 minutes from the release of the exam on Canvas to write the exam + 10 minutes to submit the problems on Gradescope. Do not submit the quiz on Canvas before you submit your exam on Gradescope (I am not sure if all devices allow accessing the quiz questions after submission, so if you submit the quiz too quickly you might lose access to the problems. Alternatively, take a picture of your exam problems at the beginning of the exam.)
  - Each student will get a random selection of problems of equal difficulty and covering similar topics.
  - Students taking exams at different times will have their problems been selected from different subsets of problems; there is no advantage in taking the exam at later time slots.
  - You have to write your solutions on paper/tablet and submit them through Gradescope. Your answers in Canvas will not be graded.
  - This is an open-book exam. You are allowed to use the textbook, lecture notes, your personal notes. You are not allowed to use the outside assistance. Outside assistance includes but is not limited to other people, the internet and unauthorized notes.
  - You are not allowed to use the calculator or analogous software. All intermediate steps of your computations (computing integrals, solving systems of linear equations etc) should be included in you solutions.
- Oral part:
  - The Zoom meeting will start 60 minutes after the beginning of the exam.
  - You have to join the meeting not later than 110 minutes after the beginning of the exam (not later than 20 minutes after the end of the written part).
  - You will receive the access codes for the Zoom meeting via email one day before the exam.
  - After joining the meeting, you will be placed into the waiting room. You will be then added to the conversation room one by one in the order of the submission of your exams on Gradescope for a discussion with the instructors. It is important that you are ready to start the conversation at any time while in the waiting room.
  - The goal of the oral part is to make sure that the students do not use outside help during the unproctored exams. You will be asked questions about your solutions to the written part of the exam submitted on Gradescope. Most of the conversations will be very short. In case of serious inconsistencies between your written and oral answers some additional questions might be asked. If it will become clear that the written part is written using the outside help, the case will be reported to AI. If you write your exam honestly, the oral part is a simple formality.
  - The oral part will not be graded.
- Time framework: if T is the scheduled starting time of your exam, then
  - T: problems become available on Canvas
  - T+60 min: Zoom conversation starts
  - T+90 min: the end of the written part
  - T+100 min: Gradescope submission deadline
  - T+110 min: Zoom meeting locks
  - T+180 min: the end of the exam
- Academic integrity pledge:
  "I pledge to be fair to my classmates and instructors by completing all of my academic work with integrity.
  This means that I will respect the standards set by the instructor and institution, be responsible for the consequences of my choices, honestly represent my knowledge and abilities, and be a community member that others can trust to do the right thing even when no one is watching. I will always put learning before grades, and integrity before performance. I pledge to excel with integrity.
  In addition to the above, I pledge that I did not receive outside assistance with this exam. Outside assistance includes but is not limited to other people, the internet and unauthorized notes."
  To acknowledge that you agree to this pledge, you must copy the sentence:
  I choose to excel with integrity as a member of the University of California, San Diego.
  and submit it with your exam on Gradescope. Make sure to sign your name below it and date it as well
- On the day of final:
  - (0): Prepare the notes that you plan to use during the exam. Write, date and sign the academic integrity pledge (see above).
  - (1): Go to the Canvas page of the course, get the exam problems. Start writing the exam.
  - (2): Submit the exam (with the AI pledge) on Gradescope. Join the Zoom meeting.
  - (3): Wait in Zoom for the oral follow-up conversation.
- Practice final exam has been published on the Canvas page of this course. It has similar length and structure to the real final exam. Report as soon as possible any technical issues related to the practice exam.
June 5: Please read this message from the Department of Mathematics pdf in case you have not received it via email.
June 5: Several office hours as well as discussion sections will be held next week. For the exact times of the discussion sections and the office hours during the next week check the Google calendar below.
June 5: Here is a list of what your are expected to know for the final exam pdf.
May 31: Solutions to Midterm 2 are available for download pdf.
May 31: Homework 8 is now available for download (see below). Due Saturday, June 6, 23:59pm.
May 26: please fill in this form and indicate when you want to write the final exam. I remind you that you have to choose one of the three options: either your scheduled time, or one of the two additional time slots.
May 26: Information about the final
- The exam will have two parts, written and oral.
- The written part will be open book, 90 minutes long, and you will have to upload your exam to Gradescope.
- The oral part will be held via Zoom. It will consist of a short follow-up conversation with me and one of the TA's, mostly about your written exam. It will not be recorded. Please make sure that you have access to Zoom during your chosen time slot.
- The detailed instructions for the final will be posted on the course web site next week.
May 23: Homework 7 is now available for download (see below). Due Friday, May 29, 23:59pm.
May 20: Problems for Midterm 2 are available for download pdf. Read carefully the instructions on the first page. You should spend no more than one hour on these problems before submitting your exam to Gradescope.
May 19: Midterm 2 will take place on May 20-22. This will be an open-book take-home exam. The problems will be published on this website on Wednesday, May 20, 11 PM, and the submission deadline will be Friday, May 22, 11 PM (via Gradescope). You are supposed to spend not more than one hour composing your exam. Midterm 2 will cover the following topics: conditioning on continuous random variables; renewal processes; martingales. This corresponds to Lectures 7-12 and Homeworks 4-6.
May 4: Solutions to Midterm 1 are available for download pdf.
April 22: Problems for Midterm 1 are available for download pdf. Read carefully the instructions on the first page. You should spend no more than one hour on these problems before submitting your exam to Gradescope.
April 19: Midterm 1 will take place on April 22-24. This will be an open-book take-home exam. The problems will be published on this website on Wednesday, April 22, 11PM, and the submission deadline will be Friday, April 24, 11PM (via Gradescope). You are supposed to spend not more than one hour composing your exam. I would like to remind you that according to the new grading scheme you all get 50 points to your final point score independently of your performance on the midterm.
April 19: Homework 3 is now available for download (see below). Due Saturday, April 25, 23:59pm.
April 16: Submission deadline for Homework 2 has been extended to Saturday, April 18, 23:59pm. Check also the recent post on Piazza concerning Problem 6.3.1.
April 15: Important announcement. The grading policy has been updated. A new (additional) grading scheme is available offering a 50% Bonus to all students: Final grade = 15% Homework, 35% Final Exam, 50% Bonus. The midterm exams will be take-home exams within 48-hour time windows (Wednesday to Friday of corresponding weeks). Although with the new grading scheme the midterm exams will not have direct impact on you final grades, I strongly encourage you to take the midterm exams in order to estimate your progress.
April 12: Homework 2 is now available for download (see below). Due Friday, April 17, 23:59pm.
April 4: Homework 1 is now available for download (see below). Due Friday, April 10, 23:59pm.
April 3: Please fill in this form if you are experiencing any troubles related to the remote format of this course (limited access to the course materials, time difference issues etc)
You might find this information about grading policies in Spring 2020 useful
Welcome

Course Information

Textbook: The required textbook for this course is

An Introduction to Stochastic Modeling, by Mark A. Pinsky and Samuel Karlin; 4th edition
The link above goes to UCSD library website, where the textbook can be downloaded freely and legally if you are connecting from a UCSD IP address. Reading and homework assignments will refer to this textbook as PK.

Coursework: There will be weekly homework assignments due on Fridays (starting in Week 1); they are posted below. There will be two midterm exams and a final exam; dates, times and Zoom links posted below.

Piazza is an online discussion forum. It will allow you to post messages (openly or anonymously) and answer posts made by your fellow students, about course content, homework, exams, etc. The instructors and TAs of both lectures (A00 and B00) will also monitor and post to Piazza regularly. You can sign up here. Note: Piazza has an opt-in "Piazza Careers" section which, if you give permission, will share statistics about your Piazza use with potential future employers. It also has a "social network" component, based on other students who've shared a Piazza-based class with you, that comes with the usual warnings about privacy concerns. Piazza is fully FERPA compliant, and is an allowed resource at UCSD. Nevertheless, you are not required to use Piazza if you do not wish.

Gradescope is an online tool for uploading and grading assignments an exams (it is now under the umbrella of Turnitin). You will turn in your homework through Gradescope, and you will access your graded exams there as well. Access the class Gradescope site here.

Instructional Staff and Office Hours

Name	Role	Office	E-mail	Office hours
Yuriy Nemish	Instructor	-	ynemish@ucsd.edu	Monday 2-3PM Zoom Wednesday 2-3PM Wednesday 5-7PM
Toni Gui	Teaching Assistant	-	ttgui@ucsd.edu	Thursday 12-2PM Zoom
Alec Todd	Teaching Assistant	-	altodd@ucsd.edu	Tuesday 2-4PM Zoom

Please, check the following calendar for possible reschedulings of the office hours.

Calendar

Lectures

	Date
Lecture A00/B00 (Nemish)	Monday, Wednesday, Friday	-	-

Zoom Meetings

	Date	Time	Link
Q&A A00 (Nemish)	Monday, Wednesday, Friday	1:00pm - 1:25pm	Zoom
Q&A B00 (Nemish)	Monday, Wednesday, Friday	4:00pm - 4:25pm	Zoom
Discussion A01 (Gui)	Monday	7:00pm - 7:50pm	Zoom
Discussion A02 (Gui)	Monday	6:00pm - 6:50pm	Zoom
Discussion B01 (Todd)	Monday	7:00pm - 7:50pm	Zoom
Discussion B02 (Todd)	Monday	6:00pm - 6:50pm	Zoom
First Midterm Exam A00	Wednesday, Apr 22	1:00pm - 1:50pm	??
First Midterm Exam B00	Wednesday, Apr 22	4:00pm - 4:50pm	??
Second Midterm Exam A00	Wednesday, May 20	1:00pm - 1:50pm	??
Second Midterm Exam B00	Wednesday, May 20	4:00pm - 4:50pm	??
Final Exam A00	Thursday, Jun 11	11:30am - 2:29pm	???
Final Exam B00	Thursday, Jun 11	3:00pm - 5:59pm	???

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Syllabus

Welcome to Math 180C: a one quarter course introduction to stochastic processes (II). According to the UC San Diego Course Catalog, the topics covered are Markov chains in discrete and continuous time, random walk, recurrent events and other topics.

Here is a more detailed listing of course topics, in the sequence they will be covered, together with the relevant section(s) of the textbook. While each topic corresponds to approximately one lecture, there will be some give and take here.

Q&A	Week	Topic	PK	Slides	Video
03/30	1	Administrivia	-	-	-
04/01	1	Birth processes	6.1	Slides 1	Video 1
04/03	1	Birth and death processes	6.2 - 6.3	Slides 2	Video 2
04/06	2	Birth and death processes	6.2 - 6.3
04/08	2	Hitting probabilities	6.5	Slides 3	Video 3
04/10	2	General continuous-time Markov chains	6.6	Slides 4	Video 4
04/13	3	General continuous-time Markov chains	6.6
04/15	3	Kolmogorov's forward and backward equations	6.3, 6.6	Slides 5	Video 5
04/17	3	Kolmogorov's forward and backward equations	6.3, 6.6
04/20	3	Stationary distributions and long-run behavior	6.4	Slides 6	Video 6
04/22	3	Stationary distributions and long-run behavior	6.4
04/24	4	Midterm 1		-	-
04/27	5	Conditioning on a continuous random variable	2.4	Slides 7	Video 7
04/29	5	Introduction to renewal processes	7.1	Slides 8	Video 8
05/01	5	Introduction to renewal processes	7.1
05/04	6	Examples of renewal processes	7.2 - 7.3	Slides 9	Video 9
05/06	6	Examples of renewal processes	7.2 - 7.3
05/08	6	Asymptotic results for renewal processes	7.4	Slides 10	Video 10
05/11	7	Asymptotic results for renewal processes	7.4
05/13	7	Generalizations of renewal processes	7.5	Slides 11	Video 11
05/15	7	Generalizations of renewal processes	7.5
05/18	8	Martingales	2.5	Slides 12	Video 12
05/20	8	Midterm 2		-	-
05/22	8	Martingales	2.5
05/25	9	Memorial Day
05/27	9	Definition and basic properties of Brownian motion	8.1	Slides 13	Video 13
05/29	9	The reflection principle	8.2	Slides 14	Video 14
06/01	10	Processes derived from Brownian motion	8.3-8.4	Slides 15	Video 15
06/03	10	Processes derived from Brownian motion	8.3-8.4
06/05	10	Review	-

Prerequisite: MATH 180B or concent of instructor.

Lecture: You are responsible for material presented in the lecture whether or not it is discussed in the textbook. You should expect questions on the exams that will test your understanding of concepts discussed in the lecture.

Homework: Homework assignments are posted below, and will be due at 11:59pm on the indicated due date. You must turn in your homework through Gradescope; if you have produced it on paper, you can scan it or simply take clear photos of it to upload. Your lowest homework score will be dropped. It is allowed and even encouraged to discuss homework problems with your classmates and your instructor and TA, but your final write up of your homework solutions must be your own work.

Midterm Exams: The two midterm exams will take place during the lecture time at the dates listed above.

You may bring one 8.5 by 11 inch sheet of paper with handwritten notes (on both sides) with you to each midterm exam; no other notes (or books) will be allowed.
No calculators, phones, or other electronic devices will be allowed during the midterm exams.
There will be no makeup midterm exams.

Final Exam: The final examination will be held at the date and time stated above.

It is your responsibility to ensure that you do not have a schedule conflict involving the final examination; you should not enroll in this class if you cannot take the final examination at its scheduled time.
You may bring two 8.5 by 11 inch sheets of paper with handwritten notes (on both sides) with you to the final examination; no other notes (or books) will be allowed.
No calculators, phones, or other electronic devices will be allowed during the final examination.
There will be no makeup final exam.

Administrative Links: Here are two links regarding UC San Diego policies on exams:

Exam Responsibilities An outline of the responsibilities of faculty and students with regard to final exams

Policies on Examinations The Academic Senate policy regarding final examinations (These are the rules!)

Regrade Policy:

Your exams and homeworks will be graded using Gradescope. You will be able to request regrades directly from your TA through Gradescope for a specified window of time. Be sure to make your request within the specified window of time; no regrade requests will be accepted after the deadline. Note: Your grader will consider your regrade request only if you have explained clearly, thoroughly, and politely why you think an error in grading was made.

Grading: Your cumulative average will be the best of the following three weighted averages:

15% Homework, 25% Midterm 1, 25% Midterm 2, 35% Final Exam
15% Homework, 25% Best Midterm Exam, 60% Final Exam
15% Homework, 35% Final Exam, 50% Bonus

Note also: there are no makeup exams, if you miss a midterm exam for any reason then your course grade will be computed with the second or third option. There are no exceptions; this grading scheme is intended to accommodate emergencies that require missing a midterm exam.

Your course grade will be determined by your cumulative average at the end of the quarter, and will be based on the following scale:

A+	A	A-	B+	B	B-	C+	C	C-
97	93	90	87	83	80	77	73	70

The above scale is guaranteed: for example, if your cumulative average is 80, your final grade will be at least B-. However, your instructor may adjust the above scale to be more generous.

Academic Integrity: UC San Diego's code of academic integrity outlines the expected academic honesty of all studentd and faculty, and details the consequences for academic dishonesty. The main issues are cheating and plagiarism, of course, for which we have a zero-tolerance policy. (Penalties for these offenses always include assignment of a failing grade in the course, and usually involve an administrative penalty, such as suspension or expulsion, as well.) However, academic integrity also includes things like giving credit where credit is due (listing your collaborators on homework assignments, noting books or papers containing information you used in solutions, etc.), and treating your peers respectfully in class. In addition, here are a few of our expectations for etiquette in and out of class.

Noise and common courtesy: When class/section begins, please stop your conversations. Wait until class/section is over before putting your materials away in your backpack, standing up, or talking to friends. Do not disturb others by engaging in disruptive behavior. Disruption interferes with the learning environment and impairs the ability of others to focus, participate, and engage.
Electronic devices: Please do not use devices (such as cell phones, laptops, tablets, iPods) for non-class-related matters while in class/section. No visual or audio recording is allowed in class/section without prior permission of the instructor (whether by camera, cell phone, or other means).
E-mail etiquette: You are expected to write as you would in any professional correspondence. E-mail communication should be courteous and respectful in manner and tone. Please do not send e-mails that are curt or demanding.

Accommodations:

Students requesting accommodations for this course due to a disability must provide a current Authorization for Accommodation (AFA) letter issued by the Office for Students with Disabilities (OSD) which is located in University Center 202 behind Center Hall. The AFA letter may be issued by the OSD electronically or in hard-copy; in either case, please make arrangements to discuss your accommodations with me in advance (by the end of Week 2, if possible). We will make every effort to arrange for whatever accommodations are stipulated by the OSD. For more information, see here.

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Homework

Weekly homework assignments are posted here. Homework is due by 11:59pm on the posted date, through Gradescope. Late homework will not be accepted.

Homework 0, due Wednesday, April 1.

Homework 1, due Friday, April 10.

Homework 2, due Saturday, April 18.

Homework 3, due Saturday, April 25.

Homework 4, due Friday, May 8.

Homework 5, due Friday, May 15.

Homework 6, due Saturday, May 23.

Homework 7, due Friday, May 29.

Homework 8, due Saturday, June 6.