Math 180A

Fall 2019, Lecture A00 (MWF 9:00-9:50am)

Introduction to Probability

Announcements
Calendar
Syllabus
Piazza
Gradescope
Homeworks

Announcements

Regrades for the final will be active on Gradescope on Thursday, January 16, from 8am to 11pm.
The office hours dedicated to the final exam will take place on Wednesday, January 15, from 5pm to 7pm in APM 6422.
About computing your final grade:
- Homework: all 8 homeworks have equal weight; for each assignment, divide your score for this homework by the maximal number of points (e.g. divide your score for HW1 by 20, HW2 by 19, HW8 by 12 etc); then compute the average of the 7 highest numbers and then multiply this average by 20.
  E.g., if your HW scores are 16, 19, 15, 20, 20, 10, 16, 10, you first compute your relative scores 16/20, 19/19, 15/20, 20/20, 20/20, 10/20, 16/20, 8/12, which gives 0.8, 1, 0.75, 1, 1, 0.5, 0.8, 0.75, then drop the lowest (0.5 in this case), compute the average of the remaining 7 (0.8 + 1 + 0.75 + 1 + 1 + 0.8 + 0.75)/7 and multiply the obtained number by 20. This will give the number of points you get for the homework assignments.
- Your final numerical grade will be computed as the maximum of the following four numbers (here HW denotes your HW points computed as above, M1, M2 and F are your grades for midterms 1 and 2 and final):
  - HW points + 0.2*M1 + 0.2*M2 + 0.4*F
  - HW points + 0.2*M1 + 0.6*F
  - HW points + 0.2*M2 + 0.6*F
  - HW points + 0.8*F
- To translate your numerical grade into the letter grade, please use the following (updated) table
  
  F C- C C+ B- B B+ A- A A+
  
  < 34 34-46 46-51 51-57 57-62 62-67 67-73 73-88 81-88 > 88
- Results of the final exam have been released on Gradescope. Passing grade for the final is 20 out of 100. Regrades for the final will be postponed to the beginning of the second quarter (you will receive a reminder).
- Regrades for HW8 will be active on Gradescope on Friday, December 13 from 8am to 11pm.
- Solutions to the final exam can be found here.
- Solutions to all problems from HW8 can be found here, solutions to the practice problems from sections 6,8 and 9 are available here (Important there was mistake in the previous version of the last file in the solution of the problem 5(d). It has been fixed. See the discussion on Piazza for more details).
- Final exam will take place on Wednesday, December 11, 8:00am-10:59am in CENTR113.
- Office hours during the exam week (check the Google calendar below and on Professor Au's course web site for updates on time/place of the office hours):
  - Sunday, December 8, 2pm-4pm, Professor Au, AP&M 6303
  - Monday, December 9, 1pm-2pm, Professor Au, AP&M 6303
  - Tuesday, December 11, 6pm-8pm, Toni Gui, AP&M 1220
- Practice problems for sections 6,8,9 are available here. Note that the final exam will include problems from all section that were discussed in this course, i.e. sectioins 1,2,3,4,5,6,8,9.
- Regrades for HW7 will be active on Gradescope on Thursday, December 5, 8am-11pm.
- Homework 8 is now ready for download (see below). This assignment has 10 problems. You have to turn in only first five of them, and only first five problems will be taken into account for your final grade. Due date: Friday, December 6, 11:59pm. The solutions to the other problems will be published on this web site later.
- Results of Midterm 2 are now available on Gradescope. The regrade requests will be active on Gradescope on Tuesday, December 3, 8am-11pm. Please, read this short summary of your performance pdf.
- Regrade requests for HW6 will be active on Tuesday, November 26, 8am - 11pm.
- Homework 7 is now ready for download (see below). Due date: WEDNESDAY, November 27, 11:59pm.
- The solutions to the second midterm can be founde here.
- The link for the anonymous survey is here.
- Midterm 2 will take place on Wednesday, November 20, 9:00am-9:50am in CENTR113.
- Solutions to the practice exams can be found here practiceMidterm2solutions_a.pdf (note that problem 2 was slightly modified: 100 interviewed instead of 250) and practiceMidterm2solutions_b.pdf.
- Two practice midterm exams are available for download: pdf and pdf (with some additional problems).
- Regrade requests for HW4 and HW5 will be active on Tuesday, November 19, 8am - 11pm.
- Homework 6 is now available for download (see below). Due date: November 15 11:59pm.
- Homework 5: error in problem 8 (exercise 4.40) The exact probability that the number one appears at most 3 times is 0.00327556 and not 0.000949681 as stated in the book.
- Homework 5 is now available for download (see below). Due date: November 8 11:59pm.
- Regrades of Midterm 1 will be active on Gradescope on Wednesday, October 30 from 8am to 11pm. Please, check carefully the solutions to Midterm 1 (available here) before requesting a regrade.
- Results of Midterm 1 are now available on Gradescope. You will be notified when the regrade requests are active. It seems like many of you found the exam slightly too difficult, this might be taken into account when computing your final grade. Please, read this short summary of your performance pdf.
- Homework 4 is now available for download (see below). Due date: November 1 11:59pm.
- Mistake in the solution to problem 1(b) in the list of additional practice problems for Midterm 1 has been corrected (see updated slides of lecture 11).
- Midterm 1 will take place on Wednesday, October 23, 9:00am-9:50am in CENTR113.
- Practice midterm exam #1 is now avalable (pdf), as well as a collection of additional problems (Updated: pdf). We will do the practice midterm exam during the lecture on Monday, Oct 21.
- Regrade requests (homework #2) will be active on Gradescope on Tuesday, October 22 from 8am to 11pm ONLY (after October 22, 11pm the grade will become final). I recall that you should write a separate request for each problem, and your requests should be detailed and polite.
- Regrade requests (homework #1) will be active on Gradescope on Tuesday, October 15 from 8am to 11pm ONLY (after October 15, 11pm the grade will become final). I recall that you should write a separate request for each problem, and your requests should be detailed and polite.
Course Information
- Textbook: The required textbook for this course is
  
  Introduction to Probability, by David F. Anderson, Timo Seppäläinen, and Benedek Valkó; DOI 10.1017/9781108235310
  Reading and homework assignments will refer to this textbook as ASV.
- Coursework: There will be weekly homework assignments due on Fridays (starting in Week 1); they are posted below. There will be two in class midterm exams and a final exam; dates, times, and locations 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 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	AP&M 6422	ynemish@ucsd.edu	Tuesday 6:00pm-8:00pm (AP&M 6303) Thursday 2:00pm-3:00pm (AP&M 6303)
Toni Gui	Teaching Assistant	AP&M 1220	ttgui@ucsd.edu	Thursday 3:30pm-5:30pm (AP&M 1220)
Andrew Ying	Teaching Assistant	AP&M 1111	anying@ucsd.edu	Thursday 1:00pm-3:00pm (AP&M 1111)

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

Calendar

Class Meetings

	Date	Time	Location
Lecture A00 (Nemish)	Monday, Wednesday, Friday	9:00am - 9:50am	CENTR 113
Discussion A01 (Gui)	Monday	6:00pm - 6:50pm	CENTR 218
Discussion A02 (Gui)	Monday	7:00pm - 7:50pm	CENTR 218
Discussion A03 (Ying)	Monday	8:00pm - 8:50pm	CENTR 218
Discussion A04 (Ying)	Monday	9:00pm - 9:50pm	CENTR 218
First Midterm Exam	Wednesday, Oct 23	9:00am - 9:50am	CENTR 113
Second Midterm Exam	Wednesday, Nov 20	9:00am - 9:50am	CENTR 113
Final Exam	Wednesday, Dec 11	8:00am - 10:59am	CENTR 113

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Syllabus

Welcome to Math 180A: a one quarter course introduction to probability theory. This course is the prerequisite for the subsequent courses Math 180B/C (Introduction to Stochastic Processes) and Math 181A/B (Introduction to Mathematical Statistics) and Math 189 (Exploratory Data Analysis and Inference). It is also prerequisite for the new Data Science topics course DSC 155 (Hidden Data in Random Matrices) in Winter 2020. According to the UC San Diego Course Catalog, the topics covered are probability spaces, random variables, independence, conditional probability, discrete and continuous probability distributions, joint distributions, variance and moments, the Laws of Large Numbers, and the Central Limit Theorem.

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

Date	Week	Topic (updated)	ASV (updated)	Preliminary slides	Final slides
09/27	0	Definition of Probability	1.1	-	-
09/30	1	Random sampling	1.2	-	-
10/02	1	Basic Properties of Probability	1.4	-	-
10/04	1	Conditional Probability	2.1	-	-
10/07	2	Bayes' Rule. Independence	2.2-2.3	-	-
10/09	2	Random Variables	1.5, 3.1	-	Lecture 6
10/11	2	Probability Distributions	3.1-3.2	-	-
10/14	3	Independent Trials and Sampling	2.4-2.5	Lecture 8	Lecture 8
10/16	3	Binomial, Geometric, and Poisson Distributions	2.4-2.5, 4.4	Lecture 9	Lecture 9
10/18	3	Expected Value	3.3	Lecture 10	Lecture 10
10/21	4	Review		Lecture 11	Lecture 11 (updated)
10/23	4	Midterm 1
10/25	4	Variance	3.4	Lecture 13	Lecture 13
10/28	5	Normal (Gaussian) Distribution	3.5	Lecture 14	Lecture 14
10/30	5	Normal Approximation	4.1-4.2	Lecture 15	Lecture 15
11/1	5	Confidence Intervals	4.3	Lecture 16	Lecture 16
11/4	6	Poisson Approximation	4.4	Lecture 17	Lecture 17
11/6	6	Exponential Distribution	4.5	Lecture 18	Lecture 18
11/8	6	Moment Generating Function	5.1-5.2	Lecture 19	Lecture 19
11/11	7	Veterans Day
11/13	7	Joint Distributions	5.2-6.1	Lecture 20	Lecture 20
11/15	7	Joint distrubutions	6.1-6.2	Lecture 21	Lecture 21
11/18	8	Review
11/20	8	Midterm 2
11/22	8	Independence of Random Variables	6.3	Lecture 22	Lecture 22
11/25	9	Expectations of sums and products	8.1-8.3	Lecture 23	Lecture 23
11/27	9	Covariance, correlation, and variance of sums	8.4	Lecture 24	Lecture 24
11/29	9	Thanksgiving
12/2	10	Tail probabilities	9.1	Lecture 25	Lecture 25
12/4	10	Law of Large Numbers. Central Limit Theorem	9.2-9.3	Lecture 26	Lecture 26
12/6	10	Review

Prerequisite: The only prerequisites are calculus up to and including Math 20C (Multivariate Calculus). Math 109 (Mathematical Reasoning) is also strongly recommended as a prerequisite or corequisite.

Lecture: Attending the lecture is a fundamental part of the course; 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:

20% Homework, 20% Exam I, 20% Exam II, 40% Final Exam
20% Homework, 20% Best Midterm Exam, 60% Final Exam
20% Homework, 80% Final Exam

In addition, you must pass the final examination in order to pass the course. 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.

Entering/exiting class: Please arrive on time and stay for the entire class/section period. If, despite your best efforts, you arrive late, please enter quietly through the rear door and take a seat near where you entered. Similarly, in the rare event that you must leave early (e.g. for a medical appointment), please sit close to the rear exit and leave as unobtrusively as possible.
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 Monday, September 30.

Homework 1, due Friday, October 4.

Homework 2, due Friday, October 11.

Homework 3, due Friday, October 18.

Homework 4, due Friday, November 1.

Homework 5, due Friday, November 8.

Homework 6, due Friday, November 15.

Homework 7, due WEDNESDAY, November 27.

Homework 8, due Friday, December 6.

F	C-	C	C+	B-	B	B+	A-	A	A+
< 34	34-46	46-51	51-57	57-62	62-67	67-73	73-88	81-88	> 88