Instructor: David A. Meyer
Office hours: AP&M 7218, M 11:00am-12:50pm, or by appointment
Lecture: Solis 107, MWF 9:00am-9:50am
Email: dmeyer "at" math "dot" ucsd "dot" edu
Teaching assistant: Zequn ZHENG
Office hours: AP&M6132, Th 5:00pm-9:00pm, or by appointment
Section A01: Center 203, F 5:00pm-5:50pm
Section A02: Center 203, F 6:00pm-6:50pm
Email: zez084 "at" ucsd "dot" edu
Teaching assistant: Xiaoou PAN
Office hours: AP&M 1121, Th 3:00pm-5:00pm, or by appointment
Section A03: WLH 2112, F 5:00pm-5:50pm
Email: xip024 "at" ucsd "dot" edu
Teaching assistant: Qingyuan CHEN
Office hours: AP&M 6446, TuTh 1:00pm-2:00pm, or by appointment
Section A04: WLH 2112, F 6:00pm-6:50pm
Email: qic069 "at" ucsd "dot" edu
Teaching assistant: Alec TODD
Office hours: AP&M 6414, W 1:00pm-2:50pm, 4:00pm-5:50pm, or by appointment
Section A05: Center 217B, F 5:00pm-5:50pm
Section A06: Center 217B, F 6:00pm-6:50pm
Email: altodd "at" ucsd "dot" edu
Teaching assistant: Phong CHAU
Office hours: AP&M 5720, Th 9:00am-1:00pm, or by appointment
Section A07: WLH 2115, F 5:00pm-5:50pm
Section A08: WLH 2115, F 6:00pm-6:50pm
Email: phchau "at" ucsd "dot" edu
This course is an introduction to probability. The mathematical analysis of probabilities originated with attempts to optimize play in various gambling games, and probability continues to be a useful tool for describing many situations in the real world. In this course we will learn the basic ideas of both discrete and continuous probability.
Especially for the latter, the prerequisite for this course is a thorough knowledge of calculus. Math 109, taken at least concurrently, is strongly recommended as we will prove some theorems. The textbook is David F. Anderson, Timo Seppäläinen and Benedek Valkó, Introduction to Probability (Cambridge: Cambridge University Press 2018). We will cover most of chapters 1-6, 8, and 9. Other useful texts include Andrei Nikolaevich Kolmogorov, Foundations of Probability [1], Ani Adhikari and Jim Pitman, Probability for Data Science [2], and Gian-Carlo Rota and Kenneth Baclawski, Introduction to Probability and Random Processes [3].
There will be weekly homework assignments, due in section on Fridays, or before 7:00pm Friday in the appropriate drop box (A01-A04 or A05-A08) in the basement of AP&M. Students are allowed to discuss the homework assignments among themselves, but are expected to turn in their own work — copying someone else's is not acceptable. Homework scores will contribute 15% to the final grade. Occasional extra credit problems are due by specific dates; each worth not more than 2% of the final grade.
There will be two midterms, currently planned for Week 4 and Week 8. The final is scheduled for 8:00am Wednesday, March 18. Scores on the two midterms and final will contribute 25%, 25% and 35% to the final grade, respectively^{*}. There will be no makeup tests.
^{*}To be precise, let H_{i}, M1_{i}, M2_{i}, and F_{i} be student i's scores on the homework, on the first and second midterms, and on the final, respectively; and let μ_{H} and σ_{H} be the average and standard deviation of the homework scores for the class, respectively. Student i's homework score is rescaled using the average and standard deviation, to get ZH_{i} = (H_{i} - μ_{H})/σ_{H}, with analogous notation for the exam averages, exam standard deviations, and exam Z-scores. Then student i's total Z-score is Z_{i} = 0.15ZH_{i} + 0.25ZM1_{i} + 0.25ZM2_{i} + 0.35ZF_{i}. Any positive Z-scores on extra credit problems will be multiplied by 0.01 each and added to Z_{i}. Student i's letter grade will be assigned based upon max{Z_{i},ZF_{i}}. The cutoffs for grades will be no higher than A-, 0.5; B-, -0.3; C-, -1.3; these cutoffs correspond to about 30% A+,A,A-; 30% B+,B,B-; and 30% C+,C,C-.
Apr 10 | Application deadline for Air Force Research Lab Summer of Topological Data Analysis Intern. |
Mar 9 | Application deadline for UC San Diego Physical Sciences Undergraduate Summer Research Award. |
Feb 19 |
MATLAB seminars,
"Data Analysis and Visualization with MATLAB for Beginners", 10:00am-12:00nn, Geisel Library, Classroom 2, "What's New in MATLAB?", 1:00pm-3:00pm, Geisel Library, Classroom 2. |
Feb 17 | Application deadline for University of Washington Data Science for Social Good Summer Program. |
Feb 6 |
Alex Hening,
"Stochastic persistence and extinction", 11:00am-11:50am, AP&M 6402. |
Jan 9 |
Alexander Dunlap,
"Stationary solutions for the stochastic heat, KPZ, and Burgers equations", 11:00am-11:50am, AP&M 6402. |
Jan 6 |
§1.1. Sample spaces and probabilities §1.2. Random sampling counting license plates [slides] HWK (for Friday, Jan 10). Read Chapter 1. Do Chapter 1, exercises 1.2, 1.6, 1.10, 1.12, 1.20, 1.30. [solutions] |
Jan 8 |
§1.3. Infinitely many outcomes §1.4. Consequences of the rules of probability |
Jan 10 |
divisor probabilities [slides] §2.1. Conditional probability HWK (for Friday, Jan 17). Read Chapter 2. Do Chapter 1, exercises 1.14, 1.34, 1.40. Do Chapter 2, exercises 2.3, 2.10, 2.16, 2.22, 2.26, 2.46. 1% Extra Credit (for Friday, Jan 17); not required. Do Chapter 1, exercise 1.57 (on separate piece of paper from HWK, marked "Extra Credit"). [solutions] |
Jan 13 |
§2.2. Bayes' formula §2.3. Independence |
Jan 15 |
§2.4. Independent trials §2.5. Further topics on sampling and independence |
Jan 17 |
§1.5. Random variables §3.1. Probability distributions of random variables HWK (for Friday, Jan 24). Read §3.1, §3.2, §3.3. Do Chapter 1, exercise 1.18. Do Chapter 3, exercises 3.2, 3.3, 3.6, 3.19, 3.40, 3.43, 3.44, 3.46. 1% Extra Credit (for Friday, Jan 24); not required. Do Chapter 2, exercise 2.83 (on separate piece of paper from HWK, marked "Extra Credit"). [solutions] |
Jan 20 |
No lecture. Martin Luther King, Jr. Day. |
Jan 22 |
§3.1. Probability distributions of random variables §3.2. Cumulative distribution function [practice midterm problems] |
Jan 24 |
§3.3. Expectation HWK (for Friday, Jan 31). Read §3.4, §3.5. Do Chapter 3, exercises 3.9, 3.12, 3.14, 3.23, 3.30, 3.52. 1% Extra Credit (for Friday, Jan 31); not required. Do Chapter 3, exercise 3.79 (on separate piece of paper from HWK, marked "Extra Credit"). [solutions] |
Jan 27 |
Midterm 1. Will cover material through Wednesday, Jan 22. Please bring a bluebook and your student ID. You may bring a page of handwritten notes, but nothing else. [seat assignments] [exam] [solutions] [results] |
Jan 29 |
§3.4. Variance |
Jan 31 |
§3.5. Gaussian distribution HWK (for Monday, Feb 10). Read §4.1-4.4. Do Chapter 3, exercises 3.18, 3.64, 3.65, 3.67. Do Chapter 4, exercises 4.2, 4.4, 4.5, 4.7, 4.20. 1% Extra Credit (for Monday, Feb 10); not required. In [3] do Chapter 4, exercise 22 (on separate piece of paper from HWK, marked "Extra Credit"). You can ignore the part of the problem that asks about rejecting at the 5% level. [solutions] |
Feb 3 |
§8.1. Linearity of expectation §8.2. Expectation and independence §4.1. Normal approximation §9.1. Estimating tail probabilities |
Feb 5 |
§4.1. Normal approximation §4.2. Law of large numbers §4.3. Applications of the normal approximation |
Feb 7 |
§4.4. Poisson approximation HWK (for Friday, Feb 14). Read §4.5, §4.6. Do Chapter 4, exercises 4.10, 4.14, 4.27, 4.30, 4.36, 4.39. 1% Extra Credit (for Friday, Feb 14); not required. Do Chapter 4, exercise 4.56 (on separate piece of paper from HWK, marked "Extra Credit"). [solutions] |
Feb 10 |
No lecture. |
Feb 12 |
Premier League goals [data] [code] §4.5. Exponential distribution |
Feb 14 |
§4.6. Poisson process Premier League goals [data] [code] HWK (for Friday, Feb 21). Read §5.1, §5.2. Do Chapter 4, exercises 4.15, 4.51, 4.52. Do Chapter 5, exercises 5.2, 5.5, 5.11. 1% Extra Credit (for Friday, Feb 21); not required. Find a data set and show that it consists of samples from one of the probability distributions we have studied, as I did with the Premier League data in lecture (on separate piece of paper from HWK, marked "Extra Credit"). [solutions] |
Feb 17 |
No lecture. Presidents' Day. |
Feb 19 |
§5.1. Moment generating function [practice midterm problems] [distributions] |
Feb 21 |
§5.2. Distribution of a function of a random variable |
Feb 24 |
Midterm 2. Will cover material through Wednesday, Feb 19. Please bring your student ID. You may bring a page of handwritten notes, but nothing else; you do not need a blue book. [seat assignments] [exam] [solutions] [results] |
Feb 26 |
§6.1. Joint distribution of discrete random variables §6.2. Jointly continuous random variables HWK (for Monday, Mar 2). Read §6.1-6.3 and §8.1-8.3 Do Chapter 5, exercises 5.7, 5.14, 5.21. Do Chapter 6, exercises 6.3, 6.7, 6.22. 1% Extra Credit (for Monday, Mar 2); not required. Do Chapter 5, exercise 5.40 (on separate piece of paper from HWK, marked "Extra Credit"). [solutions] |
Feb 28 |
§6.3. Joint distributions and independence HWK (for Friday, Mar 6). Read §8.1-8.4. Do Chapter 6, exercises 6.10, 6.12, 6.25, 6.28. Do Chapter 8, exercises 8.3, 8.7, 8.11, 8.16, 8.43. 1% Extra Credit (for Friday, Mar 6); not required. Do Chapter 6, exercise 6.58 (on separate piece of paper from HWK, marked "Extra Credit"). [solutions] |
Mar 2 |
§8.1. Linearity of expectation §8.2. Expectation and independence |
Mar 4 |
§8.3. Sums and moment generating functions |
Mar 6 |
§8.4. Covariance and correlation HWK (for Friday, Mar 13). Read §9.1-9.3. Do Chapter 8, exercises 8.49, 8.50, 8.52. Do Chapter 9, exercises 9.2, 9.3, 9.4, 9.5, 9.11, 9.14, 9.19. 1% Extra Credit (for Friday, Mar 13); not required. Do Chapter 8, exercise 8.65 (on separate piece of paper from HWK, marked "Extra Credit"). [solutions] |
Mar 9 |
§9.1. Estimating tail probabilities §9.2. Law of large numbers |
Mar 11 |
§9.3. Central limit theorem |
Mar 13 |
No lecture. |
Mar 18 |
Final exam due at 11:00am. [exam] [solutions] [results] |
[1] |
Andrei Nikolaevich Kolmogorov,
Grundbegriffe der Wahrscheinlichkeitrechnung (1933); translation edited by Nathan Morrison, Foundations of the Theory of Probability (New York: Chelsea 1956). |
[2] | Ani Adhikari and Jim Pitman, Probability for Data Science (2019). |
[3] | Gian-Carlo Rota and Kenneth Baclawski, Introduction to Probability and Random Processes (1979). |