Our capacity to fathom the world around us hinges on our ability to understand quantities which are inherently unpredictable. Therefore, in order to gain more accurate mathematical models of the natural world we must incorporate probability into the mix. This course will serve as an introductions to the foundations of probability theory. Topics covered will include some of the following: (discrete and continuous)random variable, random vectors, multivariate distributions, expectations; independence, conditioning, conditional distributions and expectations; strong law of large numbers and the central limit theorem; random walks and Markov chains. There is an honors version of this course: see MATH 60.
Introduction to Probability (2nd edition) by Charles M. Grinstead and J. Laurie Snell, American Mathematical Society. By courtesy of the authors, this book is free to access here
Introduction to Probability (2nd edition) by D. Bertsekas and J. Tsitsiklis, Athena Scientific
| Instructor | Bohan Zhou |
|---|---|
| Class | MWF 13:10 - 14:15 |
| Office-hour | (DX) Tu 13:40 - 14:30 |
| bzhou AT math.dartmouth.edu |
This course will run as synchronous activities online. Live lectures will be deliveried through zoom.
There will two midterm exams and a cumulative final exam. Exams will be posted on Gradescope. Exams are required to be submit to Gradescope.
If you have a question about how your exam was graded, you can ask your instructor; to have your exam regraded, please submit your question in writing to your instructor.
The exams are scheduled as follows:
Written homework assignments will be assigned weekly and will be posted on the gradescope. Homework will be assigned each Wednesday and must be uploaded to Gradescope by the next Wednesday at 6pm Eastern Time. No late homework will be accepted. The lowest homework grade will be dropped. For the homework the Honor Principle below applies.
Academic integrity is at the core of our mission as mathematicians and educators, and we take it very seriously. We also believe in working and learning together.
Cooperation on homework is permitted and encouraged, but if you work together, try not take any paper away with you—in other words, you can share your thoughts (say on a blackboard), but try to walk away with only your understanding. In particular, you must write the solution up individually, in your own words. This applies to working with tutors as well: students are welcome to take notes when working with tutors on general principles and techniques and on other example problems, but must work on the assigned homework problems on their own. Please acknowledge any collaborators at the beginning of each assignment.
On exams, you may not give or receive help from anyone. Exams in this course are closed book, and no notes, calculators, or other electronic devices are permitted.
Plagiarism, collusion, or other violations of the Academic Honor Principle will be referred to the Committee on Standards.
The course grade will be based upon reading and class participation, the scores on the short exams, homework, and the final exam as follows:
| Written homework | 20% |
| Attendance, Participation | 10% |
| Midterm 1 | 20% |
| Midterm 2 | 20% |
| Final Exam | 30% |
Some students may wish to take part in religious observances that occur during this academic term. If you have a religious observance that conflicts with your participation in the course, please meet with your instructor before the end of the second week of the term to discuss appropriate accommodations.
Students who need academic adjustments or alternate accommodations for this course are encouraged to see their instructor privately as early in the term as possible. Students requiring disability-related academic adjustments and services must consult the Student Accessibility Services office (Carson Suite 125, 646-9900, Student.Accessibility.Services@Dartmouth.edu). Once SAS has authorized services, students must show the originally signed SAS Services and Consent Form and/or a letter on SAS letterhead to their professor. As a first step, if students have questions about whether they qualify to receive academic adjustments and services, they should contact the SAS office. All inquiries and discussions will remain confidential.
We reserve the right to make changes to this syllabus and to course policies during the term. Such changes will be announced by email when they are made.