| ABOUT THE COURSE |
| BASIC INFORMATION |
| ASSESSMENT |
| LATE ASSIGNMENTS |
| HOMEWORK |
| QUIZZES |
| EXAMS |
| LECTURE NOTES |
| CONDUCT |
NOTE: all course information announced here, including the meeting time, is subject to change! The date for the in-class midterm exam is tentative, and also subject to change (though plenty of notice will be given if it does change).
The tools that are used to tackle discrete problems come from all over mathematics. The method of generating function is a powerful tool in enumeration problems, and draws heavily on both real and complex analysis. Algebraic tools, particularly tools from linear algebra, are invaluable in extremal problems. Differential equations are used to track the growth rates of discretely defined families. Methods from probability and information theory are ubiquitous.
This course acts as an introduction to contemporary discrete mathematics. Roughly, the plan is to touch on the following topics:
The course will have no assigned text --- I will provide notes as the semester progresses. The following books well represent the level of the course, and will prove useful as reference resources:
Beyond familiarity with the basics of calculus, real analysis, linear algebra and algebra at the undergraduate level, the course has no real prerequisites other than a willingness to work hard and engage with the material. As such it is appropriate for all graduate students, and junior or senior honors undergraduates. Feel free to contact me if you want to discuss the suitability of the course for you.
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Basic information
Back to the top of the page Assessment
Back to the top of the page Late assignments
Detailed solutions to homeworks and quizzes will be posted here on their due dates, so late work cannot be accepted. All homework must be done by the due date to receive credit, and all quizzes and exams must be taken at the assigned times. I will not consider requests for homework extensions, or make-up quizzes and/or exams, except in the case of legitimate, university-sanctioned conflicts. It is your responsibility to let me know the full details of these conflicts before they cause you to miss an assignment! Excepting university-sanctioned conflicts, it is your responsibility to be in class for all scheduled lectures. Back to the top of the page Homework
Homework 5 due in class Wednesday April 12: Section 50, questions 1 through 5, of the lecture notes. Homework 4 due in class Monday March 27: Section 40, questions 1 through 3, of the lecture notes. Homework 3 due in class Friday March 3: (Section 15, Q5) AND (Section 22, Q1) AND (Section 25, EITHER Q1 OR Q2) AND (Section 29, EITHER Q1 OR Q2 OR Q3) AND (Section 32, Q1) of the lecture notes. Homework 2 due in class Wednesday February 15: Section 8, questions 13, 14, 12; Section 11, question 4; Section 13, question 2, and Section 8, question 11, of the lecture notes. Homework 1 due in class Monday January 30: Section 5, questions 1 through 5, of the lecture notes. The weekly/biweekly homework is an integral part of the course; it gives you a chance to think more deeply about the material, and to go from seeing (in lectures) to doing. It's also your opportunity to show me that you are engaging with the course topics. Homework is an essential part of your learning in this course, so please take it very
seriously. It is extremely important that you keep up with the homework, as if you do not, you may quickly
fall behind in class and find yourself at a disadvantage during exams and quizzes. You are permitted, in fact encouraged, to work together and help one another with homework, although what you turn in should be written by you. Providing detailed arguments in your homework is important, since learning how to write mathematics in a rigorous and yet concise and readable way is an essential part of graduate school in mathematics. Back to the top of the page Quizzes
Quizzes will be posted
here
in a single file that will be updated throughout the semester. Quizzes will not be totally problem-oriented, but rather will test basic understanding of definitions and theorems. Quiz solutions will also be posted
here. Back to the top of the page
The midterm exam was held on Wednesday March 22, in class. The exam, together with solutions, is incorporated into the class lecture notes. The final is take-home, and is due back on Thursday, May 11 by 6.15pm. Back to the top of the page Lecture notes
Here is where I will post the lectures notes, quizzes, homework, etc., in a file that will be updated as the semester progresses: Back to the top of the page Conduct
Honor code: This hardly needs to be said, but there's no harm in it: I expect all students to abide by the university's Honor Code pledge, to not participate in or tolerate
academic dishonesty. For this course, that means that although you may (and should) discuss assignments
with your colleagues, you must write the final version of each of your assignments on your own; if you use
any external sources to assist you (such as other textbooks, computer programmes, etc.), you should cite
them clearly; your work on the mid-semester exam and the final exam should be your own; and you will adhere
to all announced exam policies. Class conduct: The lecture room should be a place where you should feel free to engage in
lively discussion about the course topic; don't be shy! But non course related interruptions should
be kept to a minimum. In particular, you should turn off or switch to silent all phones, etc.,
before the start of class. If for some good reason you need to have your phone on during class, please
mention it to me in advance. Back to the top of the page
Exams
Lecture notes.