**Instructor:** Igor Pak

See email instructions below.

**Class schedule:** MWF 9:00 - 9:50 am, LA time, online.

Zoom meeting link and password will be sent by email from the course my.ucla site.

They are also permanently displayed on the course CCLE website.

**Discussion Section:** Tue 9:00 - 9:50, online (address to be announced)

**Office Hours:** Mon 10:00-10:50 am (right after class), Mon 2:00-2:30 am (for other time zones), or by appointment.

For all these, use the course Zoom link.

**Teaching Assistant:** Jason Snyder (see that website for email)

**TA Office Hours: **Tue 10-11 am (regular), Fri 12-1 pm (open)

Discussions and TA OH Zoom meeting links are posted on the CCLE website.

**Note:** University deadlines and holidays according to the
UCLA academic calendar.

**Textbooks:** J. Matousek, J. Nesetril (MN), *Invitation to Discrete Mathematics*,
Oxford Univ Press, Second Edition

Online content (UCLA library)

MN Table of content (see also MN Amazon
page)

Additional reading will be posted on this page if necessary.

**Grading:** Homeworks: 20%, Midterm: 20%, Final: 60%.

**Difficulty:** This is an introductory course in Graph Theory and related topics.
The students are expected to learn the theory and solve problems on the homeworks.
The problems will be both computational and require some proof abilities.

**Other expectations:**
I would guess that the average student
should spend about 8-10 hours per week outside of class to get a decent grade
(incuding discussion sections and study group meetings).
Much of this time should be spent on the homeworks, but some should
be spent on reading the book and absorbing the class material.

Although much of the material will follow the textbook, I will change the order of sections and some additional material will be presented in class, so class participation is very important. More specific info on the order of sections will be posted soon.

**Lecture notes and videos:**
The class will follow the book fairly closely, so I will not be making regular lecture notes.
However, I will be making in-class *Zoom videos* available to accommodate students unable
to join during the lecture. I expect students to view all lectures either in class or after hours.
Occasionally, additional reading materials will be posted here (or on CCLE website if copyright
restricted to UCLA students), as they come available.

**HA1** is here, due Jan 13.

**HA2** is here, due Jan 20.

**HA3** is here, due Jan 27.

**HA4** is here, due Feb 3.

No HA due Feb 10 -- Midterm! Consider using 2016 midterm as a practice test.

**HA5** is here, due Feb 17.

**HA6** is here, due Feb 24.

**HA7** is here, due Mar 3.

**HA8** is here, due Mar 10.

**Midterm:** Wed Feb 10, 2021, online, 24 hr window, exact times 8:00 am PT -- 7:59 am PT next day.

*Midterm problems* are available here.

*Midterm answers: *

**1.** 1260, 26208 (or, using the book's definition of P_{5}, 169344), 0, 1980, 26208, 138600

**2.** 2308, not unique (if 610 used in place of 61 a correct solution is accepted)

**3.** 38610

**4.** 4, infinite

**5.** FFFTT, TTTFF, FTTTF, TFFTT

**Final:** Mon Mar 15, 2021, online, 24 hr window, exact times 8:00 am PT -- 7:59 am PT next day.

**Practice final answers:**

**1.** all edges (1,j') and (i,1'),

**2.** 94.5

**3.** Hint: number of spanning trees is at most |E|-choose-n, and |E| <3n.

**4.** Hint: use Euler's formula

**5.** Hint: d_{1} >2 because otherwise the graph is a union of at least two connected components which are paths

**6.** Hint: cliques give lower bound for the chromatic number

**8.** 112

**9.** Hint: use induction

**10.** TTTFT, T (n/6 typo) FT(we didn't cover that) T, F(we didn't cover that) FTTT

**Note:** On CCLE, I opened a discussion forum where you can post replies in case
you are looking for study partners.

Put

Please put in your first line "Dear Professor Pak," -- no other salutations are allowed in the first line of the message.

At the end of your email, you must include your full name, UCLA id, and your official

Click here to return to Igor Pak Home Page.

*Last updated 3/13/2021*