Course: MCS 421, Combinatorics

CRN: 34232 and 34233

Time: MWF 900-950pm

Place: ONLINE through Zoom till Jan 21, in person after that in Taft 215 (as per guidelines)

Professor: Dhruv Mubayi

Office: 620 SEO

Tel:
3-8036

E-mail: mubayi@uic.edu

Course Web Page:
http://www.math.uic.edu/~mubayi/421/Spring22/421Spring22info.html

Office Hours: To be decided

Grading Policies:

Attendance and class participation: 10%

Homework (due Friday roughly every two weeks): 15%

Two in-class midterms, 25% each

Final Exam: 25%

Be sure to staple your homework. No late homework will be
accepted.

Disability Policy: Students with disabilities who require accommodations for access and participation in this course must be registered with the Office of Disability Services (ODS). Please contact ODS a 312/413/-2183 (voice) or 312/413-0123 (TTY).

Prerequisite: Prerequisite(s): Grade of C or better in MATH 215; and Grade of C or better in MATH 310 or Grade of C or better in MATH 320; or consent of the instructor.

Description: The pigeonhole principle, permutations and combinations, generating permutations and combinations, binomial coefficients, inclusion-exclusion principle, recurrence relations and generating functions, special counting sequences, Polya theory of counting. We will attempt to cover most of Chapters 1--8, 10, and 14 from the text.

Text: Brualdi, Introductory Combinatorics, Prentice Hall. The text is not required; class notes will suffice for everything. But the text has many extra problems (and more details of various math concepts) that you can do for practice.

Homework 1, Due Friday January 28:

Chapter 1: 1, 2, 3, 25, 38, 43

Solutions to HW1

Homework 2, Due Friday February 11 (its somewhat long so start early)

Chapter 2: 1,2,5 a,b, 8,11,16,28 a, 38, 39 a,c, 42, 45 a,b

Chapter 3: 1, 2, 4, 5, 8, 22, 27

Solutions to HW2

Homework 3, Due Friday February 25:

Chapter 4: 5, 8a, 20, 35, 37, 47,

Chapter 5: 11, 16, 18, 25, 48, 49

Solutions to HW3

Homework 4, Due Friday March 11:

Chapter 6: 2, 5, 6, 7, 10, 13, 19, 22, 23, 26

Solutions to HW4

Homework 5, Due Friday April 1:

Chapter 7: 1 (all parts), 5, 8, 9, 16, 17, 21, 26, 33, 34, 42, 47

Solutions to HW5

Homework 6, Due Friday April 15

Chapter 8: 1, 2, 9, 12, 19, 25, 26d

Chapter 10: 19, 26, 28, 32, 38

Solutions to HW6

Homework 7, Due Friday April 29

Chapter 10: 42

Chapter 14: 7, 8, 12, 13d, 15, 19, 26, 35, 48

Solutions to HW7