Course: MCS 421, Combinatorics

CRN: 34232 and 34233

Time: MWF 900-950pm

Place: ONLINE through Zoom

Professor: Dhruv Mubayi

Office: 620 SEO

E-mail: mubayi@uic.edu

Course Web Page:
http://www.math.uic.edu/~mubayi/421/Spring21/421Spring21info.html

Office Hours: W 10-12

Grading Policies:

Attendance and class participation: 10%

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

Two in-class midterms, 25% each: 50%

Final Exam: 25%

HW should be scanned and turned in on Blackboard.
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 5th edition. Note that the text is not required for the mathematics (class lectures and notes should suffice for this) but you will need the text to find the homework problems.

Homework 1, Due Wednesday January 27:

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

Solutions to HW1

Homework 2, Due Friday February 12 (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 26:

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

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

Solutions to HW3

Test 1: Friday February 26

Homework 4, Due Friday March 12:

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

Solutions to HW4

Spring Break - March 22-26

Homework 5, Due Friday April 2:

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

Solutions to HW5

Test 2, Friday April 2

Homework 6, Due Friday April 16

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

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

Solutions to HW6

Homework 7, Due Friday April 30

Chapter 10: 42

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

Solutions to HW7