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