Version of Feb 13, 2007.
MATH 413 (Spring 2007)
Combinatorics
MWF11 at 148 Henry
Zoltan Furedi
The aim of this course is to give an introduction to finite mathematics,
like enumerations, sieve method, designs and other symmetric configurations,
(no or very little about graphs).
We emphasize techniques, but also present proofs of theorems.
LECTURES, DISCUSSION: Monday, Wed. and Friday 11:00-11:50 in 148 Henry.
INSTRUCTOR: Prof. Zoltan Furedi, 233B Illini Hall
Telephone 333-3355.
E-mail address: z-furedi@math.uiuc.edu
OFFICE HOURS: Wednesday 9:30-10:20
I can often see you if you come by without an appointment
(whether or not during office hours).
TEXT: Introductory Combinatorics, by
Richard A. Brualdi, Prentice-Hall, 2004, Fourth Edition
We leave out (among others) entirely Chapters 4, 9, 11-14.
SYLLABUS:
What is Combinatorics (Sections 1.1, 1.2, 1.4 only) Class hours: 4
Pigeonhole (Ch. 2.1, 2.2) 2
Permutations and Combinations (Ch. 3) 6
Binomial coefficients (Ch. 5 minus 5.7) 6
Inclusion-Exclusion (Ch. 6.1, 6.2, 6.3, 6.4 only) 4
Recurrence and generating functions (Ch. 7) 8
Special sequences (Catalan, Stirling) (Ch. 8.1, 8.2, 8.3 only ) 5
Combinatorial Designs (Ch. 10) 4
Exams + leeway 4
Total 43
HOMEWORK:
Recommended homework will be assigned. I will not collect
homework this semester, but rather give QUIZZES once a week
(almost every Wednesday) whose questions come directly from the homework.
3rd quiz: on Feb 16 Friday!
Recommended HW
Ch.1 page 20-22: Exercise 1, 2, 3, 4, 5, 6, 8, 9, 10, 21
Ch.2 page 40-41: Exercise 3, 4, 5, 8, 12, 14, 15, 16, 17, 18
Ch.3 page 75-81: Exercise 1, 2, 3, 4, 5, 8, 9, 10, 11, 12, 15, 16,
19, 20, 28, 29, 30, 31, 34, 37, 38, 41, 45
Ch.5 page 153-158: Exercise 2, 3, 4, 5, 6, 7, 8, 11, 13, 14, 16,
20, 21, 22, 25, 45
Ch.6 page 200-202: Exercise 1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 17, 24, 25
Ch.7 page 259-264: Exercise 1, 2, 3, 4, 5, 12, 13, 14, 15, 16, 17,
19, 20, 23, 24, 26, 27, 35, 36, 37
Ch.8 page 317-319 : Exercise 1, 2, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19
Ch.10 page 415-421: Exercise 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11,
12, 13, 14, 15, 16, 18, 19, 20, 37, 58, 59, 60, 61
HOURLY EXAMS: Three evening exams are planned tentatively Feb 21, March 28
and April 25
at 5-6:50 pm (all Wednesdays). Location: 347 Altgeld Hall
(the Math building).
FINAL EXAM: The final exam will be on May 8, Tuesday, 8:00-11:00am,
here in our usual classroom.
NO CLASS: on Feb. 14 (snow emergency), March 16, April 18, 20.
These are cancelled for the 3 evening exams.
No classes on March 19, 21, 23 (Spring break!).
GRADING:
Quizzes (Homework) -- 18% ; Hour Exams -- 3x14% ;
Final Exam -- 40%
WEB:
http://www.math.uiuc.edu/~z-furedi/TAN/413math.html