MATH 503 Discrete Mathematics 2016 Fall
Instructor: Jozsef Solymosi
Office: MATH 220
Prerequisites: Familiarity with discrete structures (such as MATH 443)
is desirable but not imperative. Talented undergraduate students are
welcome however good grades and some honours math courses are required.
Tue Thu 11:00 - 12:30 (no
class on Tuesday, Sep.
Mathematics Annex 1118
Grading: Homework assignments 40%, Take home midterm 20%, Take home
Course book (recommended):
Laszlo Lovasz, Combinatorial
Problems and Exercises
There is another nice book which is a great read; it is Stasys Jukna’s Extremal
Course Material and Topics:
Discrete mathematics (combinatorics) is a fundamental mathematical
discipline as well as essential component of many mathematical areas,
and its study has experienced an impressive growth in recent years.
While in the past many results in this area were obtained mainly by
ingenuity and detailed reasoning, the modern theory has grown out of
this early stage and often relies on deep, well-developed tools.
The main aim of this course is to introduce many core ideas from this
topic, such as extremal set theory, Ramsey theory and design theory as
well as some of the dominant proof techniques such as probabilistic
methods and algebraic methods.
The course outline follows (with sections taken from Lovasz’ book) with
approximately 1 to 2 lectures being spent on each topic.
. Basic enumeration methods
. Connectivity in Graphs and
Menger’s theorem (section 6)
. Factors of Graphs and Tutte’s
theorem (section 7)
. Graph colourings and perfect
graphs (section 9)
. Block designs and Wilson’s theorem
. Extremal graph theory and Turan’s
theorem (section 10)
. Strongly regular graphs and
algebraic methods (section 11)
. Hypergraphs and extremal set
theory (section 13)
. Ramsey Theory and probabilistic
methods (section 14)
Further Notes (Check the course books above for the details):
- Enumerations. (Due Sept 22.) Solutions (thanks to Robert)
- Counting. (Due Oct 6.)
- Probability. (Due Oct 18.)
- Ramsey Theory. (Due Nov 17.)