WESTERN UNIVERSITYDEPARTMENT OF MATHEMATICSLONDON, ONTARIO, CANADAM. ChudnovskyR. StanleyFALL 2019K. WickelgrenB. GreenT. TaoCOMBINATORIAL MATHEMATICS – Mathematics 3152AInstructorEmailOffice Hours: after eachclass in the sameclassroom and also byappointment and also byaccidental meetingOffice TelephoneClass TimesClass LocationTextbookPrerequistesFinal Examination DateEvaluationFunCombinatorial ClaimThe Art of Studying andResearchJán Mináč (also known as Professor Maniac J)minac@uwo.ca / and / jminac1811@gmail.comMy indoor office is in Middlesex College. The number of my office is a 32nd primenumber. Exercise 0: Find the number of my office. (You can find the solution inthe rotunda in Middlesex College.) I also use the university campus as a large,outdoor office. J(519) 661-2111, extension 86519Monday / Wednesday / Friday 10:30 a.m. – 11:30 a.m.
Middlesex College room 107Introductory Combinatorics (Classic Version), 5th Edition, by Richard A. Brualdi,Pearson, 2017. There are some copies available in the Book Store. I will alsorequest that the Taylor Library place a copy of this book on 2-hour reserve loan tobe available for students. (This book is optional – recommended but not required,as the main source of information will be your lecture notes.)0.5 course from: Mathematics 2120A/B, 2155A/B, 2211A/B, AppliedMathematics 2811B or permission of the Department. Some basic knowledge oflinear algebra and an introduction to mathematical structures may be useful. Alsoan interest in the magic of mathematics is very welcome. The courage to try andwrite neat proofs will be encouraged. If you are unsure about the backgroundrequirements, please speak with me or email me.
To be announced when the Office of the Registrar final exam schedule is in place.
The final examination period this semester falls between December 8th - 19th.
Homework 60% and Final Examination 40%During the entire semester. JCombinatorial Mathematics is delightful magic, filled with surprises andinteresting, challenging problems. (This claim will be proved in class.)We shall discuss and practice, and enjoy the art of studying and research.J. ChayesCombinatorial Math Course Outline: Permutations, inversions in permutations, the binomial theorem,Pascal’s triangle, the Inclusion-Exclusion Principle, Polya’s counting formula for permutations and symmetrygroups, Möbius inversion, recurrence relations, generating functions, Catalan numbers, difference sequencesand Stirling numbers, partition numbers, introduction to graphs, trees, chromatic numbers, and magic squares.
We shall also add some ad hoc interesting and I hope fascinating material, enhancing this basic subject andconnecting it with current research in the field.
After the presentation of the basic course material, we shall select some delicious topics from an appetizingtray of tasty mathematical treats such as finite groups, networks, probability, distribution of prime numbers,finite fields, finite projective planes, codes, counting in groups, and some open problems.

L. EulerJ. LabuteR. MurtyJ. BirmanThe basic course material is the core of the course which we shall try to develop with many details and we shallaim at a full understanding of the basics.
In the other part of this course, we shall bravely make an attempt to understand the “big picture” and the latestdevelopments. This will often be done with bold strokes of our brushes, aiming our imagination and letting itloose; as well as freeing us from worries about the details. Perhaps some of you will decide to climb this hill orthat hill, or to examine certain deep topics with a microscope and the obsession that such an examination mayrequire.
Remark. Combinatorics has a great tradition and a rich history. However during the last century combinatorics often played the role of Cinderella although there was also some very interesting research going on incombinatorics at that time as well. Combinatorics was often not considered a part of “mainstream” mathematicsbut this view has changed dramatically, also due to some spectacular applications and developments incomputer science and in science in general, including artificial intelligence and networks.
In the past, only a few of the most outstanding mathematicians devoted their energy to this fascinating subject.
Today combinatorics is becoming quite popular and remarkable success has been obtained in recent years. I willtry and systematically develop parts of this area, and I will try and preserve some of the charm, beauty, andromantic dreams contained within it.When I was a teenager I often daydreamed and lived in my own world full of fantasy and magic. Sometimescombinatorial considerations snuck into this world. These were puzzling and fascinating. And then I learnedthat there were others dreamers called mathematicians who explore this combinatorial world as well as othermathematical worlds in a detailed way. And what a wonderful world all of this belongs to! I long to share thisworld with you.

Maryam Mirzakhani (Fields Medal 2014)Karen Uhlenbeck (Abel Prize 2019)Further Information:Final Examination: There will be one written final examination.

Common Course Policies for 2019/20 Mathematics Undergraduate coursesThe following is a list of course policies which are common to all undergraduate courses run by theMathematics department at Western for the academic year 2019/20.
Senate Policy on Prerequisites:	  Unless you have either the requisites for this course or written special permission from your Dean to enroll in it,you may be removed from this course and it will be deleted from your record. This decision may not beappealed. You will receive no adjustment to your fees in the event that you are dropped from a course forfailing to have the necessary prerequisites.
Course Websites:Students should check OWL (http://owl.uwo.ca) or the course website (if not hosted on OWL) on a regularbasis for news and updates for all of the courses in which they are enrolled. This is the primary method bywhich information will be disseminated to all students in each class. Students are responsible for checkingOWL on a regular basis.Accommodation and Accessibility:	  If you are unable to meet a course requirement due to illness or other serious circumstances, you must seekapproval for the absence as soon as possible. Approval can be granted either through a self-reporting of absenceor via the Dean’s Office/Academic Counselling unit of your Home Faculty. If you are a Science student, theAcademic Counselling Office of the Faculty of Science is located in NCB 280, and can be contactedat scibmsac@uwo.ca.
For further information, please consult the university’s policy on academic consideration for studentabsences: https://www.uwo.ca/univsec/pdf/academic_policies/appeals/Academic_Consideration_for_absences.pdf.
If you miss the Final Exam, please contact your faculty’s Academic Counselling Office as soon as you are ableto do so. They will assess your eligibility to write the Special Exam (the name given by the university to amakeup Final Exam).
You may also be eligible to write the Special Exam if you are in a “Multiple Exam Situation”(see http://www.registrar.uwo.ca/examinations/exam_ schedule.html).
Academic Policies:The website for Registrarial Services is http://www.registrar.uwo.caIn accordance with policy, http://www.uwo.ca/its/identity/activatenonstudent.html, the centrally administered email account provided to students will be considered the individual's official university e-mail address. It is theresponsibility of the account holder to ensure that e-mail received from the University at his/her officialuniversity address is attended to in a timely manner.
Students must use their Western (@uwo.ca) email addresses when contacting their instructors.
Electronic devices (including cell phones and calculators) are NOT allowed on exams and may be confiscated.
Scholastic offences are taken seriously and students are directed to read the appropriate policy, specifically, thedefinition of what constitutes a Scholastic Offence, at the following Web site:http://www.uwo.ca/univsec/pdf/academic_policies/appeals/scholastic_discipline_undergrad.pdf.
Support Services:Please contact the course instructor if you require lecture or printed material in an alternate format or if anyother arrangements can make this course more accessible to you. You may also wish to contact StudentAccessibility Services (SAS) at 661-2147 if you have any questions regarding accommodations.
The policy on Accommodation for Students with Disabilities can be foundhere: https://www.uwo.ca/univsec/pdf/academic_policies/appeals/Academic%20Accommodation_disabilities.pdf.
The policy on Accommodation for Religious Holidays can be found here:http://www.uwo.ca/univsec/pdf/academic_policies/appeals/accommodation_religious.pdf.
Learning-skills counsellors at the Student Development Centre (http://www.sdc.uwo.ca) are ready to help youimprove your learning skills. They offer presentations on strategies for improving time management, multiple-choice exam preparation/writing, textbook reading, and more. Individual support is offered throughout theFall/Winter terms in the drop-in Learning Help Centre, and year-round through individual counselling.
Students who are in emotional/mental distress should refer to Mental Health@Western(http://www.health.uwo.ca/mental_health) for a complete list of options about how to obtain help.
Additional student-run support services are offered by the USC, http://westernusc.ca/services.
Acknowledgment of the Science Student Donation Fund:Mathematics undergrad courses are supported by the Science Student Donation Fund. If you are a BSc or BMScstudent registered in the Faculty of Science or Schulich School of Medicine and Dentistry, you pay the ScienceStudent Donation Fee. This fee contributes to the Science Student Donation Fund, which is administered by theScience Students' Council (SSC). One or more grants from the Fund have allowed for the purchase ofequipment integral to teaching this course. You may opt out of the Fee by the end of September of eachacademic year by completing the online form linked from the Faculty of Science's Academic Counselling site.
For further information on the process of awarding grants from the Fund or how these grants have benefittedundergraduate education in this course, consult the Chair of the Department or email the Science Students'Council at ssc@uwo.ca.