Math447/557Combinatorial MathematicsSpring2017MWFPAS224http://alamos.math.arizona.edu/~rychlik/math447http://marekrychlik.com/math447ProfessorMarek RychlikMathematics605rychlik@email.arizona.edu
15206216865
1-520-621-6865 Marek RychlikMMathematics605Regular Office Hours in my office Marek RychlikMMathematics605Regular Office Hours in my office Marek RychlikFMathematics220Math Upper-Division TutoringApplied CombinatoricsSixth EditionAlan TuckerJohn Wiley & Sonsrequired
Two 1-hour Midterms, worth 20% of the course grade
each, and a 2-hour Final Exam worth 30%.
Homework is assigned weekly and graded, and it counts for 30% of
course grade. The grade for each assignment shall be based on a
representative sample of the assigned problems. Homework shall be
submitted as a typed paper, with the exception of these graphs and
figures which cannot be easily drawn with software. Recommended
tools for preparing the homework paper are LaTeX and Graphviz or
TikZ for drawing graphs. They will be briefly discussed in
class. Proofs should be complete, concise and clear in terms of
reasoning and presentation.
Mastermind Extra Credit
In the first month of the course, there will be weekly
Mastermind puzzles posted on this webpage each Monday at 10:00
pm. Mastermind is explained in the Prelude at the front of the
textbook. The first five students to email the correct
solution (with an explanation of their reasoning) will get 3
extra points on the first test; the next five students to
e-mail me the correct sequence will get 2 extra points on the
first test and the next 5 students will get one extra point on
the first test.
Strengthen logical reasoning skills to solve combinatorial problems using:
elements of propositional calculus;proof by contradiction;logical consequences of assumptions.
Learn to find multiple (equally valid) ways to solve a combinatorics problem:
apply a top-down strategy (breaking a problem into parts and subparts);apply a bottom-up strategy (solving special subcases and building up);learn to solve problems from first principles, rather than looking for existing templates or formulas;solve a complementary problem;use different strategies to categorize subcases of a problem;use different techniques (e.g., generating functions, inclusion-exclusion).
Learn basic graph theory results and apply them in problem-solving:
isomorphism;planar graphs;Hamilton circuits and Euler cycles;graph coloring;trees and ways to search them;
Use formulas for counting basic combinatorial outcomes to
construct solutions to more complex combinatorial enumeration
problems:
permutations, with and without repetition;combinations, with and without repetition.
Apply counting strategies to solve discrete probability problems.
Use specialized techniques to solve combinatorial enumeration problems:
generating functions;recurrence relations;inclusion-exclusion principle.12Jan112017Jan202017Graph Theory Basics, Isomorphism1.11.21.3Feb11.1169141620231.245bck6cdef71.3 16103Jan23Jan27Planar Graphs, Euler Cycles1.42.1Feb81.43bh7befgh811151620252.1249104Jan30Feb3Planar Graphs, Euler Cycles and Trails1.42.15Feb6Feb10Hamilton Circuits, Graph Coloring2.22.32.4Feb152.234bjko7b9162.31bcgl14156Feb13Feb17Graph Coloring, Trees and Searching2.43.13.2Feb222.4 7a3.11a4611131925293.21ab47Feb20Feb24
Graph Coloring, Trees and Searching, Traveling Salesperson
Problem
2.43.13.23.3Feb273.2516b253.3158Feb27Review for Midterm 18Mar1Midterm 18Mar3Basic Permutations and Combinations5.15.2Mar225.1679121316abc2022252633365.24581016bcd25425369a9Mar6Mar10Counting Problems with Repetition5.35.4Mar295.12429305.23238555.32457912215.41119212847486.12b4bc6710Mar11Mar19Spring Recess10Mar20Mar24Counting Problems with Repetition, Generating Function Models5.35.46.111Mar27Mar31Generating Function Models, Evaluating Generating Function Coefficients6.16.2Apr125.22646565.31519225.42ab3ab710276.13ac8131612Apr3Review for Midterm 212Apr5Midterm 212Apr7Evaluating Generating Function Coefficients, Recurrence Relations6.27.1Apr196.21251315b17ab202213Apr10Apr14Recurrence Relations7.17.3Apr267.1246ab7111215192028307.3123a14Apr17Apr21Inclusion-Exclusion Principle8.18.2Apr308.191011121516242629368.22581113151923b15Apr24Apr28Chromatic Polynomials, Rook Polynomials, Review and/or
Optional Topics8.3Apr308.231328.32b4616May1May3Review and/or Optional TopicsFinals WeekMay5Final Exam, 1:00 pm - 3:00 pm (regular room)Attendance Policy
Students are expected to attend every scheduled
class and to be familiar with the University Class Attendance policy
as it appears in the General Catalog. It is the student's
responsibility to keep informed of any announcements, syllabus
adjustments or policy changes made during scheduled classes.
Expected Classroom Behavior
Students are expected to behave in accordance with the Student
Code of Conductand the Code of Academic Integrity. The guiding principle of academic
integrity is that a student's submitted work must be the student's
own. University policies can be found
at http://policy.arizona.edu/academic.
Threatening Behavior
See http://policy.web.arizona.edu/threatening-behavior-students.
No prohibited behavior will be tolerated.
Administrative Drop
Students who miss the first two class meetings will be
administratively dropped unless they have made other
arrangements with the instructor.
Missed Exams
Students are expected to be present for all exams. If a
verifiable emergency arises which prevents you from taking an
in-class exam at the regularly scheduled time, the instructor must be
notified as soon as possible, and in any case, prior to
the next regularly scheduled class. Make-up exams and quizzes
will be administered only
at the discretion of the instructor
and only under extreme circumstances. If a
student is allowed to make up a missed exam, (s)he must take
it at a mutually arranged time. No further opportunities will
be extended. Failure to contact your instructor as stated
above or inability to produce sufficient evidence of a real
emergency will result in a grade of zero on the exam. Other
remedies, such as adjusting credit for other exams, may be
considered.
Accessibility and Accommodations
Disabled students must register with Disability Resources and be
identified to the course instructor through the University's
online process in order to use reasonable accommodations.
It is the University's goal that learning experiences be as
accessible as possible. If you anticipate or experience
physical or academic barriers based on disability, please let me
know immediately so that we can discuss options. You are also
welcome to contact Disability Resources
15206213268
520-621-3268
to establish reasonable accommodations.
Please be aware that the accessible table and chairs in this room
should remain available for students who find that standard
classroom seating is not usable.
Policy on the grade of "I" (incomplete)
The grade of "I" will be awarded if all of the following conditions are met:
The student has completed all but a small portion of the required work.The student has scored at least 50% on the work completed.The student has a valid reason for not completing the course on time.The student agrees to make up the material in a short period of time.The student asks for the incomplete before grades are
due, 48 hours after the final exam.Changes to the Syllabus
The information contained in the course syllabus, other than
the grade and absence policies, is subject to change with
reasonable advance notice, as deemed appropriate by the
instructor.