Math447/557Combinatorial MathematicsSpring2019MWFPAS414http://alamos.math.arizona.edu/~rychlik/math447http://marekrychlik.com/math447ProfessorMarek RychlikMathematics605rychlik@email.arizona.edu
15206216865
1-520-621-6865 Marek RychlikMMathematics220Upper Division Tutoring Room Marek RychlikWMathematics605Regular Office Hours in my office Marek RychlikFMathematics605Regular Office Hours in my officeApplied 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 submit the correct
solution (with an explanation of their reasoning if required)
will get 3 extra points on the first test; the next five
students to submit 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.12Jan92017Jan182017Graph Theory Basics, Isomorphism1.11.21.3Jan301.1169141620231.245bck6cdef71.3 16103Jan21Jan25Planar Graphs, Euler Cycles1.42.1Feb61.43bh7befgh811151620252.1249104Jan28Feb1Planar Graphs, Euler Cycles and Trails1.42.15Feb4Feb8Hamilton Circuits, Graph Coloring2.22.32.4Feb202.234bjko7b9162.31abcgl14156Feb11Feb15Graph Coloring, Trees and Searching2.43.13.2Feb212.4 7a3.11a4611131925293.21ab47Feb18Feb22
Graph Coloring, Trees and Searching, Traveling Salesperson
Problem
2.43.13.23.3Feb253.2516b253.3158Feb25Review for Midterm 18Feb27Midterm 18Mar1Basic Permutations and Combinations5.15.2Mar215.1679121316abc2022252633365.24581016bcd25425369aMar2Mar10Spring Recess9Mar11Mar15Counting Problems with Repetition5.35.4Mar205.12429305.23238555.32457912215.41119212847486.12b4bc671010Mar18Mar22Counting Problems with Repetition, Generating Function Models5.35.46.111Mar25Mar29Generating Function Models, Evaluating Generating Function Coefficients6.16.2Apr105.22646565.31519225.42ab3ab710276.13ac8131612Apr1Review for Midterm 212Apr3Midterm 212Apr1Evaluating Generating Function Coefficients, Recurrence Relations6.27.1Apr176.21251315b17ab202213Apr8Apr12Recurrence Relations7.17.3Apr247.1246ab7111215192028307.3123a14Apr15Apr19Inclusion-Exclusion Principle8.18.2Apr288.191011121516242629368.22581113151923b15Apr22Apr26Chromatic Polynomials, Rook Polynomials, Review and/or
Optional Topics8.3Apr308.231328.32b4616Apr28May1Review and/or Optional TopicsFinals WeekMay3Final 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.