**Math 724 -- Combinatorics I**I

**Spring 2014, TuTh 1:30--2:45 PM, SAS 1220**

**Instructor:** Seth Sullivant, office: 3114 SAS Hall, email: smsulli2@ncsu.edu

**Syllabus:** Syllabus

**Office Hours: **Tu 3:00- 4:00, W 2:00-3:00,
Or by appointment

**Text:** G. Ziegler.* Lectures on Polytopes* Springer, Graduate Texts in Mathematics **152** ISBN: 978-0387943657

**Recommended Texts:** R.Thomas, *Lectures in Geometric Combinatorics*, American Mathematical Society, ISBN: 978-0821841402

**Prerequisites: **Math 524

**Course Description: ** Combinatorics is the part of
mathematics concerned with discrete structures and finite sets. Anytime we need to answer the question "how many ways are there to do X?" we are usually solving a combinatorial problem. These discrete structures arise in more than just counting problems, and combinatorial reasoning pervades modern mathematics. This is the second course of a year-long series on combinatorics. The first semester was on algebraic and enumerative combinatorics and the second semester will focus on geometric combinatorics. Main topics for the fall semester are: Polyhedral Geometry Basics: V-polyhedra and H-Polyhedra, Fourier-Motzkin elimination, Schlegel diagrams, linear programming for geometers, Steinitz theorem (6 weeks), Simplicial and polyhedral complexes, regular subdivisions and triangulations, Kruskal-Katona theorem, shellability (4 weeks), Lattice polytopes, Ehrhart theory, toric varieties (4 weeks)

Learning Objectives (This document will be updated throughout the course and can be used as a study guide.)

** Schedule: ** Is available here.

** Homework: ** Homework will be assigned weekly and is due in class on Thursday, unless otherwise indicated. Students must write up their own solutions. Working with other students is allowed, however, you must first attempt all problems on your own before discussing solutions with other students. Limit your group size to at most four students. Each student must write up their own solutions.
Please indicate on your homework any sources that you used in preparing
solutions (e.g. if another student helped with a solution, or you found the
solution in a book).

It is acceptable to use other sources besides the course notes and the text to aid your learning. However, using other student's homework solutions from previous courses, online homework solutions from courses at other universities, or copying the solutions out of books are unacceptable sources for preparing your homework, and violate the university's academic integrity policy.

Students are encouraged to prepare homework solutions in LateX. Homework assignments can be found at the course website as well as information on preparing your homework in LateX.

A file explaining how to prepare your homework can be found here. Homework assignments can be found here.

**Policy on Late Homework:** Homework is due in class on Thursdays, unless otherwise indicated. Late homework will be accepted up to Friday at 5 PM of the week it was due, either to my mailbox, delivered to me in person, or by email and will received 80% of the points.** Any homework turned in after Friday at 5 PM will receive a zero.** If you must miss a class on the day a homework is due and you want full credit, it is your responsibility to get the homework to me by the beginning of class on Thursday. This could be delivered to my mailbox, delivered to me in person, turned in by another student, or by email.

**Quizzes:** There will be two 20-minute quizzes. Each quiz will be worth 5% of your grade. The quizzes will cover basic definitions and theorem statements only. The quizzes will be on February 11 and April 8.

**Exams: ** There will be one in-class midterm exam and an in-class final exam. The midterm will be on February 25. The final exam will take place in the usual classroom from 1-4 PM on Tuesday, April 29.

** Grades: **Grades will be based on Homework (40%), Quizzes (10%), Midterm (20%), and Final Exam (30%). Grades are based on the following scale: A : (> 85%), B: (70-85 %) C: (60-70%) D-F: (<60%).

**Attendance and Participation: **Participation in class activities, group work, and class discussions will be a key contributor to your understanding of the material. To encourage your participation, I will provide up to one third of a letter grade "bonus" to students that attend regularly and participate actively in group work in class (fyi: one third of a letter grade means B would become B+, B+ would become A-, etc.).

**Adverse Weather:** Announcements regarding scheduled delays or the closing of the University due to adverse weather conditions will be broadcast on local radio and television stations and posted on the University homepage.

**Electronic Devices:** You may use your electronic devices in class as long as it is not distracting to the other students or me. (Warning: I get distracted very easily.) Acceptible: Using a tablet to take notes. Unacceptible: Answering your phone in class, typing on a laptop.

**Academic Integrity Statement: **Students are required to follow the NCSU policy . “Academic dishonesty is the giving, taking, or presenting of information or material by a student that unethically or fraudulently aids oneself or another on any work which is to be considered in the determination of a grade or the completion of academic requirements or the enhancement of that student's record or academic career.’’ (NCSU Code of Student Conduct). The Student Affairs website has more information.

**Students with Disabilities:** Reasonable accommodations will be made for students with verifiable disabilities. In order to take advantage of available accommodations, students must register with Disabilities Services for Students at 1900 Student Health Center, Campus Box 7509, 515-7653. For more information on NC State's policy on working with students with disabilities, please see the Academic Accommodations for Students with Disabilities Regulation (REG02.20.01).

**Class Evaluations:** Online class evaluations will be available for students to complete during the last two weeks of class. Students will receive an email message directing them to a website where they can login using their Unity ID and complete evaluations. All evaluations are confidential; instructors will never know how any one student responded to any question, and students will never know the ratings for any particular instructors.

**LateX Resources:**

- Essential LateX
- Essential Mathematical LateX
- LateX 2e introduction
- LATEX Software and Documentation
- Easy to install LateX for Windows
- Easy to install LateX for Macs