**Math 416/ CSC 416-- Introduction to Combinatorics**

**Spring 2013, TuTh 10:15--11:30 am, SAS Hall 2102**

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

**Office Hours: **Tu 1:30-2:30, W 2:30-3:30,
Or by appointment

**Text:** R. Merris, *Combinatorics*, Wiley-Interscience, 2003, ISBN-13: 978-0471262961

**Prerequisites: **Math 225 or CSC 226.

**Course Description: **Combinatorics is the part of mathematics concerned with discrete structures. This will be an introduction to enumerative combinatorics with an emphasis on theoretical aspects and proofs. Below is a rough outline of the topics to be covered (Chapters 1, 2, 4, 5 in the text).

- The Mathematics of Choice (binomial and multinomial coefficients, combinatorial identities, partitions, symmetric functions): 5 weeks
- The Combinatorics of Finite Functions (Stirling numbers, Bell numbers, principle of inclusion/exclusion): 4 weeks
- Generating Functions (ordinary and exponential generating functions, applications): 4 weeks
- Enumeration in Graphs: 2 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 at the beginning of class on Thursday. 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. 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:** No late homework will be accepted. The lowest homework score will be dropped. If you must miss a class on the day a homework is due, it is your responsibility to get the homework to me by the beginning of class on Thursday.

**Quizzes:** There will be a weekly quiz at the beginning of class on Tuesday of every week. In each quiz, you will be asked one question, which will be to repeat a key definition, theorem, or formula from the previous week's lectures and readings. There will be no make-up quizzes. The two lowest quiz scores will be dropped.

**Exams: ** There will be two in-class midterm exams (February 21 and April 4), and an in-class final exam. The final exam will take place in the usual classroom from 8:00-11:00 AM, May 2nd.

** Grades: **Grades will be based on Homework (25%), Quizzes (5%), Midterms (20% each), and Final Exam (30%). Grades are based on the following scale: A : (> 85%), B: (70-85 %) C: (60-70%) D-F: (<60%).

**Attendance:** Students are expected to arrive on time, to contribute to group work and class discussions, and to stay until the class ends. Attendance at all meetings of the class is expected. Occasional absences will be approved if they meet University policies.

**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.

**Cell Phones:** Pagers, cellular phones, iphones, jpods, laptops and other types of telecommunication equipment are prohibited from use during class. If you have a special need to have your phone on during class, please let me know.

**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