Math 454, Section E1
Summer 2015

Instructor

Timothy Naumovitz

tnaumovi@math.rutgers.edu

Office Hours

Hill Center 626

Tuesdays and Wednesdays 2:30-3:30pm, or by appointment

Textbook

Roberts and Tesman, Applied Combinatorics (2nd edition) Prentice-Hall, ISBN # 0-13-079603-4

Prerequisites

Calc 2 and 01:640:250

Lecture

MTWR 12:20-2:10

ARC-105

Busch Campus

Calculators

Neither required for the course nor permitted on exams.

Grade Breakdown

Homework: 25%

Quizzes: 15%

Midterm: 25%

Final: 35%

Description

There will be one in class midterm on the third Thursday of the class, and a final which will take place on the last day of class. The final will start at 12:20pm and take 3 hours (more than the allotted time), so any conflicts due to this lengthened period should be brought up with me as early as possible. Quizzes will take place on the first, second, fourth, and fifth Thursdays of the class. These quizzes will be of approximately 30 minutes in length. Makeup quizzes and exams will not be offered. If an exam is missed for a truly compelling, DOCUMENTED reason (e.g. "I was in a car accident this morning and had to go to the emergency room"), the other elements of the final grade will count proportionally more for that student.

Students are expected to attend all lectures, which is especially important as a lot of material will be covered in each lecture. In general, the pace of the course will be very rapid, meaning it can be very hard to catch up if you find yourself falling behind. The best way to avoid this is to make a point of not missing any lectures, to do the homework the day it is assigned, and to attend office hours when the lecture and/or homework leaves you at all confused.

Homework will be assigned according to the schedule below, which will be updated throughout the course. Due dates will be posted with each assignment, but in general homework will be due two class days after it is assigned. Homework assignments will be graded for correctness. Your solutions should contain adequate justifications. You are permitted, and in fact encouraged, to work together on homework problems, but all written work which you submit must ultimately be your own.

You may turn in a late assignment by the beginning of class the next day for half of the credit you would normally receive. Any assignments submitted later than that will not be graded. Homework should be turned in at the beginning of the class it is due. Handing in homework after a significant portion of the class has elapsed may be considered late.

All students in the course are expected to be familiar with and abide by the academic integrity policy (http://academicintegrity.rutgers.edu/academic-integrity-at-rutgers). Violations of the policy are taken very seriously.

Full disability policies and procedures are indicated at http://ods.rutgers.edu/. Students with disabilities requesting accommodations must present a Letter of Accommodations to the instructor as early in the term as possible (see https://ods.rutgers.edu/my-accommodations/letter-of-accommodations).

Schedule

Here is a tentative course plan. Be aware that I may deviate from this plan as I see necessary. I will attempt to adjust this accordingly, but it is important to understand that if I make changes to the schedule and assigned homework in class, these changes trump what is written below.

DATE TOPIC HOMEWORK
M 6/22 Basic Counting HW1: due W 6/24
T 6/23 Combinations and Identities HW2: due R 6/25
W 6/24 Poker Hands, Integer Solutions HW3: due M 6/29
R 6/25 Balls and Bins, Estimates, Quiz 1
Solutions
HW4: due T 6/30
M 6/29 Probability HW5: due W 7/1
T 6/30 Multinomials, Binomial Theorem HW6: due R 7/2
W 7/1 Recurrences, Characteristic Roots HW7: due M 7/6
R 7/2 Generating Functions, Quiz 2
Solutions
HW8: due T 7/7
M 7/6 Solving Recurrences using Gen Fncs HW9: due W 7/8
T 7/7 Exponential Gen Fncs HW10: due M 7/13
W 7/8 Inclusion Exclusion HW11: due T 7/14
R 7/9 Midterm Review Problems
Solutions
M 7/13 Introduction to Graph Theory HW12: due W 7/15
T 7/14 Bipartite Graphs, Isomorphism, Trees HW13: due R 7/16
W 7/15 Trees HW14: due M 7/20
R 7/16 Coloring, Quiz 3
Solutions
HW15: due T 7/21
M 7/20 Matchings HW16: due W 7/22
T 7/21 Euler Tours and Hamilton Cycles HW17: due R 7/23
W 7/22 Ramsey Theory, Pigeonhole Principle HW18: due M 7/27
R 7/23 Probabilistic Method, Quiz 4
Solutions
HW19: due T 7/28
M 7/27 Posets, Lattices, and antichains HW20: due W 7/29
T 7/28 Combinatorial Games HW21: due R 7/30
W 7/29 Review Review Problems
R 7/30 Final Exam
12:20pm - 3:20pm
includes all material covered
Solutions

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