DISCRETE MATHEMATICS

Spring 2017

New Computer Science Department, room 208;

phone: 632-8458

e-mail: anita@cs.stonybrook.edu

Office Hours: Monday, Wednesday
12:30 pm - 2: 00pm, and by appointment

e-mail:

Office Hours: tba

Office Location: tba

CONCRETE MATHEMATICS

A Foundation for Computer Science

Graham, Knuth, Patashnik

Addison- Wesley, Third Edition

Part ONE: **Concrete Mathematics **as
presented in the Textbook

We will cover all or parts of Chapters 1-5 of the book

Part TWO: **Discrete Mathematic:**
if time allows will cover some chosen topics in classical Discrete
Mathematics.

I will provide Lecture Notes and sets of Problems and you can use any Discrete Mathematics book as an extra reading

There will be two Practice Tests, three One Question Quizzes, a Midterm and a FINAL examination

There also will be assigned sets of
homework problems students must work out and learn for
the tests

The complete solutions to all problems are posted on the course
webpage

The book also contains majority of solutions but they are are not
complete

All tests are **CLOSED NOTES** and **CLOSED
BOOK**

If a student is found using notes or a book during a test, he/she
will receive **AUTOMATICALLY 0pts**
for a given test.

There are 6 sets of Homework problem

Not all of them might be covered.
**None will be collected or graded**. You will be tested
Homework problems dealing with material covered in class. Some
solutions (very short) of homework problems are also in the text
book.

Students are responsible for working out and writing DETAILED
solutions explaining all steps and methods used, as it is done in
our Lecture Notes. We will cover
some of such detailed solutions in class and ALL of them are
POSTED on our web page for you to study and learn how to write
them.

Your GRADES on the tests will depend on the form, attention to details, and carefulness of your written solutions.

The course will follow the book very closely and in particular we will cover some, or all of the following chapters and subjects.

PART ONE: CONCRETE MATHEMATICS

the course will follow the book very closely and in
particular we will cover some, or all of the following chapters
and subjects.

Chapter 1: Recurrent Problems

Chapter 2: Sums

Chapter 3: Integer functions

Chapter 4: Number Theory

Chapter 5: Binomial Coefficients pp 153- 204

Chapter 6: Special numbers pp 243- 264 (reading)

PART TWO : DISCTETE MATHEMATICS

Some Lecture Notes and Problems (Hmk 6) are posted. More to
follow.

HOMEWORK 1, Chapter 1: Problems on pages 17 -20.

Write carefully a detailed solution to problems 2, 6, 7, 8, 9, 11,
12, 14, 15, 16, 19, 18, 20,

write details of pp 12-13 discussion of cyclic properties of J(n)
and the false guess that J(n) = n/2,

write details of pp 15-16 binary solutions to generalized
recurrence.

HOMEWORK 2, Chapter 2 part one: Problems on pages 62-63.

Write and present a detailed solution to problems 5 ,6, 7, 8, 9,
10, 11, 13, 14, 15, 16,

HOMEWORK 2, Chapter 2 part two: Problems on pages 63-66.

Write and present a detailed solution to problems 16, 18, 19, 20,
21, 23, 24, 25, 26, 27, 29, 30, 31.

HOMEWORK 3, Chapter 3: Problems on pages 96- 101.

Write and present a detailed solution to problems 10, 11, 12, 14,
16, 17, 19, 20, 23, 28, 31, 33, 35, 36.

HOMEWORK 4, Chapter 4: Problems on pages 144 - 149.

Write and present a detailed solution to problems 2, 6, 14, 15,
45.

HOMEWORK 5, Chapter 5: Problems on pages 230 - 235.

Write and present a detailed solution to problems 2, 4, 6, 7, 8,
15, 16, 17, 18, 35, 43, 45.

HOMEWORK 6, Discrete Mathematics- some problems posted- more to come

This is a preliminary schedule. The changes and updates, if any, will be advertised in the NEWS section

Q1: Monday, February 13

PRACTICE TEST 1: Wednesday, March 8, in class

Use it as your own PRACTICE- write carefully all solutions. ONLY One Problem will be corrected

Spring Break: March 13 - 19

MIDTERM: Monday, March 20, in class

Midterm covers problems from Homework sets 1 and 2 (chapters
1 and 2 ) plus content and problems in the Lecture Slides that
were covered in class **before** the Practice
Test 1

All solutions are posted on the course web page.

Q2: Monday, April 10

Q3: Monday, April 24

PRACTICE TEST 2 Wednesday, May 3, in class

It covers material covered in class **after** MIDTERM and**
before **the TEST and corresponding Homework sets as posted

LAST DAY OF CLASSES- May 3

FINAL: will be given during the Finals week, May 9 - 17, exact time and place t.b.a

Final covers problems from all hmks and testsIs it possible to obtain Zn regions with n bent lines when the angle at each zig is 30 degrees?

Answer: Here we will need 12 such bent lines, when the first overlap occurs. This is because a complete circle is of 360 degrees and each zig is 30 degrees. So, till n=11 we will get Zn regions. On the 12th bent line, it will overlap with one of the previous lines in order to give Zn regions.

Original textbook was an extension of "Mathematical Preliminaries" of Knuth book of ART OF COMPUTER PROGRAMMING. Concrete Mathematics is supposed (and hopefully will) to help you in the art of writing programs, or thinking about them.

The second part of the course will cover some chosen topics in Number Theory and classical Discrete Mathematics, if times permits.