cse547, ams547

DISCTRETE MATHEMATICS

Spring 2012



GENERAL NEWS:

  • FINAL: Tuesday, May 8, 2:15PM - 4:45PM;
  • PLACE: HARRIMAN HALL, rooms 112 and 116
  • FINAL COVERS Chapter1 1-5.
  • Practice Final corected. E-mail TA for your grade.
  • New improved version of chapter 1, problem 20 posted in Student's Input
  • Ch2 Homeworks posted in Student's Input
  • Ch2 lecture notes posted in Student's Input
  • My Chapter 5 last lecture POSTER as LECTURE 18
  • More students input lectures/hmks will be posted as I receive it


  • Time:

    11:20am - 12:40pm

    When:

    Tuesday, Thursday

    Place:

    2311 Wireless Seminar Room CS Building

    Professor:

    Anita Wasilewska

    1428 CS Building; 632-8458
    e-mail: anita@cs.sunysb.edu
    Office Hours: Tuesday, Thursday, 3:00pm - 4:00 pm, and by appointment

    Teaching Assistant : Junxing Yang

    e-mail: junyang@cs.stonybrook.edu
    Office Hours: 1:00PM - 2:00PM on Monday and Wednesday and by appointment
    Office Location: Room 2110, CS department.

    Course Texbook

    CONCRETE MATHEMATICS
    A Foundation for Computer Science
    Graham, Knuth, Patashnik
    Addison- Wesley

    General Course Information

    There will be TWO MIDTERMS 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 will be three, or four Homework sets. NONE will be collected or graded. Solutions (very short) of all homework problems are 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 post ALL of them 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.

    COURSE CONTENT

    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: Classical Discrete Mathematics - Lecture Notes and Problems (HMK4) posted.

    HOMEWORK PROBLEMS

    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 1, 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.

    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 2, 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 3, Chapter 4: Problems on pages 144 - 149.
    Write and present a detailed solution to problems 2, 6, 14, 15, 45.

    HOMEWORK 3, 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 4, Discrete Mathematics Lecture - problems posted

    TESTS SCHEDULE

    Practice Midterm 1: Tuesday, March 6, in class

    Midterm 1: Tuesday, March 13, in class
    Midterm 1 covers problems from homeworks 1 and 2 (chapter 1 and 2 ) plus content and problems in the Lecture Notes. All solutions are posted on the course web page.

    Spring Break: April 2 - April 8

    Midterm 2: Tuesday, April 24, in class.
    Midterm 2 covers ch3 and ch4 homework problems PLUS Lectures proofs and examples.

    LAST DAY OF CLASSES- MAY 5

    FINAL: Tuesday, May 8, 2:15PM - 4:45PM; room to be announced
    Final covers problems from homework 3, 4 and some problems from Hmks 1, 2.

    DOWNLOADS

    Syllabus
    Writing Mathematical Texts

    STUDENTS INPUT

    Chapter 1 Lecture Notes
    SLIDES Chapter 1, Lecture 2
    SLIDES Chapter 1 Problem 16
    Chapter 1 Problem 20 (new)
    SLIDES Chapter 1 RADIX Representation
    INFINITE SUMS 1 -Prepared by Sivaranjini Dharmalingam and Vidhya Ramanathan
    INFINITE SUMS 2 (Examples) -Prepared by Sivaranjini Dharmalingam and Vidhya Ramanathan
    CHAPTER 2 LECTURE NOTES-Prepared by Shingo Omori and his group
    CHAPTER 2 Homeworks Solutions -Prepared by Pramod Ganapathy, Sheetal Tare, Ayon Chakraborty

    HOMEWORK PROBLEMS SOLUTIONS: CHAPTER 1

    Corrected Solution of Question 19, Chapter 1:

    Is 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.

    Chapter 1, Problem on pages 11-12
    Chapter 1, Problem 2
    Chapter 1, Problem 6
    Chapter 1, Problem 7
    Chapter 1, Problem 8
    Chapter 1, Problem 9
    Chapter 1, Problems 14, 2
    Chapter 1, Problem 16
    Chapter 1, Problem 16 Generalization
    Chapter 1, Problems 18, 19
    Chapter 1, Problem 20
    Chapter 1, Problem 20, solution 2

    HOMEWORK PROBLEMS SOLUTIONS: CHAPTER 2


    Chapter 2, Problem 6 Corrected
    Chapter 2, Problem 11
    Chapter 2, Problems 13, 14
    Chapter 2, Problem 15
    Chapter 2, Problem 19
    Chapter 2, Problems 20, 21 Corrected
    Chapter 2, Problem 23
    Chapter 2, Problem 29 full solution
    Chapter 2, Problem 29 short solution
    Chapter 2, Problem 29
    Chapter 2, Problem 31

    HOMEWORK PROBLEMS SOLUTIONS: CHAPTER 2


    Chapter 2, Problems 5,7
    Chapter 2, Problem 8
    Chapter 2, Problems 9, 10
    Chapter 2, Problems 16, 17
    Chapter 2, Problems 27,29
    Chapter 2, Problem 29
    Chapter 2, Problem 29 short solution

    HOMEWORK PROBLEMS SOLUTIONS: CHAPTER 3


    Chapter 3, Problem 10, 12
    Chapter 3, Problem 11
    Chapter 3, Problem 14
    Chapter 3, Problem 16
    Chapter 3, Problem 17
    Chapter 3, Problem 19, 20
    Chapter 3, Problem 23
    Chapter 3, Problem 31
    Chapter 3, Problem 33, 36
    Chapter 3, Problem 35

    HOMEWORK PROBLEMS SOLUTIONS: CHAPTER 4


    Chapter 4, Problem 2, 14
    Chapter 4, Problem 6
    Chapter 4, Problem 14
    Chapter 4, Problem 15
    Chapter 4, Problem 45

    HOMEWORK PROBLEMS SOLUTIONS: CHAPTER 5

    Chapter 5, Problem 2 Solution
    Chapter 5, Problem 3 Solution
    Chapter 5, Problem 4 Solution
    Chapter 5, Problems 4, 6 Solution
    Chapter 5, Problem 7 Solution
    Chapter 5, Problem 8 Solution
    Chapter 5, Problem 8 Solution 2
    Chapter 5, Problem 14 Solution
    Chapter 5, Problem 15 Solution
    Chapter 5, Problem 16, Chapter 4 Problem 15 Solution
    Chapter 5, Problems 15, 43 Solution
    Chapter 5, Problem 17 Solution
    Chapter 5, Problem 18 Solution
    Chapter 5, Problems 18, 45 Solution
    Chapter 5, Problem 35 Solution
    Chapter 5, Problem 74 Solution

    HOMEWORK 4 DEFINITIONS and PROBLEMS


    Descrete Mathenatics Definitions 1
    Descrete Mathenatics Definitions 2
    Descrete Mathenatics Definitions 3
    Descrete Mathenatics Definitions 3
    HOMEWORK 4 PROBLEMS
    HOMEWORK 4 SOLUTIONS

    PREVIOUS TESTS TO STUDY FOR FINAL


    Practice Midterm 1
    Midterm 1
    Practice Midterm 2
    Midterm 2
    PRACTICE FINAL

    LECTURE NOTES


    Lecture 1
    Lecture 2
    Lecture 3
    Lecture 4
    Lecture 5
    Lecture 6
    Lecture 7 Corrected pg(119-123a)
    Lecture 7
    Lecture 8
    Lecture 9
    Lecture 9a (Chapter 2, Infinite Sums 1)
    Lecture 9a (Chapter 2, Infinite Sums 1 SLIDES)
    Lecture 9b (Chapter 2, Infinite Sums 2)
    Lecture 10
    Lecture 11
    Lecture 12
    Lecture 13
    Lecture 14
    Lecture 15
    Lecture 16
    Lecture 17
    Lecture 18

    EXTRA SLIDES


    Chapter 2 Method 5
    Few Practice Midterm 1 Review Problems
    SPECTRUM THEOREM PROOF


    Academic Integrity Statement

    Each student must pursue his or her academic goals honestly and be personally accountable for all submitted work. Representing another person's work as your own is always wrong. Any suspected instance of academic dishonesty will be reported to the Academic Judiciary. For more comprehensive information on academic integrity, including categories of academic dishonesty, please refer to the academic judiciary website at Academic Judiciary Website

    Stony Brook University Syllabus Statement

    If you have a physical, psychological, medical, or learning disability that may impact your course work, please contact Disability Support Services at (631) 632-6748 or Disability Support ServicesWebsite They will determine with you what accommodations are necessary and appropriate. All information and documentation is confidential. Students who require assistance during emergency evacuation are encouraged to discuss their needs with their professors and Disability Support Services. For procedures and information go to the following website: Disability Support Services Website

    General Course Description:

    The course will have two parts: Concrete Mathematics as presented in the textbook and Concrete Mathematics is "a controlled manipulation of (some) mathematical formulas using a collection of techniques for solving problems "(textbooks introduction). We will cover book chapters 1- 5.
    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.