MA 2201 / CS 2022 - Discrete Mathematics

Homework

Change Game

On a table is placed a penny, two dimes and a nickel. The player can move coins from the table to his hand according to the following rules:
  1. If the penny is on the table, he may pick it up, either alone or with exactly one other coin.
  2. If the penny is in his hand, he may put it back on the table, either alone or with exactly one other coin.
The opponent can take all the coins on the table if they total 1, 11, 15, or 25 cents. The player wants to get as much money as possible.

Your task

  1. produce a list of states (vertices)
  2. List the pairs of states (red edges) which are related by a single move of the player.
  3. List the pairs of states (blue edges) which are related by a single move of the opponent.
  4. Produce a drawing of the graph of states.
  6. Decide whether the resulting graph is connected.
Text:
Discrete Mathematics with Algorithms
M. O. Albertson and J. P. Hutchinson
Text is freely downloadable.
Instructor:
Herman Servatius

EMAIL: hservat@wpi.edu

Office Hours: MTRF - 8:30 - 9:00 AM in the classroom - or by appointment.

TA: Guillaume Marceau gmarceau@WPI.EDU
Feel free to email Mr. Marceau with those homework problems you particularly would like to see solved in conference. You should always do the homework on your own before the conference. Even if you believe you have solved all the exercises correctly, you ought to attend the conference to see if an alternate solution is of interest, and to get an example for how to present the work correctly.

Syllabus

This course provides an introduction to the mathematical structures of computer science. Discrete mathematics includes topics on set theory, logic, proofs, relations, functions, orders of growth, induction, recursion, and graphs.

This course is recommended background for: CS2223, CS3133, CS3431, ECE3801 and most of upper-level mathematics.

Grading

There will be a quiz each Friday.

Your homework altogether will count for one quiz.

The quizzes altogether count for 60% of your grade.

There will one final exam, worth 40% of your grade.

Plan for the week

Mondays - Quizes are returned.

Tuesday - Two homework problems are collected.

Wednesday - Conferences. (gmarceau will present problems - particularly those problems you have emailed.)

Thursday - Collected homework is returned.

Friday - Quiz. Homework sections to be prepared for Tuesday are announced.

Homework
Exercises from the text: 
Chapter 1:
   Section  1 -  1,  2, 11, 13
   Section  2 -  2,  3,  6,  9, 10, 11c
   Section  3 -  1,  3,  5
   Section  4 - 1f, 3,  6,  7, 10
   Section  5 -  1,  2,  3,  6
   Section  6 -  1,  4
   Section  7 -  1,  6,  8, 10
   Section  8 -  1,  3,  6, 13
   Section  9 -  1,  2,  4,  8, 16, 10, 18, 20
   Section 10 -  1,  2,  3,  7,  8
Chapter 2:
   Section  1 -  1,  5,  6
   Section  2 - 1b, 1c,  4
   Section  3 -  1,  3, 10, 12, 14
   Section  4 -  1,  2,  3,  4,  8, 12, 13, 15
   Section  5 -  4,  6
   Section  6 -  2,  5, 16, 17, 19
   Section  7 -  1,  2, 11
   Section  8 -  1,  2,  3,  9
   Section  9 -  2,  3,  4,  5
   Section 10 -  1,  5
Chapter 3:
   Section  1 -  1,  2,  5,  6
   Section  2 -  4,  5,  8, 13
   Section  3 -  1,  2,  4, 10, 17, 24
   Section  4 -  1,  4,  7, 10
   Section  6 -  1,  2,  4,  6,  7,  
Chapter 5:
   Section  1 -  3,
   Section  2 -  2, 4, 5, 6, 8, 10a, 10d, 11c, 12, 13, 14
   Section  3 -  1, 2, 3, 6, 7, 10
   Section  4 -  1, 2, 5, 7