**MTH 221 Discrete and Combinatorial Mathematics_All 5 Weeks_Discussion Questions_Individual Assignments_Research Paper_A+_Detailed Answer**

MTH 221 Discrete and Combinatorial Mathematics_All 5 Weeks_Discussion Questions_Individual Assignments_Research Paper_A+_Detailed Answer

MTH 221 Discrete and Combinatorial Mathematics_All 5 Weeks_Discussion Questions_Individual Assignments_Research Paper_A+_Detailed Answer

Week One: Basic Enumeration and Logic & Set Theory

Details Due Points

Objectives 1.1 Apply basic enumeration techniques.

1.2 Simplify assertions and compound statements in first-order

logic.

1.3 Apply basic set-theoretic concepts.

Readings Read Ch. 1, sections 1.1–1.4, of Discrete and Combinatorial

Mathematics.

Read Ch. 2, “Fundamentals of Logic,” of Discrete and Combinatorial

Mathematics.

Read Ch. 3, sections 3.1–3.3, of Discrete and Combinatorial

Mathematics.

Read the Week One Read Me First.

Read this week’s Electronic Reserve Readings.

Participation &

Discussion

Questions

Respond to weekly discussion questions by Saturday and follow-up

on other’s responses by Monday

Monday 4

Nongraded

Activities and

Preparation

Select a method for turning in textbook exercises. Due to the nature

of this course, symbols are actively used in individual assignments.

You may choose one of the following methods to complete the

assignments:

• Write out the names of symbols rather than using the symbols.

• Download Microsoft® Equation Editor. There is a tutorial

available on your student website if you choose this method.

• Handwrite your assignments and scan them if you have access

to a scanner.

Learning Team

Instructions

Resources: The Association of Computing Machinery (ACM)

website, the Society of Individual and Applied Mathematics (SCIAM)

website, and the University Library

Create the Learning Team Charter.

Sunday 2

Course Design Guide

MTH/221 Version 1

3

Begin working on the Research Paper & Presentation, due in Week

Five.

Prepare a 12-15 pages Paper describing existing research efforts in

one of the following areas:

• Computer vision, such as automatic recognition of objects,

boundaries, and so on

• Computational linguistics, such as information extraction, corpus

analysis, and so on

• Automatic proof programs

• Automated routing programs, such as shipping, circuitry, electric

power, and so on

• Ultra-high-speed or high-precision computation

Include a discussion of concepts discussed in this course, such as

the following:

• Logic and set theory

• Enumeration

• Algorithmic concepts

• Relations and functions

• Graph theory

• Trees

• Boolean algebra

Based on the same paper, prepare 15- to 20-slide Microsoft®

PowerPoint® presentation with detailed notes.

Individual

Selected Textbook

Exercises

Complete 12 questions below by choosing at least four from each

section.

• Ch. 1 of Discrete and Combinatorial Mathematics

o Supplementary Exercises 1, 2, 7, 8, 9, 10, 15(a), 18, 24, &

25(a & b)

• Ch. 2 of Discrete and Combinatorial Mathematics

o Exercise 2.1, problems 2, 3, 10, & 13,

o Exercise 2.2, problems 3, 4, & 17

o Exercise 2.3, problems 1 & 4

o Exercise 2.4, problems 1, 2, & 6

o Exercise 2.5, problems 1, 2, & 4

• Ch. 3 of Discrete and Combinatorial Mathematics

o Exercise 3.1, problems 1, 2, 18, & 21

o Exercise 3.2, problems 3 & 8

o Exercise 3.3, problems 1, 2, 4, & 5

Monday 10

Course Design Guide

MTH/221 Version 1

4

Week Two: Algorithmic Concepts and Relations & Functions, Part 1

Details Due Points

Objectives 2.1 Apply the principles of mathematical induction and recursion.

2.2 Solve problems of iteration.

2.3 Manipulate relations and simple functions, and their inverses.

2.4 Apply the basic concepts of computational complexity and

algorithmic analysis.

Readings Read Ch. 4, “Properties of the Integer: Mathematical Induction,” of

Discrete and Combinatorial Mathematics.

Read Ch. 5, “Relations and Functions,” of Discrete and

Combinatorial Mathematics.

Read the Week Two Read Me First.

Read this week’s Electronic Reserve Readings.

Participation &

Discussion

Questions

Respond to weekly discussion questions by Saturday and follow-up

on other’s responses by Monday

Monday 4

Individual

Selected Textbook

Exercises

Complete 12 questions below by choosing at least three from each

section.

• Ch. 4 of Discrete and Combinatorial Mathematics

o Exercise 4.1, problems 4, 7, & 18

o Exercise 4.2, problems 11 & 16

• Ch. 4 of Discrete and Combinatorial Mathematics

o Exercise 4.3, problems 4, 5, 10, & 15

o Exercise 4.4, problems 1 & 14

o Exercise 4.5, problems 5 &12

• Ch. 5 of Discrete and Combinatorial Mathematics

o Exercise 5.1, problems 5 & 8

o Exercise 5.2, problems 2, 5, 12, & 27(a & b)

o Exercise 5.3, problems 1 & 8

o Exercise 5.4, problems 13 & 14

o Exercise 5.5, problems 2 & 7(a)

o Exercise 5.6, problems 2, 3, 4, & 5

• Ch. 5 of Discrete and Combinatorial Mathematics

o Exercise 5.7, problems 1 & 6

o Exercise 5.8, problems 5 & 6

Monday 12

Learning Team Discuss with your team mates and arrive at the topic due in week 5 Saturday 2

Course Design Guide

MTH/221 Version 1

5

Week Three: Relations & Functions, Part 2, and More Enumeration

Details Due Points

Objectives 3.1 Use the properties of relations.

3.2 Apply the properties of equivalence relations and partitions.

3.3 Use the principle of inclusion and exclusion.

Readings Read Ch. 7, sections 7.1–7.4, of Discrete and Combinatorial

Mathematics.

Read Ch. 8, sections 8.1–8.2, of Discrete and Combinatorial

Mathematics.

Review Ch. 5, “Relations and Functions,” of Discrete and

Combinatorial Mathematics.

Read the Week Three Read Me First.

Read this week’s Electronic Reserve Readings.

Participation &

Discussion

Questions

Respond to weekly discussion questions by Saturday and follow-up

on other’s responses by Monday

Monday 4

Individual

Selected Textbook

Exercises

Complete 12 questions below by choosing at least four from each

section.

• Ch. 7

o Exercise 7.1, problems 5, 6, 9, & 14

o Exercise 7.2, problems 2, 9, &14 (Develop the algorithm

only, not the computer code.)

o Exercise 7.3, problems 1, 6, & 19

• Ch. 7

o Exercise 7.4, problems 1, 2, 7, & 8

• Ch. 8

o Exercise 8.1, problems 1, 12, 19, & 20

o Exercise 8.2, problems 4 & 5

Monday 12

Learning Team Decide on the sections you will be working on and start working –

show your work to your team mates

Saturday 2

Week Four: Graph Theory and Trees

Details Due Points

Course Design Guide

MTH/221 Version 1

6

Objectives 4.1 Apply properties of general graphs.

4.2 Identify graph isomorphisms, planarities, connected

components, and chromatic numbers.

4.3 Identify properties of a tree.

Readings Read Ch. 11, “An Introduction to Graph Theory,” of Discrete and

Combinatorial Mathematics.

Read Ch. 12, sections 12.1–12.3 & 12.5, of Discrete and

Combinatorial Mathematics.

Read the Week Four Read Me First.

Read this week’s Electronic Reserve Readings.

Participation &

Discussion

Questions

Respond to weekly discussion questions by Saturday and follow-up

on other’s responses by Monday

Monday 4

Individual

Selected Textbook

Exercises

Complete 12 questions below by choosing at least four from each

section.

• Ch. 11 of Discrete and Combinatorial Mathematics

o Exercise 11.1, problems 3, 6, 8, 11, 15, & 16

• Ch. 11 of Discrete and Combinatorial Mathematics

o Exercise 11.2, problems 1, 6, 12, & 13,

o Exercise 11.3, problems 5, 20, 21, & 22

o Exercise 11.4, problems 14, 17, & 24

o Exercise 11.5, problems 4 & 7

o Exercise 11.6, problems 9 &10

• Ch. 12 of Discrete and Combinatorial Mathematics

o Exercise 12.1, problems 2, 6, 7, & 11

o Exercise 12.2, problems 6 & 9

o Exercise 12.3, problems 2 & 3

o Exercise 12.5, problems 3 & 8

Monday 12

Learning Team Post your individual contributions towards the team assignment and

review each other’s work

Saturday 4

Week Five: Boolean Logic and Algebra

Details Due Points

Objectives 5.1 Apply the basic concepts of Boolean algebra.

5.2 Use the basic laws of Boolean algebra.

5.3 Convert Boolean expressions into a disjunctive or conjunctive

normal form.

Course Design Guide

MTH/221 Version 1

7

Readings Read Ch. 15, of Discrete and Combinatorial Mathematics.

Read the Week Five Read Me First.

Read this week’s Electronic Reserve Readings.

Participation &

Discussion

Questions

Respond to weekly discussion questions by Saturday and follow-up

on other’s responses by Monday

Monday 4

Individual

Selected Textbook

Exercises

Complete 12 questions below.

• Ch. 15 of Discrete and Combinatorial Mathematics

o Supplementary Exercises, problems 1, 5, & 6

• Ch. 15 of Discrete and Combinatorial Mathematics

o Exercise 15.1, problems 1, 2, 11, 12, 14, & 15

• Ch. 15 of Discrete and Combinatorial Mathematics

o Exercise 15.2, problems 4, 5, 8b, & 9

Monday 12

Learning Team

Research Paper &

Presentation

Submit the final Research Presentation.

• Submit the paper and power-point presentation with detailed

speaker notes.

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