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

MTH 221 Statistics for Decision-Making_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

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.
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.

Participation &
Discussion
Questions
Respond to weekly discussion questions by Saturday and follow-up
on other’s responses by Monday
Monday 4
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.
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.
Discrete and Combinatorial Mathematics.
Read Ch. 5, “Relations and Functions,” of Discrete and
Combinatorial Mathematics.

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.
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.

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 –
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.

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

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

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