MASTER SYLLABUS

2020-2021

A.	Academic Division: Liberal Arts

B.	Discipline: Mathematics

C.	Course Number and Title: MATH2000 Discrete Mathematics

D.	Course Coordinator: Christine Shearer

Assistant Dean: Dr. Steve Haynes

Instructor Information:

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E.	Credit Hours: 3

F.	Prerequisites:	MATH 1110 (Minimum grade of C- required)

-OR- A COMPASS College Algebra score of 46 or higher

-OR- ACT Math 26 or higher

-OR- ACCUPLACER College Level Math score of 55 or higher

G.	Syllabus Effective Date: Fall, 2020

H.	Textbook(s) Title:

Discrete Mathematics

Author: Richard Johnsonbaugh

Year: 2009

Edition: 7th

ISBN # 9780131593183

I.	Workbook(s) and/or Lab Manual:	None

J.	Course Description: This course presents topics in sets, logic, proofs, functions/sequences/relations, algorithms, counting methods, recurrence relations, graph theory, and trees. Emphasis is placed on proper notation and terminology as well as problem solving and proofs. Prerequisite MATH1110 (minimum grade of C- required) or COMPASS College Algebra score of 46 or higher or ACT math score of 26 or higher or ACCUPLACER College Level Math Score of 55 or higher.

K.	College Wide Learning Objectives:

College-Wide Learning Outcomes	Assessments - - How it is met & When it is met
Communication – Written
Communication – Speech
Intercultural Knowledge and Competence
Critical Thinking
Information Literacy
Quantitative Literacy	Cumulative Review Problem Sets: Weeks 3,7,11 Quantitative Literacy VALUE Rubric Tests: Weeks 4,8,12; Final Exam: Week 16

L.	Course Outcomes and Assessment Methods:

Upon successful completion of this course, the student shall:

Outcomes	Assessments – How it is met & When it is met
Find sets/subsets based upon given criteria	HW:Wk#1 Test:Wk#4 F.Ex.:Wk#16
Perform unary and binary set operations both symbolically and visually	HW:Wk#1 Test:Wk#4 F.Ex.:Wk#16
Use quantifiers when describing set relationships	HW:Wk#2 Test:Wk#4 F.Ex.:Wk#16
Analyze simple or compound propositions by using truth tables and/or Venn diagrams	HW:Wk#1 Test:Wk#4 F.Ex.:Wk#16
Analyze arguments using rules of inference.	HW:Wk#2 Test:Wk#4 F.Ex.:Wk#16
Describe and use methods of proof including direct proofs, indirect proofs, resolution proofs, and mathematical induction	HW:Wk#3,4 Test:Wk#4 F.Ex.:Wk#16
Provide examples of and/or identify functions that are injections, surjections, bijections, and composite functions	HW:Wk#1 Test:Wk#8 F.Ex.:Wk#16
Find terms of a sequence, both specific terms and the general term	HW:Wk#5 Test:Wk#8 F.Ex.:Wk#16
Define sequences and answer questions about them	HW:Wk#5 Test:Wk#8 F.Ex.:Wk#16
Define strings and answer questions about them	HW:Wk#5 Test:Wk#8 F.Ex.:Wk#16
Compute the resulting string from string operations	HW:Wk#5 Test:Wk#8 F.Ex.:Wk#16
Prove or disprove discrete mathematical assertions	HW throughout the course
Verify characteristics of relations	HW:Wk#5 Test:Wk#8 F.Ex.:Wk#16
Use digraphs to describe relations	HW:Wk#6 Test:Wk#8 F.Ex.:Wk#16
Use matrices to describe relations	HW:Wk#6 Test:Wk#8 F.Ex.:Wk#16
Define and analyze algorithms, including recursive algorithms	HW:Wk#6,7 Test:Wk#8 F.Ex.:Wk#16
Use counting techniques including permutations and combinations to compute the number of ways an event can occur	HW:Wk#8,9 Test:Wk#12 F.Ex.:Wk#16
Calculate discrete probabilities	HW:Wk#10 Test:Wk#12 F.Ex.:Wk#16
Compute binomial coefficients, with and without using Pascal’s triangle	HW:Wk#10 Test:Wk#12 F.Ex.:Wk#16
Prove combinatorial identities	HW:Wk#10 Test:Wk#12 F.Ex.:Wk#16
Solve problems by using the Pigeonhole Principle	HW:Wk#10 Test:Wk#12 F.Ex.:Wk#16
Use recurrence relations to analyze the times algorithms require	HW:Wk#11 Test:Wk#12 F.Ex.:Wk#16
Define both directed and undirected graphs in terms of vertices and edges and visually represent these graphs	HW:Wk#12 F.Ex.:Wk#16
Identify paths and cycles in a graph or sub-graph	HW:Wk#12 F.Ex.:Wk#16
Recognize graphs with/without Euler cycles and Hamiltonian cycles	HW:Wk#13 F.Ex.:Wk#16
Define and recognize trees	HW:Wk#13 F.Ex.:Wk#16
Show the relationship of a tree to Huffman codes	HW:Wk#13 F.Ex.:Wk#16
Characterize trees using proper terminology	HW:Wk#13 F.Ex.:Wk#16
Find spanning trees and minimal spanning trees	HW:Wk#14 F.Ex.:Wk#16
Analyze combinatorial circuits	HW:Wk#14 F.Ex.:Wk#16
Represent circuits using Boolean Algebra expressions	HW:Wk#15 F.Ex.:Wk#16
Use Boolean Algebra to synthesize circuits	HW:Wk#15 F.Ex.:Wk#16

M.	Topical Timeline (Subject to Change):

Week 1

Sets

Propositions

Conditional propositions and logical equivalence

Week 2

Arguments and rules of inference

Quantifiers

Nested quantifiers

Week 3

Mathematical systems, direct proofs, and counterexamples

More methods of proof

Resolution proofs

Week 4

Mathematical induction

Strong form of induction and the well-ordering property

Test 1

Week 5

Functions

Sequences and strings

Relations

Week 6

Equivalence relations

Matrices of relations

Introduction to algorithms

Week 7

Examples of algorithms

Analysis of algorithms

Recursive algorithms

Week 8

Test 2

Basic counting principles

Permutations and combinations

Week 9

Generalized permutations and combinations

Algorithms for generating permutations and combinations

Introduction to discrete probability

Week 10

Discrete probability theory

Binomial coefficients and combinatorial probabilities

The pigeonhole principle

Week 11

Introduction to recurrence relations

Solving recurrence relations

Applications to the analysis of algorithms

Week 12

Test 3

Introduction to graph theory

Paths and cycles

Week 13

Hamiltonian cycles and the traveling salesperson problem

Introduction to trees

Terminology and characterization of trees

Week 14

Spanning trees

Minimal spanning trees

Introduction to and properties of combinatorial circuits

Week 15

Boolean algebras

Boolean functions and synthesis of circuits

Applications

Week 16

Review

Review

Comprehensive final exam

N.	Course Assignments:

10% Homework will be assigned over each topic. Homework will be graded for approach, communication, and completeness.

30% Cumulative review homework will be assigned and graded for accuracy prior to each of the three tests and for the material covered after the third test and before the final exam.

40% Tests will cover two or three chapters. (3 tests)

20% Final Exam will be a comprehensive departmental exam.

O.	Recommended Grading Scale:

NUMERIC	GRADE	POINTS	DEFINITION
93–100	A	4.00	Superior
90–92	A-	3.67	Superior
87–89	B+	3.33	Above Average
83–86	B	3.00	Above Average
80–82	B-	2.67	Above Average
77–79	C+	2.33	Average
73–76	C	2.00	Average
70-72	C-	1.67	Below Average
67–69	D+	1.33	Below Average
63-66	D	1.00	Below Average
60-62	D-	0.67	Poor
00-59	F	0.00	Failure

P.	Grading and Testing Guidelines:

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Q.	Examination Policy:

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R.	Class Attendance and Homework Make-Up Policy:

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S.	Classroom Expectations:

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T.	College Procedures/Policies:

Important information regarding College Procedures and Policies can be found on the syllabus supplement located at

http://catalog.ncstatecollege.edu/mime/download.pdf?catoid=5&ftype=2&foid=3