ESSEX COUNTY COLLEGE
ESSEX COUNTY COLLEGE
Mathematics and Physics Division
MTH 136 – Discrete Mathematics
Course Outline
Course Number & Name: MTH 136 Discrete Mathematics
Credit Hours: 3.0 Contact Hours: 3.0 Lecture: 3.0 Lab: N/A Other: N/A
Prerequisites: Grade of “C” or better in MTH 113 or MTH 119 or placement
Co-requisites: None Concurrent Courses: None
Course Outline Revision Date: Fall 2010
Course Description: This is a course in finite mathematical structures relevant to computer science and computer information systems. Topics include sets, relations, functions, graphs, trees, methods of proof including mathematical induction, Boolean algebras and their use in circuit design, elementary combinatorics, coding theory and formal languages.
General Education Goals: MTH 136 is affirmed in the following General Education Foundation Category: Quantitative Knowledge and Skills. The corresponding General Education Goal is as follows: Students will use appropriate mathematical and statistical concepts and operations to interpret data and to solve problems.
Course Goals: Upon successful completion of this course, students should be able to do the following:
1. demonstrate knowledge of the fundamental concepts and theories from discrete mathematics;
2. utilize various discrete math problem-solving and critical-thinking techniques to set up and solve applied problems in finance, economics, geometry, sciences, and other fields; and
3. communicate accurate mathematical terminology and notation in written and/or oral form in order to explain strategies to solve problems as well as to interpret found solutions.
Measurable Course Performance Objectives (MPOs): Upon successful completion of this course, students should specifically be able to do the following:
1. Demonstrate knowledge of the fundamental concepts and theories from discrete mathematics:
1.1 describe and correctly use structures such as graphs, trees and Boolean algebras; and
1.2 identify computable problems and model them using formal language theory
Measurable Course Performance Objectives (MPOs) (continued):
2. Utilize various discrete math problem-solving and critical-thinking techniques to set up and solve applied problems in finance, economics, geometry, sciences, and other fields
2.1 solve counting problems using combinatorics; and
2.2 use and/or construct algorithms and determine algorithm efficiency
3. Communicate accurate mathematical terminology and notation in written and/or oral form in order to explain strategies to solve problems as well as to interpret found solutions:
3.1 interpret and write proofs using formal logic; and
3.2 use the language of mathematics to describe sets, number systems and relations between mathematical objects
Methods of Instruction: Instruction will consist of a combination of lectures, class discussion, group work, individual study/projects, and computer/calculator projects.
Outcomes Assessment: Test and exam questions are blueprinted to course objectives. Data is collected and analyzed to determine the level of student performance on these assessment instruments in regards to meeting course objectives. The results of this data analysis are used to guide necessary pedagogical and/or curricular revisions.
Course Requirements: All students are required to:
1. Maintain regular attendance.
2. Complete homework assignments in a timely manner.
3. Participate in class discussion and present problem solutions when required.
4. Complete computer/calculator lab assignments and projects.
5. Take quizzes, tests and exams in class as required or make up quizzes, tests or exams if permitted by the instructor.
Methods of Evaluation: Final course grades will be computed as follows:
% of
Grading Components final course grade
• Homework, projects and class participation 0 – 15%
This combination indicates the extent to which students master course objectives.
• 4 or more Quizzes/Tests (dates specified by the instructor) 10 – 25%
Quizzes/tests provide evidence of the extent to which students master course objectives, including, but not limited to, identifying and applying concepts, analyzing and solving problems, estimating and interpreting results, and stating appropriate conclusions using correct terminology.
• Midterm Exam 20 – 30%
The midterm exam, being more comprehensive than quizzes/tests, provides evidence as to how well students synthesize a combination of concepts developed during the semester.
• Final Exam 30 – 40%
The comprehensive final exam will examine the extent to which students have understood and synthesized all course content and achieved all course objectives.
Note: The instructor will provide specific weights, which lie in the above-given ranges, for each of the grading components at the beginning of the semester.
Academic Integrity: Dishonesty disrupts the search for truth that is inherent in the learning process and so devalues the purpose and the mission of the College. Academic dishonesty includes, but is not limited to, the following:
• plagiarism – the failure to acknowledge another writer’s words or ideas or to give proper credit to sources of information;
• cheating – knowingly obtaining or giving unauthorized information on any test/exam or any other academic assignment;
• interference – any interruption of the academic process that prevents others from the proper engagement in learning or teaching; and
• fraud – any act or instance of willful deceit or trickery.
Violations of academic integrity will be dealt with by imposing appropriate sanctions. Sanctions for acts of academic dishonesty could include the resubmission of an assignment, failure of the test/exam, failure in the course, probation, suspension from the College, and even expulsion from the College.
Student Code of Conduct: All students are expected to conduct themselves as responsible and considerate adults who respect the rights of others. Disruptive behavior will not be tolerated. All students are also expected to attend and be on time all class meetings. No cell phones or similar electronic devices are permitted in class. Please refer to the Essex County College student handbook, Lifeline, for more specific information about the College’s Code of Conduct and attendance requirements.
Course Content Outline: based on the text Discrete Mathematics and its Applications, 6th edition, by K Rosen; published by McGraw-Hill, 2007; ISBN #: 978-0-07-288008-3
Class Meeting
(80 minutes) Chapter/Section
Chapter 1 The Foundations: Logic and Proofs, Sets and Functions
1. 1.1 Logic
1.2 Propositional Equivalences
2 1.6 Introduction to Proofs
1.7 Proof Methods and Strategy
Chapter 2 Basic Structures: Sets, Functions, Sequences, and Sums
3 2.1 Sets
2.2 Set Operations
4 2.3 Functions
2.4 Sequences and Summations
5 Quiz #1 on Chapters 1 & 2
Chapter 3 The Fundamentals: Algorithms, the Integers, and Matrices
3.1 Algorithms
3.3 Complexity of Algorithms
6 3.4 The Integers and Division
7 3.6 Integers and Algorithms
8 3.7 Applications of Number Theory
9 3.8 Matrices
10 Quiz #2 on Chapter 3
Chapter 4 Mathematical Reasoning, Induction, and Recursion
4.1 Mathematical Induction
11 4.2 Strong Induction and Well Ordering
4.3 Recursive Definitions and Structural Induction
12 4.4 Recursive Algorithms
13 Review for Midterm
14 Midterm Exam
Chapter 5 Counting
15 5.1 The Basics of Counting
5.2 The Pigeonhole Principle
16 5.3 Permutations and Combinations
17 Chapter 8 Relations
8.1 Relations and Their Properties
8.2 n-ary Relations and Their Applications (optional)
18 8.3 Representing Relations
8.4 Closures of Relations (optional)
19 8.5 Equivalence Relations
Class Meeting
(80 minutes) Chapter/Section
20 Quiz #3 on Chapters 5 & 8
Chapter 9 Graphs
9.1 Graphs and Graph Models
21 9.2 Graph Terminology and Special Types of Graphs
22 9.3 Representing Graphs and Graph Isomorphism
9.4 Connectivity
Chapter 10 Trees
23 10.1 Introduction to Trees
24 10.2 Applications of Trees
25 10.3 Tree Traversal
10.4 Spanning Trees
26 Quiz #4 on Chapters 9 & 10
Chapter 12 Modeling Computation
12.1 Languages and Grammars
27 12.2 Finite-State Machines with Output
28 12.4 Language Recognition
29 Review for Final Exam
30 Comprehensive Final Exam on all course material covered
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