| 12/22/2024 3:49:11 AM |
| New Course (First Version) |
| CATALOG INFORMATION
|
| Discipline and Nbr:
MATH 4 | Title:
DISCRETE MATH |
|
| Full Title:
Discrete Mathematics |
| Last Reviewed:9/14/2020 |
| Units | Course Hours per Week | | Nbr of Weeks | Course Hours Total |
| Maximum | 4.00 | Lecture Scheduled | 4.00 | 17.5 max. | Lecture Scheduled | 70.00 |
| Minimum | 4.00 | Lab Scheduled | 0 | 17.5 min. | Lab Scheduled | 0 |
| | Contact DHR | 0 | | Contact DHR | 0 |
| | Contact Total | 4.00 | | Contact Total | 70.00 |
| |
| | Non-contact DHR | 0 | | Non-contact DHR Total | 0 |
| | Total Out of Class Hours: 140.00 | Total Student Learning Hours: 210.00 | |
Title 5 Category:
AA Degree Applicable
Grading:
Grade Only
Repeatability:
00 - Two Repeats if Grade was D, F, NC, or NP
Also Listed As:
Formerly:
Catalog Description:
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A lower division Discrete Mathematics course including formal logic, Boolean logic, and logic circuits, mathematical induction, introduction to number theory, set theory, principles of combinatorics, functions, relations, recursion, algorithm efficiency, and graph theory.
Prerequisites/Corequisites:
Completion of Math 27 (formerly MATH 57).
Recommended Preparation:
Math 1A.
Limits on Enrollment:
Schedule of Classes Information
Description:
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A lower division Discrete Mathematics course including formal logic, Boolean logic, and logic circuits, mathematical induction, introduction to number theory, set theory, principles of combinatorics, functions, relations, recursion, algorithm efficiency, and graph theory.
(Grade Only)
Prerequisites:Completion of Math 27 (formerly MATH 57).
Recommended:Math 1A.
Limits on Enrollment:
Transfer Credit:CSU;UC.
Repeatability:00 - Two Repeats if Grade was D, F, NC, or NP
ARTICULATION, MAJOR, and CERTIFICATION INFORMATION
| Associate Degree: | Effective: | Fall 1981
| Inactive: | |
| Area: | B
MC
| Communication and Analytical Thinking
Math Competency
|
| |
| CSU GE: | Transfer Area | | Effective: | Inactive: |
| | B4 | Math/Quantitative Reasoning | Fall 2001 | |
| |
| IGETC: | Transfer Area | | Effective: | Inactive: |
| | 2A | Mathematical Concepts & Quantitative Reasoning | Fall 2001 | |
| |
| CSU Transfer: | Transferable | Effective: | Fall 2001 | Inactive: | |
| |
| UC Transfer: | Transferable | Effective: | Fall 2001 | Inactive: | |
| |
| C-ID: |
Certificate/Major Applicable:
Not Certificate/Major Applicable
COURSE CONTENT
Outcomes and Objectives:
At the conclusion of this course, the student should be able to:
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tudents will be able to :
1. Properly structure mathematical algorithms and proofs.
2. Do proofs by induction.
3. Apply elementary number theory.
4. Be able to apply set theory.
5. Apply combinatorics including use of pigeonhole principle,
permutations, combinations, and probability.
6. Apply functions, inverse functions, and finite state automata.
7. Solve recurrence relations.
8. Analyze the efficiency of algorithms.
Topics and Scope
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1. Logic
Logical form and equivalence, conditional statements, valid and invalid
arguments, predicates, quantified statements, and arguments with
quantified statements.
2. Elementary number theory.
Direct proofs, conterexamples, rational numbers, divisibility, floor
and ceiling functions, proofs by contradiction, proofs by
contraposition, and algorithms.
3. Mathematical Induction
Sequences, weak and strong induction, well ordering principle,
orrectness of algorithms.
algorithms.
correctness of algorithms. n
rule, inclusion/exclusion, permatutations, combinations, and counting
of multisets.
5. Set Theory
Definitions, binary operations, properties, partitions, power sets,
and Boolean algebras.
6. Functions
Definition, one-to-one, onto, inverse functions, finite state automata,
and composition of functions.
7. Recursion
Sequences defined recursively, solving recurrence relations by
iteration, and solutions of second-order linear homogeneous recurrence
relations with constant coefficients.
8. Algorithm Efficiency
Comparison of real valued functions and their graphs, O-notation,
and calculations of efficiency.
9. Relations
Relations on sets, reflexivity, symmetry, transitivity, and equivalence
relations.
10.Graph Theory
Definitions, paths and circuits, matrix representations, and trees.
Assignments:
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1. Students will have daily outside readings, problem set assignments
from required text(s), or instructor chosen supplementary materials.
2. Instructional methodology may include, but not be limited to, lecture,
demonstrations, oral recitation, discussion, supervised practice,
independent study, outside project(s), or other assignments.
Methods of Evaluation/Basis of Grade.
| Writing: Assessment tools that demonstrate writing skill and/or require students to select, organize and explain ideas in writing. | Writing
0 - 0% |
| None | |
| This is a degree applicable course but assessment tools based on writing are not included because problem solving assessments are more appropriate for this course. |
|
| Problem solving: Assessment tools, other than exams, that demonstrate competence in computational or non-computational problem solving skills. | Problem Solving
30 - 90% |
| Homework problems, Quizzes, Exams | |
| Skill Demonstrations: All skill-based and physical demonstrations used for assessment purposes including skill performance exams. | Skill Demonstrations
0 - 0% |
| None | |
| Exams: All forms of formal testing, other than skill performance exams. | Exams
10 - 70% |
| Multiple choice, True/false, Matching items, Completion | |
| Other: Includes any assessment tools that do not logically fit into the above categories. | Other Category
0 - 0% |
| None | |
Representative Textbooks and Materials:
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1. Discrete Mathematics, Second Edition by Susanna S. Epp
PWS Publishing Company
ITP, An International Thompson Publishing Company, 1995.
2. Discrete Mathematics, Fifth Edition by Richard Johnsonbaugh
Prentice Hall, 2000.
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