SRJC Course Outlines

9/24/2022 9:00:30 AMMATH 4 Course Outline as of Fall 2001

New Course (First Version)
CATALOG INFORMATION

Discipline and Nbr:  MATH 4Title:  DISCRETE MATH  
Full Title:  Discrete Mathematics
Last Reviewed:9/14/2020

UnitsCourse Hours per Week Nbr of WeeksCourse Hours Total
Maximum4.00Lecture Scheduled4.0017.5 max.Lecture Scheduled70.00
Minimum4.00Lab Scheduled017.5 min.Lab Scheduled0
 Contact DHR0 Contact DHR0
 Contact Total4.00 Contact Total70.00
 
 Non-contact DHR0 Non-contact DHR Total0

 Total Out of Class Hours:  140.00Total 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: Untitled document
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:
 B4Math/Quantitative ReasoningFall 2001
 
IGETC:Transfer Area Effective:Inactive:
 2AMathematical Concepts & Quantitative ReasoningFall 2001
 
CSU Transfer:TransferableEffective:Fall 2001Inactive:
 
UC Transfer:TransferableEffective:Fall 2001Inactive:
 
C-ID:

Certificate/Major Applicable: Not Certificate/Major Applicable



COURSE CONTENT

Outcomes and Objectives:
Upon completion of the course, students will 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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