SRJC Course Outlines

 9/12/2024 2:55:21 PM MATH 4 Course Outline as of Fall 2001 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
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.

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: BMC Communication and Analytical ThinkingMath 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.