GAVILAN COLLEGE
CURRICULUM DEVELOPMENT
Date:
Department:
1.
2.
4/5/2015
Business
FORM C
Modify or Inactivate an Existing Course
Prepared & Submitted by:
Venable
Course Discipline and Number:
CSIS 26
What is the effective term?
Fall
Spring
Summer
Year: 2015
Inactivate Course(s): (Inactivating a course will remove it from the course catalog. Courses may be reactivated by updating the course and bringing it back to the Curriculum Committee for approval. Transferable
courses will need to be re-articulated, should you decide to reactivate the course.)
Reason for inactivation:
3.
Modification of the following: (Attach existing course outline, note changes as appropriate. Update
Prerequisite/Advisory Form, if appropriate )
Number
Hours
Prerequisite/Advisory
Discipline
Title
Units
Description
Content
Grading
GE Applicability
Repeatability
Transferability
General Update
Reinstate Course
Cross list course with
Update Textbook
Other (please describe.)
FROM:
CSIS 26
Discrete Structures
Discipline & Number
TO:
CSIS 26
4
Course Title
Units
Discrete Structures
Discipline & Number
3
Course Title
Units
4
0
Lec
Hours per
week
Lab
Hours per
week
3
0
Lec
Hours per
week
Lab
Hours per
week
Reason for modification: Lower units to fit into AS-T degree. Align with C-ID descriptor for
COMP 152 Discrete Structures
4.
Will this course be offered via distance education? Yes
If yes, fill out Form D – Distance Education form.
5.
Routing/Recommendation for Approval
No
Signatures
Approval
Dept. Approval (Chair Sign)
__________________________________
Date ______________
Yes___ No___
Area Dean
__________________________________
Date ______________
Yes___ No___
Curriculum Committee Chair __________________________________
Date ______________
Yes___ No___
VP of Instruction
__________________________________
Date ______________
Yes___ No___
Superintendent/President
For District Board
__________________________________
Date ______________
Yes___ No___
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GAVILAN COLLEGE
CURRICULUM DEVELOPMENT
COURSE OUTLINE
DISCIPLINE:
CSIS
DEPARTMENT:
Business
(Discipline and Number)
COURSE TITLE:
Discrete Structures
(Maximum of 58 spaces)
ABBREVIATED TITLE:
DISCRETE STRUCTURES
(Maximum of 28 spaces)
SEMESTER UNITS: 4
LEC HOURS PER WEEK: 4
Classification:
N/A
TOP Code: 0000.00
LAB HOURS PER WEEK: 0
Non Credit Category:
Y Not Applicable, Credit Course
LEH Factor:
Occupational Code (SAM):
N/A
FTE Load:
CATALOG DESCRIPTION:
No Change
Change
COURSE REQUISITES:
List all prerequisites separated by AND/OR, as needed. Also fill out and submit the Prerequisite/Advisory form.
No Change
Replaces existing Advisory/Prerequisite
In addition to existing Advisory/Prerequisite
Prerequisite:
Advisory:
Co-requisite:
GRADING SYSTEM:
No Change
REPEATABLE FOR CREDIT:
(Note: Course Outline must include additional skills that will be acquired by repeating this course.)
No Change
Credit Course
Non Credit Course
Yes
Yes
No
No
If yes, how many times?
If yes, how many times?
1
1
2
2
3
3
Unlimited
(Noncredit only)
STAND ALONE:
No Change
METHODS OF INSTRUCTION:
No Change
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RECOMMENDED OR REQUIRED TEXT/S:
(The following information must be provided: Author, Title, Publisher, Year of Publication, Reading level and Reading level
verification)
Required:
Recommended:
n/a
Author: Epp Title: Discrete Mathematics with Applications (most recent edition) Publisher: Brooks/Cole Year
of Publication: 2011, or other appropriate college level text.
ISBN:
(if available)
Reading level of text, Grade: 12+
Verified by: ev
Other textbooks or materials to be purchased by the student: none
CULTURAL DIVERSITY:
Does this course meet the cultural diversity requirement? Yes
No
If Yes, please indicate which criteria apply. At least two criteria must be selected and evidenced in the course
content section and at least one Student Learning Outcome must apply to cultural diversity.
This course promotes understanding of:
Cultures and subcultures
Cultural awareness
Cultural inclusiveness
Mutual respect among diverse peoples
Familiarity with cultural developments and their complexities
SLO #
PROGRAM LEARNING OUTCOMES:
Is this course part of a program (degree or certificate)? If yes, copy and paste the appropriate Program Learning
Outcomes and number them. Enter the PLOs by number in the Student Learning Outcomes below.
1) Student will code, debug, document, test, and run programs.
2) Student will write programs in at least three different programming languages, and compare and contrast
the philosophies and comparative advantages of each these languages.
3) Students will demonstrate professional conduct by meeting project deadlines, and participating in selfmanaged teams.
4) Student will create algorithms to solve programming problems, and implement those algorithms.
STUDENT LEARNING OUTCOMES:
1.
2.
3.
4.
5.
6.
Complete this section in a manner that demonstrates student’s use of critical thinking and reasoning skills. These include
the ability to formulate and analyze problems and to employ rational processes to achieve increased understanding.
Reference Bloom's Taxonomy of action verbs.
List the Type of Measures that will be used to measure the student learning outcomes, such as written exam, oral exam,
oral report, role playing, project, performance, demonstration, etc.
Identify which Program Learning Outcomes (PLO) are aligned with this course. List them by number in order of
emphasis.
Identify which Institutional Learning Outcomes (ILO) are aligned with this course. List them, by number in order of
emphasis. For example: "2, 1" would indicate Cognition and Communication.
(1) Communication, (2) Cognition, (3) Information Competency, (4) Social Interaction, (5) Aesthetic Responsiveness,
(6) Personal Development & Responsibility, (7) Content Specific.
For GE courses, enter the GE Learning Outcomes for this course. For example "A1, A2". GE Learning Outcomes are
listed below.
Indicate when the course was last assessed.
Indicate by number which Program Learning Outcomes, Institutional Learning Outcomes and GE Learning
Outcomes are supported by each of the Student Learning Outcomes.
1. Student uses logically valid forms of argument and avoids common logical errors
GE-LO: B3, B7, B8
Year assessed or
Measure: homework,
PLO: 1
ILO: 2, 7
anticipated year of
exam, problem sets
assessment: 2015
2. Student can provide examples of recurrence relations that give rise to formulas that are verified by
induction.
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Measure: homework,
exam, problem sets.
PLO: 1
ILO: 7, 2
GE-LO:
3. Student can describe different traversals of trees and graphs.
Measure: homework,
PLO: 2,1
ILO: 7,2
GE-LO:
exam, problem sets
4. Student can apply the binomial theorem and Bayes’ theorem as appropriate.
ILO7,2,3
GE-LO: B3, B7, B8
Measure: homework,
PLO:
exam, problem sets
Year assessed or
anticipated year of
assessment: 2015
Year assessed or
anticipated year of
assessment: 2015
Year assessed or
anticipated year of
assessment: 2015
5.
Measure:
PLO:
ILO:
GE-LO:
Year assessed or
anticipated year of
assessment:
6.
Measure:
PLO:
ILO:
GE-LO:
Year assessed or
anticipated year of
assessment:
7.
Measure:
PLO:
ILO:
GE-LO:
Year assessed or
anticipated year of
assessment:
8.
Measure:
PLO:
ILO:
GE-LO:
Year assessed or
anticipated year of
assessment:
9.
Measure:
PLO:
ILO:
GE-LO:
Year assessed or
anticipated year of
assessment:
10.
Measure:
PLO:
ILO:
GE-LO:
Year assessed or
anticipated year of
assessment:
GENERAL EDUCATION LEARNING OUTCOMES
AREA A Communications in the English Language
After completing courses in Area A, students will be able to do the following:
A1. Receive, analyze, and effectively respond to verbal communication.
A2. Formulate, organize and logically present verbal information.
A3. Write clear and effective prose using forms, methods, modes and conventions of English grammar that best achieve
the writing’s purpose.
A4. Advocate effectively for a position using persuasive strategies, argumentative support, and logical reasoning.
A5. Employ the methods of research to find information, analyze its content, and appropriately incorporate it into written
work.
A6. Read college course texts and summarize the information presented.
A7. Analyze the ideas presented in college course materials and be able to discuss them or present them in writing.
A8. Communicate conclusions based on sound inferences drawn from unambiguous statements of knowledge and belief.
A9. Explain and apply elementary inductive and deductive processes, describe formal and informal fallacies of language
and thought, and compare effectively matters of fact and issues of judgment and opinion.
AREA B Physical Universe and its Life Forms
After completing courses in Area B, students will be able to do the following:
B1. Explain concepts and theories related to physical and biological phenomena.
B2. Identify structures of selected living organisms and relate structure to biological function.
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Recognize and utilize appropriate mathematical techniques to solve both abstract and practical problems.
Utilize safe and effectives laboratory techniques to investigate scientific problems.
Discuss the use and limitations of the scientific process in the solution of problems.
Make critical judgments about the validity of scientific evidence and the applicability of scientific theories.
Utilize appropriate technology for scientific and mathematical investigations and recognize the advantages and
disadvantages of that technology.
B8. Work collaboratively with others on labs, projects, and presentations.
B9. Describe the influence of scientific knowledge on the development of world’s civilizations as recorded in the past as
well as in present times.
B3.
B4.
B5.
B6.
B7.
AREA C Arts, Foreign Language, Literature and Philosophy
After completing courses in Area C, students will be able to do the following:
C1. Demonstrate knowledge of the language and content of one or more artistic forms: visual arts, music, theater,
film/television, writing, digital arts.
C2. Analyze an artistic work on both its emotional and intellectual levels.
C3. Demonstrate awareness of the thinking, practices and unique perspectives offered by a culture or cultures other than
one’s own.
C4. Recognize the universality of the human experience in its various manifestations across cultures.
C5. Express objective and subjective responses to experiences and describe the integrity of emotional and intellectual
response.
C6. Analyze and explain the interrelationship between self, the creative arts, and the humanities, and be exposed to both
non-Western and Western cultures.
C7. Contextually describe the contributions and perspectives of women and of ethnic and other minorities.
AREA D Social, Political, and Economic Institutions
After completing courses in Area D, students will be able to do the following:
D1. Identify and analyze key concepts and theories about human and/or societal development.
D2. Critique generalizations and popular opinion about human behavior and society, distinguishing opinion and values
from scientific observation and study.
D3. Demonstrate an understanding of the use of research and scientific methodologies in the study of human behavior
and societal change.
D4. Analyze different cultures and their influence on human development or society, including how issues relate to race,
class and gender.
D5. Describe and analyze cultural and social organizations, including similarities and differences between various
societies.
AREA E Lifelong Understanding and Self-Development
After completing courses in Area E, students will be able to do the following:
E1. Demonstrate an awareness of the importance of personal development.
E2. Examine the integration of one’s self as a psychological, social, and physiological being.
E3. Analyze human behavior, perception, and physiology and their interrelationships including sexuality, nutrition,
health, stress, the social and physical environment, and the implications of death and dying.
AREA F Cultural Diversity
After completing courses in Area F, students will be able to do the following:
F1. Connect knowledge of self and society to larger cultural contexts.
F2. Articulate the differences and similarities between and within cultures.
CONTENT, STUDENT PEFORMANCE OBJECTIVES and OUT-OF CLASS ASSIGNMENTS.
No Change
Copy and paste the existing content from the official course outline of record. Edit the content as needed.
WEEK 1
(3 hours)
Topics:
Variables
•
Using Variables in Mathematical Discourse;
•
Introduction to Universal, Existential, and Conditional Statements
The Language of Sets
•
Set-Roster and Set-Builder Notations;
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•
Subsets;
•
Cartesian Products
Homework: Read assigned pages in text, work assigned problems.
WEEK 2
(3 hours)
Topics:
Relations and Functions
•
Definition of a Relation from One Set to Another;
•
Arrow Diagram of a Relation;
•
Definition of Function;
•
Function Machines;
•
Equality of Functions
The Logic of Compound Statements
Logical Form and Logical Equivalence
•
Statements;
•
Compound Statements;
•
Truth Values;
•
Evaluating the Truth of More General Compound Statements;
•
Logical Equivalence;
•
Tautologies and Contradictions;
Interpret truth tables to determine whether a compound statement is a tautology, contradiction or neither, and
whether two logical statements are equivalent
WEEK 3
(3 hours)
Topics:
Conditional Statements
•
Negation of a Conditional Statement;
•
The Contrapositive of a Conditional Statement;
•
The Converse and Inverse of a Conditional Statement;
•
Only If and the Biconditional;
•
Necessary and Sufficient Conditions;
Student Performance Objectives:
State the converse, inverse, contrapositive and negation of a conditional statement
Valid and Invalid Arguments
•
Modus Ponens and Modus Tollens;
•
Additional Valid Argument Forms: Rules of Inference;
•
Fallacies; Contradictions and Valid Arguments;
Student Performance Objectives:
Explain whether a given argument form is valid or invalid
•
WEEK 4
(3 hours)
Topics:
The Logic of Quantified Statements
Predicates and Quantified Statements
•
The Universal Quantifier
•
The Existential Quantifier
•
Formal Versus Informal Language;
•
Universal Conditional Statements;
•
Equivalent Forms of Universal and Existential Statements;
•
Implicit Quantification;
Statements with Multiple Quantifiers
•
Translating from Informal to Formal Language;
•
Ambiguous Language;
•
Negations of Multiply-Quantified Statements;
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•
Order of Quantifiers;
Formal Logical Notation;
Student Performance Objectives:
State the converse, inverse, contrapositive and negation of a quantified statement
WEEK 5
(3 hours)
Topics:
Arguments with Quantified Statements
•
Universal Modus Ponens;
•
Use of Universal Modus Ponens in a Proof;
•
Universal Modus Tollens;
•
Proving Validity of Arguments with Quantified Statements;
•
Using Diagrams to Test for Validity;
•
Creating Additional Forms of Argument;
•
Remark on the Converse and Inverse Errors
Methods of Proof
•
Direct Proof and Counterexample
•
Definitions;
•
Proving Existential Statements;
•
Disproving Universal Statements by Counterexample;
•
Proving Universal Statements;
•
Directions for Writing Proofs of Universal Statements;
•
Variations among Proofs;
•
Common Mistakes;
Student Performance Objective:
Student writes direct proofs
WEEK 6
(3 hours)
Topics:
Methods of Proof
•
Showing That an Existential Statement Is False;
•
Conjecture, Proof, and Disproof
•
Indirect Argument: Contradiction and Contraposition
•
Proof by Contradiction; Argument by Contraposition;
Relation between Proof by Contradiction and Proof by Contraposition;
Student Performance Objective:
Construct a counterexample to disprove a statement
Mathematical Induction
•
Principle of Mathematical Induction
•
Comparison of Mathematical Induction and Inductive Reasoning;
Student Performance Objective:
Write inductive proofs
WEEK 7
(3 hours)
Topics:
Strong Mathematical Induction and the Well-Ordering Principle for the Integers
Defining Sequences Recursively
•
Definition of Recurrence Relation:
•
Examples of Recursively Defined Sequences;
•
Recursive Definitions of Sum and Product
Solving Recurrence Relations by Iteration
•
The Method of Iteration;
•
Using Formulas to Simplify Solutions Obtained by Iteration;
•
Checking the Correctness of a Formula by Mathematical Induction;
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WEEK 8
(3 hours)
Topics:
Set Theory
Definitions and the Element Method of Proof
•
Subsets;
•
Proof and Disproof;
•
Set Equality;
•
Venn Diagrams;
•
Operations on Sets;
•
The Empty Set;
•
Partitions of Sets;
•
Power Sets;
•
Cartesian Products;
Properties of Sets
•
Set Identities;
•
Proving that a set is empty
Student Performance Objectives:
Student proves simple set identities.
Student finds complements, unions, intersections and differences of sets
WEEK 9
(3 hours)
Topics:
Disproofs, Algebraic Proofs and Boolean Algebras
Functions
Functions defined on General Sets
One-to-One and Onto,
Student Performance Objective:
Student will determine whether a function is one-to-one and onto or not.
WEEK 10
(3 hours)
Topics:
Inverse Functions
One-to-One Correspondences and Inverse Functions
Composition of Functions
•
Composition of One-to-One Functions;
•
Composition of Onto Functions
Cardinality with Applications to Computability
Definition of Cardinal Equivalence; Countable Sets;
The Search for Larger Infinities
Student Performance Objective:
Student will determine the inverses of functions.
WEEK 11
(4 hours)
Topics:
Relations on Sets
•
The Inverse of a Relation;
•
Directed Graph of a Relation;
Reflexivity, Symmetry, and Transitivity
Equivalence Relations
Student Performance Objective:
Student will identify relations and functions
Student will determine whether a relation is reflexive, symmetric or transitive
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WEEK 12
(3 hours)
Topics:
Counting and Probability
•
Definition of Sample Space and Event;
•
Probability in the Equally Likely Case;
•
Counting
Possibility Trees and the Multiplication Rule
Counting Elements of Disjoint Sets
•
The Addition Rule;
•
The Difference Rule;
•
The Inclusion/Exclusion Rule
Student Performance Objective:
Student will apply the rules to solve problems.
Student will apply counting techniques to calculate the probabilities.
WEEK 13
(3 hours)
Topics:
The Pigeonhole Principle
•
Statement and Discussion of the Principle;
•
Applications;
•
Decimal Expansions of Fractions;
•
Generalized Pigeonhole Principle;
•
Proof of the Pigeonhole Principle
Counting Subsets of a Set: Combinations
WEEK 14
(3 hours)
Topics:
Pascal's Formula and the Binomial Theorem
•
Combinatorial Formulas;
•
Pascal's Triangle;
•
Algebraic and Combinatorial Proofs of
Pascal's Formula;
Binomial Theorem and Algebraic and Combinatorial Proofs for It;
WEEK 15
(3 hours)
Topics:
Probability Axioms and Expected Value
Conditional Probability. Bayes' Formula, and Independent Events
Student Performance Objective:
Student can apply the binomial theorem and Bayes’ theorem as appropriate.
WEEK 16
(3 hours)
Topics:
Graphs: Definitions and Basic Properties
•
Matrix Representations of Graphs
•
Directed Graphs;
•
Undirected Graphs;
•
Counting Walks of Length N
WEEK 17
(3 hours)
Topics:
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Isomorphisms of Graphs
Trees
•
Rooted Trees
•
Binary Trees
•
Spanning Trees and Shortest Paths
•
Minimum Spanning Trees
Student Performance Objective:
Student can describe several different traversals of trees or graphs.
Homework for all weeks: read the assigned material and work the assigned problems.
WEEK 18
(2 hours)
Final Exam
The content should include:
1. Hours it will take to cover each topic - Hours are based on an 18 week term, even though the instruction is
compressed into a 16 week calendar. For example, a 3 unit course should have 54 hours (3 hours per week
times 18 weeks = 54 Total Contact Hours). 2 hours should be set aside for the final.
2. Topic
3. Student Performance Objectives
4. Out of Class Assignments - Out of Class Assignments: essays, library research, problems, projects required
outside of class on a 2 to 1 basis for Lecture units granted. Include specific examples of reading and writing
assignments.
METHODS OF EVALUATION:
No Change
METHODS OF EVALUATION:
CATEGORY 1 - The types of writing assignments required:
Percent range of total grade:
% to
%
Written Homework
Reading Reports
Lab Reports
Essay Exams
Term or Other Papers
Other:
If this is a degree applicable course, but substantial writing assignments are not appropriate,
indicate reason:
Course is primarily computational
Course primarily involves skill demonstration or problem solving
CATEGORY 2 -The problem-solving assignments required:
Percent range of total grade:
% to
%
Homework Problems
Field Work
Lab Reports
Quizzes
Exams
Other:
CATEGORY 3 -The types of skill demonstrations required:
Percent range of total grade:
% to
%
Class Performance/s
Field Work
Performance Exams
CATEGORY 4 - The types of objective examinations used in the course:
Percent range of total grade:
% to
%
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Multiple Choice
True/False
Matching Items
Completion
Other:
CATEGORY 5 - Any other methods of evaluation:
Percent range of total grade:
% to
%
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