Course Discipline and



GAVILAN COLLEGE

CURRICULUM DEVELOPMENT

|form C |

|Modify or Inactivate an Existing Course |

|Date: |4/5/2015 |Prepared & Submitted by: |Venable |

|Department: |Business |Course Discipline and Number: |CSIS 26 |

|1. |What is the effective term? |

| |Fall Spring Summer Year: 2015 |

|2. | Inactivate Course(s): (Inactivating a course will remove it from the course catalog. Courses may be re-activated 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 |4 |4 |0 |

| |Discipline & Number |Course Title |Units |Lec |Lab |

| | | | |Hours per |Hours per |

| | | | |week |week |

|TO: |CSIS 26 |Discrete Structures |3 |3 |0 |

| |Discipline & Number |Course Title |Units |Lec |Lab |

| | | | |Hours per |Hours per |

| | | | |week |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 No |

| |If yes, fill out Form D – Distance Education form. |

5. Routing/Recommendation for Approval

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___

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 |LAB HOURS PER WEEK: 0 |

|Classification: |Non Credit Category: |Occupational Code (SAM): |

|TOP Code: 0000.00 |LEH Factor:       |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: Co-requisite:      

Advisory:      

GRADING SYSTEM:

No Change

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REPEATABLE FOR CREDIT:

(Note: Course Outline must include additional skills that will be acquired by repeating this course.)

No Change

Credit Course Yes No If yes, how many times? 1 2 3

Non Credit Course Yes No If yes, how many times? 1 2 3 Unlimited

(Noncredit only)

STAND ALONE:

No Change

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[pic]

METHODS OF INSTRUCTION:

No Change

     

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 self-managed teams.

4) Student will create algorithms to solve programming problems, and implement those algorithms.

STUDENT LEARNING OUTCOMES:

1. 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.

2. 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.

3. Identify which Program Learning Outcomes (PLO) are aligned with this course. List them by number in order of emphasis.

4. 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.

5. For GE courses, enter the GE Learning Outcomes for this course. For example "A1, A2". GE Learning Outcomes are listed below.

6. 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 |

|Measure: homework, exam, problem |PLO: 1 |ILO: 2, 7 |GE-LO: B3, B7, B8 |Year assessed or anticipated year |

|sets | | | |of assessment: 2015 |

|2. |Student can provide examples of recurrence relations that give rise to formulas that are verified by induction. |

|Measure: homework, exam, problem |PLO: 1 |ILO: 7, 2 |GE-LO:       |Year assessed or anticipated year |

|sets. | | | |of assessment: 2015 |

|3. |Student can describe different traversals of trees and graphs. |

|Measure: homework, exam, problem |PLO: 2,1 |ILO: 7,2 |GE-LO:       |Year assessed or anticipated year |

|sets | | | |of assessment: 2015 |

|4. |Student can apply the binomial theorem and Bayes’ theorem as appropriate. |

|Measure: homework, exam, problem |PLO:       |ILO7,2,3 |GE-LO: B3, B7, B8 |Year assessed or anticipated year |

|sets | | | |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:

1. Receive, analyze, and effectively respond to verbal communication.

2. Formulate, organize and logically present verbal information.

3. Write clear and effective prose using forms, methods, modes and conventions of English grammar that best achieve the writing’s purpose.

4. Advocate effectively for a position using persuasive strategies, argumentative support, and logical reasoning.

5. Employ the methods of research to find information, analyze its content, and appropriately incorporate it into written work.

6. Read college course texts and summarize the information presented.

7. Analyze the ideas presented in college course materials and be able to discuss them or present them in writing.

8. Communicate conclusions based on sound inferences drawn from unambiguous statements of knowledge and belief.

9. 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:

1. Explain concepts and theories related to physical and biological phenomena.

2. Identify structures of selected living organisms and relate structure to biological function.

3. Recognize and utilize appropriate mathematical techniques to solve both abstract and practical problems.

4. Utilize safe and effectives laboratory techniques to investigate scientific problems.

5. Discuss the use and limitations of the scientific process in the solution of problems.

6. Make critical judgments about the validity of scientific evidence and the applicability of scientific theories.

7. Utilize appropriate technology for scientific and mathematical investigations and recognize the advantages and disadvantages of that technology.

8. Work collaboratively with others on labs, projects, and presentations.

9. Describe the influence of scientific knowledge on the development of world’s civilizations as recorded in the past as well as in present times.

AREA C Arts, Foreign Language, Literature and Philosophy

After completing courses in Area C, students will be able to do the following:

1. Demonstrate knowledge of the language and content of one or more artistic forms: visual arts, music, theater, film/television, writing, digital arts.

2. Analyze an artistic work on both its emotional and intellectual levels.

3. Demonstrate awareness of the thinking, practices and unique perspectives offered by a culture or cultures other than one’s own.

4. Recognize the universality of the human experience in its various manifestations across cultures.

5. Express objective and subjective responses to experiences and describe the integrity of emotional and intellectual response.

6. Analyze and explain the interrelationship between self, the creative arts, and the humanities, and be exposed to both non-Western and Western cultures.

7. 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:

1. Identify and analyze key concepts and theories about human and/or societal development.

2. Critique generalizations and popular opinion about human behavior and society, distinguishing opinion and values from scientific observation and study.

3. Demonstrate an understanding of the use of research and scientific methodologies in the study of human behavior and societal change.

4. Analyze different cultures and their influence on human development or society, including how issues relate to race, class and gender.

5. 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:

1. Demonstrate an awareness of the importance of personal development.

2. Examine the integration of one’s self as a psychological, social, and physiological being.

3. 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:

1. Connect knowledge of self and society to larger cultural contexts.

2. 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; |

|• 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; |

|• 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; |

|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 |

| |

|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: |

|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: |

|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. |

|Topic |

|Student Performance Objectives |

|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       % |

| 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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