ࡱ> \ Objbj >b8T` p-:--&./*+00P}}}}}}}$}1//11}-&._I9I9I91-&.}I91}I9I9Jprv-|gʉp10rF}u0s^;/3;rvrvJ;v11I911111}}?6 1111111;111111111 : GAVILAN COLLEGE CURRICULUM DEVELOPMENT form C Modify or Inactivate an Existing CourseDate:4/5/2015Prepared & Submitted by:  FORMTEXT VenableDepartment: FORMTEXT BusinessCourse Discipline and Number: FORMTEXT CSIS 26 1.What is the effective term? Fall  FORMCHECKBOX  Spring  FORMCHECKBOX  Summer  FORMCHECKBOX  Year: 2015 2. FORMCHECKBOX  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:  FORMTEXT       3. FORMCHECKBOX  Modification of the following: (Attach existing course outline, note changes as appropriate. Update Prerequisite/Advisory Form, if appropriate ) FORMCHECKBOX  Number FORMCHECKBOX  Hours FORMCHECKBOX  Prerequisite/Advisory FORMCHECKBOX  Discipline FORMCHECKBOX  Title FORMCHECKBOX  Units  FORMCHECKBOX  Description FORMCHECKBOX  Content  FORMCHECKBOX  Grading  FORMCHECKBOX  GE Applicability FORMCHECKBOX  Repeatability FORMCHECKBOX  Transferability FORMCHECKBOX  General Update FORMCHECKBOX  Reinstate Course FORMCHECKBOX  Cross list course with  FORMTEXT       FORMCHECKBOX  Update Textbook FORMCHECKBOX  Other (please describe.)  FORMTEXT       FROM: FORMTEXT CSIS 26Discrete Structures44 FORMTEXT 0Discipline & NumberCourse TitleUnitsLec Hours per weekLab Hours per weekTO: FORMTEXT CSIS 26 FORMTEXT Discrete Structures33 FORMTEXT 0Discipline & NumberCourse TitleUnitsLec Hours per weekLab Hours per weekReason for modification: Lower units to fit into AS-T degree.  FORMTEXT Align with C-ID descriptor for COMP 152 Discrete Structures 4.Will this course be offered via distance education? Yes  FORMCHECKBOX  No  FORMCHECKBOX 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: FORMTEXT CSISDEPARTMENT:  FORMTEXT Business(Discipline and Number)COURSE TITLE: FORMTEXT Discrete Structures (Maximum of 58 spaces) ABBREVIATED TITLE: FORMTEXT DISCRETE STRUCTURES (Maximum of 28 spaces) SEMESTER UNITS:  FORMTEXT 4LEC HOURS PER WEEK:  FORMTEXT 4LAB HOURS PER WEEK:  FORMTEXT 0 Classification:  FORMDROPDOWN Non Credit Category:  FORMDROPDOWN Occupational Code (SAM):  FORMDROPDOWN TOP Code:  FORMTEXT 0000.00LEH Factor:  FORMTEXT      FTE Load:  FORMTEXT       CATALOG DESCRIPTION: No Change  FORMCHECKBOX  Change  FORMCHECKBOX   FORMTEXT       COURSE REQUISITES: List all prerequisites separated by AND/OR, as needed. Also fill out and submit the Prerequisite/Advisory form. No Change  FORMCHECKBOX  Replaces existing Advisory/Prerequisite  FORMCHECKBOX  In addition to existing Advisory/Prerequisite  FORMCHECKBOX  Prerequisite:  FORMCHECKBOX  Co-requisite:  FORMCHECKBOX   FORMTEXT       Advisory:  FORMCHECKBOX   FORMTEXT       GRADING SYSTEM: No Change  FORMCHECKBOX   CONTROL Forms.OptionButton.1   CONTROL Forms.OptionButton.1   CONTROL Forms.OptionButton.1   CONTROL Forms.OptionButton.1  REPEATABLE FOR CREDIT: (Note: Course Outline must include additional skills that will be acquired by repeating this course.)  FORMCHECKBOX _No Change  FORMCHECKBOX  Credit Course Yes  FORMCHECKBOX  No  FORMCHECKBOX  If yes, how many times? 1  FORMCHECKBOX   FORMCHECKBOX _ 2  FORMCHECKBOX   FORMCHECKBOX _ 3  FORMCHECKBOX  Non Credit Course Yes  FORMCHECKBOX  No  FORMCHECKBOX  If yes, how many times? 1  FORMCHECKBOX   FORMCHECKBOX _ 2  FORMCHECKBOX   FORMCHECKBOX _ 3  FORMCHECKBOX  Unlimited  FORMCHECKBOX  (Noncredit only) STAND ALONE: No Change  FORMCHECKBOX   CONTROL Forms.OptionButton.1 \s   CONTROL Forms.OptionButton.1 \s  METHODS OF INSTRUCTION: No Change  FORMCHECKBOX   FORMTEXT       RECOMMENDED OR REQUIRED TEXT/S: (The following information must be provided: Author, Title, Publisher, Year of Publication, Reading level and Reading level verification)  FORMCHECKBOX _Required:  FORMCHECKBOX  Recommended:  FORMCHECKBOX  n/a  FORMCHECKBOX  Author:  FORMTEXT Epp Title:  FORMTEXT Discrete Mathematics with Applications (most recent edition) Publisher:  FORMTEXT Brooks/Cole Year of Publication:  FORMTEXT 2011, or other appropriate college level text. ISBN:  FORMTEXT       (if available) Reading level of text, Grade:  FORMTEXT 12+ Verified by:  FORMTEXT ev Other textbooks or materials to be purchased by the student:  FORMTEXT none CULTURAL DIVERSITY: Does this course meet the cultural diversity requirement? Yes  FORMCHECKBOX  No  FORMCHECKBOX  If Yes, please indicate which criteria apply. At least two criteria must beselected andevidenced in the course content section and at least one Student Learning Outcome must apply tocultural diversity. This course promotes understanding of:  FORMCHECKBOX  Cultures and subcultures  FORMCHECKBOX  Cultural awareness  FORMCHECKBOX  Cultural inclusiveness  FORMCHECKBOX  Mutual respect among diverse peoples  FORMCHECKBOX  Familiarity with cultural developments and their complexities SLO #  FORMTEXT       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: Complete this section in a manner that demonstrates students 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. FORMTEXT Student uses logically valid forms of argument and avoids common logical errorsMeasure:  FORMTEXT homework, exam, problem sets PLO:  FORMTEXT 1ILO:  FORMTEXT 2, 7GE-LO: B3, B7, B8Year assessed or anticipated year of assessment: 20152. FORMTEXT Student can provide examples of recurrence relations that give rise to formulas that are verified by induction.Measure:  FORMTEXT homework, exam, problem sets.PLO:  FORMTEXT 1ILO:  FORMTEXT 7, 2GE-LO:  FORMTEXT      Year assessed or anticipated year of assessment: 20153. FORMTEXT Student can describe different traversals of trees and graphs.Measure:  FORMTEXT homework, exam, problem setsPLO:  FORMTEXT 2,1 ILO:  FORMTEXT 7,2GE-LO:  FORMTEXT      Year assessed or anticipated year of assessment: 20154. FORMTEXT Student can apply the binomial theorem and Bayes theorem as appropriate.Measure:  FORMTEXT homework, exam, problem setsPLO:  FORMTEXT      ILO7,2,3GE-LO: B3, B7, B8Year assessed or anticipated year of assessment: 20155. FORMTEXT      Measure:  FORMTEXT      PLO:  FORMTEXT      ILO:  FORMTEXT      GE-LO:  FORMTEXT      Year assessed or anticipated year of assessment:  FORMTEXT      6. FORMTEXT      Measure:  FORMTEXT      PLO:  FORMTEXT      ILO:  FORMTEXT      GE-LO:  FORMTEXT      Year assessed or anticipated year of assessment:  FORMTEXT      7. FORMTEXT      Measure:  FORMTEXT      PLO:  FORMTEXT      ILO:  FORMTEXT      GE-LO:  FORMTEXT      Year assessed or anticipated year of assessment:  FORMTEXT      8. FORMTEXT      Measure:  FORMTEXT      PLO:  FORMTEXT      ILO:  FORMTEXT      GE-LO:  FORMTEXT      Year assessed or anticipated year of assessment:  FORMTEXT      9. FORMTEXT      Measure:  FORMTEXT      PLO:  FORMTEXT      ILO:  FORMTEXT      GE-LO:  FORMTEXT      Year assessed or anticipated year of assessment:  FORMTEXT      10. FORMTEXT      Measure:  FORMTEXT      PLO:  FORMTEXT      ILO:  FORMTEXT      GE-LO:  FORMTEXT      Year assessed or anticipated year of assessment:  FORMTEXT       GENERAL EDUCATION LEARNING OUTCOMES FORMTEXT  AREA A Communications in the English Language After completing courses in Area A, students will be able to do the following: Receive, analyze, and effectively respond to verbal communication. Formulate, organize and logically present verbal information. Write clear and effective prose using forms, methods, modes and conventions of English grammar that best achieve the writings purpose. Advocate effectively for a position using persuasive strategies, argumentative support, and logical reasoning. Employ the methods of research to find information, analyze its content, and appropriately incorporate it into written work. Read college course texts and summarize the information presented. Analyze the ideas presented in college course materials and be able to discuss them or present them in writing. Communicate conclusions based on sound inferences drawn from unambiguous statements of knowledge and belief. 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: Explain concepts and theories related to physical and biological phenomena. Identify structures of selected living organisms and relate structure to biological function. 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. Work collaboratively with others on labs, projects, and presentations. Describe the influence of scientific knowledge on the development of worlds 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: Demonstrate knowledge of the language and content of one or more artistic forms: visual arts, music, theater, film/television, writing, digital arts. Analyze an artistic work on both its emotional and intellectual levels. Demonstrate awareness of the thinking, practices and unique perspectives offered by a culture or cultures other than ones own. Recognize the universality of the human experience in its various manifestations across cultures. Express objective and subjective responses to experiences and describe the integrity of emotional and intellectual response. Analyze and explain the interrelationship between self, the creative arts, and the humanities, and be exposed to both non-Western and Western cultures. 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: Identify and analyze key concepts and theories about human and/or societal development. Critique generalizations and popular opinion about human behavior and society, distinguishing opinion and values from scientific observation and study. Demonstrate an understanding of the use of research and scientific methodologies in the study of human behavior and societal change. Analyze different cultures and their influence on human development or society, including how issues relate to race, class and gender. 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: Demonstrate an awareness of the importance of personal development. Examine the integration of ones self as a psychological, social, and physiological being. 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: Connect knowledge of self and society to larger cultural contexts. Articulate the differences and similarities between and within cultures. CONTENT, STUDENT PEFORMANCE OBJECTIVES and OUT-OF CLASS ASSIGNMENTS. No Change  FORMCHECKBOX 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. 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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 ExamThe 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. 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