6. Minimum hours per week of independent work done outside of class: 8
Course Preparation – (Supplemental form B required)


7a. Prerequisite(s): (Course and/or other preparation/experience that is REQUIRED to be completed previous to enrollment in this course.)

Completion of MATH 30 with grade of "C" or better


7b. Corequisite(s): (Courses and/or other preparation that is REQUIRED to be taken concurrently with this course.)



7c. Advisory: (Minimum preparation RECOMMENDED in order to be successful in this course. Also known as “Course Advisory”.)




Catalog Description And Other Catalog Information


8. Repeatability:

Not Repeatable

Please Note: 8. (Repeatability) does not refer to repeating courses because of substandard grades or a lapse of time since the student took the course. A course may be repeated only if the course content differs each time it is offered and the student who repeats it is gaining an expanded educational experience as stipulated in Title 5.
Skills or proficiencies are enhanced by supervised repetition and practice within class periods.
Active participatory experience in individual study or group assignments is the basic means by which course objectives are attained.
Course content differs each time it is offered.
Explanation for above repeatability selection:


9a. Grading Option:

Standard Grade

9b. Catalog Description:

Study of set theory, relations and functions, logic, combinatorics and probability, algorithms, computability, matrix algebra, graph theory, recurrence relations, number theory including modular arithmetic. Various forms of mathematical proof are developed: proof by induction, proof by contradiction.



Course Outline Information


10. Course Objectives: (Course
objectives for all credit courses must indicate that students will learn critical thinking and will be able to apply concepts at college level. Course
objectives must be related to items listed in Section 11.)

1. create mathematical proofs directly, indirectly, and by contradiction; 2. use mathematical induction to create a mathematical proof; 3. create a mathematical proof with truth tables and logical equivalences; 4. translate mathematical statements using universal and existential quantifiers; 5. use sets to organize and quantify data; 6. create an algorithm using pseudocode; 7. evaluate a series; 8. model using permutations and combinations and numerically evaluate appropriate applied problems; 9. model using probabilities, including conditional probabilities; 10. solve counting problems using a generating function; 11. assess that a relation is an equivalence relation; 12. create a graph and a tree to describe the structure of a system; 13. use Boolean algebra to mathematically model electronic circuits; 14. verify functions are onetoone and onto; 15. use matrices to solve applied problems.


11. Course Content Outline: (Provides a comprehensive, sequential outline of the course content, including all major subject matter and the specific body of knowledge covered.)

I. Predicate Calculus A. Propositional Equivalences B. Universal and Existential Quantifiers II. Proofs A. Counterexample B. Direct C. Indirect D. Contradiction E. Mathematical Induction F. Truth Tables G. Logical Equivalences III. Algorithms A. Complexity B. Growth C. The Division Algorithm D. The Euclidean Algorithm E. Number Bases IV. Counting Principles A. Combinatorics B. Generating Functions C. Difference Equations V. Probability A. Conditional Probability B. Independence C. Expected Value VI. Relations A. Equivalence Relation VII. Graphs and Trees A. Euler and Hamiltonian Paths B. Shortest Distance Applications VIII. Boolean Algebra A. Logic Gates and Switching Circuits IX. Matrices A. Operations B. Applications C. Systems of Equations


12. Typical OutofClass Assignments: Credit courses require two hours of independent work outside of class per unit of credit for each lecture hour, less for lab/activity classes. List types of assignments, including library assignments.)


a. Reading Assignments: (Submit at least 2 examples)

1. Throughout the course, read assigned topics from text. For example, how to verify the validity of a mathematical formula by mathematical induction.
2. Search the library or the internet for applications of the golden ratio and the Fibonacci sequence.


b. Writing, Problem Solving or Performance: (Submit at least 2 examples)

1. Write mathematical proofs. For example, given a function f, prove that the image of the intersection of two sets is a subset of the intersection of the images of those two sets.
2. Prove that the limit of the ratio of a Fibonacci number to its predecessor is the golden ratio.


c. Other (Term projects, research papers, portfolios, etc.)



13. Required Materials:

a. All Textbooks, resources and other materials used in this course are College Level?

Yes
No

b. Representative collegelevel textbooks (for degreeapplicable courses) or other print materials.

Book 1:

Author:

Kenneth Rosen

Title:

Discrete Mathematics and Its Applications

Publisher:

McGraw Hill

Date of Publication:

2012

Edition:

seventh

Book 2:

Author:

Susanna Epp

Title:

Discrete Mathematics with Applications

Publisher:

Brooks Cole

Date of Publication:

2011

Edition:

fourth

Book 3:

Author:


Title:


Publisher:


Date of Publication:


Edition:


Book 4:

Author:


Title:


Publisher:


Date of Publication:


Edition:


Book 5:

Author:


Title:


Publisher:


Date of Publication:


Edition:


c. Other materials and/or supplies required of students:


Methods of Instruction


14a. Check all instructional methods used to present course content.

Lecture/Discussion


Laboratory
and/or Activity


Distance Learning (requires supplemental form)


Other:


14b. Provide
specific examples for each method of instruction checked above; include a
minimum of two examples total. Reference the course objective(s) addressed by
instructional method(s). Explain both what the instructor and students are
expected to be doing and experiencing.

1. create mathematical proofs directly, indirectly, and by contradiction:
The instructor will provide through a lecture format mathematical proofs of various types, including proof by contradiction. The instructor will then ask the student to construct a proof of this type. An example is: prove that sqr(2) is irrational. Typically, a student will provide his/her proof to the class and both students and instructor will evaluate the correctness, the level of rigor, and the clarity of presentation.
2. use mathematical induction to create a mathematical proof:
The instructor will provide through a lecture format mathematical proofs of various types, including mathematical induction. The instructor will then ask the student to construct a proof of this type. An example is: prove that the sum of the first n integers is n(n+1)/2. Typically, a student will provide his/her proof to the class and both students and instructor will evaluate the correctness, the level of rigor, and the clarity of presentation.





15. Methods of Assessing Student Learning
15a. Methods of Evaluation:
Essay Examinations


Objective Examinations


Problem Solving Examinations


Skill Demonstrations


Projects 

Classroom Discussions 

Reports 

Other
(explain below) 





15b. Based upon course objectives, give examples of how student performance will be evaluated. Provide examples for each method checked above; include a minimum of two examples total.




1. Exams will determine a student's ability to independently construct a mathematical proof. For example, a student might be asked to write a formal proof that sqr(2) is irrational. The instructor will assess the success of the proof by determining if the appropriate proof format is used (i.e., proof by contradiction), that the guidelines of such a proof are being employed (i.e., the negation of the conclusion of the conditional statement in the theorem is stated), and that the remaining body of the proof meets college level rigor and clarity.
2. A classroom discussion will be employed upon the completion of a presentation from a student, particularly with an example of proof writing. The instructor will assess the rigor, clarity, and correctness of the proof. In addition, the instructor will assess the level of understanding of the student presenting such a proof through that student's answers to questions from other students and from the instructor.








SECTION C


1. Program Information:


In an approved program.


Part of a new program.


Not part of an approved program.

2.
Course TOP Code:

Program title  TOP Code:

Mathematics, General 170100


3.
Course SAM Code:

A
Apprenticeship
B
Advanced Occupational
C
Clearly Occupational
D
Possibly Occupational
E
NonOccupational


4. Faculty Discipline Assignment(s):
Comments:





SECTION D


General Education Information:

1. College Associate Degree GE Applicability:


Communication & Analytic Thinking Math Competency

2. CSU GE Applicability (Recommendedrequires CSU approval):


B4 Mathematics/Quantitative Reasoning

3. IGETC Applicability (Recommendedrequires CSU/UC approval):


2: Mathematical Concepts & Quantitative Reasoning

4. CID:



SECTION E


Articulation Information: (Required for Transferable courses only)

1.



CSU Transferable.


UC Transferable.


CSU/UC major requirement.


If CSU/UC major requirement, list campus and major. (Note: Must be lower division)



2.

List at least one community college and its comparable course. If requesting CSU and/or UC transferability also list a CSU/UC campus and comparable lower division course.


Laney College, Math 11, Discrete Mathematics Humboldt State University, Math 253, Discrete Mathematics San Diego State University, Math 245 Discrete Mathematics University of California, Riverside, Math 11, Introduction to Discrete Structures


SECTION F


Planning and Resources  Please address the areas below:

1. Evidence of Planning: connection to existing or planned degrees/certificates,
place in general education; relationship to mission (basic skills, transfer,
career technical education, lifelong learning); transfer university requirements;
advisory/regional/national needs; or other planning considerations.

recommendations of advisory committee, connection to existing or planned degrees or transfer university requirements. connection to transfer or lifelong learning. relationship to student learning outcomes identified by program, connection to general education, or articulation with other institutions. Meets all four student learning outcomes for the math program.


2. Potential Impact on Resources: faculty, facilities,
computer support/lab, library, transportation, equipment, or other needs. 
Minimum qualifications to teach the course. No special qualifications or training to teach the course. There is no impact on library, computer support, transportation, equipment, or other needs.



SECTION G

1. Maximum Class Size (recommended): 35

2. If recommended class size is not standard, then provide rationale:







