College of San Mateo
Official Course Outline
1. COURSE ID: MATH 268 TITLE: Discrete Mathematics
Units: 4.0 units Hours/Semester: 64.0-72.0 Lecture hours; and 16.0-18.0 TBA hours
Method of Grading: Letter Grade Only
Prerequisite: MATH 251
Recommended Preparation:
Any READ 400 level course.
2. COURSE DESIGNATION:
Degree Credit
Transfer credit: CSU; UC
CSU GE:
CSU GE Area B: SCIENTIFIC INQUIRY AND QUANTITATIVE REASONING: B4 Mathematics/Quantitative Reasoning
IGETC:
IGETC Area 2: MATHEMATICAL CONCEPTS AND QUANTITATIVE REASONING: A: Math
3. COURSE DESCRIPTIONS:
Catalog Description:
Covers topics in discrete mathematics with particular emphasis on applications to computer science.
Includes logic, sets, functions and relations, mathematical induction, recursion, Boolean algebra,
elementary number theory, and probability. Extra supplies may be required.
4. STUDENT LEARNING OUTCOME(S) (SLO'S):
Upon successful completion of this course, a student will meet the following outcomes:
1. Demonstrate understanding of Formal logic, (both predicate and propositional) Set theory, Number theory,
Combinatorics, and additional selected topics, as well as their their applications, especially to computer
science at a level appropriate to a first course.
2. Be able to read, create, and effectively communicate mathematical proofs
5. SPECIFIC INSTRUCTIONAL OBJECTIVES:
Upon successful completion of this course, a student will be able to:
1. Build and interpret logical statements with proper quantification.
2. Recognize valid and invalid logical arguments.
3. Use basic argument forms singly and in complex combinations.
4. Use quantifiers and predicates.
5. Build correct logical arguments to prove or disprove logical statements.
6. Prove or disprove statements in elementary number theory using direct and indirect proof methods.
7. Use unique factorization, the quotient remainder theorem and the Euclidean algorithm.
8. Prove statements using mathematical induction.
9. Perform basic operations with sets.
10. Prove and disprove statements about sets.
11. Solve counting problems using elementary laws for counting, permutations, combinations
12. Find probabilities using counting ideas.
13. Work with functions, and inverse functions, composition of functions, recognizing domain, co-domain, and
range, and recognizing one to one and onto.
14. Use one-to-one correspondence to prove sets countably infinite.
6. COURSE CONTENT:
Lecture Content:
1. Logical statements, truth tables, arguments.
2. Conditionals, contrapositive.
3. Argument forms.
4. Quantifiers and predicates.
5. Direct and indirect proof, proof by cases.
6. Proof in elementary number theory.
7. Unique factorization, quotient-remainder theorem, Euclidian algorithm.
8. Build and interpret logical statements with proper quantification.
8. Build and interpret logical statements with proper quantification.
9. Set, basic set operations, proof propositions involving sets.
10. Counting theory, permutations, combinations, basic probability.
11. The Binomial theorem.
12. The Pigeon Hole principle.
13. Functions, inverse functions, composition of functions.
14. One to one and onto.
Lab Content:
no lab
TBA Hours Content:
TBA assignments will provide additional practice for targeted student learning outcome. These assignments may be remedial,
reinforcement, or extension of ideas presented in class. The assignments may be individualized or designed for all members of the
class. TBA work will be completed with supervision of mathematics faculty.
7. REPRESENTATIVE METHODS OF INSTRUCTION:
Typical methods of instruction may include:
A. Lecture
B. Discussion
C. Observation and Demonstration
8. REPRESENTATIVE ASSIGNMENTS
Representative assignments in this course may include, but are not limited to the following:
Writing Assignments:
Students will be required to explain concepts and compose logical arguments in writing assignments.
Example: Prove or disprove: If an integer is a perfect square then its cube root is irrational.
Reading Assignments:
Assignments requiring the student to read sections of the (discrete mathematics) textbook and/or selected
materials supplied by the teacher. Example: Read the section in the textbook on Division into Cases and the
Quotient-Remainder Theorem. Example: Read the instructor's handout on RSA Cryptography.
Other Outside Assignments:
Students will be assigned problem sets requiring students to compute, solve, construct, prove, and assess.
Example: A group of 8 people are attending the movies together. Two of them insist on sitting together. In
how many ways may the 8 be seated in a row? Example: Prove: The product of any four consecutive
integers is divisible by 8.
Also students will be encouraged to discuss and debate conceptual questions in classroom discussion and in
study groups and students are encouraged to question whatever the teacher or other students do. Example:
f(n) = 2n is a mapping from the integers into the integers. Is f one to one? Prove or give a counter-example.
Is f onto? Prove or give a counter-example Example: Do the set of real numbers more than 0 and less than
one and the set of real numbers more than 0 and less than 2 have the same cardinality? Why or why not?
Collaborative work in or out of class may be assigned.
Work using computer software may be assigned.
To be Arranged Assignments:
TBA assignments will be extension of other assigned work or investigation of questions/ideas arising in
other assigned work. Thus they will reflect all assignment structures listed in representative assignments.
9. REPRESENTATIVE METHODS OF EVALUATION
Representative methods of evaluation may include:
A. Class Participation
B. Class Performance
C. Class Work
D. Exams/Tests
E. Group Projects
F. Homework
G. Oral Presentation
H. Papers
I. Projects
J. Quizzes
K. Written examination
L. A. Problem sets – These consist of sets of exercises assigned frequently. Questions may require proof,
calculation (calculate the number of arrangements), proof, construction of discrete mathematical objects
(construct a quotient finite state automaton), judgments about discrete mathematical objects (are these two
sets equal), and explanation of why. B. Quizzes – These are short examinations on the areas covered in the
problem set. C. Exams – Longer examinations. May be cumulative. D. Writing assignments – Require
extended logical argument and explanation of mathematical assertions, concepts, and processes.
10. REPRESENTATIVE TEXT(S):
Possible textbooks include:
A. Epp, Susanna S.. Discrete Mathematics with Applications, 4 ed. Cengage, 2011
B. Rosen, Kenneth. Discrete Mathematics and Its Applications, 7 ed. McGraw-Hill, 2012
Origination Date: August 2010
Curriculum Committee Approval Date: November 2012
Effective Term: Fall 2013
Course Originator: Cheryl Gregory