Palomar Logo Effective Term: Fall 2007
Status: Historical
 
PALOMAR COLLEGE
 COURSE OUTLINE FOR CREDIT COURSE
 
  • Courses numbered 1 - 49 are remedial or college preparatory courses which do not apply toward an A. A. Degree and are not intended for transfer.
  • Courses numbered 50-99 apply toward an AA Degree, but are not intended for transfer.
  • Courses numbered 100 and higher apply toward an AA Degree and/or are intended for transfer to a four-year college or university.
 
Course Number and Title: MATH 245 Discrete Mathematics
 

Unit Value: 3  

Lecture Hours Per Week: 3  

Lab Hours Per Week:  

Lecture/Lab Hours Per Week:  

 

Grading Basis: Grade/Pass/No Pass
 
Basic Skills Requirements: Appropriate Language and/or Computational Skills.
 
Requisite(s)
To satisfy a prerequisite, the student must have earned a letter grade of A, B, C or P(Pass) in the prerequisite course, unless otherwise stated.
Prerequisite:
A minimum grade of 'C' in MATH 130 or MATH 140 , or a passing score on the appropriate placement test
Corequisite:
None
Prerequisite: Completion of, or concurrent enrollment in
None
Recommended Preparation:
None
Limitation on Enrollment:
None
Catalog Description:
The study of prepositional and predicate logic, number theory and methods of proof, elements of set theory, relations and functions, the Pigeonhole Principle, sequences, infinite sets, basic counting techniques, permutations, combinations, and applications directed to the field of computer science.
 
Specific Course Objectives:
Upon successful completion of the course the student will be able to:
  1. Use logic to explore the truth and falsity of statements and patterns of proofs, and apply basic principles of logical reasoning in set theory, mathematical induction, functions and relations, and in solving recurrence relations.
  2. Apply the logic of compound and quantified statements, translate these statements into symbolic form, and test symbolic arguments for validity.
  3. Use properties of mathematical concepts, such as sets, relations, and functions in logical derivations and theorem proving.
  4. Perform various operations with relations and functions, define and solve different types of recurrence relations, and analyze functions such as one-to-one and onto functions.
  5. Solve problems using permutations and combinations, calculate the probability of a given event occurring, and solve problems by applying the exclusion -inclusion and Pigeonhole Principle.
  6. Apply critical thinking skills to express mathematical ideas with clarity and precision both orally and in writing.
 
Methods of Instruction:
Methods of Instruction may include, but are not limited to, the following:
  1. Lecture
 
Content in Terms of Specific Body of Knowledge:
  1. The logic of compound statements and of quantified statements
    1. Logical form and logical equivalence
    2. Conditional statements
    3. Valid and invalid arguments
    4. Predicate and quantified statements
    5. Arguments with quantified statements
  2. Elementary number theory and methods of proof
    1. Direct proof and counterexample
    2. Indirect argument: contradiction and contrapositive
    3. Classical proof: The irrationality of  2
  3. Sequences and mathematical induction
    1. Sequences
    2. Mathematical induction
    3. Strong mathematical induction and the Well -Ordering Principle
  4. Set theory
    1. Basic definitions of set theory
    2. Properties of sets
    3. The empty set, partitions, power sets, and Boolean algebras
  5. Counting
    1. Counting and probability
    2. Permutations and combinations
    3. The Binomial Theorem
  6. Functions
    1. Functions defined on general sets
    2. One-to-one, onto, and inverse functions
    3. The Pigeonhole Principle
    4. Composition of functions
  7. Relations
    1. Relations on sets
    2. Reflexivity, symmetry, and transitivity
    3. Equivalence relations
  8. Additional topics may be included at instructor's discretion
Textbooks/Resources:
May Include Textbooks, Manuals, Periodicals, Software, and Other Resources
  1. Susanne S. Epp. Discrete Mathematics with Applications. 3rd ed. Boston: PWS Publishing Company, 2004.
Required Reading:
 
Suggested Reading:
Ralph P. Grimaldi. Discrete and Combinatorial Mathematics. An Applied Introduction. 5th ed. Addison Wesley, 2004
 
Critical Thinking:
Among other topics, students will study the basic properties of sets and logic, and learn how to construct proofs from elementary number theory. Students will be able to analyze problems from mathematics and computer science, formulate and test their problem solving techniques, and hence improve their critical thinking skills throughout the course.
 
Required Writing:
Problem-solving exercises on homework assignments and written tests are more appropriate. In addition, students may be required to write reports from one paragraph to several pages explaining concepts or explaining and interpreting solutions to non-routine or applied problems.
 
Outside Assignments:
Students are expected to spend a minimum of three hours per unit per week in class and on outside assignments, prorated for short-term classes.

Students are expected to read the text, study lecture notes, and complete daily homework Homework assignments may include practice solving routine problems, explaining concepts, and solving applications or non-routine problems. Other outside assignments may include problem-solving reports or journals.
 
Methods of Assessment:
Methods of Assessment may include, but are not limited to, the following:
  • Exams/Tests
  • Homework
  • Papers
 
Open Entry/Open Exit:
No, course is not offered as open entry/open exit.
 
Is Course Repeatable for Reason(s) Other Than Deficient Grade? No
 
Contact Person: Monika Brannick