Course Outline of Record

Item	Value
Eff Term	Fall 2026
Curriculum Committee Approval Date	11/12/2025
Top Code	170100 - Mathematics, General
Units	4 Total Units (Lecture Units 4)
Hours	72 Total Hours (Lecture Hours 72)
Total Outside of Class Hours	144
Total Student Learning Hours	216
Course Credit Status	Credit: Degree Applicable (D)
Material Fee	No
Basic Skills	Not Basic Skills (N)
Repeatable	No
Open Entry/Open Exit	No
Grading Policy	Standard Letter (S)
California General Education Transfer Curriculum (Cal-GETC)	Cal-GETC 2A Math Concepts (2A)
Intersegmental General Education Transfer Curriculum (IGETC)	IGETC 2A Math Concepts (2A)

Course Description

This course is an introduction to proof writing and mathematical reasoning. Topics include logic, set theory, functions, induction, equivalence relations, cardinality, and proof writing techniques. PREREQUISITE: MATH A185 or MATH A185H. Transfer Credit: CSU; UC.

Course Level Student Learning Outcome(s)

1. Students will be able to write elementary proofs including direct proof, proof by contradiction, proof by contrapositive, and proof by induction.
2. Students will be able to perform operations on sets using appropriate notation.
3. Students will be able to draw conclusions about the veracity of a statement with appropriate mathematical justification.

Course Objectives

• 1. Distinguish between definition, conjecture, theorem, and proof.
• 2. Write proofs using a variety of proof techniques.
• 3. Perform mathematical operations on sets.
• 4. Utilize quantifiers in mathematical arguments.
• 5. Identify cardinality of sets.
• 6. Calculate greatest common divisors using the Euclidean Algorithm.
• 7. Prove equivalence relations
• 8. Prove a definition is well-defined.

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Lecture Content

1. Mathematical Structure
   1. Proof
   2. Definition
   3. Theorem and Conjecture
   4. Planning and Writing a Proof
2. Logic
   1. Propositions
   2. Functions and Quantifiers
   3. Proof
      1. Direct
      2. Contradiction
      3. Contrapositive
3. Sets and Functions
   1. Set Notation
   2. Subsets
   3. Unions, Intersections, and Compliments
   4. Functions
   5. Cartesian Products
   6. Power Sets
   7. Indexed Collections of Sets
4. Divisibility and the Euclidean Algorithm
   1. Remainders and Congruence
   2. Greatest Common Divisors and the Euclidean Algorithm
5. Mathematical Induction and Well-Ordering
   1. Recursive Processes
   2. Proof by Induction
   3. Well-Ordering and the Principle of Mathematical Induction
   4. Strong Induction
6. Relations and Partitions
   1. Relations
   2. Equivalence Relations
   3. Partitions
   4. Functions
   5. Well-Definition
   6. Congruence
7. Cardinalities of Infinite Sets
   1. Cardinality
   2. Countable Sets
   3. Uncountable Sets

Method(s) of Instruction

• Lecture (02)

Instructional Techniques

Lecture, Discussion, Collaborative Learning

Reading Assignments

Students will spend approximately 1 hour per week reading from the assigned text.

Writing Assignments

Students will spend approximately 1 hour per week on written assignments.

Out-of-class Assignments

Students will spend approximately 6 hours per week on homework assignments as given by the instructor.

Study Non-Contact Hours Recommended

144

Methods of Student Evaluation

• Midterm Exam
• Final Exam
• Short Quizzes
• Written Assignments
• Projects (Individual/Group)
• Problem Solving Exercises

Demonstration of Critical Thinking

Problem solving is foundational to a course in abstract mathematics which requires deep critical thinking. Critical thinking is an integral part of an abstract mathematics course.

Required Writing, Problem Solving, Skills Demonstration

Problem sovling exercises commonly appear on exams or quizzes. These require written responses of the students.  Grades are determined by performance on quizzes and exams. Some instructors may also include grades on homework, cooperative assignments, or participation in cooperative learnign sessioons. A comprehensive final exam is par tof this course.

Textbooks Resources

1. Required Sundstrom, T. Mathematical Reasoning: Writing and Proof, 2nd ed. Pearson, 2020

Other Resources

1. Other appropriate textbook as chosen by full-time faculty.

Resources Subscreen

• Textbook: Sundstrom, T.. Mathematical Reasoning: Writing and Proof. Pearson (2020).

Eligible Discipline(s)

• Mathematics: Master’s degree in mathematics or applied mathematics OR bachelor’s degree in either of the above AND master’s degree in statistics, physics, or mathematics education OR the equivalent. Master's degree required.