SRJC Course Outlines

7/3/2022 8:36:27 PMMATH 6 Course Outline as of Fall 2019

Changed Course
CATALOG INFORMATION

Discipline and Nbr:  MATH 6Title:  INTRO TO HIGHER MATH  
Full Title:  An Introduction to Higher Mathematics
Last Reviewed:12/10/2018

UnitsCourse Hours per Week Nbr of WeeksCourse Hours Total
Maximum4.00Lecture Scheduled4.0017.5 max.Lecture Scheduled70.00
Minimum4.00Lab Scheduled06 min.Lab Scheduled0
 Contact DHR0 Contact DHR0
 Contact Total4.00 Contact Total70.00
 
 Non-contact DHR0 Non-contact DHR Total0

 Total Out of Class Hours:  140.00Total Student Learning Hours: 210.00 

Title 5 Category:  AA Degree Applicable
Grading:  Grade Only
Repeatability:  00 - Two Repeats if Grade was D, F, NC, or NP
Also Listed As: 
Formerly: 

Catalog Description:
Untitled document
A lower division course introducing topics in higher mathematics including introductory set theory and formal logic, proof techniques, mathematical induction, equivalence relations, functions and cardinalities of sets as applied to number theory, calculus and modern algebra.

Prerequisites/Corequisites:
Course Completion of MATH 1B


Recommended Preparation:

Limits on Enrollment:

Schedule of Classes Information
Description: Untitled document
A lower division course introducing topics in higher mathematics including introductory set theory and formal logic, proof techniques, mathematical induction, equivalence relations, functions and cardinalities of sets as applied to number theory, calculus and modern algebra.
(Grade Only)

Prerequisites:Course Completion of MATH 1B
Recommended:
Limits on Enrollment:
Transfer Credit:CSU;UC.
Repeatability:00 - Two Repeats if Grade was D, F, NC, or NP

ARTICULATION, MAJOR, and CERTIFICATION INFORMATION

Associate Degree:Effective:Inactive:
 Area:
 
CSU GE:Transfer Area Effective:Inactive:
 
IGETC:Transfer Area Effective:Inactive:
 
CSU Transfer:TransferableEffective:Spring 2013Inactive:
 
UC Transfer:TransferableEffective:Spring 2013Inactive:
 
C-ID:

Certificate/Major Applicable: Major Applicable Course



COURSE CONTENT

Student Learning Outcomes:
Upon completion of the course, students will be able to:
Untitled document
1.  Identify valid forms of arguments using predicate logic.
2.  Construct mathematical proofs of theorems in number theory, calculus and modern algebra.
3.  Determine the properties of functions and relations.
4.  Determine the cardinalities of important sets.
 

Objectives: Untitled document
Upon successful completion of the course, students will be able to:
1. Use set theory and logic to convey and understand mathematical concepts.
2. Prove and disprove mathematical conjectures.
3. Provide proper counterexamples.
4. Prove mathematical theorems using mathematical induction and strong mathematical
    induction.
5. Characterize functions as injective, surjective, bijective or otherwise.
6. Characterize relations in terms of the reflexive, symmetric and transitive properties.
7. Determine when a relation is an equivalence relation.
8. Characterize a set in terms of its cardinality.
9. Apply techniques of proofs to number theory, calculus, and topics in modern algebra.

Topics and Scope
Untitled document
I. Logic
    A. Negation, conjunction and disjunction
    B. Logical form and equivalence
    C. Conditional statements
    D. Biconditional statements
    E. Valid and invalid arguments
    F. Predicates
    G. Quantified statements
    H. Arguments with quantified statements
II. Set Theory
    A. Introduction to sets
    B. Algebra of sets
    C. Venn diagrams and conjectures
    D. Arbitrary unions and intersections
III. Proofs
    A. Trivial and vacuous proofs
    B. Direct proofs
    C. Indirect proofs
           1. Proof by contradiction
           2. Proof by contrapositive
    D. Existence proofs
    E. Counterexamples
    F. Proofs by cases
IV. Mathematical Induction
    A. Introduction to mathematical induction
    B. Proof by minimum counterexample
    C. Strong mathematical induction
V. Functions
    A. Definition
    B. Injective and surjective functions
    C. Bijective functions
    D. Composition of functions
    E. Inverse functions
    F. Permutations
VI. Relations
    A. Relations on sets
    B. Properties of relations
    C. Equivalence relations
    D. Equivalence classes
    E. Congruence modulo n
    F.  Integers modulo n
VII. Cardinalities of Sets
    A. Numerically equivalent sets
     B. Denumerable sets
    C. Uncountable sets
    D. Comparison of set cardinalities
VIII. Topics in Number Theory
    A. Divisibility properties of integers
    B. The division algorithm
    C. Greatest common divisors
    D. The Euclidean algorithm
    E. Relatively prime integers
    F. The Fundamental Theorem of Arithmetic
    G. Concepts involving sums of divisors
IX. Topics in Calculus
    A. Limits of sequences
    B. Infinite series
    C. Limits of functions and fundamental properties
    D. Continuity
    E. Differentiability
X. Various Topics from Modern Algebra that Could Include:
    A. Binary operations
    B. Groups
    C. Rings
    D. Fields
    E. Integral domains
    F. Fundamental properties
    G. Isomorphism
    H. Homomorphisms
    I. Subgroups

Assignments:
Untitled document
1. Daily reading outside of class (10-50 pages per week).
2. Homework assignments (15-30) consisting of problems (5-35) from required text(s) or
    supplementary materials chosen by the instructor.
3. Quizzes (0-8) and exams (2-6), including final exam.
4. Projects (0-3): research papers on a specific topic (5 to 10 pages) or presentations given as
    posters or short talks. Papers and presentations must be related to topics taught in the course.

Methods of Evaluation/Basis of Grade.
Writing: Assessment tools that demonstrate writing skill and/or require students to select, organize and explain ideas in writing.Writing
0 - 0%
None
This is a degree applicable course but assessment tools based on writing are not included because problem solving assessments are more appropriate for this course.
Problem solving: Assessment tools, other than exams, that demonstrate competence in computational or non-computational problem solving skills.Problem Solving
5 - 20%
Homework problems
Skill Demonstrations: All skill-based and physical demonstrations used for assessment purposes including skill performance exams.Skill Demonstrations
0 - 0%
None
Exams: All forms of formal testing, other than skill performance exams.Exams
70 - 95%
Quizzes; exams, including final exam: problem solving and objective questions
Other: Includes any assessment tools that do not logically fit into the above categories.Other Category
0 - 10%
Projects: research papers or presentations


Representative Textbooks and Materials:
Untitled document
Mathematical Proof: A Transition to Advanced Mathematics. 4th ed. Chartrand, Gary and Polimeni, Albert and Zhang, Ping. Pearson. 2018
A Concise Introduction to Pure Mathematics. 4th ed. Liebeck, Martin. Routledge. 2015
Introduction to Advanced Mathematics. 2th ed. Barnier, William and Feldman, Norman. Pearson. 2000 (classic)

Print PDF