SRJC Course Outlines

10/1/2022 6:03:39 PMMATH 5 Course Outline as of Spring 2010

Changed Course
CATALOG INFORMATION

Discipline and Nbr:  MATH 5Title:  INTRO TO LINEAR ALGEBRA  
Full Title:  Introduction to Linear Algebra
Last Reviewed:2/8/2021

UnitsCourse Hours per Week Nbr of WeeksCourse Hours Total
Maximum3.00Lecture Scheduled3.0017.5 max.Lecture Scheduled52.50
Minimum3.00Lab Scheduled017.5 min.Lab Scheduled0
 Contact DHR0 Contact DHR0
 Contact Total3.00 Contact Total52.50
 
 Non-contact DHR0 Non-contact DHR Total0

 Total Out of Class Hours:  105.00Total Student Learning Hours: 157.50 

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:
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An introduction to linear algebra including the theory of matrices, determinants, vector spaces, linear transformations, eigenvectors, eigenvalues and applications.

Prerequisites/Corequisites:
Completion of MATH 1B or higher (VF)


Recommended Preparation:
Concurrent enrollment in MATH 1C or MATH 2

Limits on Enrollment:

Schedule of Classes Information
Description: Untitled document
An introduction to linear algebra including the theory of matrices, determinants, vector spaces, linear transformations, eigenvectors, eigenvalues and applications.
(Grade Only)

Prerequisites:Completion of MATH 1B or higher (VF)
Recommended:Concurrent enrollment in MATH 1C or MATH 2
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 1989Inactive:
 
UC Transfer:TransferableEffective:Spring 1989Inactive:
 
C-ID:
 CID Descriptor: MATH 250 Introduction to Linear Algebra SRJC Equivalent Course(s): MATH5

Certificate/Major Applicable: Major Applicable Course



COURSE CONTENT

Outcomes and Objectives:
Upon completion of the course, students will be able to:
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Upon successful completion of the course, students will be able to:
1. Solve systems of linear equations using Gauss-Jordan elimination and Cramer's rule.
2. Define operations on matrices, invertibility, elementary matrices, orthogonal matrices.
3. Apply properties of determinants to matrices.
4. Evaluate determinants using row reduction techniques.
5. Define cofactors and adjoints of determinants to determine the inverse of a matrix.
6. Define properties of vectors, subspace, span, linear independence,
  bases, inner product spaces, and orthonormal bases.
7. Define and determine dimension rank of solution space of a system of linear equations.
8. Define kernel, range, rank, nullity, matrix representation of
  linear transformation, similarity, and change of basis.

Topics and Scope
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I.   Matrices
    A.  Systems of linear equations
    B.  Gauss-Jordan elimination
    C.  Operations on matrices
    D.  Invertibility
    E.  Elementary matrices
    F.  Orthogonal matrices
II.  Determinants
    A.  Properties
    B.  Evaluation by row reduction
    C.  Cofactors and adjoints
    D.  Formula for inverse of a matrix
    E.  Cramer's rule
III. Vector Spaces
    A.  Defining properties
    B.  Subspace
    C.  Span
    D.  Linear independence
    E.  Basis
    F.  Dimension
    G.  Rank
    H.  Solution space of a system of linear equations
    I.  Inner product spaces
    J.  Orthonormal bases
    K.  Gram-Schmidt process
IV.  Linear Transformations
    A.  Kernel
    B.  Range
    C.  Rank and nullity
     D.  Matrix representation of linear transformation
    E.  Similarity
    F.  Change of basis
V.   Eigenvectors and Eigenvalues
    A.  Characteristic equations
    B.  Eigenspaces
         1.  Diagonalization of matrices
         2.  Orthogonal diagonalization of symmetric matrices
VI.  Applications may include:
    A.  Differential equations
    B.  Fourier series
    C.  Quadratic forms
    D.  Gauss-Seidel method
    E.  Partial pivoting
    F.  Eigenvalue approximation
    G.  Others

Assignments:
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1.  Reading outside of class (0-50 pages per week)
2.  Problem set assignments (15-30)
3.  Midterm exams (2-5), quizzes (0-20) and final exam

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 assignments
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
80 - 95%
Multiple choice, Free response exams, quizzes
Other: Includes any assessment tools that do not logically fit into the above categories.Other Category
0 - 0%
None


Representative Textbooks and Materials:
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Elementary Linear Algerbra (9th). Anton, Howard. Wiley: 2005 (classic)
Linear Algebra and Its Applications (3rd). Lay,  David C. Addison Wesley: 2003 (classic)

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