COLLEGE OF ALAMEDA COURSE OUTLINE

COLLEGE: STATE APPROVAL DATE: 09/27/2010
ORIGINATOR: Vanson Nguyen STATE CONTROL NUMBER: CCC000373222
BOARD OF TRUSTEES APPROVAL DATE: 05/08/2008
CURRICULUM COMMITTEE APPROVAL DATE: 03/17/2015
CURRENT EFFECTIVE DATE:
 
DIVISION/DEPARTMENT:

1. REQUESTED CREDIT CLASSIFICATION:
  Credit - Degree Applicable
Course is not a basic skills course.
Program Applicable
2. DEPT/COURSE NO: 3. COURSE TITLE:
  MATH 003E   Linear Algebra
4. COURSE: COA Course Changes only in Non-Catalog Info   TOP NO. 1701.00
5. UNITS: 3.000   HRS/WK LEC: 3.00 Total: 52.50
  HRS/WK LAB:

6. NO. OF TIMES OFFERED AS SELETED TOPIC:       AVERAGE ENROLLMENT:
7. JUSTIFICATION FOR COURSE:
  Satisfies the General Education Analytical Thinking requirement for Associate Degrees. Provides foundation for more advanced study in mathematics, and related fields such as Physics. Satisfies the Quantitative Reasoning component required for transfer to UC, CSU, and some independent four-year institutions. Acceptable for credit: CSU, UC.
8. COURSE/CATALOG DESCRIPTION
  Linear spaces and linear transformations: Development of techniques and theory for solving and classifying linear systems, including row operations, Gaussian elimination, and matrix algebra; properties of vectors in two and three dimensions, matrix theory, abstract vector spaces, linear transformations, inner products, norms, orthogonality, eigenvalues, eigenspaces; selected applications of linear algebra. MATH 3E and 3F are equivalent to MATH 3D. Not open for credit to students who have completed or are currently enrolled in MATH 3D.
9. OTHER CATALOG INFORMATION
 
  1. Modular: No     If yes, how many modules:
  2. Open entry/open exit: No
  3. Grading Policy: Letter Grade Only
  4. Eligible for credit by Exam: No
  5. Repeatable according to state guidelines: No
  6. Required for degree/certificate (specify):
    New - Mathematics AS-T
  7. Meets GE/Transfer requirements (specify):
    Acceptable for credit: UC/CSU. AA/AS area 4b, 4e CSU area B4. IGETC area 2A.
  8. C-ID Number: MATH 250 Expiration Date:

  9. Are there prerequisites/corequisites/recommended preparation for this course? Yes
    Date of last prereq/coreq validation: 03/17/2015
  10. Acceptable for Credit: CSU/UC
10. LIST STUDENT PERFORMANCE OBJECTIVES (EXIT SKILLS): (Objectives must define the exit skills required of students and include criteria identified in Items 12, 14, and 15 - critical thinking, essay writing, problem solving, written/verbal communications, computational skills, working with others, workplace needs, SCANS competencies, all aspects of the industry, etc.)(See SCANS/All Aspects of Industry Worksheet.)

Students will be able to:
  1. solve system of equations using Gaussian elimination and other methods
  2. determine whether a set, with given operations, is a vector space
  3. use bases and orthonormal bases to solve linear algebra problems
  4. find the dimension of a space such as those associated with matrices and linear transformations
  5. find eigenvalues and eigenvectors and use them in applications
  6. prove basic results in linear algebra using appropriate proof-writing techniques together with concepts such as those of linear independence of vectors, properties of subspaces, linearity, injectivity and surjectivity of functions, and properties of eigenvectors and eigenvalues
  7. apply systems of equations to solving problems from areas such as statistics (curve fitting), physical science (electrical circuits), and business (economic models)
11A. COURSE CONTENT: List major topics to be covered. This section must be more than listing chapter headings from a textbook. Outline the course content, including essential topics, major subdivisions, and supporting details. It should include enough information so that a faculty member from any institution will have a clear understanding of the material taught in the course and the approximate length of time devoted to each. There should be congruence among the catalog description, lecture and/or lab content, student performance objectives, and the student learning outcomes. List percent of time spent on each topic; ensure percentages total 100%.

LECTURE CONTENT:

1. Systems of Linear Equations and Matrices (20%)
      a. Systems of Linear Equations
      b. Gaussian and
Gauss-Jordan elimination
      c. Matrices and matrix operations
      d. Inverse matrices and the relationship between the inverse of the coefficient matrix and solutions to systems of equations
      e. Matrix arithmetic and matrix algebra
      f. Elementary matrices
      g. Transpose of a matrix
      h. Special matrices: Diagonal, triangular and symmetric

      i. Matrix generated spaces: row space, column space, null space, rank and nullity

2. Determinants (6%)
      a. Evaluating determinants by row reduction
      b. Properties of determinants
      c. Cramer's Rule

3. Vectors in R2 and R3 (10%)
      a. Introduction to vectors (geometric)
      b. Norm of a vector; vector arithmetic
      c. Dot product; projections
      d. Cross product
      e. Lines and planes in 3-space

4. Euclidean vector spaces (10%)
      a. Euclidean n-space
      b. Linear transformations from Rn to Rm
      c. Properties of linear transformations from Rn to Rm

      d.
Vector Algebra for Rn

5. General vector spaces (22%)
      a. Real vector spaces
      b. Subspaces
      c. Linear independence and dependence
      d. Basis and dimension of a vector space
      e. Row and column spaces, nullspace
      f. Rank and nullity


6. Inner product spaces
(12%)
      a. Inner products on real vector spaces
      b. Orthogonality in inner product spaces
      c. Orthonormal bases
      d. Gram-Schmidt process, QR-decomposition
      e. Best approximation; least squares
      f. Orthogonal matrices
      g. Change of basis
      h. Angle in inner product space


7. Eigenvalues, Eigenvectors
(10%)
      a. Eigenvalues and eigenvectors
      b. Diagonalization
      c. Orthogonal diagnonalization
      d. Eigenspace

8. Linear transformations
(10%)
      a. General linear transformations
      b. Kernel and range
      c. Inverse linear transformations
      d. Matrices of general linear transformations
      e. Similarity

11B. LAB CONTENT:
N/A
12. METHODS OF INSTRUCTION (List methods used to present course content.)
  1. Threaded Discussions
  2. Other (Specify)
  3. Discussion
  4. Lecture

  5. Other Methods:
    Instructor-focused lecture on theory and the language of calculus. Question and answer periods based on worksheets and in-class examples to encourage class discussion and demonstrations which emphasize alternative approaches to problem solving and their underlying rationales. Video demonstration of tools specific to this level of calculus. Distance Ed addendum for hybrid instruction use.
13. ASSIGNMENTS: 0.00 hours/week (List all assignments, including library assignments. Requires two (2) hours of independent work outside of class for each unit/weekly lecture hour. Outside assignments are not required for lab-only courses, although they can be given.)

Out-of-class Assignments:
Out-of-class Assignments: College-level textbook chapter readings that reinforce lecture material. Problem sets including computational problems equivalent in content and level of difficulty to those covered in the lectures. Additional problems that introduce supplemental concepts and formulas and require the synthesis and analysis of various concepts. Graphical representation and analysis specific to the study of linear algebra.


ASSIGNMENTS ARE: (See definition of college level):
Primarily College Level
14. STUDENT ASSESSMENT: (Grades are based on):
ESSAY (Includes "blue book" exams and any written assignment of sufficient length and complexity to require students to select and organize ideas, to explain and support the ideas, and to demonstrate critical thinking skills.)
COMPUTATION SKILLS
NON-COMPUTATIONAL PROBLEM SOLVING (Critical thinking should be demonstrated by solving unfamiliar problems via various strategies.)
OTHER (Describe):
Assess essay for understanding and application of concepts presented in classwork and supplemental material. Evaluate computation skills for accurate application of steps and correct answers. Evaluate students' ability to analyze given information and apply it in terms of the question
15. TEXTS, READINGS, AND MATERIALS
  A. Textbooks:
 
  • Anton, Howard. 2013. Elementary Linear Algebra 11th. John Wiley Publishing Company
    Rationale: -
 
  • Anton, Howard. 09-30-2013. Elementary Linear Algebra (Student Solutions Manual). John Wiley Publishing Company
 

*Date is required: Transfer institutions require current publication date(s) within 5 years of outline addition/update.

  B. Additional Resources:
 
  • Library/LRC Materials and Services:

    The instructor, in consultation with a librarian, has reviewed the materials and services of the College Library/LRC in the subject areas related to the proposed new course
  • Are print materials adequate?     Yes
  • Are nonprint materials adequate?     No
  • Are electronic/online resources available?     Yes
  • Are services adequate?     Yes
  • Specific materials and/or services needed have been identified and discussed. Librarian comments:
    Collection adequate to support course. Department Chair to donate additional texts as needed.
  C. Readings listed in A and B above are: (See definition of college level):
 

Primarily college level

16. DESIGNATE OCCUPATIONAL CODE:
E - Non-Occupational
17. LEVEL BELOW TRANSFER:
Y - Not Applicable
18. CALIFORNIA CLASSIFICATION CODE:
Y - Credit Course
19. NON CREDIT COURSE CATEGORY:
Y - Not Applicable
20. FUNDING AGENCY CATEGORY:
Not Applicable - Not Applicable
SUPPLEMENTAL PAGE

Use only if additional space is needed. (Type the item number which is to be continued, followed by "continued." Show the page number in the blank at the bottom of the page. If the item being continued is on page 2 of the outline, the first supplemental page will be "2a." If additional supplemental pages are required for page 2, they are to be numbered as 2b, 2c, etc.)

1a. Prerequisites/Corequisites/Recommended Preparation:
    PREREQUISITE:
  • MATH 003A: Calculus I