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LINEAR ALGEBRA

Dr. Ray Rosentrater Office hours: Mon. 9:00 – 10:20
Office: Mathematics Building (next to Post Office) Thurs. 10:00 – 11:30
Phone: 6185 Fri. 9:00 – 10:20

Prerequisites: The mathematical content required to function successfully in this course is minimal. You
should be familiar and comfortable with mathematical notation and algebraic manipulations. You
should be able to solve simultaneous linear equations with symbolic coefficients. You should also
be acquainted with the idea of a mathematical proof.

Far more important, though much harder to quantify, is a level of mathematical maturity. This
course will be concerned with investigating relationships between concepts, understanding
definitions, and developing theorems. You should be able to work with definitions and should be
able to distinguish between valid and invalid proofs. Successful completion of Math 10, Math 15
or Math 19 is considered sufficient evidence of the required mathematical maturity.

Texts: Lay, Linear Algebra and its Applications (3rd Ed.).
Solow, How to Read and Do Proofs (4th Ed.).

Objectives:
1. To understand the relationship between matrices and linear functions .
2. To understand the relationships between invertability, determinants, Eigenvalues, characteristic
roots , rank and characteristic polynomials.
3. To understand the concepts of vector space, linear independence , basis, and dimension.
4. To gain an appreciation for the beauty of the subject of linear algebra.
5. To develop the ability to read and write proofs.
6. To learn to ask mathematical questions and to begin pursuing answers.
7. To develop the ability to express mathematical ideas and questions in writing.

Outline: The course will consist of three major sections with an exam at the end of each section. The
mathematical content of the course, for the most part, can be found in the first six chapters of Lay.
Topics from Solow will be interspersed with the material from Lay as the term progresses. For
additional details, see the attached schedule of topics.

Evaluation: Evaluation will be based on the following criteria

Weekly homework (Lay)  27%
Weekly homework (Solow)  8%
Class Contribution  5%
Definition Quizzes  5%
Regular Exams (2)  35%
Cumulative Final  20%

1. Homework from Lay will be assigned weekly and will generally be due on Wednesdays at the
beginning of class. The readings, problems and due dates will be posted to the course web site.
Homework papers should be neat, organized, and clearly presented . Multiple pages should include
your name at the top of each page and should be stapled together.

The majority of assigned problems will involve proofs. Solutions to such problems
should be carefully written using complete sentences. Your sentences should maintain proper form
including capitalization, punctuation, the inclusion of both a subject and a verb, and agreement of
subject and predicate. Notation and equations should be properly set up by means of introductory
sentences and phrases. In particular, you should identify the meaning of any variable before using
it in your proof.

Each assignment will be worth 25 points and will consist of both computational and
theoretical problems. You may do extra even- numbered problems on one assignment to
compensate for an assignment for which you did not do well on the assigned problems. Though
you may do as many extra problems as you desire, your total score on any given assignment is
limited to 30 points. Extra computational problems are worth 1 point each (maximum 3 points per
assignment) and theoretical problems are worth 2 points each. Any extra problems should be
placed after the required problems and should be ordered by section.

The problems from Solow without solutions in the back of the book or on the web are
worth 2 points each. You should read the material from Solow at the rate of one chapter per week
and turn in 8 points worth problems each Friday. You may do extra problems on one assignment
to compensate for an assignment for which you received less than 8 points. You may also do extra
problems up to 120% of the total value of the homework from Solow for the semester.

Collaboration on homework is expected and encouraged. There is no reduction in score
due to working with others provided the following guidelines are adhered to:

• All students in the group understand the solution and are not merely copying solutions.
• All collaboration is credited. This will generally take the form of a note at the end of a
solution like “this solution was developed in collaboration with Jane Smith and Sam Jones.”
Alternatively or in addition, you may choose to include a note at the top of the first page like
“the solutions in this assignment were compared with those of John Martin for verification” or
“ I received help from Prof. Rosentrater on problems 12 and 18.”
• Any paper that does not include acknowledgements must include a statement indicating that
the work was done without assistance.

2. Each class period will begin with a vocabulary quiz. A term from the current lectures or readings
will be written on the board and you will be given a minute to write its correct definition on a sheet
of paper. You should come to class with a sheet of paper appropriate to the occasion.

3. Exam dates are included on the accompanying schedule of topics.

4. The final exam will be Wednesday, May 6 at 12:00 noon. Exceptions can be made only by
petition to the registrar and are rarely granted.

Absence: While attendance is expected and absence is unwise, there is no formal penalty for absence.
Responsibility is expected. If you are forced to miss class for some reason, you should make
arrangements for your homework to be brought to class for you. If you know you will be absent on a
particular day or for several days, you should make prior arrangements with me to get a list of
assignments and to make up the work.

Dishonesty: Dishonesty of any kind will result in loss of credit for the work involved. Major or repeated
infractions will result in dismissal from the course with a grade of F. Collaboration is encouraged, but
you must do your own, independent write up. Mere copying of another's work is dishonest. Give credit
on all collaborative work.

Schedule of Topics:
 

January 12 Linear Equations
  14 Row Operations
  16 Vector and Matrix Equations
  19 Martin Luther King Holiday
  20 Solutions of linear systems (Monday Schedule)
  21 Linear Independence
  23 Applications
  26 Matrices
  28 Matrix Operations
  30 Inverses
February 2 Factorizations
  4 Application
  6 Determinants
  9 Properties
  11 Review
  13 Exam 1(Through Matrices)
  16 President's Holiday
  18 Applications
  20 Vector Spaces
  23 Subspaces
  25 Special Subspaces
  27 Bases
March 2 Coordinate Systems
  4 Dimension and Rank
  6 Change of Basis
  9 Applications
  11 Review
  13 Exam 2(Through Vector Spaces)
  16 Spring
  18 Recess
  20  
  23 Eigenvectors and Eigenvalues
  25 Characteristic Equation
  27 Diagonalization
  30 Linear Transformations
April 1 Applications
  3 Orthogonality
  6 Inner product
  8 Orthogonal Sets
  10 Easter
  13 Recess
  15 Gram-Schmidt
  17 Least Squares and Projection
  20 Inner product Spaces
  22 Applications
  24  
  27 Review
  29 Review
     
May 6 12:00 - 2:00 Final Exam
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