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 (3^{rd} Ed.).
Solow, How to Read and Do Proofs (4^{th} 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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