# Math 200 Linear Algebra

## Course Description

This course will be an introduction to linear algebra. Our
main goal for this class will be to work

our way from the concrete to the abstract. We will begin with a situation which
is familiar to

you: solving small systems of linear equations. We will use this to springboard
into a discussion

of matrices, solving vector equations, linear transformations, and properties of
the familiar vector

space R^{n}. (A note on notation: R^{1} is the real line, R^{2}
is the real plane, R^{3} is three-dimensional

space, and so on.)

Once we have the basics in place for this concrete
setting, we will consider abstract vector spaces

and see how the topics we have studied in R^{n} apply to vector spaces
in general. While in the

general vector space setting, we will consider eigenvalues and eigenvectors as
well as inner products

and orthogonality.

As we work our way through the course, our other goal will
be to work on writing proofs. For

many of you, this will be the first time you have written mature mathematical
proofs so this course

serves as a place for your to try your hand at it and begin to work on
developing your style.

## Text

We will work from Linear Algebra and Its Applications, 3rd
ed., update by David C. Lay.

Note that the third edition update comes with a CD that contains the Student
Study Guide for

the text. I highly encourage you to make use of this resource.

## Homework

Homework assignments will be posted on the course website.

Homework will be assigned after class each day and will be
due at the start of the following class.

Please write neatly and staple your work. Working problems is the only way to
really learn

math so therefore I strongly encourage you to work carefully through each
exercise in

order to develop intuition for the subject. You will find that by being diligent
about doing your

homework, you will be much more well-prepared for the exams. In a typical
non-exam week, you

should expect to spend about two to three hours of work outside of class for
every hour spent in

class.

Homework is graded on a 0-1-2 scale. A zero is given for
little or no work shown (even if the answer

is correct), a one is given if the exercise is attempted but incomplete, and a
two is given for a

mostly or totally correct answer.

Note that no late homework will be accepted, even for
reasons of mild illness. Late homework

will receive a score of zero. You may however, hand in homework early if a
conflict arises. I will

drop your lowest three homework scores when I calculate your final average.

## Exams

There will be two midterm exams and one final exam. The midterm exams are scheduled for

Monday, March 9 at 7:30pm

Wednesday, April 15 at 7:30pm

The final exam will be scheduled by the registrar. Do not
try to determine our exam date from

the "Outline" that is posted on the college website. The outline does not apply
to our class.

As with homework, no late exams will be given. If you have
a conflict with either midterm

exam date, please see me at least two weeks before the exam so that we can make
arrangements

for you to take the exam early. Vacation plans are not a legitimate reason for
arranging an early

exam so please plan to be on campus until after our final exam date.

## Honor Code

You may (in fact you are encouraged to!) work together in
pairs or groups while you are figuring

out homework assignments. However, your final write-up of each assignment must
be your own.

Copying is considered a breach of the honor code.

You are expected to complete exams entirely on your own.
All exams will be closed-book and there

will be no calculators allowed.

## Grading

I will determine final grades according to whichever of
the the following percentages gives the better

score:

Exam 1 | 30% |

Exam 2 | 30% |

Final Exam | 30% |

Homework and Class Participation | 10% |

Exam 1 | 27.5% |

Exam 2 | 27.5% |

Final Exam | 35% |

Homework and Class Participation | 10% |

**Tentative Schedule of Topics**

Week Beginning | Topics |

Feb 9 | Solving systems of linear equations, row reduction, vector equations |

Feb 16 | Matrix equation Ax = b, solution sets of linear systems (Winter Carnival) |

Feb 23 | Linear independence, linear transformations and matrices |

Mar 2 | Matrix operations, inverting matrices, characterizations of invertible matrices |

Mar 9 | Introduction to and properties of determinants, (Exam 1) |

Mar 16 | Determinants and volume, vector spaces and subspaces |

Mar 23 | Spring Break! |

Mar 30 | Null and column spaces, bases, coordinate systems |

Apr 6 | Dimension of a vector space, rank, change of basis |

Apr 13 | Markov chains, eigenvalues and eigenvectors, the characteristic equation (Exam 2) |

Apr 20 | Diagonalization, eigenvectors and linear transformations |

Apr 27 | More eigenvectors and linear transformations, inner products, orthogonality |

May 4 | Orthogonal sets, orthogonal projections, the Gram-Schmidt process |