# Math 110: Linear Algebra

### Announcements

• Thanks for a great summer! Hopefully you learned a thing or two!
• Final Exam solution here.
• Midterm 2 solution here.
• Midterm 1 solution here.
• Please note - class meets from 10-12 EVERY DAY Mon - Thurs. There was some confusion about this from the berkeley schedule website.

### Homework

 Assignment Solution HW1 Solved! HW2 Solved! HW3 Solved! HW4 Solved! HW5 Solved! HW6 Solved! HW7 Solved!

### Worksheets

 Date Solution June 25th page 1 page 2 July 3rd Solution Practice Midterm 1 Solution July 18th Solution Practice Midterm 2 Solution August 5th Solution August 7th Solution Practice Final Solution

#### Overview

Math 110 is a second course in linear algebra, focusing more on theory and proof than computations. We will begin with the abstract notions of vector spaces and linear transformations, and relate these to the more familiar column vectors and matrices. We will see that finite-dimensional vector spaces are classified by their dimension, which is to say two spaces having the same dimension are essentially the same. Thus the more interesting thing to study is a linear transformation between two vector spaces. This is a very interesting theory, and will occupy us for most of the back half of the course. This class, however, is focused at least as much on developing your ability to write and read proofs as it is on the material itself. As such, a lot of time will be spent discussing various strategies for writing and understanding proofs. I will also emphasize where possible geometric interpretations, since I think this is helpful and often overlooked.

#### Prerequisites

Math 54, officially, but math 55 may also be helpful.

#### Textbook

"Linear Algebra Done Right", by Sheldon Axler. This book tends to be focused on the abstract theory. I will try to emphasize examples in my lectures to supplement your readings.

Grades will be calculated on a 500-point scale, as follows:
• Midterm Exams - 100 points each; two midterms (20% each)
• Final Exam - 200 points (40%)
• Homework - 15 points each; seven assignments (note this comes to 105 points, so extra credit is possible here). (20%)

You must take the final exam to pass the course. In the event of a serious medical emergency, you may miss ONE midterm if you have written documentation of your illness; in this case the final exam will then count for 60% of your grade. You cannot miss both midterms.

#### Homework

Homework is due every Wednesday (except the first week) at the beginning of class. There are seven assignments in all. Late HW will count for 3 points less per day late.

In doing your homework, you should work with others, but please write the names of your collaborators at the top of the assignment. You must write clearly - points will be taken off if your explanations are confusing or illegible. When writing proofs, you must use complete sentences.

#### Exams

There are two midterm exams, on July 16th and August 1st, weighted equally at 20% each. There are no make-up exams. If you miss the midterm, you must provide written evidence from a doctor of serious illness. In this case I will count your final exam at 60% instead. The final exam will be two hours long and will be on the final day of class, Thursday August 15th.

#### Lectures

Schedule of Lectures

We meet for two hours each session. The first fifty minutes will be a lecture. After a ten minute break, the second hour will be a problem session.

As mentioned above, I will try to supplement the textbook by giving many examples in my lectures. You will be responsible for these (and possibly other) examples on the exams and homework, so it's a good idea to come to class.