# Math 54, Fall 2016

This is the homepage for Fall 2016 Math 54 discussion sessions 115 and 116.

**GSI:** Kyle Miller

**E-mail:** kmill at math.berkeley.edu

**Meeting times:** MWF 12-1pm (Disc 115) or MWF 1-2pm (Disc 116) in 110 Barrows Hall

**Office hours:** T 1-2pm and Th 4-5pm in 1066 Evans, or by appointment

**bCourses:**
https://bcourses.berkeley.edu/courses/1453155 (lecture)

The math department publishes a rough course overview. There is also a collection of some past exams.

## 1. Information

**Textbook:** Lay-Nagle-Saff-Snider, *Linear Algebra &
Differential Equations*. A specially priced UC Berkeley paperback
edition is available. This is a combination of

- Lay,
*Linear Algebra and Its Applications*(4th ed.); and - Nagle, Saff, and Snider,
*Fundamentals of Differential Equations*(8th ed.).

**Homework and quizzes:** Homework is due Wednesdays by
11:59pm. No late homework will be accepted. Quizzes will take
place Fridays in discussion in the first twenty minutes or so.
Quizzes will cover homework material. It is your responsibility to
make your work clear: if you are “right” but the grader did not
notice, you will lose points.

The lowest homework score and the lowest quiz score will be dropped.

**Attendance:** I do not keep track of attendance (though you
should appear for the quizzes!). It is up to you to determine how
you are going to learn the material.

**DSP accommodations:** Please tell me by 9/9 so that
arrangements can be made.

## 2. Worksheets

- Aug 26
- Aug 29
- Aug 29
- Sep 2
- Sep 7 (notes): Disc 115, Disc 116
- Sep 9
- Sep 12
- Sep 14
- Sep 16
- Sep 19
- Sep 21: midterm 1 schemata
- Sep 26
- Sep 27: Determinants in detail
- Sep 28, Determinants geometrically
- Oct 3 (partial solutions)
- Oct 5
- Oct 10
- Oct 12
- Oct 17
- Oct 19
- Oct 24
- Oct 26
- Oct 29: midterm 2 schemata
- Nov 2
- Nov 7
- Nov 9
- Nov 21

The department publishes worksheets on the Lower Division Course Outlines page, Math 54 Worksheet (pdf).

## 3. Quizzes

- Quiz 1 (solutions)
- Quiz 2 (solutions)
- Quiz 3 (solutions)
- Quiz 4 (solutions)
- Quiz 5 (solutions)
- Quiz 6 (solutions)
- Quiz 7 (solutions)
- Quiz 8 (solutions)
- Quiz 9 (solutions)
- Quiz 10 (solutions)
- Quiz 11 (solutions)
- Quiz 12 (solutions)
- Quiz 13 (solutions)

## 4. Programs

The following are some programs to illustrate some computations and concepts from the course.- Row reducer. Computes the reduced row echelon form of a matrix using the book’s algorithm, and displays every step.
- Cat transformation. Experiment with $2\times 2$ matrix transformations by transforming the image of a cat.
- Basis toy. Experiment with bases of ${\mathbb{R}}^{2}$.
- Interactive cofactor expansion
Complex polynomials. Type in a polynomial (for instance, “x(x+2i)^2+1”), then drag the circle ($r{e}^{i\theta}$) on the left side around to see its image ($p(r{e}^{i\theta})$) on the right. One reason every polynomial has a root is for large radii the image will wrap around zero $\mathrm{deg}p$ times, but for very small radii the image will wrap tightly around $p(0)$ — and somewhere in between the image must pass through zero.