*Director of the Center*

(This page is like a cathedral: always under reconstruction ;-)

**Common Guidelines & Topics Schedule:**

All nine learning sections of Spring 2017 Math 235 will follow the Common Guidelines & Topics Schedule

**Our Learning Sections:**

TuTh at 11:30AM-12:45PM (235.3) & 1:00PM-2:15PM (235.7) in Goessmann 51

**Office Hours:**

Immediately after my afternoon classes (about 2:15PM) in Goessmann 51; or in LGRT 1435G (office) or 1535 (lab) with an advance appointment via email: profkusner@gmail.com

**Prerequisites:**

Familiarity with basic algebra, vector geometry and (later in the course) a bit of calculus and differential equations

**Remarks:**

We're looking for some class note-takers, particularly from Section 7
(a few folks from Section 3 have kindly volunteered).

Please talk with Rob after class if you're interested in this
important project.

Here's some possibly useful (or useless ;-) information:

⇒ Before the first midterm, you may enjoy reviewing Basic Linear Algebra in 7 Easy Pages prepared by my former student (2011-14) Andrew Maurer (he's now in grad school at the University of Georgia; and his advisor Dan Nakano took my linear algebra course at Berkeley in the early 1980's - years later Dan told me that my course made him want to become a mathematician).

⇒ Before the second midterm, you may appreciate this Linear Algebra Review Sheet by your generous fellow student Jonah Palmer (with a couple comments from yours truly).

⇒ Several past exams are available here or at the Kusner's Math Classes page.

⇒ For you hardcore linear algebra students: the usual multiplication algorithm has complexity O(n^3) for n × n matrices; here's a recent paper on the latest complexity bound: O(n^2.3726...). (Conjecture: O(n^2) is best.)

⇒ The last part of the course uses the relation AE=ED (for any matrix E whose columns form a basis of real eigenvectors of a real 2 × 2 matrix A with distinct real eigenvalues) to factor A=EDE^{-1}, where D is the real diagonal 2 × 2 matrix whose nonzero entries are the eigenvalues, i.e. A is similar to D. This is useful to compute powers of A and the exponential of A. But what if A has repeated real eigenvalue (a, a), or if the eigenvalues are complex conjugate pairs (a+bi, a-bi) with nonzero b? How does one decompose A=aI+bJ where J^2=-I in the latter case, or decompose A=aI+N where N^2=0 in the former? Some texts (e.g. Bretscher) find a 2 × 2 matrix aI+bJ_o to which A is similar; here J_o is the standard 90-degree rotation matrix. Here's another approach, suggested by my emeritus colleague Arunas Rudvalis, which seems simpler - and more general since it also deals with the N (nilpotent) case.

**MyMathLab:**

• *To register for* **Math 235 Linear Algebra Spring 2017 Kusner Sections
3 & 7**:

1. Go
to www.pearsonmylabandmastering.com

2. Under Register, select Student.

3. Confirm you have the information needed, then select OK! Register now.

4. Enter our learning sections' course ID: **kusner44207**, and Continue.

5. Enter your existing Pearson account username and password to Sign In.

→You have an account if you have ever used a Pearson MyLab & Mastering
product, such as MyMathLab, MyITLab, MySpanishLab, MasteringBiology or
MasteringPhysics.

⇒ If you donâ€™t have an account, select Create and complete the required fields.

6. Select an access option.

⇒ Enter the access code that came with your textbook or was purchased
separately from the bookstore.

⇒ Buy access using a credit card or PayPal account.

⇒ If available, get temporary access by selecting the link near the
bottom of the page.

7. From the You're Done! page, select Go To My Courses.

8. On the My Courses page, select the course name **Math 235 Linear
Algebra Spring 2017 Kusner Sections 3 & 7** to start your work.

• *To sign in later:*

1. Go
to www.pearsonmylabandmastering.com

2. Select Sign In.

3. Enter your Pearson account username and password, and Sign In.

4. Select the course name **Math 235 Linear Algebra Spring 2017 Kusner
Sections 3 & 7** to start your work.

• *To upgrade from temporary to full access:*

1. Go
to www.pearsonmylabandmastering.com

2. Select Sign In.

3. Enter your Pearson account username and password, and Sign In.

4. Select Upgrade access for **Math 235 Linear Algebra Spring 2017
Kusner Sections 3 & 7**.

5. Enter an access code or buy access with a credit card or PayPal
account.

*!!!DRAFT!!! (Still under reconstruction! ;-)*