*Director of the Center*

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

• • • Here's how to get
the e-text and sign up for
on-line homework **for Rob's section (235.2) only!**

• • • Course-wide logistical details
appear here.

**Common Guidelines & Topics Schedule:**

All seven learning sections of Fall 2019 Math 235 will follow the Common Guidelines & Topics Schedule

**Our Learning Sections:**

MW at 4:00PM-5:15PM (235.2) in LGRT 121

**If you are Waiting to Enroll:**

Please come to class, introduce yourself, and in a short time we should be able to officially enroll you (we don't want to deal with over-rides until we know they're necessary).

**Office Hours:**

Immediately after (about 5:15PM) my class
in LGRT 121; and in LGRT 1435G (office) or LGRT 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 always looking for some class note-takers! 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 a recent (Spring 2017) 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 the e-text and e-homework* **Fall2019KusnerMath235** (Math 235 - Introduction to Linear Algebra - Rob Kusner's Section 2 only!)
here are
instructions in .pdf or in text:

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: **kusner20653**, 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 **Fall2019KusnerMath235** 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 **Fall2019KusnerMath235** 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 **Fall2019KusnerMath235**.

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

**Accommodation Policy Statement:**

UMass Amherst is committed to providing an equal educational
opportunity for all students. A student with a documented physical,
psychological, or learning disability on file with Disability Services
may be eligible for academic accommodations to help them succeed in
this course. If you have a documented disability that requires an
accommodation, **please notify your instructor during the first two
weeks of the semester** so that we can make appropriate
arrangements. It is also **your responsibility** to notify
Disability Services (normally at least one week in advance) if you
wish to take an exam there.