Linear Algebra

Last update: December 12, 2004

*This page will be updated at least once a week. Check for announcements and postings regularly, mostly at the bottom of the page!*

**Lecture 1:** Valentina Kiritchenko, Math 3-102

Phone: 632-8884.
Email: *vkiritch@math.sunysb.edu*

Classes: MWF 9:35-10:30, Light Engineering 152

Office Hours: MWF 11-12:20 (Math 3-102)

**Lecture 2:** Detlef Gromoll, Math 5-110

Phone: 632-8286,
Email: *detlef@math.sunysb.edu*

Classes: MWF 9:35-10:30, Mathematics P-131

Office Hours: M 3-4, F 11-12 (both UG Office P-143), W 2:30-3:30 (Math 5-110), and by appointment

**Grader:** Fan Zhu, Math S-240C

Email: *fzhu@math.sunysb.edu*

Office Hours: F 5-6 (S-240C), Th 3-4 Math Learning Center [MLC] S-240A

**About this Course:** This is an advanced undergraduate linear algebra course, which will be more rigorous and also cover additional material needed in various areas of mathematics and its applications - including vector spaces, linear transformations, eigenvalues, and inner product spaces. Optional projects may address further topics like elementary Jordan forms and very basic multilinear algebra (including bilinear forms).

**Prerequisites:** MAT 211 or equivalent, MAT 200 or permission of instructor.

**Text:** Kenneth Hoffman, Ray Kunze: *Linear Algebra*, second edition, Prentice Hall (1971).

For a little more than 7 weeks, the course will cover the basic chapters 1,2,3 pretty much in detail. We will then discuss more selected topics from the chapters 5,6,8.

**Grading:** There will be 3 short tests, 40 minutes each, about once a month; all given in class - *no makeups*. If one short exam is missed because of a serious (documented) illness or emergency, the semester grade will be determined based on the balance of the work in the course. A final examination will be held on Wednesday, December 15, 8-10:30am (Period 1).
Students are expected to ensure when they register for this course that they will be available for the final examination, and that they do not have too many final exams on that date.
The final course grades in MAT 310 will be determined as follows:

Homework/Class Participation 25%, Short Tests 15% each, Final Exam 30%

We will give up to 30% extra credit for at most 3 projects, to be assigned below.
*Incompletes* will be granted only if documented circumstances beyond your control prevent you from completing the course work, according to strict University rules.

**Homework/Class Participation:** You can not learn mathematics without doing mathematics. It is essential to be an active participant in class and to solve problems: Each week a homework assignment will be posted further down on this page, normally on Monday. It is due the following week by M noon in class or directly with our grader. While you may work together with others in the class (which can be a rewarding experience), write up your own solutions in your own words. Since homework earns credit, it is assumed that everyone submitting particular problems has solved them individually. The goal of the homework is to understand the material, not to merely hand in some paper. This is a more advanced math course where coherent arguments and rigorous proofs are often required. Late homework will *not* be accepted.

**Approximate Course Schedule:**

*Weeks of* *Sections*

8/30-9/20 1.1 through 1.6

9/24-10/11 2.1 through 2.6

Short Test 1 - F 9/24 [in class; on Chapter 1]

10/13-11/03 3.1 through 3.5 (basics from 3.6 and 3.7 recommended optional reading)

Short Test 2 - F 11/05 [in class; on Chapters 2 and 3]

11/08-11/17 5.1 through 5.4 (basic material)

11/19-12/03 6.1-2 in more detail; topics from 6.3 and 6.4

Short Test 3 - W 12/01 [in class; 5.1-4, to the extent of homework and the summaries below]

12/06-12/10 8.1 and 8.2

Final Exam - W 12/15 [in our classroom; cumulative]

**Special Needs:**
If you have a physical, psychological, medical or learning disability that
may impact your course work, please contact Disability Support Services,
ECC (Educational Communications Center) Building, room 128, (631) 632-6748.
They will determine with you what accommodations are necessary and
appropriate. All information and documentation is confidential.

Students requiring emergency evacuation are encouraged to discuss their
needs with their professors and Disability Support Services. For procedures
and information, go to the following web site.

*http://www.stonybrook.edu/facilities/ehs/fire/disabilities.shtml*

**Week by Week Details:** Assignments are listed here.

8/30-9/03 | Study 1.1, 1.2, and 1.3 in detail | Homework problems:

p5 1,3,8 Bonus: 6 pp10-11 2,5,6,7 [due F 9/10, in class]

9/06-10 | Review 1.2 | Study 1.3 and 1.4 in detail | Homework problems:

pp15-16 2,3,5,7,9 Bonus: 10
[due W 9/15, in class]

9/13-17 | Review 1.4 | Study 1.5 and 1.6 in detail | Homework problems:

p21 1,3,5,7 pp26-27 3,4,8,9
Bonus: 12 [due W 9/22, in class]

9/20-24 | Review Chapter 1 for F test | Study 2.1 in detail | Homework problems:

pp33-34 1,3,6,7 [due W 9/29, in class]

9/27-10/01 | Review 2.1 | Study 2.2 and 2.3 in detail; begin reading 2.4 | Homework Problems:

pp39-40 1,2,3,4,7 pp48-49 1,3,6,7,10 Bonus: 14 [due F 10/08, in class]

10/04-08 | Review 2.3 | Study 2.4 and 2.5 in detail | Homework problems:

pp54-55 1,4,6,7 p66 2,4,6
Bonus: 7 [due F 10/15, in class]

10/11-15 | Review 2.5 | Study 2.6 and 3.1 in detail; begin reading
3.2 | Homework Problems:

pp73-74 1,3,5,6,8,10,13 Bonus: 12 [due F 10/22, in class]

10/18-22 | Review 3.1 | Study 3.2 in detail; read 3.3 | Homework Problems:

pp83-84 1,3,4,7,9 Bonus: 11 p86 2,4 Bonus: 7 [due F 10/29, in class]

10/25-29 | Review 3.3 | Study 3.4 in detail | Homework Problems:

pp95-97 2,3,5,7,8 Bonus: 12 [due F 11/05, in class]

11/01-05 | Review 2.1-6 and 3.1-4 for Test 2 F | Study 3.5 in detail | Homework Problems:

pp105-107 2,3,4,8,11 Bonus: 14 [due W 11/10, in class]

11/08-12 | Study 5.1 through 5.3 (basic material) | Homework Problems:

pp148-150 2,4,9 Bonus: 12 pp155-156 1,2,5,6,7 Bonus: 8 [due F 11/19, in class]

11/15-19 | Review Summary 5.1-3 (to be posted here) and study 5.4 | Homework Problems:

*Summary_1.pdf*

pp162-163 1,2,3,4,6 Bonus: 9 [due W 11/24, in class]

*Summary_2.pdf*

11/22-24 | Review 5.4 and its summary (to be posted here) | Study 6.1 and 6.2 in detail | Homework Problems:

pp189-190 3,4,6,7,10,11,13 Bonus: 8,9 [due F 12/03, in class]

11/29-12/03 | Read 6.3 and 6.4 | Study pp1-9 of the following link as alternate reference | Homework Problems:

pp197-198 1,3,4 Bonus: 5 pp205-206 1,4,5,10 Bonus: 11
[due F 12/10, in class]

Summary_3.pdf (Do not take the title of this excellent article too seriously!)

12/06-10 | Study 8.1 and 8.2 | Homework Problems:

pp275-277 2,3,5,9,10 pp288-290 1,2,4 Bonus: 16

[This last HW is optional; do as soon as you can; absolute deadline: Final, Wednesday 12/15]

Begin review of all course materials.

**Announcement:** We will have a joint review and extended problem session in preparation for the Final on Sunday, December 12, 2-4pm, in Math P-131.

Printout of homework:

*hw1.pdf*
*hw2.pdf*
*hw3.pdf*
*hw4.pdf*
*hw5.pdf*
*hw6.pdf*
*hw7.pdf*

*hw8.pdf*
*hw9.pdf*
*hw10.pdf*
*hw11.pdf*

But you will need the text book!

*Note:* Test 1 was given on Friday 9/24, in class.

Test 2 was given on Friday 11/05, in class.

Test 3 was given on Wednesday 12/01, in class.

Solutions for the assigned homework sets will always be posted on the page
*http://www.math.sunysb.edu/~vkiritch/*.

Direct links to the solution files are:

*sol1.pdf*
*sol2.pdf*
*sol3.pdf*
*sol4.pdf*
*sol5.pdf*
*sol6.pdf*
*sol7.pdf*

*sol8.pdf*
*sol9.pdf*
*sol10.pdf*
*sol11.pdf*
*sol12.pdf*
*sol13.pdf*

*sol_test1.pdf*

*sol_test2.pdf*

*sol_test3.pdf*

**Optional Projects:** You may submit work on not more than three of the following 10 independent study type problems, each worth extra credit up to 10% of the course grade. Problems are in essence taken from our text. It will usually be necessary to first read and understand much of the material of the corresponding section. Sometimes consulting additional sources may be helpful. Problems marked with an asterisk are more difficult or elaborate. If you want to earn extra credit toward a higher course grade you must work on at least one of those. All presentations should be reasonably detailed and neatly typed. Formulas can be entered by hand, if necessary. On the average, an optimal treatment of a topic would probably take 2 pages. Keep it short, but complete. Projects will be added through November. Of course, partial solutions will earn partial credit. Good luck!

*Deadline:* Wednesday, December 15 by the end of the Final (turn papers in with the Final).

1*. *Jordan forms* (.pdf file)

We also recommend the reference
*jordan.pdf*

2*. Solve Problem 14 on p49 in Section 2.3. Find and describe an argument that V has a basis. Argue that any such basis must be an uncountable set. Do you think it is possible to construct a basis explicitly?

3. *Vector spaces and operators* (.pdf file)

4. *Paints* (.pdf file)

5. *Determinants* <.pdf file>

6. *Eigenvalues and Eigenvectors* (.pdf file)

7. (*Rotation in 3-space*) Work out Problem 5 on p309.

Another useful link is
*cross.pdf*

8*. (*Cayley Transform*) Solve Problem 7 on p309.

9. (*Rigid Motion*) Discuss Problem 14 on p310.

10*. (*Lorentz Transformation*) Work out Problem 15 on p311.