Introduction to Linear Algebra

Last update: May 27, 2003

*Check regularly the end of this page for announcements and postings!*

**Lecture 2:** Detlef Gromoll (Course Coordinator), Math 5-116

Phone: 632-8290,
Email: *detlef@math.sunysb.edu*

Classes: MW 7-8:20pm, Physics 113

Office Hours: M 1-2 (5-116) & Th 2-3 (UG Office P-143), and by appointment

**Lecture 1:** Paul Kumpel, Math 3-120

Phone: 632-8264,
Email: *pkumpel@math.sunysb.edu*

Classes: MWF 2:15-3:10, Physics 113

Office Hours: MW 3:30-4:30 (3-120) & F 3:30-4:30 (UG Office P-143)

**Teaching Assistant:** Lucas Finco, Physics B-119

Phone: 632-4624,
Email: *lfinco@grad.physics.sunysb.edu*

Office Hours: MW 11:30-12:30 (Physics B-119) & Tu 7-8 (MLC S-240A)

**Course Description:** MAT 211 is the basic standalone introduction to the theory of linear algebra with some applications. Mastering this subject is essential all across Mathematics, the Sciences, and beyond. Topics include: Systems of linear equations and the Gauss-Jordan Algorithm, vectors, vector spaces, bases and dimension, inner products, applications to geometry, linear transformations, determinants, eigenvalues and eigenvectors.

**Prerequisites:** C or higher in AMS 151 or MAT 131 or 141, or coregistration in MAT 126, or level 7 on the mathematics placement examination, or permission of instructor. Anyone lacking these prerequisites risks deregistration.

**Text:** Howard Anton, Chris Rorres: *Elementary Linear Algebra* (Applications Version), John Wiley & Sons, 8th Edition (2000).

The shrinkwrapped version costs $124 at the bookstore. It includes the eGrade Student Learning Guide (ISBN 0471-22628-9), which will give you a necessary one-time only access code to the web component of our course. Homework will be done over the web. You can also try to purchase the textbook used more economically. In that case you must buy the eGrade Guide separately. It normally sells for $15, but we have a special arrangement with the publisher, and the bookstore will have a reasonable supply of the Guides for $5 a piece by Monday 1/27, or Tuesday.

The course will cover Chapters 1 through 5 quite completely and rigorously. Optional independent study projects will touch on some aspects of Chapters 9 through 11. Further supplementary materials for students are listed on page ix in the Preface to our text.

**Grading:** There will be 4 short tests, approximately every 3-4 weeks, 30 minutes each, all given in class; no makeups. A final examination will be held on

Wednesday, May 14, 8-10:30pm (Lecture 02),

Monday, May 19, 2-4:30pm (Lecture 01).

Students are expected to ensure when they register for the courses 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 211 will be determined as follows:

Homework 25%, four short tests 10% each, final exam 35%

We will give up to 20% extra credit for independent study type projects on materials from Chapters 9-11, to be assigned somewhat later; details will follow. Incompletes will be granted only if documented circumstances beyond your control prevent you from completing the course work, according to strict University rules.

**Homework:** You need to register at *http://egrade.brownstone.net/live/classes/gromoll/*.

Go to this page and bookmark it. Then follow further online instructions.

The only way to learn the course material is to work problems for yourself. Each week, you need to do the corresponding interactive assignment. Your homework will be graded online and will give you vital feedback on where you are making mistakes. Homework is a means to an end, the "end" being for you to learn the material. It is generally a good idea to work together with others in the class. However, since homework earns credit, it is understood that everyone submitting particular problems has solved them individually. It has been our experience after many years of teaching that those who consistently do the homework are those that learn the most and do the best in the course. Trying to learn the material in any math course just before the exams rarely produces good results. Never be shy about asking how to approach a problem, we are always happy to help you.

**Approximate Course Schedule:**

Week of Sections

1/22-24 1.1, 1.2

1/27-31 1.2, 1.3

2/03-07 1.4, 1.5

2/10-14 1.6, 1.7
(Test 1 on 1.1-5)

2/17-21 2.1, 2.2

2/24-28 2.3, 2.4

3/03-07 3.1, 3.2, 3.3
(Test 2 on 1.6-7 & Chapter 2)

3/10-14 3.3, 3.4, 3.5

3/17-21 Spring Recess

3/24-28 4.1, 4.2
(Test 3 on Chapter 3)

3/31-4/04 4.2, 4.3

4/07-11 5.1, 5.2

4/14-18 5.3, 5.4
(Test 4 on Chapter 4 & 5.1-2)

4/21-25 5.4, 5.5

4/28-5/02 5.5, 5.6

5/05-09 A topic from Chapter 11 & Review

5/14-20 Comprehensive Finals (with emphasis on Chapter 5)

**Special Needs:** If you have a physical, psychiatric,
medical, or learning disability that could adversely affect
your ability to carry out assigned course work, we urge you to contact
the staff in the Disabled Student Services office (DSS),
Room 133 Humanities, 632-6748/TDD. DSS will review your
situation and determine, with you, what accomodations are
necessary and appropriate. All information and documentation
of disability is confidential.

**Week by Week Details:** We will list here also some selected typical exercises from the text. They are independent of the regular web homework and will not be collected and graded. Almost all of the book problems have solutions in the Answer Section at the end of the text, pp753. You could find more detailed solutions in the Student Solution Manual (ISBN 0-471-38248-5), which can be ordered and purchased separately. You should look at these typical problems: beyond our regular web homework, they are primarily meant as a guide to what kind of questions to expect in the short tests and the final exam. Working out some of them in addition to the homework will be good further practice and can only help you with doing well in the course.

1/22-24 | Study 1.1 in detail; read through 1.2 | Sample exercises:

p6 1,3,4,5,7,11

1/27-31 | Review 1.1 | Study in detail Sections 1.2 and 1.3 | Sample exercises:

p19 1-14,17,22,26,28,31,32 p33 1-6,12-14,20,23,28,29

2/03-07 | Review 1.3 | Study in detail 1.4 and 1.5 | Sample exercises:

p47 4,7,11,13,16,20,23,33,35 p56 1-11,19,21

2/10-14 | Review 1.4 | Study in detail 1.5-7 | Sample exercises:

p64 1-9,14,16,19,22,29 p71 1-8,10,17,22,26,27,30

2/17-21 | Review 1.6 | Study in detail 1.7 and 2.1 | Sample exercises:

p71 1-8,10,17,22,26,27,30 p87 1,2,4-12even,13,16,17,23,25

2/24-28 | Review 2.1 | Study in detail 2.2-3 | Sample exercises:

p94 1-5,10-12 p102 1-5,12,14,15,20,21

3/03-07 | Review 2.3 | Study in detail 2.4 | Sample exercises:

p112 1-5,7,10,12,15,18,22,24,33,35 p115
2,4,5,10,18 p117 T3

3/10-14 | Review 2.4 | Study in detail 3.1-3 | Sample exercises:

p125 1-10,11,14,17
p128 1-4,6-8,14 p136
1-6,9,11,14,16,18,19,24,28

3/17-21 | Spring Break.

3/24-28 | Review 3.1-2 | Study in detail 3.3-5 | Sample exercises:

pp136 1-6,9,11,14,16,18,19,24,28 p147
1-4,7-13,16,17,30,37 p155 1-8,10,11,15,20,25,39

3/31-4/04 | Review 3.5 | Study in detail 4.1-2 | Sample exercises:

p170 1-4,6,7,10,11,15,16,20,22,26,35,37 p185
1-6,8,11,13,16,18,21,28,30,32

4/07-11 | Review 4.1 | Study in detail 4.2-3 | Sample exercises:

p198 1-10,13,14,18,19,23,25

4/14-18 | Review 4.3 | Study in detail 5.1-2 | Sample exercises:

p208 1-4,6,9-12,15,21-24,28 p219
1-5,7-9,11,14,21,23,26

4/21-25 | Review 5.2 | Study in detail 5.3-4 | Sample exercises:

p229 1,2,4-7,10,13,18,19,26 p243
1-5,7-10,11,16,21,23,28,31,35

4/27-5/02 | Review 5.3 | Study in detail 5.4-5 | Sample exercises:

p257 2-6,8-10,13,15,17

5/05-5/09 | Review 5.4 | Study 5.5-6 | Sample exercises:

p269 2-8,13,16,17,19

*The last online assignment "Homework #11" has been activated and will remain accessible until Wednesday, May 14, 7pm. A score of 20 points will be considered perfect. Note that the system is set to allow multiple tries; the highest score will be recorded automatically. Feedback for a running assignment will be off during the time scheduled for an assignment, but turned on once it has expired. So you can check your solutions, as long as all assignment copies are graded. (Some bugs have been fixed by the publisher; please report any problems that you think still exist to the course coordinator.) *

Test 1 was given W 2/12 in class (both lectures), covering Sections 1.1 through 1.4.

Test 2 was given W 3/5 in class (both lectures), covering 1.6-7 and 2.1-3. It will be returned W 3/12.

Test 3 was given W 4/2 in class (both lectures), covering 2.4 and all of Chapter 3. To be returned W 4/09.

Test 4 was given W 4/23 in class (both lectures), covering all of Chapter 4 and 5.1-2. To be returned W 4/30.

**Practice Final.** There will be 10 problems on the actual exam, all worth 10 points, plus 1 bonus problem worth up to 20 points.

*Sample problems:* p20/10c p113/11 p156/29 p199/13b p220/13 p229/3b p271/3b p269/2c p258/6c p244/8a

**Note.** For all official standard information on final exams consult the web page *http://www.stonybrook.edu/sb/finalss03.shtml*

The Final of Lecture 02 will be given in the regular location, Physics 113.

The Final of Lecture 01 will be given in a *different* location, Javits 105.

Click to see the *Solutions* for the Final of Lecture 02.

**Optional Projects:** You may submit work on not more than two of the following independent study type problems, each worth extra credit up to 10% of the course grade. All problems are taken from the various applications of Linear Algebra in Chaper 11. It will usually be necessary to first read and understand much of the material of the corresponding section. All work should be detailed and neatly presented. On the average, an optimal treatment of a topic would probably take 2-3 pages. Keep it short, but complete. As a guideline note however, that the format of the presentation of these independent study projects should be such that they could be read and understood by a mathematically literate reader, who has not necessarily studied the accompanying sections in Chapter 11, so you should explain the basic setup and what you are doing. You may work together with one person, however, in that case both names must appear on the paper, amd by doing so you attest that both of you have contributed substantially to the work. Good luck!

*Deadline:* Friday, May 16, noon (firm). Deliver papers to Math 5-116 after classes are over.

11.2 p541 T2, 11.3 p553 9+10, 11.4 p564 8 or T1, 11.5 p575 T1, 11.6 p586 5,

11.7 p598 T2, 11.8 p607 7, 11.9 p616 8, 11.10 p625 4, 11.11 p635 T1,

11.12 p644 4, 11.13 p657 3, 11.14 p677 T1, 11.15 p690 7+8, 11.16 p703 10,

11.17 p715 T1, 11.18 p725 2+3, 11.19 p734 T1, 11.20 p741 6+7, 11.21 p750 6 or T1.

Projects were completed by almost 60% of the class, with many nice efforts.

Overall course work has been at a good level.

*Have a great summer!
*