Sylvain BONNOT
Section I
|
MAT 211
Introduction to linear algebra
|
 |
We will meet on MWF : 9:35 am to 10:30 am in Harriman Hll 108.
First day of class: Wedn. Sept 6, 2006.
Final exam : it will take place on Wed. Dec 20, 8 to 10:30 am in Harriman Hll 108 (the usual room).
Office hours:
every Wedn. from 2:00 pm to 5:00 pm in my office, 5D-148 in the Math Tower.
My office is in the I.M.S (Institute for Math. Sciences), located on floor 5 and a half (true!)
I offer you a campus map,
in case you don't know where is the Math Tower...
How to contact me?
the best way is to email me there:
bonnot at math dot sunysb dot edu
Our textbook:
Otto Bretscher: Linear Algebra with applications, 3rd Ed., Pearson/Prentice-Hall
We will cover the first seven chapters.
Link to Current Homework:
Please have a look at the syllabus to know when it is due. See below if you want to know the grading policy.
Click here to go to the homework page.
Course notes and announcements:
The Final Exam has been graded, I posted your final grades on the Solar system, so you should
be able to access them very soon, probably tonight or tomorrow...
You did a good job, I think, and in many cases your final grade was much better than the beginning of the semester
so for those cases, I was glad to apply my grading scheme...I have graded from 20/100 to 100/100, the average
was around 72/100. By the way, I wrote some comments about the final, so read
them, if you are bored during the break...
Also I scanned a detailed correction of the final exam: the numbering of the questions is a bit different, but the
content is what you want.
final1,
final2,
final3,
final4,
final5.
Anyway, it was nice having you as my students, I wish you good luck for your studies, and an excellent break!!!
Au revoir!
FINAL EXAM: Wed. Dec 20, 8:00am to 10:30am (morning), in Harriman 108.
This is the usual room. Please arrive 5 minutes earlier (I know it will be really early...) so that
we can start on time. For this final, you are not allowed to use calculators. Good luck, and see you on
Wednesday!
If you want to find me, send an email or stop by my office on monday afternoon starting at 2, and also on
tuesday afternoon.
I made a mistake in the correction of #3 second practice exam: the rank is 3 and not
2 as I said...
Here comes the correction of the second practice exam!
scan1,
scan2,
scan3,
scan4,
scan5,
scan6,
scan7,
scan8.
Correction of the last homework is available.
Try this at home: second practice exam !
You will have a correction of this available on Thursday.
Correction for Homework 11 is available on HW page
Correction for the practice final: part1,
part2, part3,
part4, part5,
part6.
Brand new: a Practice Final exam for you
.
The correction will be available in few days, together with another practice exam...
The new HW 12 is on the homework page, due on Monday 12/11.
There might be one last HW, that I will give you on friday, due on Friday december 15th(last day of class).
Special office hours: Tuesday 21st from 2pm to 5pm
.
Depending on the number of people who will go to these, I might have to find a larger room...I will put a
note at the door of 5D-148...
Also the correction of HW9 is on the homework page.
Correction for Midterm II has arrived:
scan1, scan2, scan3,
scan4, scan5, scan6,
scan7.
Midterm II is graded:
You will have it tomorrow. Lowest grade: 12/100 ----- Highest grade: 98/100. Average grade is 73/100.
On Friday, you will have a correction available on the web as usual.
Solutions of the new practice problems!
You can now check the
solutions1, solutions2.
Some more problems for you to practice!
I knew you wanted some more, so here is some
new stuff.
On monday I will post the solutions for that...
Midterm is next week on Wednesday 15th, in Harriman Hll 108, 9:35am to 10:30am
(Usual place and time)
Content: everything from 1.1 to 5.1 included.
The focus is on chapter 4, but you need to remember the previous chapters, that's why it is cumulative...
The class on Monday will be a review session, so prepare your questions for that day!
The office hours next week will be on Tuesday afternoon (from 2pm to ??...whatever you will need!However it must end before
9:35am on wednesday for obvious reasons)
The correction for the practice exam has arrived:
read it just to make sure that
you would have obtained 100pts...
Page1, Page2,
Page3,Page4.
Correction for HW8 is on HW page
a Practice exam is ready
Please try both of these: scan1,
scan2.
Also new HW is on HW page.
HW8 is now on HW page
Hum Hum
Ok, now you have the correction of the correction available on the page!
(Thanks to Joe Pastore for telling me I was
wrong...)
I still have some midterm papers with me
For the people who weren't here last friday: I still have your midterm, I will bring it back on wednesday,
so don't forget to claim your paper at the end of the class! Otherwise, you can also find me in my office.
Correction for HW5 is on HW page
About the lecture notes: I treated most of the content this morning, so I am not sure to write them actually,
I will see...
< New HW is on HW page
Coming soon: (soon or never...) some lectures notes about 3.2, 3.3. (You will have to read them in detail, all of them, and yes
you will need them for the next midterm...)
Correction of the midterm is here:
Please have a look at these scans: correc1,
correc2,correc3,
correc4,correc5,
correc6.
MIDTERM I
Date: Wednesday Oct. 11th, from 9:35 am to 10:30 am in Harriman Hll 108 (usual time and hour).
Please arrive 5 minutes in advance so that we can start on time!
(Posted on Monday 10/09) A remark about the correction of the practice exam
This morning No Eul told me that my correction for question (g) was wrong: so the answer is that question
(g) is False, but the matrix I provided doesn't work...Instead Min Sung proposed to take a 2 by 2 matrix with
first column made of 1, second column made of 0, and this works...Thanks to both of you!
Joe Pastore also told me there was a mistake in (5): for the case b=0, a=4/3, the solutions are actually
given by (x1, x2, x3)=s(0,1,0)+t(-3,0,1)...thanks for the remark!
(Posted on Monday 10/09) Solutions of HW4 !
scan1,
scan2.
(Posted on Friday 10/06) < Solutions of the PRACTICE EXAM !
Try it first by yourself and then have a look at these scan1,
scan2,scan3,scan4.
(Posted on Thursday 10/05) NEW!!! PRACTICE EXAM !
Here is a brand new practice exam.Please try it...you will have a correction
for this...
(Posted on Wednesday 10/04) Correction for HW3
Here are the scans of my correction for HW3:
scan #3.1, scan #3.2, scan #3.3,
scan #3.4.
(Posted on friday 09/29)
Please see the HW page for the next homework...
Lecture notes, please read!!!!
Click on this link.
(Posted on monday 09/25) Correction for HW2
Here are the scans of my correction for HW2:
scan #2.1, scan #2.2.
Some hints for #48: actually I gave you an answer this morning. You just need to understand the difference
between these two phrases:"for any vector y the system A.x=y has a unique solution" (meaning that A is invertible),
and "there exists a vector y such that the system A.x=y"...
(Posted Friday 09/22) HW3 is assigned on HW page
Since I already defined the product, you can already solve most of them. I'll give some hints on monday.
Coming soon: scans of the correction for HW2, available on monday.
(Posted on monday 09/18) Correction for HW1
Scans of my correction are now available:
scan #1.1, scan #1.2,scan #1.3,
scan #1.4,scan #1.5.
(Posted on Friday 09/15) HW 2 is on homework page
I scanned my detailed correction for HW1, it will be available on Monday.
(Posted on Monday 09/11) Some hints for HW 1 :
Please have a look at the following lecture notes #1 (.pdf file),
it might help you for HW 1!! Here are the same notes #1(.ps) in Postscript (.ps).
(Posted on Friday 09/08)Please read 1.1 and 1.2 for monday (1.1 is just an introduction). We will cover on monday 1.2 and therefore the
first HW will be due on FRIDAY Sep. 15 (and NOT Wedn. as I said earlier). HW1 is about the solution of linear
systems. Don't worry about what we saw today, it will be covered again later (2.1).
See below for the link to HW1: please notice that I will give indications about it on monday, so basically
you don't need to start it right now...
HW1 is posted now, see below for the link.
Quick intro:
Linear algebra is all about solving systems of linear equations (a nice circular "definition"...).
It's an old subject
where all the main concepts
have been clarified and polished over the years, that's why it's possible now to present them in a concise
way.
Even if the subject is pretty old, there are applications everywhere nowadays. I found some examples just for you:
- Face recognition by computers (related to biometry,etc...): have a quick look at that
page, you'll see eigenvectors everywhere (we will see these in the class);
- Information retrieval (data mining);
- Compression of pictures (for the Web);
- Quantum mechanics (where "physical observables such as energy and momentum are no longer
considered as functions on some phase space, but as eigenvalues of operators which act on
such functions"):
check this
link;
- Cryptography
(you can read this);
- Search engines
(read this article if
you want to know how Google works!)...
And the list goes on and on...
Prerequisites:
You must have had at least one semester of calculus. If you have not yet studied integration, you should be taking
the relevant calculus course (e.g. MAT 126) concurrently with this one, as some important problems and examples in this
course require a knowledge of integration.
Math Learning Center:
This is a very useful place for you: there you can ask questions about the class or the homework problems. It is located
in the Math Tower S-240A (basement level). You should definitely check
their webpage.
Link to Current Homework:
Please have a look at the syllabus to know when it is due. See below if you want to know the grading policy.
Click here to go to the homework page.
Syllabus (very tentative schedule):
| Day of |
Homework due |
Sections Covered |
September 6
|
|
1.1 (Introduction to Linear Systems) |
September 8
|
|
Intro to linear transformations |
September 11
|
|
1.2 (Matrices, Vectors, and Gauss-Jordan Elimination) |
September 13
|
|
1.3 (On the Solutions of Linear Systems; Matrix Algebra)
|
September 15
|
Homework 1 |
2.1 (Introduction to Linear Transformations And Their Inverses)
|
September 18
|
|
2.2 (Linear Transformations in Geometry)
|
September 20
|
|
2.3 (The Inverse of a Linear Transformation)
|
September 22
|
Homework 2
|
2.4 (Matrix Products)
|
September 25
|
|
2.4 (Continued) |
September 27
|
|
3.1 (Image and Kernel of a Linear Transformation)
|
September 29
|
Homework 3
|
3.2 (Subspaces of R^n; Bases and Linear Independence)
|
October 2:NO CLASS
|
|
|
October 4
|
|
3.2 (Continued) |
October 6
|
Homework 4
|
3.3 (The Dimension of a Subspace of R^n)
|
October 9
|
|
Review session |
October 11: Midterm I
|
|
Midterm I: Everything up to and including 3.3
|
October 13
|
Homework 5 |
3.4 (Coordinates)
|
October 16
|
|
4.1 (Introduction to linear spaces)
|
October 18
|
|
4.2 (Linear Transformations and Isomorphisms)
|
October 20
|
Homework 6 |
4.3 (The matrix of a linear transformation) |
October 23
|
|
4.3 (Continued)
|
October 25
|
|
5.1 (Orthogonal Projections and Orthonormal Bases)
|
October 27
|
Homework 7 |
5.2 (Gram-Schmidt Process and QR Factorization)
|
October 30
|
|
5.2 (Continued)
|
November 1
|
|
5.3 (Orthogonal transformations)
|
November 3
|
Homework 8
|
5.4 (Least squares and data fitting)
|
November 6
|
|
5.5 (Inner Product Spaces)
|
November 8
|
|
6.1 (Introduction to Determinants) |
November 10
|
Homework 9 |
6.1 (Continued) |
November 13
|
|
Review session |
November 15:Midterm II
|
|
Midterm II: Everything from 1.1 to 5.1 (included) |
November 17
|
Homework 10 |
6.2 (Properties of the Determinant) |
November 20
|
|
6.2 (Continued) |
November 22
|
Homework 11 |
6.3 (Geometrical Interpretations of the Determinant; Cramer's Rule) |
November 24:NO CLASS
|
|
|
November 27
|
|
Ch 7.1: Dynamical systems
and eigenvectors |
November 29
|
|
7.2 (Finding the Eigenvalues of a Matrix) |
December 1
|
Homework 12 |
7.2 (Continued) |
December 4
|
|
7.3 (Finding the Eigenvectors of a Matrix) |
December 6
|
|
7.3 (Continued) |
December 8
|
Homework 13 |
7.4 (Diagonalization) |
December 11
|
|
7.4 (Continued) |
December 13:CORRECTION DAY for 10/02
|
Homework 14 |
7.5 (Complex eigenvalues) |
December 15: LAST CLASS
|
|
Review session |
December 20:FINAL EXAM
|
|
Final Exam (Cumulative: from 1.1 to 7.4 included) |
Exams: (tentative schedule)
You will get very soon the definitive schedule.
| Midterm 1 |
October 11, Wednesday 9:35-10:30 a.m. |
Usual room |
| Midterm 2 |
November 15, Wednesday 9:35-10:30 a.m. |
Usual room |
| Final |
December 20, Wednesday 8:00-10:30 a.m. |
Usual room Harriman 108 |
Homework and grading policy:
The grading will not be based on a curve. Here is how your final grade will be computed.First I'll take a weighted average
of the following:
| Exam I |
25% |
| Exam II |
25% |
| Final Exam |
35% |
| Homework |
15% |
This gives me a first grade. A second grade is given by 90% of your final exam grade. The grade you will receive at the
end of the class will be the maximum of these two grades.
Late homework will not be accepted.
DSS advisory:
If you have a
physical,
psychological,
medical, or learning disability that may affect your course work,
please contact Disability Support
Services (DSS) office: ECC (Educational Communications Center)
Building, room 128, telephone (631) 632-6748/TDD.
DSS will determine with you what accommodations are necessary and
appropriate. Arrangements should be made early in the semester (before
the first exam) so that your needs can be accommodated. All information
and documentation of disability
is confidential.
Students requiring emergency evacuation are encouraged to discuss their
needs with
their professors and DSS. For procedures and information, go to the
following web site http://www.ehs.sunysb.edu
and search Fire safety and
Evacuation and Disabilities.
