MAT 211

MAT 211
Introduction to
Linear Algebra
Fall 2004

MAT 211 provides a basic, self-contained introduction to linear algebra and its applications. This subject-matter is now an essential tool in mathematics, the sciences, and beyond. The topics will include: Systems of linear equations and the Gauss-Jordan Algorithm, vectors, vector spaces, bases and dimension, innerproducts, applications to Geometry, linear transformations, determinants, eigenvalues and eigenvectors.

Lecture 1: Craig van Coevering, Math 2-104,
Email: craig@math.sunysb.edu
Classes: MWF 9:35-10:30 Engineering 143,
Office Hours: Monday 11:00-12:00 M.L.S S-240A; Wednesday 11:00-12:00 Math. 2-104

Textbook: Otto Bretscher,
Linear Algebra with Applications,
Prentice Hall, 3rd Edition, 2005,
ISBN 0-13-145334-3.

Prerequisites:

C or higher in AMS 151 or Mat 131 or 141; or
co-registration in MAT 126; or
level 7 on the mathematics placement examination; or
or permission of the course coordinator.

Homework:

Doing problems is essential to learning mathematics. There will be weekly homework assignments. Each assignment will be due in class the following Monday.

Announcements:

The homework due date has be changed to Wednesday, so you can get help if needed on the homework on Monday.

The midterm exam on October 6 will cover up through section 3.1.

Here is a list of things you will have to know to do well on the miderm on October 6.

The correspondence between matrices and linear systems of equations,
how to solve systems of equations using Gauss-Jordan elimination,
what the reduced row-eschelon form of a matrix is and how to find it, and how it gives the solutions to the system of equations,
what the rank of a matrix is,
how the possible number of solutions to a linear system depends on the r.r.e.f. of it's augmented matrix,
how to add, subtract, and take scalar multiples of vectors and matrices, also how to multiply matrices,
what a linear transformation is and how it is related to it's matrix, i.e. how to determine it's matrix,
how to find the parallel and perpendicular components of a vector with respect to a line,
what the basic properties of reflections and rotations are,
how to determine whether a matrix is invertible,
how to find the inverse of a matrix,
what the image and kernel of a transformation are,
how to find Im(A) and ker(A) for a matrix A, i.e. how to find vectors which span these subspaces.

Some more practice problems: I will post answers to these on Moday.
§1.2: 6,7,8,27,28,34,35
§1.3: 26,30,34,36,48; p.28:1-20
§2.1: 44
§2.3: 8,10,42
§2.4: 7,10,12,14,20,22,24; p.97: 1-15

solutions

The midterm on November 10 will cover up through section 5.2

Here are some practice problems for the midterm.

The final will be comprehensive. So in addition to what was covered in the midterms make sure you know the following:

Basic properties of the determinant, non-zero for invertible matrices etc.,
how to compute the determinant by expanding along a row or column,
how to compute the determinant using row reductions,
definition of eigenvalues and eigenvectors,
the characteristic polynomial of a matrix,
how to find the eigenvalues of a matrix, or transformation,
how to find the eigenvectors corresponding to an eigenvalue,
when a matrix is diagonalizable, and how to diagonalize a matrix with respect to an eigenbasis.

Here is a final from last years Mat211. Note that is was written by a different instructor. It's meant as practice, but not as an indiction of precisely which problems are going to be on the final. Here is another past final. Here are the solutions to the second sample final, the one we didn't go over in class last week.

Schedule:

The following schedule is preliminary and subject to change.

Week Of	Sections	Homework Problems	On Page	Due
8/30-9/3	1.1, 1.2	1-6,11-13,19,25,37	5	9/8
		1-5,10,11,18-21,24-26	20
9/6-9/10	1.3, 2.1	2-4,6,9,12,14,18,22,24,28,46,47	35	9/13
		4,6,8,10,12,16,18,20,40,41,42	51
9/13-9/15	2.2	1,4,6,7,13,20,24,25,29,32,38,43	66	9/20
9/20-9/24	2.3, 2.4	1-6,16,17,30,32,34,35,40	76	9/27
		1-6,8,13,15,16,17,18,32,34,45	89
9/27-10/1	3.1, 3.2	3-7,14,15,18,20,24,34,35	109	10/6
		2,3,5,6,7,8,12-17,28-30,36	121
10/4-10/8	3.3	9-12,16,18,21,22,26,28,30,38,47	133	10/13
10/11-10/15	3.4	6-12,16,18,22-24,32-34,38,40	146	10/20
10/18-10/22	4.1, 4.2	6-11,16,18,20,22,27,28,39,40,41	162	10/27
		4,6,7,8,10,12,13,18,20,51,65	169
10/25-10/29	4.3, 5.1	2,3,6,12,15,16,17,18,22,26,34	180	11/3
		2,3,4,8,10,11,16,21,22,28	198
11/1-11/5	5.2, 5.3	1-10,29,31,32,33,34,35	208	11/12
		3,4,5-11,14-16,21,22,28,29,36	216
11/15-11/19	6.1, 6.2	1,2,7-10,12,14,17,18,24,27,30,31-35,44,49	259	11/24
		4-8,11-14,18-20,26,29,37,38,40,41,48;§6.3:22-25,30	271
11/22-11/24	7.1, 7.2	1-10,15-20,34,35,36,40	302	11/29
		4-10,15,16,17,20,22,23,39,40,41	314
11/29-12/3	7.3, 7.4	1-10,19,20,23,24,25,35,36,38	324	12/8
		5-15,21,22,24,26,31,32,36,39-42	338
12/6-12/10	Review

Exams:

Midterm 1	October 6, Wednesday 9:35-10:30 a.m.	Eng. 143
Midterm 2	November 10, Wednesday 9:35-10:30 a.m.	Eng. 143
Final	December 15, Wednesday 8:00-10:30 a.m.	Eng. 143

Grading:

Homework: 15%
Midterm 1: 25%
Midterm 2: 25%
Final : 35%

The Math Learning Center, located in room S-240A of the Math-Tower basement, may be a useful source of help if you have difficulties with your homework. For more information about the Math Learning Center, visit their web-site.

If you have a physical, psychiatric, medical, or learning disability that may affect your ability to carry out the assigned course work, please contact the office of Disabled Student Services (DSS), Educational Communications Center (ECC) Building, room 128, (631) 632-6748. DSS will review your concerns and determine what accommodations may be necessary and appropriate. All information and documentation of disability is confidential.

MAT 211 Introduction to Linear Algebra Fall 2004

MAT 211
Introduction to
Linear Algebra
Fall 2004