Meetings: MWF 12:10pm-1pm, Room 202 Wellman

Instructor: Jesús A. De Loera.

email: deloera@math.ucdavis.edu

http://www.math.ucdavis.edu/~deloera/TEACHING/MATH22A/courseinfo/22A.html

Phone: (530)-754 70 29 Office hours: Monday and Wednesday 11:10pm-12:00pm or by appointment. My office is 580 Kerr Hall. I will be glad to help you with any questions, concerns or problems you may have! You can also go to the office hours of any of the following TAs:

Brian Wissman Kerr 565 TTh, 12-1
Spyridon Michalakis Kerr 481 3:30-5:30pm Mondays
Alice Stevens Kerr 473 MW, 11-12
Brandon Muranaka Kerr 469 T Th from 3 to 4pm

Prerequisites and expectations: 21D or permission of instructor. You are expected to work intensively outside the classroom. I estimate a minimum of 2 hours work at home per lecture. Remember, YOU learn by doing!

Text: B. Kolman and D. Hill, Linear Algebra, seventh edition.

Description and Goals: One famous statement is that ``Mathematics is the queen of science''. Well, one can easily argue that linear algebra is the heart of mathematics! This is important and beautiful material. The main topic is the study of linear transformations and the solutions of systems of linear equations. Beautiful geometry and the introduction to abstraction is part of this course.

Course outline:

(week 1) Linear systems and Matrices, Matrix multiplication, Solving linear systems of equations.

(week 2) The inverse of a matrix, Elementary matrices.

(week 3) LU decomposition, Determinants.

(week 4) Vectors, basics of linear transformations.

Midterm 1

(week 5) Vector spaces and subspaces, Linear independence

(week 6) Notion of dimension.

(week 7) Homogeneous systems, Rank of matrix,

Midterm 2

(week 8) Change of basis, orthogonal bases.

(week 9) Eigenvalues and Eigenvectors, Diagonalization.

(week 10) Kernel and range of linear transformations.

Midterm 3

Grading policy:

• There will be 3 midterms, April 30th, May 21, and on June 9th 2004, each counting 20 points. I will drop the lowest of the three for the calculation of the grade.

• I will assign 9 homeworks, 5 points each. The lowest score will be dropped from the calculation of the grade, for a maximum of 40 points. No late assignments will be accepted! No exceptions.

• A comprehensive final exam worth 20 points.

• As you see, there are 100 points possible in this course. I will assign grades based on the statistical information obtained (I compute the mean, standard deviation, etc.) and set letter grades according with those numbers. Nevertheless, it is my rule that more than 50 points are required to pass the class.

• Please remember there are NO make-up exams or late homeworks, instead I am dropping the lowest scores as a compensation of possible problems or emergencies. I will handle all grades via myucdavis grade system. This means that if you are a registered student at UC Davis you can access grade information for this class via the internet (check https://my.ucdavis.edu/ for details). This is a secure and private web page assigned to each student. You can see your standing in the class, important statistics on exams, and your final grade there! I will not disclose your grade in any other form.

HOMEWORK (DUE EVERY FRIDAY!)

Homework 1 (due April 9): 1.1 (6,14,16,19,25, T.4) 1.2 ( 4,6) 1.3 (9,15, 18,26) 1.5(13,14,20)

Homework 2 (due April 16): 1.5 (32,44, ML 4,10) 1.6 (7,10,15,16,22, T.6, ML 3) 1.7 (1,4, ML 2), Determine the elementary matrix for each step in Example 6 in sec 1.6 of the text

Homework 3 (due April 23): 3.1 (4,8,17ab,20c,T7,ML4a) 3.2 (1,2,4,12a,18a,21,22) 4.1 (6,16,24,30)

Homework 4 (due May 3): 3.2 (ALL page 169, chapter test) 4.2 (20,27,T10) 4.3 (4,14,22,26,28,page 215 chapter test EVEN problems).

MIDTERM 1 will include all sections that have been in the homeworks 1,2,3,4. Thus until section 4.3. Chapter 2 will not be included.

Homework 5 (due May 7): 6.1 (11-16) 6.2(4,6,10,15,19,20,23,T.8).

Homework 6 (due May 14): 6.3 (2,10,15,T.10) 6.4 (4,11,18,30) 6.5(6,12,22,ML3)

Homework 7 (due May 24): 6.6(4,7,12,ML4,ML5), 6.7 (8,10,18,ML2),

MIDTERM 2 will include sections covered in Homeworks 5,6,7

HERE is the Solution for Midterm2

Homework 8 (due June 2) 6.8 (2,5,6,8,10,16,ML2) 8.1 (2a,8,11,19,ML3).

Homework 9 (due June 9) 8.2 (4,7,8,11,T.7) 8.3(11,12) 10.1 (2,5,10) 10.2 (4,5,10,20)

MIDTERM 3 will include sections covered in Homeworks 8,9

FINAL will include ALL sections covered in the homeworks.

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