Section E13/14: MWF 1:00 - 1:50, 245AH
Instructor: Anton Malkin
Office: 334 IH
Office Hours: Tue 4:00 - 5:00 and by appointment
Email: malkin@math.uiuc.edu
Book: G. Strang,
Introduction to Linear Algebra. 4th edition.
MIT 18.06: A version of this course
taught by Gilbert Strang at MIT is available at
MIT 18.06 OCW (and youtube).
Of course, Math415 syllabus is not identically the same.
Syllabus: The goal of Linear Algebra is to understand
vectors and matrices: what they are, how to think about them, how
to deal/calculate with them, what they are good for.
In particular, we'll cover systems of linear equations,
inverse matrices, determinants, vector spaces and linear transformations,
orthogonality, eigenvectors and eigenvalues, and various
applications.
Homework will be assigned
after each lecture (see the table below). Problems from Mon, Wed, and Fri,
are due next Wednesday. Late homework (regardless of excuse)
will not be accepted, but two lowest problem set scores will be dropped
from the final grade calculation. Not every homework problem will be graded.
Doing (as opposed to copying) homework is essential in Math415.
You are allowed (and encouraged) to talk to other people about
the problems provided: (1) you think on your own first, (2) you
write down your own solutions.
Quizzes will be given (almost) every Wednesday.
There will be no makeup quizzes but two lowest quiz scores will be dropped.
Exams:
3 midterms (9/30, 10/21, 11/18) and the final exam (12/15).
Grading: The final grade will be determined by
homework (15%), quizzes (15%), midterms (15%+15%+15%), and the final (25%).
Letter grades: A>90%, B>75%, C>60%, D>50%, F<50%.
Scores: You can look up your scores for problem sets,
quizzes, and exams, on the math department
score report system.
Tutoring: MTuWTh, 5-7pm, in 347AH, and
MTuWTh, 7-9pm, in 243 AH.
Problem Set 1
Quiz 1
Problem Set 2
Quiz 2
Problem Set 3
Quiz 3
Problem Set 4
Problem Set 5
Test 1
Problem Set 6
Quiz 6
Problem Set 7
Quiz 7
Problem Set 8
Test 2
Problem Set 9
Quiz 9
Problem Set 10
Quiz 10
Problem Set 11
Quiz 11
Problem Set 12
Test 3
| Date | Material Covered |
Homework Problems |
Homework Due |
|---|---|---|---|
| 08/24 | 2.1 | 2.1: 26, 1, 27 | 09/02 |
| 08/26 | 1.1 | 1.1: 1, 3, 4, 10, 13 | 09/02 |
| 08/28 | 1.2 | 1.2: 1, 2, 3, 6, 7b, 16 | 09/02 |
| 08/31 | 2.4, 1.3 | x-practice; 2.4: 1, 3, 4, 5, 7 | 09/09 |
| 09/02 | 2.5 (to p. 83), 1.3 | 2.5: 1 (only B), 2 (only first P), 4, 6, 13 | 09/09 |
| 09/04 | 1.3, 2.1, 2.2 | 1.3: 3, 10; 2.2: 3, 5, 8, 12, 13 | 09/09 |
| 09/07 | no class | ||
| 09/09 | 2.3 | 2.3: 1, 7, 10, 26; 2.4: 18 | 09/16 |
| 09/11 | 2.6 (to p. 97), 2.5 (Gauss-Jordan) |
2.6: 5;
LDU problem; 2.5: 10, 22 (1st matrix), 25 (A), 27 (2nd matrix), 32 |
09/16 |
| 09/14 | 3.1 | 3.1: 1, 2, 10, 12, 17 | 09/23 |
| 09/16 | 3.1, p. 132 | 3.1: 19, 20b | 09/23 |
| 09/18 | 3.2, 3.3, 3.4 | 3.2: 1-4, 9, 15, 17, 21 | 09/23 |
| 09/21 | 3.2, 3.3, 3.4 | 3.3: 2; 3.4: 1, 2, 4, 5, 16, 17 | 09/30 |
| 09/23 | 3.5 | 3.5: 5, 9, 10, 11, 15, 28 | 09/30 |
| 09/25 | p. 107 (transpose)
3.6 |
2.7: 1 (1st matrix only);
three problems; 3.6: 1, 3 (except for left null space), 6B, 7, 11 |
09/30 |
| 09/28 | review | none | -- |
| 09/30 | test | ||
| 10/02 | 4.1 | nonbook problem; 4.1: 3, 5, 11A, 13, 17 | 10/07 |
| 10/05 | 4.2 | 4.2: 1a, 3a, 5, 18, 27; nonbook problem | 10/14 |
| 10/07 | 4.3 | 4.3: 1, 9, 10 (in 9 and 10
find and draw the best parabola and cubic, no discussion about p, e, fig. 4.9b, required) |
10/14 |
| 10/09 | 4.4 to p. 233 | 4.4: 2, 7, 30, 31, 33 | 10/14 |
| 10/12 | bases note, 4.4, QR note | 4.4: 13, 14, 18, 23, nonbook problem | 10/21 |
| 10/14 | 4.1-4.4 | 4.1: 21, 22; 4.4: 15 | 10/21 |
| 10/16 | 8.5 | 8.5: 2, 3, 4 (also find lengths of the four polynomials),
8a, 8c (f(x) is a function on [0, 2pi]), 12 |
10/21 |
| 10/19 | review | none | -- |
| 10/21 | test | ||
| 10/23 |
determinant as volume, pp. 244-245, 271-277 |
5.1: 22, 23; 5.3: 16, 20 (find det up to sign only), 21 |
10/28 |
| 10/26 | 5.1 | 5.1: 2, 3, 14, 15 (1st matrix only), 16, 18, 19 (1st matrix only) | 11/04 |
| 10/28 | 5.2 (Big Formula) 5.3 (Cramer's Rule) |
5.2: 1A, 1B (use the mnemonic rule
for 3x3 det from class/problem 28); 5.3: 1a, 2, 3 |
11/04 |
| 10/30 | 5.2, 5.3 (cofactors) | 5.2: 11 (detB only), 13;
5.1: 14 by cofactors (1st matrix only) 5.3: 6a, find L-inverse in 14a, do 14c |
11/04 |
| 11/02 | 6.1 | 6.1: 2, 4, 5, 6, 29A, 29C | 11/11 |
| 11/04 | 6.1, 6.2 | 6.1: 15 (2nd matrix only, find eigenvalues and
a basis of eigenvectors); 6.2: 1, 2 |
11/11 |
| 11/06 | 6.1, 6.2,
matrix functions pp. 319-21 |
6.1: 19; 6.2: 11, 12; nonbook problems | 11/11 |
| 11/09 | 8.3, 6.2 (Fibonacci) | nonbook problem; 8.3: 3 (3rd matrix only), 5; 6.2: 9 | 11/18 |
| 11/11 | 6.3 (skip pp. 316-318) | 6.3: 4, 8, 10, 11 | 11/18 |
| 11/13 | 10.1 | 10.1: 1, 2, 14, 17, 21, 23b, 24; nonbook problem | 12/02 |
| 11/16 | review | none | -- |
| 11/18 | test | ||
| 11/20 | 6.4, 6.5 | 6.5: 6, 10, 24, 29 (F2 only); nonbook problems | 12/02 |
| 11/21 11/29 |
fall break | ||
| 11/30 | |||
| 12/02 | |||
| 12/04 | |||
| 12/07 | |||
| 12/09 | |||
| 12/15 | final exam | ||