Math 320 – Linear Algebra I

Syllabus -- Thulin 2012 spring

Course Objectives:

This course introduces students to linear algebra. The topics of the course are: matrices, Gaussian elimination, vector spaces, linear transformations, orthogonality, Gram-Schmidt process, determinants, inner products, eigenvalue problems, and an introduction to Jordan canonical form. Successful students will learn to solve both computational problems and problems requiring the students' own proofs.

Prerequisite: Concurrent registration in Math 215 (Introduction to Advanced Mathematics).

Text:

Linear Algebra by Jim Hefferon. The book and the solutions are freely available here:
http://joshua.smcvt.edu/linearalgebra/
ftp://joshua.smcvt.edu/pub/hefferon/book/book.pdf
ftp://joshua.smcvt.edu/pub/hefferon/book/jhanswer.pdf

Supplemental text (not required):

Linear Algebra by Lipschutz (Schaum’s Outline Series).

Time and location: MWF AH 306 9-9:50 AM

Call Number: 16474

Instructor: Fred Thulin, 426 SEO, 312.413.7872, fthulin @ uic.edu

Office Hours: 10-11 MWF and by appt.

TA: Jim Freitag; hours 5-6 WTh in the MSLC (430 SEO)

Grading: There will be two hour exams (100 points each), a number of quizzes (about 11, total 100 points) and a comprehensive final exam (200 points), for a total of 500 points. Homework from the text will be assigned but not collected (for now), since the solutions are available with the text. There may be some future homeworks collected.

Qizzes: Quizzes will be given normally on Fridays in non-exam weeks.

Exams:

Week 6: Exam 1, Friday 2/17.

Week 12: Exam 2, Friday 4/6.

Final exam: 10:30-12:30 Tuesday, May 1

 

Homework problems (For most problems solutions should be written down, but not turned in):

Week 1:

One.I.1, pp. 8-11, ## 1.16, 1.17, 1.19, 1.21, 1.22
One.I.2,
pp. 18-20, ## 2.15, 2.16, 2.17, 2.18, 2.20, 2.21, 2.23, 2.30

One.I.3, pp. 29-30, # 3.15

One.III.1, pp. 51-52, ## 1.7, 1.8, 1.9, 1.10

One.III.2, p. 59, # 2.11

 

Week 2: 

Two.I.1, pp. 86-88, ## 1.18(a,c), 1.19(a,c), 1.20(d), 1.21(a,c), 1.26(a), 1.40

Two.I.2, pp. 95-96, ## 2.20(a,d), 2.22(a,c), 2.24, 2.25(a,c), 2.26(a,d)

 

Week 3:

Two.II.1, pp. 106-108, ## 1.18(a,c), 1.19(b,d), 1.24, 1.28, 1.29

Two.III.1, pp. 114-116, ## 1.16(b,c), 1.17, 1.18, 1.19, 1.24(b,d), 1.28(a,c),  1.33


Week 4:

Two.III.2, pp. 120-121, ## 2.15, 2.18(b), 2.21, 2.22

Two.III.3, pp. 127-128, ## 3.16(a,c), 3.17(a), 3.18(a), 3.19, 3.20(b), 3.21(a,c), 3.24, 3.28

Week 5:

Two.III.4, pp. 135-136, ## 4.20(a,d), 4.21, 4.23, 4.26, 4.34

Three.I.1, pp. 164-165, ## 1.11, 1.13, 1.14, 1.19, 1.26

Week 7:

Three.I.2, pp. 172-173, ## 2.8, 2.12, 2.14
Three.II.1, pp. 179-180, ## 1.17(a,c), 1.18(b,c), 1.19
Three.II.2, pp. 190-191, ## 2.22, 2.23(a,b), 2.24(a,c)

 

Week 8:

Three.III.1, pp. 200-202, ## 1.14, 1.15, 1.16, 1.22, 1.26
Three.III.2, pp. 207-208, ## 2.9(b,c), 2.10, 2.11, 2.13, 2.18

Three.IV.1, pp. 212-213, ## 1.8, 1.13, 1.14, 1.15

Week 9:

Three.IV.2, pp. 218-219, ##  2.14, 2.16, 2.17
Three.IV.4, pp. 234-235, ##  4.14, 4.16, 4.18, 4.19

Three.V.1, pp. 239-240, ## 1.6, 1.7(b,d), 1.8(b,d), 1.9(a,c), 1.10(b,c), 1.11

 

Week 10:

Three.V.2, pp. 245-246, ## 2.10, 2.12

Four.I.1, pp. 295-296, ## 1.1(a,b), 1.4(c), 1.5(b), 1.7, 1.8

Four.I.2, pp. 299-300, ## 2.7(a,b), 2.9, 2.13, 2.16

Week 11:

Four.I.3, pp. 308-309, ## 3.22, 3.27, 3.33
Four.Cramer's rule, pp. 330-331, ## 1, 2, 4

Five.II.1, pp. 352-353, ## 1.4, 1.6, 1.10, 1.11

 

Week 13:

Five.II.2, pp. 356-357, ## 2.7(a,b), 2.8, 2.9, 2.17

Five.II.3, pp. 362-364, ## 3.20(a,b,c,e), 3.21, 3.22, 3.23, 3.24(a), 3.28, 3.34, 3.37(a,b), 3.42

Three.VI.2, pp. 256-258, ##2.9(a,b), 2.10(a), 2.12, 2.16, 2.17, 2.19

Week 14:

Five.IV.1, pp. 384-385, ## 1.13, 1.14(a,b,c,e), 1.16, 1.23

Five.IV.2, pp. 396-397, ## 2.19, 2.21(a,b,c,e), 2.22, 2.24