| Course: | MTH U371, Linear Algebra |
| Time and place: | MWTh 1:35-2:40 PM, 7 Snell Library |
| Textbook: | O. Bretscher, Linear Algebra with Applications, Third Edition. Prentice Hall, 2005 |
| Instructor: | Professor Andrei Zelevinsky |
| Office and phone: | 431 LA, x5648 |
| Email: | andrei@neu.edu |
| Office hours: | Mon., Wed. 10:30 - 11:35 AM, or by appointment |
The course introduces basic concepts, algorithms and applications of linear algebra. Starting with linear systems and their solution via Gauss - Jordan elimination, the course covers most of the material in the book, with the exception of Chapter 4. An approximate work schedule contains the following topics and suggested homework problems (subject to change):
1.1 Introduction to linear systems // 1,7,10,20-22,34
1.2 Matrices, vectors and Gauss - Jordan elimination // 2,4,5,7,18,20-22,29-31,34,35,41
1.3 On the solutions of linear systems // 1-8,10-15,21-32,34,36,47,55
2.1 Linear transformations and their inverses // 1-3,5,6,24-30,35,42
2.2 Linear transformations in geometry // 1,4,6-10,17,19,21,23-26,49
2.3 The inverse of a linear transformation //1-5,17,19,25,35-41(odd)
2.4 Matrix products //3,5,11,13,16-25,47,65,76
3.1 Image and kernel of a linear transformation // 1-7(odd), 14,15,23,25,33,35,42
3.2 Subspaces of R^n; bases and linear independence // 1,3,11-17(odd),21-33(odd)
3.3 The dimension of a subspace of R^n // 1-7,11,13,17,21,23,27,37,39,49,52
5.1 Orthogonal projections and orthonormal bases //1,3,5,13,15,17,27,35
5.2 Gram-Schmidt process and QR factorization // 5,7,19,21,33,35
5.3 Orthogonal transformations and orthogonal matrices // 5-8,13-17,27-29
5.4 Least squares and data fitting // 8,11,13,17-25,31-33
5.5 Inner product spaces // 1, 2, 3b
6.1 Introduction to determinants // 1-11(odd),17,27
6.2 Properties of the determinant // 1,6,24-26,31
7.1 Dynamical systems and eigenvectors // 1-7,9,15-22,34
7.2 Finding the eigenvalues of a matrix // 1-13(odd), 28
7.3 Finding the eigenvectors of a matrix// 1-13(odd), 21,44,46
7.4 Diagonalization // 1,3,5,17,31,33,35,41
7.5 Complex eigenvalues // 1, 2, 5, 8, 20, 23
7.6 Stability //1, 11, 17
8.1 Symmetric matrices // 1,3,7
8.2 Quadratic forms // 1, 4, 9
8.3 Singular values // 1, 2, 4
The grading will be based on weekly half-hour quizzes (60%), and the final exam (40%). Two lowest scores on the quizzes will be dropped at the end of the semester. There will be no make up for quizzes or the final exam. Homework will be regularly assigned and discussed in class. Although the homework is not counted in grading, the quizzes and the final exam will consist of similar problems so working on the homework is crucial for the success in this course.
It is your responsibility to be aware of any changes in the syllabus announced in class. Students are responsible for all information given when they are absent.
If you have a concern about the course or the instructor that cannot be resolved by speaking with the instructor, please contact Professor S. Eigen (vice chair), 527 LA, x5647, eigen@neu.edu.
It is University policy that no grade, including an incomplete, can be changed after one year. Exceptions must be authorized by the Academic Standing Committee.
All students without legitimate conflicts will take the final exam at the scheduled time. Do not make travel plans that conflict with the final exam.
Homework:
Sep. 7: Section 1.1; pp. 5-7, #1, 7, 10, 21-22, 34.
Sep. 8: Section 1.2; pp. 20-21, #2, 4, 5, 7, 18, 31.
Sep. 12: Section 1.3; p. 22, #34, 35; pp. 35-36, #1-4, 22-28.
Sep. 14: Section 1.3; pp. 35-36, #5-8, 11-15, 34, 36.
Sep. 15: pp. 37-38, #47, 54-58; read Section 2.1.
Sep. 19: pp. 51-53, #1-3, 5, 6, 9-12, 32, 42 (a).
Sep. 21: read Section 2.2 (especially projections and reflections );
pp. 66-68, #6-8, 10-12, 19, 23, 30.
Sep. 22: read Section 2.3; pp. 76-77, #4-5, 19, 29, 34, 39, 41 (a-c).
Sep. 26: read Section 2.4; p. 89, #3, 5, 11, 13, 16-17, 19-20.
Sep. 28: pp. 89-91, #21, 22, 47; read Section 3.1; p. 109, #1, 3, 5, 7, 15.
Sep. 29: pp. 110-111, #33-35, 44; read (relevant parts of) Section 3.2; pp. 121-122, #1, 3, 11, 13, 15, 17, 27, 29.
Oct. 3: p. 122, #31, 33, 34, 42; read Section 3.3; p. 133, #21, 23, 27, 37.
Oct. 5: p. 134, #38-39; p. 150, #1-5, 7-8, 11-14.
Oct. 6: p. 150, #16-18, 20, 23, 28; read Section 5.1; pp. 198-200, #1, 3, 15, 17, 27, 29.
Oct. 12: read Section 5.2; p. 208, #5, 7, 9, 19, 21.
Oct. 13: p. 208, #33, 35; read Section 5.3; pp. 216-217, #5-8, 27, 31-33, 41.
Oct. 17: pp. 217-218, #40, 46-48; review Sections 5.1-5.3; p. 245, #1, 2, 6, 7, 9, 17, 22, 23.
Oct. 19: review Sections 5.1-5.3; p. 245, #24, 31, 33, 34, 45.
Oct. 20: read Section 5.4; pp. 228-229, #5, 17, 19, 21, 22.
Oct. 24: pp. 229-230, #23-25, 31-32.
Oct. 26: review Section 5.4; pp. 229-230, #15, 29.
Oct. 27: read Section 6.1; p. 259, #1, 3, 5, 7, 11, 17.
Oct. 31: read Section 6.2; p. 259, #27; p. 271, #1, 6, 31, 33.
Nov. 2: p. 259, #31, 33, 35, 37, 43; pp. 290-291, #1, 2, 7, 14.
Nov. 3: read Section 7.1; p.302, #1-7, 9.
Nov. 7: p.303, #15-17; read Section 7.2; pp.314-315, #1, 3, 7, 13, 25.
Nov. 9: read Section 7.3; p.324, #1, 3, 5, 7, 9.
Nov. 10: pp.324-325, #11, 21, 23; read Section 3.4; p.146, #1, 5, 7, 13.
Nov. 14: p.146, #19, 21, 23, 27.
Nov. 16: read Section 7.4; p.338, #1, 3, 5, 17, 31.
Nov. 17: pp.338-339, #33, 35, 37, 38, 54.
Nov. 21: read Section 8.1; pp.370-371, #3, 5, 9, 11, 15, 25.
Nov. 28: read Section 8.2; p.378, #1, 3, 4, 7.
Nov. 30: p.379, #11, 13, 14, 23-25.
Dec. 1: read Section 8.3; pp.389-390, #4, 5, 7, 12, 13.
Dec. 5: work on practice exam.
Quizzes and tests:
Quiz 1: Thursday, Sep. 15 (Sections 1.1, 1.2, 1.3).
Quiz 2: Thursday, Sep. 22 (Sections 2.1, 2.2
(projections and reflections)).
Quiz 3: Thursday, Sep. 29 (Sections 2.3, 2.4, 3.1).
Quiz 4: Thursday, Oct. 6 (Sections 3.1, 3.2, 3.3).
Quiz 5: Thursday, Oct. 20 (Sections 5.1, 5.2, 5.3).
Quiz 6: Thursday, Oct. 27 (Section 5.4).
Quiz 7: Thursday, Nov. 3 (Sections 6.1, 6.2).
Quiz 8: Thursday, Nov. 10 (Sections 7.1, 7.2, 7.3).
Quiz 9: Thursday, Nov. 17 (Sections 7.3, 3.4, 7.4).
Quiz 10: Thursday, Dec. 1 (Sections 8.1, 8.2).
Quiz 10 proved to be more time-consuming than I thought, so I will be dropping three lowest quizzes out of ten.
I will be available for last minute questions on Monday December 12 at 11:00 AM - 3:00 PM.
Final Exam: Monday December 12 at 3:30 PM in 70 Dodge Hall.
Allowed: calculators (for arithmetic calculations only), one sheet of notes.