Meets MTWR 3-5pm at MCS 148
Instructor: A. Levichev, MCS 168, tel.3-1481 (e-mail is more reliable), office hrs MTR 5-5.45 or by appointment
E-mail: levit@math.bu.edu
levit@bu.edu (when the above does not work)
get to http://math.bu.edu/people/levit for an info about the Instructor as well as for the course updates
To read and to understand the content of respective sections is part of each and every HW assignement
Homework is assigned on a regular basis. It is not collected but you are welcome to turn (part of) it (you'll get it back with my comments which might be helpful as part of your tests' preparation).
There are two in-class tests (Tue June 7, Tue June 21), and a Final (on Thursday, June 30).
The final test average was 28.9, in 12 through 40 range. Class statistics: two A, six A-, five B+, four B, four B-, three C+ or lower.
(Preliminary) attendance grade is posted.
L-16: 6.2,6.3,6.7. HW 6.2: 1-23odd, 27,29; 6.3: 1-11odd,19; 6.4: 1-9odd; 6.7: 1-7odd, 15,21,23,25.
6/26: Pp.398, 399 won't be tested. The last subsection in 6.4 won't be tested. P.431 won't be tested.
Test 2 average was 25, in the 13-37 range. Test 2 access will be arranged on Tue (at about 4.30pm). Course review - on Wed (attendance will be taken).
L-15: 5.3(Examples 1,2 won't be tested), 5.4, 6.1. HW 5.3: 1,5-25odd; 5.4: 1-29odd; 6.1: 1-17odd,19 (except the d-part),25,27,29.
L-14: 5.1, 5.2 (in each of them the last subsection won't be tested), 5.3 (up to Example 5). HW 5.1: 1-17odd, 21,25,31,32; 5.2: 1-15odd,19.
Test 1 covers 1.1 - 1.5, 1.7, 1.8, 1.9, and 2.1 (part of).
Test 2 covers 2.1, 2.2, 2.3, 3.1, 3.2, 4.1-4.7. It is book-open, you can use your lecture notes. Other (hand written) notes of yours (no more than a few pages) are allowed, too. No other sources, please.
Answers to "True-False" HW problems are provided (see below, closer to the end of the file).
L-13: 4.6, 4.7 (a simplified version of 4.7 has been presented). HW 4.6: 1-13odd, 17, 19; 4.7: 1b, 5b, 13b.
L-12: 4.4 (Example 3 won't be tested), 4.5, 4.6 (started). HW 4.4: 1-15odd, 27,29; 4.5: 1-27odd. Coordinates of a vector related HW has been given (on a separate sheet).
L-11: 4.2 (finished), 4.3, 4.4 (started) HW 4.2: 1,3,7-25odd,31,33,35; 4.3: 1-9odd, 13,19,21
IMPORTANT: On L-10 the definition of an isomorphism has been presented (p.177, or p.251 in the text). It is a fundamental notion which is not enough emphasized by the text. In 4.1 Example 8 we have proven that H is isomorphic to R^2 (by presenting an isomorphism). At the beginning of L-10 an example of a vector space like strucrure has been presented. 4.1 axioms 1, 2, 4, 6 have been satisfied but axiom 5 has been violated.
L-10: 4.1 (finished), 4.2 (part of). HW 4.1: 1-17odd, 21,23a-d,31,32.
L-9: 3.1, 3.2, 4.1 (started). HW 3.1: 1-11odd, 25,27,29,37; 3.2: 1,3,5, 15-21odd.
Test 1 scores are posted. The class performed extremely well, with 3.29 average, in the 23-40 range. To find your current standing, divide your score by 10. Monday, June 13 is the last day to drop classes with a "W" grade.
L-8: 2.1 (finished), 2.2 (Example 3 won't be tested), 2.3. HW 2.1: 15,27,31; 2.2: 1,3,5,9,13-21odd,29,31,33; 2.3: 1,3,5,11,13,15,33,37.
L-7: 2.1 (up to p.114). HW 2.1: 1,3,5,11.
L-6: 1.8, 1.9 HW 1.8: 1-33odd; 1.9: 1-27odd
L-5: 1.7 finished, 1.8 (started). HW 1.7: 1-9odd, 19,21,33,35,37.
L-4: 1.4, 1.5, and 1.7(started). HW 1.4: 1-15odd, 21, 25, 27, 31; 1.5: 1-15odd, 21,25,27,29,31.
L-3: 1.3 finished (Example 7 won't be tested), 1.4 (started). HW 1.3: 1-15odd; 23,25.
L-2: 1.2 and 1.3 (part of). HW 1.2: 1-15odd, 23.
L-1: 1.1. HW 1.1: 1-19odd, 29,31. ************************************
A (tentative) day-by-day coverage is subject to change.
L-18: 6.7, 6.8 (in 6.8 pp.440-442, only). HW 6.7: 1-11odd,15,21,23,25; 6.8: 5,7,9,11.
L-17: 6.2,6.3,6.4 (in 6.4 the last subsection won't be tested); HW 6.2: 1-23odd,27,29; 6.3: 1-19odd; 6.4: 1-9odd.
L-16 (after test 2): 6.1. HW 6.1: 1-19odd, 25,27,29.
L-15: 5.3 (Examples 1,2 won't be tested), 5.4. HW 5.3:1,5-25odd; 5.4: 1-29odd.
L-14: 5.1, 5.2 (in both, the last subsection won't be tested); some algebraic pre-requisite recalled. HW 5.1: 1-17odd,21,25,31,32; 5.2: 1-15odd,19.
Answers to "True-False" HW problems: 2.1 #15 FFTTF; 2.2 #9 TFFTT; 2.3 #11 TTTFT; 4.1 #23a-d FFFT; 4.2 #25 TFTFTT; 4.3 #21 FFTFF; 4.4 #15 TFF; 4.5 #19 TFFFT; 4.6 #17 TFTFT; 5.1 #21 FTTTF; 5.3 #21 TTFF; 6.1 #19 TTTT; 6.2 #23 TTFFF;
Grading policy: attendance=1 unit; two tests (one unit each); Final=3 units. The lowest from these 6 grades will be dropped. The average of the remaining 5 will determine the grade for the class.
40 is the possible maximum. Each half-meeting missed is 1 off. Scale: C-: [1.5, 1.8], C: [1.9, 2.1], C+: [2.2, 2.45], B-: [2.55, 2.8], B: [2.9, 3.1], B+: [3.2, 3.45], A-: [3.55, 3.8], A: [3.87, 4]. Cases which are not determined by this scale, I will decide myself about.
The students have the responsibility to know the provisions of the CAS Academic Conduct Code, copies of which are available in CAS 105. Cases of suspected academic misconduct will be referred to the Dean's Office.
The course covers chapters 1 through 7 (most parts of) from "Linear Algebra and Its Applications" by D. Lay, 3d edition. This includes
Chapter 1(Linear Equations): systems of linear equations, row reduction and echelon forms, solution sets, linear independence, introduction to linear transformations.
Chapter 2(Matrix Algebra): matrix operations, finding an inverse, partitioned matrices.
Chapter 3(Determinants): determinants and their properties, cofactor expansion, more on linear transformations, applications.
Chapter 4 (Vector Spaces): subspaces, null spaces, column spaces, linear transformations, linear independence, coordinate systems, basis and dimension, rank of a matrix, change of basis.
Chapter 5 (Eigenvalues and Eigenvectors): eigenvalues and eigenvectors, diagonalization, more on linear transformations, complex eigenvalues.
Chapter 6 (Orthogonality and Least-Squares): inner product, length, and orthogonality, orthogonal projections, the Gram-Schmidt process, inner product spaces.
Chapter 7 (Symmetric Matrices and Quadratic Forms): diagonalization of symmetric matrices, quadratic forms.