Math 4310 - Linear Algebra MWF 11:15 - 12:05, MLT 406 Fall 2009
Instructor: Becci Torrey Email: rtorrey@math.cornell.edu Phone: 255-6495 Office hours: Mon 2:30-3:30                         Thurs 3-4 Office: Malott 431	T.A.: Margarita Amchislavska Email: margo1729@math.cornell.edu Office hours: Wed 3:30-5:30                         Malott 218
Course Description: This course provides a rigorous introduction to linear algebra. By the end of the course, you should have a basic understanding of vector spaces and subspaces, systems of linear equations, linear transformations, determinants, diagonalization, eigenvalues and eigenvectors, inner product spaces and some additional topics.
Textbook: S. Friedberg, A. Insel and L. Spence, Linear Algebra, fourth edition, Pearson Hall, New Jersey, 2003 (ISBN 0-13-008451-4).
Exams: There will be two preliminary exams and one final. All exams are in-class and closed-book. The final exam will be comprehensive. Prelim 1: Tuesday, September 29, 7:30-9:00 pm, RCK 122 Last year's Prelim 1 and solutions Prelim 2: Thursday, November 19, 7:30-9:00 pm, RCK 122 Last year's Prelim 2 and solutions Final Exam: Monday, December 14, 2:00-4:30 pm, MLT 406
Homework: Solving problems on your own is essential to your understanding of the material. You may think you understand the material in class, but you will not really learn the material until you have worked through problems yourself. Homework assignments will be posted weekly on the course webpage and will be collected at the beginning of class every Friday (unless otherwise indicated below). Late homework will not generally be accepted. In the event that you cannot complete an assignment on time due to illness, contact the instructor before the assignment is due. Your lowest homework score will be dropped. Only some of the homework problems will be graded. After the assignment is turned in, those problems will be underlined below. Problems in green: optionally hand in the Monday before the assignment is due to receive commentary for revision.
Grading: The breakdown of your final grade is as follows: Homework: 30% Prelim 1: 20% Prelim 2: 20% Final exam: 30%
Evaluations: At the end of the term, you will have a chance to give me feedback on my teaching via teacher evaluations. This will provide me with valuable information for my future classes. Giving me feedback now can help me to improve this class. You may at any time download this form and leave it in the box on the door to my office. (Please indicate the course number, 4310, somewhere on the form.) Of course, you can also give me feedback directly by talking to me in office hours, or making an appointment to meet at another time. I very much appreciate all student feedback.
Academic Integrity: Each student in this course is expected to abide by the Cornell University Code of Academic Integrity. Any work submitted by a student in this course for academic credit will be the student's own work. You may work in groups or individually on the homework assignments, but each student must write up every assignment on their own.
Topics Assignment (graded probs are underlined) Due Date Solutions Preliminaries (Appendices A-C) Vector Spaces (1.2) Homework 1 (1, 2, 5, 12) Sept 4, 2009   Subspaces (1.3) Linear Combo's and Systems of Linear Equations (1.4) Linear In/dependence (1.5) 1.3: 1, 2(bgh), 8(ade), 12, 13, 19, 25, 27 1.4: 3(c), 4(c), 5(g), 8, 12 1.5: 1, 3, 8 Sept 11, 2009   Bases and Dimension (1.6) Linear Transformations, Null Spaces and Ranges (2.1) 1.6: 2(bc), 4, 13, 16, 24, 29, 31 2.1: 2, 5, 6, 9, 11, 13, 24, 28 Sept 18, 2009   Matrix Representation of a Linear Transformation (2.2) Composition of Lin. Trans. and Matrix Mult. (2.3) Invertibility and Isomorphisms (2.4) 2.2: 2(adef), 4, 9, 10, 13 2.3: 2, 3, 11, 12, 13 2.4: 2(ef), 4, 5, 14, 16, 17 Sept 25, 2009   Prelim 1   Sept 29, 2009 Solutions The Change of Coordinate Matrix (2.5) Dual Spaces (2.6) 2.5: 2(bd), 3(a), 4, 7(a), 10, 11 2.6: 3, 6, 8, 13(ab), 15, 17 Monday Oct 5, 2009 Some solutions Elementary Matrix Operations; Elementary Matrices (3.1) Rank of a Matrix; Matrix Inverses (3.2) 3.1: 2, 8 3.2: 2(bf), 3, 5(ad), 7, 8, 14, 21 Friday Oct 9, 2009 Some solutions Systems of Linear Equations I (3.3) Systems of Linear Equations II (3.4) 3.3: 1, 2(d), 3(d), 4(a), 6, 10 3.4: 2(bd), 6, 9, 10 Oct 16, 2009 Some solutions Determinants of Order n (4.2) Properties of Determinants (4.3) Eigenvalues and Eigenvectors (5.1) 4.2: 4, 10, 18, 23, 29 4.3: 6, 15, 21, 26(ad) 5.1: 2(f), 3(b), 4(f), 9, 12, 20 Oct 23, 2009 Some solutions Eigenvalues and Eigenvectors (5.1) Diagonalizability (5.2) 5.1: 8(ab), 14 5.2: 1(a-g), 2(ac), 3(be), 7, 10, 11, 18(a), 19 Oct 30, 2009 Some solutions Diagonalizability (5.2) Inv Subspaces, Cayley-Hamilton (5.4) Inner Products and Norms (6.1) 5.2: 1(hi), 20 5.4: 2(de), 5, 6(cd), 8, 15, 19, 42 6.1: 2, 5, 8(bc), 12, 16, 23(ab) Nov 6, 2009 Some solutions Gram-Schmidt Orthogonalization (6.2) Adjoint of a Linear Operator (6.3) 6.2: 2(b), 6, 9, 11, 12, 13(abc), 19(ac) 6.3: 2(b), 3(c), 12, 13, 14, 21 Nov 13, 2009 Some solutions Prelim 2   Nov 19, 2009   Normal and Self-Adjoint Operators (6.4) Unitary and Orthogonal Operators (6.5) 6.4: 2(f), 7(ab), 9, 12 6.5: 2(d), 5(cd), 10, 15, 17 Wednesday Nov 25, 2009   Orthogonal Projections, Spectral Theorem (6.6) Jordan Canonical Form (7.1) 6.6: 1, 2, 4, 6, 7(abe) 7.1: 2(c), 5, 10 Prelim 2 Revisions Friday Dec 4, 2009   Key: Underlined problems are the ones graded. Optionally hand in green problems early (see above).