Prof. Ilya Kofman
Email: ikofman
math.csi.cuny.edu
Website: http://www.math.csi.cuny.edu/~ikofman/
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Prof. Ilya Kofman |
Office: 1S-209 phone: (718) 982-3615
Email: ikofman math.csi.cuny.edu
Website: http://www.math.csi.cuny.edu/~ikofman/ |
| Course Time and Place: |
Mondays: 6:30pm - 8:10pm in 1S-115 Wednesdays: 6:30pm - 8:10pm in 1S-102 |
Textbook: Bernard Kolman and David R. Hill, Introductory Linear Algebra: An Applied First Course Eighth Edition, 2005. ISBN 0131437402. Available at the University Bookstore or online: AddALL.
Goals: Linear algebra is the study of linear equations, matrices, real vector spaces, and linear transformations. Many problems in linear algebra are computational -- the first goal is to make calculations with accuracy, intelligence and flexibility. But linear algebra is also a course filled with new concepts and new vocabulary, often with a geometric flavor -- the second goal is to explain the basic concepts clearly, reason logically with them, and use them to solve extended problems.
Homework: Assignments will be announced in class and then posted on this website in the column marked "Due". Any changes will be announced in class. Late homework will not be accepted. The listed exercises from the textbook are strongly recommended as practice, but they will not be collected. Answers for almost all of these are in the back of the book. I highly recommend working jointly on homework problems with fellow students, but in the end you must hand in your own work.
WeBWorK: WeBWorK is an online program that generates individualized computational problems, and provides immediate feedback. Incorrect answers may be corrected, so that I hope you will often submit perfect homework sets. You cannot learn linear algebra without doing these kinds of computational problems, so Webwork is the major part of your HW score.
MATLAB: MATLAB is powerful computer algebra software designed to solve linear algebra problems. The CSI Math Department has computer labs with access to MATLAB, and our textbook has many homework problems designed for MATLAB. Using MATLAB will be required for this course. For an introduction to MATLAB, see Chapter 12 of our textbook.
Grading: The course grade will be determined as follows: 18% HW and Webwork + 18% Exam 1 + 18% Exam 2 + 18% Exam 3 + 28% Final Exam. Without exception, you must take the final exam at the time scheduled by the university.
Help: My office hours are Mondays 1:30-3:00pm and Wednesdays 3:30-4:30pm in my office, 1S-209.
Optimal Method of Study: (1.) Come to class. (2.) Read the relevant sections after class. (3.) Do the homework. Leave time to think--do not put homework off until it is due! (4.) Compare your solutions with other students to improve what you hand in. (5.) Come to office hours or the help room with any remaining questions.
| Class | Topic | Read | Exercises | Due |
| Jan 26 | Linear systems, matrices | §1.1, 1.2 | 1.1: 5,7,9,11,13,15,22,27,T4
1.2: 1,5,7,9,T1,T5,T7 |
WeBWorK |
| Jan 28 | Matrix operations | §1.3, 1.4 | 1.3: 1,5,7,9,11,13,15,19,21,25,T1,T3,T4,T7,T10
1.4: 9,11,13,15,T6,T9,T23,T24,T27 |
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| Feb 02 | Solving linear systems | §1.6 | 3,5,8,9,13,19,23,27,31,47,T8,T11 | |
| Feb 04 | Inverse matrix | §1.7 | 3,5ab,11,13,15,18,25,T7,T9,T10 | problem set 1:1.1/26; 1.2/T5; 1.3/T6,T9 |
| Feb 09 | Determinants | §3.1 | 3,5abv,9,15,17,22,23,T5,T9,T16 | |
| Feb 11 | Cofactor expansion | §3.2, 3.3 | 3.2: 1,5,9,11,15,19,23,T4,T5,T10,T11 | problem set 2:1.6/T13,ML8,ML11; 1.7/T8,ML4 |
| Feb 18 | Vectors | §4.1, 4.2 | 4.1: 9,13,15,19,21,24,27,T5,T9
4.2: 1,4,11,13,17,21,23,26,27,T5,T13 |
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| Feb 23 | Review | |||
| Feb 25 | EXAM 1 | |||
| Mar 02 | Linear transformations | §4.3 | 1,7,13,15,17,21,25,27,29,T5,T11 | |
| Mar 04 | Matrix transformations | §1.5 | 1,5,9,15,19 | |
| Mar 09 | Vector spaces | §6.1, 6.2 | 6.1: 1,3,4,9,13,15,20,T5
6.2: 3,7,9,17,19,20e,23,25,27,T3,T12 |
Problem 2 on Exam 1 |
| Mar 11 | Linear independence | §6.3 | 1ab,3ac,5,7,9,11bc,12ab,13ab,14,16,T2,T8,T11,T13 | |
| Mar 16 | Basis, dimension | §6.4 | 1,3ab,5bc,9,11,13,19,23,27,29,31,33,35,T3,T4,T8,T12,T15 | |
| Mar 18 | Homogeneous systems | §6.5 | 3,5,11,13,21,T3 | |
| Mar 23 | EXAM 2, Matrix rank | §6.6 | 1,3,5,7,11,17,19,21,23,27,29,33,T7,T12 | |
| Mar 25 | Change of basis | §6.7 | 1,3,5,7,11,13,15,17,21,25,T4,T7c | |
| Mar 30 | Orthonormal bases | §6.8 | 1,3,5,9,11,15,17,19,21,T6,T9 | |
| Apr 01 | Orthogonal complements | §6.9 | 1,3,7,9ab,11,13,T5 | |
| Apr 06 | Linear transformations | §10.1, 10.2 | 10.1/1,3,5,17,19,T5; 10.2/1,3,9,11,17,T2 | |
| Apr 20 | Matrix of linear transformation | §10.3, B2 | 1,3,13,15,17 | |
| Apr 22 | Eigenvalues, eigenvectors | §8.1 | 5,9,11,13,15,17cd,19,21,25,T6,T9,T11,T15 | MIT web demo MIT web lecture |
| Apr 27 | EXAM 3 | |||
| Apr 29 | Diagonalization | §8.2 | 1,3,5,9,13,15,19,23,25,29,39,41,46,T2,T6,T7 | |
| May 04 | Symmetric matrices | §8.3 | 1,2,5,9,17,T1,T6,T8 | |
| May 06 | Dynamical systems | §9.3 | 1,2,3,4,5 | |
| May 11 | Review | |||
| May 13 | Review | Application: How Google Finds Your Needle in the Web's Haystack |