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: |
Tuesdays: 6:30pm - 8:10pm in 1S-217 Thursdays: 6:30pm - 8:10pm in 1S-116 |
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.
Material Covered: This course is an introduction to linear algebra. The central part is the study of linear equations, matrices, real vector spaces, and linear transformations.
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 problems, and provides immediate feedback. Incorrect answers may be corrected, so that I hope you will often submit perfect homework sets. These problems will be mostly computational exercises. This will count as 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: 20% HW + 20% Midterm Exam 1 + 10% Midterm Quiz + 20% Midterm Exam 2 + 30% Final Exam.
Without exception, you must take the final exam at the time scheduled by the university.
Help: My office hours are Tuesdays 2:30-4:30pm and Thursdays 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.
Written work: We write to communicate. Work must be neat and legible to receive consideration. You must explain your work to obtain full credit. For specific suggestions see A guide to writing in mathematics classes.
Goals: 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.
| Class | Topic | Read | Exercises | Due |
| Jan 30 | 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 |
| Feb 01 | Matrix multiplication | §1.3 | 1,5,7,9,11,13,15,19,21,25,T1,T3,T4,T7,T10 | |
| Feb 06 | Matrix operations | §1.4 | 9,11,13,15,T6,T9,T23,T24,T27 | |
| Feb 08 | Solving linear systems | §1.6 | 3,5,8,9,13,19,23,27,31,47,T8,T11 | |
| Feb 13 | Inverse matrix | §1.7 | 3,5ab,11,13,15,18,25,T7,T9,T10 | problem set 1:1.1/26; 1.2/6,T5; 1.3/8,T6,T9 |
| Feb 20 | Determinants | §3.1 | 3,5abv,9,15,17,22,23,T5,T9,T16 | problem set 2:1.4/14,16,ML1,ML6,ML7; 1.5/16,18 |
| Feb 22 | Cofactor expansion | §3.2, 3.3 | 3.2: 1,5,9,11,15,19,23,T4,T5,T10,T11 | |
| Feb 27 | 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 |
problem set 3:1.6/28,30,32,ML8,ML11; 1.7/8,22,T8,ML4 |
| Mar 01 | MIDTERM EXAM 1 | SAMPLE EXAM 1 (PDF) SOLUTIONS to SAMPLE EXAM 1 |
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| Mar 06 | Linear transformations | §4.3 | 1,7,13,15,17,21,25,27,29,T5,T11 | |
| Mar 08 | Matrix transformations | §1.5 | 1,5,9,15,19 | problem set 4:3.1/18, T10, ML2; 3.2/6, 18, 22, ML2 |
| Mar 13 | 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 |
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| Mar 15 | Linear independence | §6.3 | 1ab,3ac,5,7,9,11bc,12ab,13ab,14,16,T2,T8,T11,T13 | problem set 5:4.3/32, T9 |
| Mar 20 | Basis, dimension | §6.4 | 1,3ab,5bc,9,11,13,19,23,27,29,31,33,35,T3,T4,T8,T12,T15 | |
| Mar 22 | Homogeneous systems | §6.5 | 3,5,11,13,21,T3 | problem set 6:6.2/T3, T12; 6.3/10,18 |
| Mar 27 | MIDTERM QUIZ, Matrix rank | §6.6 | 1,3,5,7,11,17,19,21,23,27,29,33,T7,T12 | In class Midterm Quiz |
| Mar 29 | Change of basis | §6.7 | 1,3,5,7,11,13,15,17,21,25,T4,T7c | problem set 7:6.7/14 |
| Apr 12 | Orthonormal bases | §6.8 | 1,3,5,9,11,15,17,19,21,T6,T9 | |
| Apr 17 | Orthogonal complements | §6.9 | 1,3,7,9ab,11,13,T5 | problem set 8:6.8/10, 6.9/6,8 |
| Apr 19 | Linear transformations | §10.1, 10.2 | 10.1/1,3,5,17,19,T5; 10.2/1,3,9,11,17,T2 | |
| Apr 24 | Matrix of linear transformation | §10.3, B2 | 1,3,13,15,17 | Sample Exam 2 (PDF) |
| Apr 26 | MIDTERM EXAM 2 | SOLUTIONS to Sample Exam 2 ** NEW! ** | ||
| May 01 | Eigenvalues, eigenvectors | §8.1 | 5,9,11,13,15,17cd,19,21,25,T6,T9,T11,T15 | MIT web demo MIT web lecture |
| May 03 | Diagonalization | §8.2 | 1,3,5,9,13,15,19,23,25,29,39,41,46,T2,T6,T7 | problem set 9: 10.2/4,6,20, 10.3/20 |
| May 08 | Symmetric matrices | §8.3 | 1,2,5,9,17,T1,T6,T8 | |
| May 10 | Dynamical systems | §9.3 | 1,2,3,4,5 | |
| May 15 | Review | |||
| May 17 | Review | |||
| May ?? | FINAL EXAM | Application: How Google Finds Your Needle in the Web's Haystack |