Prof. Ilya KofmanEmail: ikofmanmath.csi.cuny.edu Website: http://www.math.csi.cuny.edu/~ikofman/ |
Textbook: Gilbert Strang, Introduction to Linear Algebra, Fifth Edition, 2016. ISBN: 978-09802327-7-6. You can rent or buy, new or used, from any store.
Videos: You are expected to view each video listed below before class, so that we can discuss the material further in class.
Homework: Webwork problems must be submitted online. To pass this course, the Webwork problems are the minimum requirement; to earn an excellent grade, you will have to do the other assigned problems in your textbook. Answers to exercises in the textbook are at https://math.mit.edu/~gs/linearalgebra. 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 a free online system that provides individualized homework problems, gives immediate feedback, and allows you to correct mistakes until the due date. Later, you can see solutions online. Webwork is required in this course, and it is a major part of your grade. Webwork website
MATLAB: MATLAB is powerful computer algebra software designed to solve linear algebra problems. Our textbook has a lot of MATLAB material, and learning to use MATLAB will help you in this course. You can access MATLAB online using CUNY Virtual Desktop.
Grading: The course grade will be determined (subject to changes announced in class) by your online participation and your scores on Webwork, homework, exams and final exam. Without exception, you must pass the exams to pass this course, and you must take the final exam at the time scheduled by the college.
Help: My office hours are Mondays and Wednesdays, 4:30pm-5:45pm. Email is the fastest way to contact me.
How to Study: (1) Watch the appropriate video before class. (2) Attend class (attendance is mandatory). (3) Read the relevant sections after class. (4) Do the homework. Leave time to think about it! (5) Use the Blackboard discussion board or visit me during office hours with any remaining questions. (6) To study for a math exam, you must DO MORE PROBLEMS from past exams, homework and textbook.
Class | Topic | Videos | Read | Exercises | Webwork |
Aug 26 | Vectors and Linear Combinations, Lengths and Dot Products | 3B1B-E1 and
3B1B-E2 and KA-dot product |
§1.1, 1.2 | 1.1: p.8: 2,4,6,9,10,17,26
1.2: p.18: 1,3,4,6,8,9,12,19,21,29 |
Set 1 |
Aug 31 | Matrices, Vectors and Linear Equations | Strang 1 | §1.3, 2.1 | 1.3: p. 29: 1,2,4,5,7
2.1: p. 41: 4,5,6,7,9,10,13,18,27 |
Set 2 |
Sep 2 | Elimination | Strang 2 and another example | §2.2, 2.3 | 2.2: p. 53: 1,2,4,5,11,12,13
2.3: p. 66: 1,3,4,8,11,14,18,25,27,28 |
Set 3 |
Sep 9 | Matrix Operations, Inverse Matrices | Strang 3 | §2.4, 2.5 | 2.4: p. 77: 1,3,5,7,13,14,15,17,19,27
2.5: p. 92: 1,4,6,7,8,11,15,16,21,22,24,27 |
Sets 4,5 |
Sep 14 | Review | ||||
Sep 16 | EXAM 1
Factorization A=LU |
§2.6 |
p. 104: 1,2,3,4,6,9,12,15, MATLAB examples for which you must import the function slu.m | ||
Sep 21 | Factorization A=LU
Transposes and Permutations |
Strang 4 Strang 5 |
§2.7 |
p.117: 2,4,8,16,17,20,22* |
Set 6 |
Sep 23 | Spaces of Vectors | Strang 6 | §3.1 | p. 131: 1,3,5,9,11,15,19,20,23,25 | Set 7 |
Sep 29 | Nullspace of A | Strang 7 | §3.2 | p. 142: 1,2,3,5,8,9,11,13,14,16,24,29 | Set 8 |
Sep 30 | Complete Solution to Ax=b | Strang 8 | §3.3 | p. 158: 1,2,4,6,8,12,13,14,16,18,25 | Set 9 |
Oct 5 | Review | ||||
Oct 7 | EXAM 2
Independence, Basis and Dimension |
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Oct 14 | Independence, Basis and Dimension | Strang 9 | §3.4 | p. 175: 1,2,3,6,8,9,11,12,15,18,20,25 | Sets 10,11,12 |
Oct 19 | Dimensions of the Four Subspaces | Strang 10 | §3.5 | p. 190: 1,2,4,6,9,11,12,16,24 | Set 13 |
Oct 21 | Orthogonality of the Four Subspaces | Strang 14 | §4.1 | p. 202: 1,3,5,6,8,9,10,11,12,16,28 | Set 14 |
Oct 26 | Projections and Least Squares Approximations | Strang 15 and Strang 16 | §4.2, 4.3 | 4.2: p. 214: 1,3,8,9,11,13,17,21,24,29
4.3: p. 229: 1,2,3,4,5,8,12 |
Sets 15,16 |
Oct 28 | Review | ||||
Nov 2 | EXAM 3
Orthogonal Bases and Gram-Schmidt |
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Nov 4 | Orthogonal Bases and Gram-Schmidt | Strang 17 | §4.4 | p. 242: 1,2,4,5,21 | Set 17 |
Nov 9 | Determinants | Strang 18 and Strang 19 | §5.1, 5.2 | 5.1: p.254: 1,3,8,9,10,11,14,23,24,27,28
5.2: p.266: 1,2,3,4,5 |
Set 18 |
Nov 11 | Cramer's Rule, Inverses, and Volumes
Eigenvalues |
Strang 20 and 3B1B-E12 | §5.3 | p. 283: 2,3,16,17 | Set 19 |
Nov 16 | Eigenvalues | Strang 21 and 3B1B-E14 | §6.1 | p. 298: 1,3,5,6,8,16,17,21,23,27. See Explained Visually | Set 20 |
Nov 18 | Diagonalizing a Matrix | Strang 22 | §6.2 | p.314: 1,3,4,6,11,12,13,14,15,21,26 | Set 21 |
Nov 23 | Review | ||||
Nov 30 | EXAM 4
Linear Transformations |
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Dec 2 | Linear Transformations | 3B1B-E3 and 3B1B-E4 and 3B1B-E5 | §8.1 | p.407: 1,3,6,10,12 | Set 22 |
Dec 7 | Matrix of a Linear Transformation | Strang 30 | §8.2 | p.418: 5,6,7,10,11,14,15,16. See Mathinsight.org applet | Set 23 |
Dec 9 | Review | Strang 34 |
Online resources:
MIT OpenCourseWare Linear Algebra Complete online linear algebra course.
Khan Academy Linear Algebra Complete online linear algebra course.
3Blue1Brown Essence of Linear Algebra Excellent online videos.
Mathmatize Linear algebra problems in an online app
Eigenvectors and Eigenvalues Explained Visually
Mathinsight.org linear transformations applet
How Google Finds Your Needle in the Web's Haystack
Attendance policy: Attendance is mandatory. Unauthorized absences from four or more classes will result in a course grade of WU (Withdrew Unofficially).
Disability policy: Qualified students with disabilities will be provided reasonable academic accommodations if determined eligible by the Office for Disability Services. Prior to granting disability accommodations in this course, the instructor must receive written verification of student's eligibility from the Office of Disability Services, which is located in 1P-101. It is the student's responsibility to initiate contact with the Office for Disability Services staff and to follow the established procedures for having the accommodation notice sent to the instructor.
Integrity policy: CUNY's Academic Integrity Policy is available online at https://www2.cuny.edu/about/administration/offices/legal-affairs/policies-procedures/academic-integrity-policy
Important Dates: www.csi.cuny.edu/currentstudents/academiccalendars