MATH 2R03 is a second course in linear algebra. From the calendar:
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Important Note:
The purpose of this webpage is to collect together all of the needed resources for the course. You should also consult the Avenue-To-Learn page and Mosaic where you will find room information.
Instructor:
Office: Hamilton Hall 419 NOTE: I'm currently using HH 326
Office Hours: Wednesdays 9:30-10:20
Email: vantuyl@math.mcmaster.ca
TA:
Silas Vriend
Email: vriendsp@mcmaster.ca
Office Hours: Thursdays 12:30-1:30; Fridays 12:00-1:00 in Math Cafe
Course Outline:
The official course outline is found on SimpleSyllabus
Place and Time:
This course will be offered in-person. The times are:
Lecture C01: Monday, Wednesday 8:30-9:20, Friday 10:30-11:20
Tutorial T01 : Monday 10:30-11:20
Tutorial T02 : Tuesday 1:30-2:20
For locations of the class and tutorials, see Mosaic
Textbook:
Linear Algebra Done Right (Fourth Edition)
by Sheldon Axler
This book can be download for free.
Here is a link to the book on the campus bookstore website: Purchase at Campus Bookstore
Important Links:
The following online resources will be used during this course:
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We will be using the following schedule.
Note 1: There may be changes so please refer back to this page to stay up-to-date
Note 2: The videos are provided as a resource -- they are based upon the third edition of the textbook (we are using the fourth edition). Our lectures may cover different topics. A detailed schedule is given below.
Math 2R03 Schedule | |||
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Week 1 (Sept 2-6) | |||
Homework: Assignment 0 (Due Sept 6) | |||
Lecture | Topic | Video | Suggested Problems |
Lecture 1 | 1.A R^n and and C^n | Video | 1.A - 10, 11, 15 |
Lecture 2 | 1.B Vector Spaces | Video | 1.B - 1, 2, 3 |
Week 2 (Sep 9-13) | |||
Homework: Assignment 1 (Due Sep 13) | |||
Lecture 3 | 1.C Subspaces I | Video | 1.C - 6, 10, 23 |
Lecture 4 | 1.C Subspaces II Writing Proofs |
Video | 1.C - 10, 19, 20 |
Lecture 5 | 2.A Span and Linear Independence I |
Video | 2.A - 2, 3, 7 |
Week 3 (Sep 16-20) | |||
Homework: Assignment 2 (Due Sep 20) | |||
Lecture 6 | 2.A Span and Linear Independence II | Video | 2.A - 3, 13 |
Lecture 7 | 2.B Bases | Video | 2.B - 3, 7, 10 |
Lecture 8 | 2.C Dimension | Video | 2.C - 11, 14, 17 |
Week 4 (Sep 23-27) | |||
Homework: Assignment 3 (Due Sep 27) | |||
Lecture 9 | 3.A Vector Space of Linear Maps | Video | 3.A - 2, 4, 7 |
Lecture 10 | 3.B Null Spaces and Ranges I | Video | 3.B - 2, 6, 9 |
Lecture 11 | 3.B Null Spaces and Ranges II 3.C Matrices |
Video | 3.C -2, 5, 6 |
Week 5 (Sep 30-Oct 4) | |||
Homework: Study for Midterm 1 (Oct 4) | |||
No class Sep 30 | |||
Lecture 12 | 3.D Invertibility and Isomorphic Vector
Spaces I |
Video | 3.D - 2, 3, 5 |
Lecture 13 | Midterm 1 (Oc. 4) | ||
Week 6 (Oc 7-11) | |||
Homework: Assignment 4 (Due Oct 15) | |||
Lecture 14 | 3.D Invertibility and Isomorphic Vector Spaces II |
Video | 3.D - 11, 14, 15 (Hint: why is T invertible?) |
Lecture 15 | 4 Polynomials | Video | 4 - 4, 5, 6 |
Lecture 16 | 5.A Invariant Subspaces I | Video | 5.A - 7, 8, 9 |
Week 7 (Oct 14-18) | |||
Reading Week (No Classes) | |||
Week 8 (Oct 21-25) | |||
Homework: Assignment 5 (Due Oct 25) | |||
Lecture 17 | 5.A Polynomials Applied to Operators 5.B Minimal Polynomials |
Video | 5.A - 2, 5, 21, 23 |
Lecture 18 | 5.B Minimal Polynomials | No Video | 5.B - 1, 3, 4 |
Lecture 19 |
5.B Minimal Polynomials II | No Video | 5.B - 6, 10, 11 |
Week 9 (Oct 28-Nov 1) | |||
Homework: Assignment 6 (Due Nov 1) | |||
Lecture 20 | 5.C Upper Triangular Matrices | Video Based on 5.B in 3rd ed |
5.C - 1, 3, 6, 8 |
Lecture 21 | 5.D Diagonalizable Opeators | Video Based on 5.C in 3rd ed |
5.D - 2, 3, 5, 7 |
Lecture 22 | 8.A Generalized Eigenvectors and Nilpotent Operators I |
Video | 8.A - 4, 6, 7, 8 |
Week 10 (Nov 4 -Nov 8) | |||
Homework: Assignment 7 (Due Nov 8) | |||
Lecture 23 | 8.A Generalized Eigenvectors and Nilpotent Operators II |
Video | 8.A - 12, 13, 17, 21 |
Lecture 24 | 8.B Generalized Eigenspace Decomposition | Video | 8.B - 2, 4, 5 |
Lecture 25 | 8.B Generalized Eigenspace Decomposition II | Video | 8.B - 7, 9, 11, 12 | Other | Videos based upon third edition may also be useful, including material on the minimal and characteristic polynomial |
Video Video Video |
Week 11 (Nov 11-15) | |||
Homework: Study for Midterm 2 (Nov 15) | |||
Lecture 26 | 6.A Inner Products and Norms I | Video | 6.A - 3, 4, 5, 9 |
Lecture 27 | 6.A Inner Products and Norms II | Video | 6.A - 13, 17, 21, 26 |
Lecture 28 | Midterm II (Nov 15) | ||
Week 12 (Nov 18-22) | |||
Homework: Assignment 8 (Nov 22) | |||
Lecture 29 |
6.B Orthonormal Bases | Video | 6.B - 2a, 3, 7, 8a |
Lecture 30 | 6.B Linear Functionals | Video | 6.B - 11, 12 |
Lecture 31 | 6.C Orthogonal Complements and Minimization |
No Video | 6.C - 1, 2, 3, 5 |
Week 13 (Nov 25-29) | |||
Homework: nothing due this week, next assingmet due next Monday | |||
Lecture 32 | 7.A Self-Adjoint and Normal Operators I | Video | 7.A - 1, 2, 3 |
Lecture 33 | 7.A Self-Adjoint and Normal Operators II | Video | 7.A - 6, 7, 15 |
Lecture 34 | 7.B The Spectral Theorem | Video | 7.B - 1, 2, 10, 14 |
Week 14 (Dec 2-4) | |||
Homework: Assignment 9 (Due Dec 2) | |||
Lecture 35 | 5.D - Gershgorin Disk Theorem | No video | |
Lecture 36 | Buffer/Review | No video |
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There will be nine homework assignments (your lowest two marks will be dropped). Assignments are posted below. Assignments will be submitted via Crowdmark. You will receive an email to your McMaster account that you will use to upload your assignment. All assignments due by 11:59PM on the due date.
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All class handouts are available as PDF files (except where indicated)
Course Information
Course handout describing the course (available online)
Midterm 1 Review Sheet
Handout describing first midterm.
Midterm 2 Review Sheet
Handout describing second midterm.
Exam Review Sheet
Handout describing final exam.
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Weighting 1
20% = 9 Assignments (best 7 used)
40% = Midterms (2 x 20%)
40% = Final Exam
Weighting 2
20% = 9 Assignments (best 7 used)
20% = Maximum of Midterm 1 and 2
60% = Final Exam
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With respect to MSAFs, missed work will be moved to final, as described in the course outline.
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