Math 1B03 -- Linear Algebra I
(Fall 2016)
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Course Information
Instructor: Adam Van Tuyl
Office: Hamilton Hall 419
Office Hours: Monday 9:30-10:20, Friday 11:30-12:20
Email: vantuyl@math.mcmaster.ca
Place and Time:
Class C01: Monday, Wednesday 8:30-9:20 and Friday 10:30-11:20 in HSC (Health Science Centre) 1A1
Tutorial T01: Tu 1:30PM - 2:20PM in HH/302
Tutorial T02: Tu 12:30PM - 1:20PM in HH/302
TA: The TA for the course is Sean Conley [conleyst@math.mcmaster.ca]. He will be running both tutorials.
Textbook:
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Elementary Linear Algebra: Applications Version 11th Edition
by Howard Anton, Chris Rorres - We will also use Chapter 10 of the 9th Edition of this textbook on complex numbers.
News (Last Updated: December 6, 2016)
Below is a summary of what we did in class, plus any relevant
news and/or information.
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FINAL EXAM Information
The final for Math 1B03 will be on Wednesday Dec. 14, 2016 at 12:30PM. Please find a review sheet below:
Here are some practice tests.
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Please take a couple of minutes to fill in the course
evaluations at
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| MIDTERM Solutions
Here are the
You can find your mark for the midterms through the homework portal.
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The bookstore has a
guarenteed buyback program. At the end of the semester, they will
buy your book (only the 11th edition) back at $80 if you sell
it to them before December 20.
Here is a summary of what we did in each class:
- December 7, 2016 Today was our last class. I had some review questions and discussed the final exam.
- December 5, 2016 We looked at an application of linear algebra today -- cryptography. See Section 10.14. Please note that in the tutorial session tomorrow, the TA will treat it as a drop-in session where you can ask questions.
- December 2, 2016 Today we finished up Sections 4.7 and 4.8. I introduced both the column space and row space of a matrix, how to find a basis for each vector space, and how to find its dimension. I then discussed the rank-nullity theorem.
- November 30, 2016 We finished our discussion of dimension and I talked about the null space of a matrix (see Section 4.7). Note that we are skipping Section 4.6.
- November 28, 2016 Today I explained how to use the Gram-Schmidt process to turn any basis into an orthogonal basis. I also started a discussion on dimension (Section 4.5).
- November 24, 2016 We started Section 6.3 on the Gram-Schmidt process. Today, I focused on the definitions of orthogonal and orthornormal, and I discussed some of their properties.
- November 23, 2016 Today we continued talking about bases, and we discussed the idea of a coordinates (see Section 4.4).
- November 21, 2016 We finished Section 4.3 on linear independence. In the last half of class, I introduced the notion of a basis, and gave some examples (see Section 4.4).
- November 18, 2016 Today we had our first class on linear independence (see Section 4.3). Please note that office hours will be cancelled today. As well, I probably won't be able to post the sides until Monday.
- November 16, 2016 We finished up Section 4.2 on subspaces. I showed that eigenspaces are subspaces. Also, I introduced the notion of a spanning set.
- Noveber 14, 2016 Today we looked at subspaces of a vector space. You should know how to decide whether a subset is a subspace or not. I also introduced the vector space of polynomials.
- November 11, 2016 We started Section 4.1 on vector spaces. I explained the definition and gave a bunch of examples.
- November 9, 2016 Today we looked briefly at Section 3.4 on understanding the geometric meaning of solutions sets of linear equations. I also defined the cross product, and gave a geometric meaning to the determinant.
- November 7, 2016 In today's class we looked at Section 3.3 on orthogonality. You should know what it means for two vectors to be orthogonal, and you should know how to find the orthogonal projection on a line.
- November 4, 2016 We looked at Section 3.2 on distance and norm. I also introduced the Cauchy-Schwarz inequality.
- November 2, 2016 We started looking at Section 3.1 today (on vectors in n-space). Of special importance is the definition of linear combinations.
- October 31, 2016 Today was our last lecture on complex numbers and complex eigenvalues. During today's class I focused on Section 5.3 on the geometric meaning of complex eigenvalues.
- October 28, 2016 We continued our discussion of complex numbers. I discussed the properties of the conjugate and modulus. I also introduced complex matrices. We also talked about the polar form of a complex number. See Section 10.2 (9th edition) and Section 5.3 for more.
- October 26, 2016 We began our three part discussion on on complex numbers. For our source material, please see Chapter 10 of the 9th edition (a free pdf version is given above). You should know how to add, subtract, multiple, and divide complex numbers. As well, you should know how to find complex eigenvalues and eigenvectors.
- October 24, 2016 We finished Section 5.5. We introduced regular Markov chains, and learned that regular Markov chains have a stable solution.
- October 21, 2016 Today we looked at dynamical systems (see Section 5.5). In particular, I introduced Markov chains, and how eigenvalues are related to the long term behaviour of a Markov chain.
- October 19, 2016 We finished up Section 5.2. In particular, I introduced the definition of the geometric multiplicity of an eigenvalue, and how to use this information to determine if a matrix was diagonalizable.
- October 17, 2016 Welcome Back - I hope you had a good break! Midterm 1 has now been graded. You can find your mark through the homework portal. In today's class we discussed diagonalization. In particular, we looked at Section 5.2; we will continue with this section on Wedneday's class.
- October 7, 2016 Last night we had the first midterm. It should be graded by the end of the week. Today, we continued our discussion on eigenvalues and eigenvectors (see Section 5.1).
- October 5, 2016 We jumped to Chapter 5 today. We will be spending the next couple of weeks looking at eigenvalues and eigenvectors. Today I started going over the material of Section 5.1.
- October 3, 2016 We went over Section 2.3 on properties of determinants, and I explained how to use Cramer's rule to solve systems of linear equations.
- Sept. 30, 2016 We went over Section 2.2. I explained how row operations change the determinant.
- Sept. 28, 2016 Today we started Chapter 2. We went over the material of Section 2.1 on how to compute the determinant of a matrix.
- Sept. 26, 2016 We went over Section 1.7 discussing some special families of matrices: diagonal, triangular, and symmetric.
- Sept. 23, 2016 In today's class we finished up Section 1.6. In particular, I discussed a number of equivalent ways to determine if a matrix is invertible, and I gave some examples of how we could use this result.
- Sept. 21, 2016 We finished up Section 1.5 (I explained what an elmentary matrix is) and then we started to discuss Section 1.6. I justified why a system of linear equations can only have 0, 1 or infinite number of solutions.
- Sept. 19, 2016 Today we looked at Section 1.5 on finding the inverse of a matrix. I described the algorithm to find the inverse. I also showed everyone WolframAlpha
- Sept. 16, 2016 We finished the material of Section 1.4 by going over some of the properties of transposes and inverses. I also explained the connection of invertible matrices and unqiue solutions.
- Sept. 14, 2016 Today we went over the material of Section 1.4. Specifically, I discussed some of the properties matrices share with integers and real numbers. I also introduced the inverse of a matrix; this idea will play a key role in future discussions.
- Sept. 12, 2016 In today's class we spent some time going over Section 1.3 on matrix operations. In particular, you should know how to to add and multiply matrices together. Note that the tutorials start tomorrow (Tuesday).
- Sept. 9, 2016 Today's class went over Section 1.2 on Gaussian elimination. The material of this section is important for the rest of the course, so it is very important you understand it. Know how to row reduce a matrix to reduced row echelon form, and how to use this form to determine the number of solutions.
- Sept. 7, 2016 In today's class we went over the course outline. I also introduced systems of linear equations (see Section 1.1).
- Sept. 6, 2016 Welcome to McMaster! Our first day of class is tomorrow. Please note that labs will start next week Tuesday.
- July 13, 2016 Just setting up the web page. Please come back!
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Homework, Labs, and Practice Assignments
HOMEWORK:
There will be five assignments made available through online submission.
They will be automatically graded if submitted before the deadline expires.
You can access the assignments though this portal:
LABS:
There will be five labs which will require the use of Matlab (version 7 or later). These will be submitted using the online lab system. You can access the assignments though this portal:
Handouts
All class handouts are available as PDF files.
Course Information
Course handout from first day of class (to be added)
Midterm 1 Review Sheet
Handout describing first midterm.
Midterm 2 Review Sheet
Handout describing second midterm.
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Grading Scheme
Your final mark is broken down as:
10% = Assignments (5 x 2%)
10% = Labs (5 x 2%)
40% = Midterms (2 x 20%)
40% = Final Exam
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Schedule
We will be using the following schedule. Please note that there may be changes; always refer to the news section above for most
recent information.
| Week 1: September 5-9 |
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| No Tutorials, Assignments, or Labs |
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| Lecture 1 |
Introduction 1.1 Systems of Linear Equations |
| Lecture 2 |
1.2 Gaussian Elimination |
| Week 2: September 12-16 | |
| ASSIGNMENT #1: Due at 11:59PM on Friday Sept. 16 |
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| Lecture 3 |
1.3 Matrices and Matrix Operations |
| Lecture 4 |
1.3 Matrices and Matrix Operations (Continued) 1.4 Inverses, Properties of Matrices |
| Lecture 5 |
1.5 Inverses, Properties of Matrices (Continued) |
| Week 3: September 19-23 | |
| LAB #1 (Matlab): Due at 11:59PM on Friday Sept. 23 |
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| Lecture 6 |
1.5 Elementary Matrices |
| Lecture 7 |
1.5 Elementary Matrices (Contiued) 1.6 More Linear Systems and Invertible Matrices |
| Lecture 8 |
1.6 More Linear Systems and Invertible Matrices (Continued) |
| Week 4: September 26-30 | |
| ASSIGNMENT #2: Due at 11:59PM on Friday Sept. 30 |
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| Lecture 9 |
1.7 Diagonal, Triangular, and Symmetric Matrices
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| Lecture 10 |
2.1 Determinant by Cofactor Expansion
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| Lecture 11 |
2.2 Evaluating Determinants by Row Reduction
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| Week 5: October 3-7 | |
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MIDTERM #1: Evening of Thursday, October 6 LAB #2 (Matlab): Due at 11:59PM on Friday Oct. 7 |
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| Lecture 12 |
2.3 Properties of Determinants (including Cramer's Rule)
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| Lecture 13 |
5.1 Eigenvalues and Eigenvectors
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| Lecture 14 |
5.1 Eigenvalues and Eigenvectors (Continued)
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| Week 6: October 10-14 | |
| FALL BREAK - no classes
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| Week 7: October 17-21 | |
| ASSIGNMENT #3: Due at 11:59PM on Friday Oct. 21 |
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| Lecture 15 |
5.2 Diagonalization
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| Lecture 16 |
5.2 Diagonalization (Continued)
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| Lecture 17 |
5.5 Dynamical Systems
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| Week 8: October 24-28 | |
| LAB #3 (Matlab): Due at 11:59PM on Friday Oct. 28 |
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| Lecture 18 |
5.5 Dynamical Systems (Continued)
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| Lecture 19 |
10.1 (from 9th Edition) Complex Numbers
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| Lecture 20 |
10.2 (from 9th Edition) Division of Complex Numbers
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| Week 9: October 31-November 4 | |
| ASSIGNMENT #4: Due at 11:59PM on Friday Nov. 4 |
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| Lecture 21 |
10.3 (from 9th Edition) Polar Form of a Complex Number
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| Lecture 22 |
3.1 Vectors in 2-space, 3-space and n-space
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| Lecture 23 |
3.2 Norm, Dot product, and Distance in R^n
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| Week 10: November 7-11 | |
| MIDTERM #2: Evening of Thursday Nov. 10 |
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| Lecture 24 |
3.3 Orthogonality 3.4 The Geometry of Linear Systems |
| Lecture 25 |
3.4 The Geometry of Linear Systems (Continued)
3.5 Cross Product
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| Lecture 26 |
4.1 Real Vector Spaces
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| Week 11: November 14-18 | |
| LAB #4 (Matlab): Due at 11:59PM on Friday Nov. 18 |
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| Lecture 27 |
4.1 Real Vector Spaces (Continued) 4.2 Subspaces |
| Lecture 28 |
4.2 Subspaces (Continued)
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| Lecture 29 |
Linear Independence
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| Week 12: November 21-25 | |
| ASSIGNMENT #5: Due at 11:59PM on Friday Nov. 25 |
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| Lecture 30 |
4.3 Linear Independence (Continued) 4.4 Coordinates and Basis |
| Lecture 31 |
4.4 Coordinates and Basis (Continued)
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| Lecture 32 |
6.3 Gram-Schmidt Process
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| Week 13: November 28-December 2 | |
| LAB #5 (Matlab): Due at 11:59PM on Friday Dec. 2 |
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| Lecture 33 |
6.3 Gram-Schmidt Process (Continued)
4.5 Dimension
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| Lecture 34 |
4.5 Dimension (Continued) 4.7 Row Space, Column Space, and Null Space |
| Lecture 35 |
4.7 Row Space, Column Space, and Null Space (Continued)
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| Week 14: December 5-7 | |
| Lecture 36 |
10.15 Cryptography
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| Lecture 37 |
10.15 Cryptograph (Continued) Review |
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Class Polices
1. Policy on Academic Ethics. You are expected to exhibit honesty and use ethical behaviour in all aspects of the learning process. Academic credentials you earn are rooted in principles of honesty and academic integrity.
Academic dishonesty is to knowingly act or fail to act in a way that
results or could result in unearned academic credit or advantage. This
behaviour can result in serious consequences, e.g. the grade of zero
on
an assignment, loss of credit with a notation on the transcript
(notation reads: Grade of F assigned for academic dishonesty),
and/or suspension or expulsion from the university.
It is your responsibility to understand what constitutes academic
dishonesty. For information on the various types of academic
dishonesty
please refer to the Academic Integrity Policy, located at:
http://www.mcmaster.ca/academicintegrity/
The following illustrates only three forms of academic dishonesty:
- plagiarism, e.g. the submission of work that is not one's own or for which other credit has been obtained.
- improper collaboration in group work,
- copying or using unauthorized aids in tests and examinations.
2. Policy regarding missed work.
If you have missed work, it is your responsibility to take action.
If you are absent from the university for
medical and non-medical (personal) situations,
lasting fewer than 3 days, you may report your absence, once per term,
without documentation, using the McMaster Student Absence Form
(MSAF). See
Requests
for Relief for Missed Academic Term Work
Absences for a longer duration or for other reasons must be reported
to
your Faculty/Program office, with documentation, and relief from term
work
may not necessarily be granted.
In Math 1B03, the percentages of the missed work will be
transferred
to the final examination.
Please note that the MSAF may not be used for term work worth 25% or
more,
nor can it be used for the final examination.
3. Student Accessibility Services.
Students who require academic accommodation must contact Student
Accessibility
Services (SAS) to make arrangements with a Program Coordinator.
Academic accommodations must be arranged for each term of study.
Student Accessibility Services can be contacted by phone
905-525-9140 ext. 28652 or e-mail sas@mcmaster.ca.
For further information, consult McMaster University's Policy for
Academic Accommodation of Students with Disabilities.
4. Important Message.
The instructor and university reserve the right to modify elements of
the course during the term. The university may change the dates and
deadlines for any or all courses in extreme circumstances. If either
type of
modification becomes necessary, reasonable notice and communication
with the students will be given with explanation and the opportunity
to
comment on changes. It is the responsibility of the student to check
their McMaster email and course websites weekly during the term and
to note any changes.
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