Math 1B03 -- Linear Algebra I
(Fall 2017)
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Course Information
Instructor: Adam Van Tuyl
Office: Hamilton Hall 419
Office Hours: Monday 9:30-10:20, Wednesday 2:30-3:20
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 Homayun Karimi (Tutorials start Tuesday, Sept 12, 2017)
Textbook:
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Elementary Linear Algebra: Applications Version 11th Edition
by Howard Anton, Chris Rorres
Note that if you buy this book new at the bookstore, the bookstore will guarentee to buy it back for $90.00 (if you return it by Dec. 21, 2017). - We will also use Chapter 10 of the 9th Edition of this textbook on complex numbers.
News (Last Updated: Dec. 20, 2017)
Below is a summary of what we did in class, plus any relevant
news and/or information.
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FINAL EXAM Information
You can see your mark on the final exam on the homework portal. Your final mark will be available on MOSAIC. |
Here is a summary of what we did in each class:
- Dec. 20, 2017 Final marks have been submitted. Have a great break!
- Dec. 15, 2017 Day of Final!
- Dec. 4, 2017 We learned how to find the basis of the row and column spaces. We also learned about the rank-nullity theorem. Here's a video.
- Dec. 1, 2017 Today we went back to Chapter 4 (Section 4.5) and talked about the dimension of a vector space. We also looked at the dimension of a null space of a matrix.
- Nov. 29, 2017 We finished Section 6.3 by describing the Gram-Schmidt process. Here's a video on the process.
- Nov. 27, 2017 We jumped to Section 6.3 to discuss the Gram-Schmidt process. Today we focused on orthogonal and orthonormal bases. Here's a video.
- Nov. 24, 2017 I talked about Section 4.4 on how to determine the coordinates of a vector relative to a basis.
- Nov. 22, 2017 We finished Section 4.3, and started our discussion on bases of vector spaces. Here's a helpful video.
- Nov. 20, 2017 Today we started Section 4.3 on sets of linearly independent vectors.
- Nov. 17, 2017 We finished our discussion on subspaces, and I introduced spanning sets.
- Nov. 15, 2017 We discussed subspaces today (see Section 4.2). I also introduced the vector space of polynomials. Here's a video about subspaces in R^2.
- Nov. 13, 2017 We started Chapter 4 on Vector Spaces. Make sure you carefully read Section 4.1, and know the examples of vector spaces.
- Nov. 10, 2017 We continued our discussion of the geometry of linear algebra, and we went over the cross product. We talked about the geometric meaning of the determinant. Here's a lecture on the cross product.
- Nov. 8, 2017 We looked at Section 3.3 and 3.4; we focused on the orthogonal project and the distance between planes and lines. Here's a video that gives a proof of the projection formula.
- Nov. 6, 2017 We finished up Section 3.2 on the norm and dot product, and we started Section 3.3 on orthogonality. Here's a helpful video.
- Nov. 3, 2017 Today we started Chapter 3. I introduced n-space and went over some of its properties. I also introduced ideas such as linear combinations and the norm of a vector.
- Nov. 1, 2017 We finished our last lecture on complex numbers. I spent today's class explaining the geometric implication (rotation) of complex eigenvalues.
- Oct. 30, 2017 We had our second lecture on complex numbers. I explained some of the properties of the conjugate and the modulus. I also introduced the polar form of a complex number.
- Oct. 27, 2017 In today's class, we started our introduction to complex numbers. You should know how to add, subtract, multiply, and divide complex numbers. As well, you should be able to find complex eigenvalues and eigenspaces involving complex numbers. Here's an video introduction to complex numbers.
- Oct. 25, 2017 We finished our discussion on dynamical systems. You should know what a regular stochastic matrix is, and how to determine the limit of a regular Markov chain.
- Oct. 23, 2017 We started Section 5.5 on dynamical systems.
- Oct. 20, 2017 We finished up Section 5.2 on diagonalization. We learned about algebraic multiplicity and geometric multiplicity, and how to use this information to determine if a matrix is diagonalizable.
- Oct. 18, 2017 Today we learned about diagonalizing a matrix (see Section 5.2 for more details). Here is a video tutorial.
- Oct. 16, 2017 We finished Section 5.1; we discussed the characteristic equation and how to use this equation to find eigenvalues of a matrix, and how to find eigenvectors. Here is a video.
- Oct. 6, 2017 We started Chapter 5 on eigenvalues and eigenvectors. I introduced these concepts with some simple examples (see Section 5.1). Note that the midterm marks will be posted by next week Tuesday. Have a good break!
- Oct. 4, 2017 In class we went over some properties of the determinant. I also introduced the adjoint and Cramer's rule. See Section 2.3. Here's a video on Cramer's rule. The first midterm was today.
- Oct. 2, 2017 We went over Section 2.2 which discussed how row operations change the determinant of a matrix. Here is a related video.
- Sept. 29, 2017 We began our discussion of Chapter 2 by going over the definition of a determinant. Here are some videos that explain how to compute the determinant: Video 1, Video 2, and Video 3
- Sept. 27, 2017 Today I introduced special types of matrices, like diagonal matrices, upper/lower triangular matrices, and symmetric matrices. For more, see Section 1.7. Note that the first midterm covers up to today's lecture.
- Sept. 25, 2017 We focused on the remainder of Section 1.6. We discussed a classification of invertible matrices, and further properties of invertible matrices.
- Sept. 22, 2017 We finished Section 1.5; in particular, we went over elementary matrices, and explained how they can be used to justify the inverse algorithm. We also started Section 1.6 to explain why inverse matrices are important when looking for system of linear equations.
- Sept. 20, 2017 Today we started Section 1.5. I explained the procedure to find the inverse of a matrix. Here is a video that also explains this procedure.
- Sept. 18, 2017 We finished Section 1.4 on the algebraic properties of matrices.
- Sept. 15, 2017 We went over the arithmetic properties of matrices. See Section 1.4 for more details.
- Sept. 13, 2017 Today we went over operations involving matrices (e.g., addition, scalar multiplication, multiplying matrices). Here is a video on matrix multiplication.
- Sept. 11, 2017 We finished our discussion of Gaussian elimination (Section 1.2). I focused on how to determine the number of solutions from the echelon form. I also introduced Matlab and explained how to do the homework. Here's another video on elimination that also uses Matlab.
- Sept. 7, 2017 I introduced Gaussian elimination (see Section 1.2). It is important you learn this procedure. Here is an online video and another video.
- Sept. 6, 2017 Today was the first day of classes. I handed out the course outline, and I went over the goals of the course. I also introduced system of linear equations (see Section 1.1).
- August 31, 2017 Please note that there are no labs or tutorials during the first week of classes. We will meet next week Wednesday at 8:30 in class.
- August 10, 2017 More information has been added to the webpage, including the course handout.
- July 31, 2017 Today I started working on the webpage. Please check back as more information is added.
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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
Midterm 1 Review Sheet
Handout describing first midterm.
Midterm 2 Review Sheet
Handout describing second midterm.
Final Exam Review Sheet
Handout describing final exam.
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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 4-8 |
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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 I |
| Week 2: September 11-15 | |
| ASSIGNMENT #1: Due at 11:59PM on Friday Sept. 15 NOTE: Matlab TA is available this week |
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| Lecture 3 |
1.2 Gaussian Elimination II |
| Lecture 4 |
1.3 Matrices and Matrix Operations |
| Lecture 5 |
1.3 Matrices and Matrix Operations (Continued) 1.4 Inverses, Properties of Matrices |
| Week 3: September 18-22 | |
| LAB #1 (Matlab): Due at 11:59PM on Friday Sept. 22 |
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| Lecture 6 |
1.4 Inverses, Properties of Matrices (Continued) |
| Lecture 7 |
1.5 Elementary Matrices |
| Lecture 8 |
1.5 Elementary Matrices (Contiued) 1.6 More Linear Systems and Invertible Matrices |
| Week 4: September 25-29 | |
| ASSIGNMENT #2: Due at 11:59PM on Friday Sept. 29 NOTE: Matlab TA is available this week |
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| Lecture 9 |
1.6 More Linear Systems and Invertible Matrices (Continued) |
| Lecture 10 |
1.7 Diagonal, Triangular, and Symmetric Matrices
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| Lecture 11 |
2.1 Determinant by Cofactor Expansion
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| Week 5: October 2-6 | |
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MIDTERM #1: Evening of Wednesday, October 4 LAB #2 (Matlab): Due at 11:59PM on Friday Oct. 6 |
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| Lecture 12 |
2.2 Evaluating Determinants by Row Reduction
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| Lecture 13 |
2.3 Properties of Determinants (including Cramer's Rule)
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| Lecture 14 |
5.1 Eigenvalues and Eigenvectors
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| Week 6: October 9-13 | |
| FALL BREAK - no classes
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| Week 7: October 16-20 | |
| ASSIGNMENT #3: Due at 11:59PM on Friday Oct. 20 |
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| Lecture 15 |
5.1 Eigenvalues and Eigenvectors (Continued)
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| Lecture 16 |
5.2 Diagonalization
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| Lecture 17 |
5.2 Diagonalization (Continued)
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| Week 8: October 23-27 | |
| LAB #3 (Matlab): Due at 11:59PM on Friday Oct. 27 NOTE: Matlab TA is available this week |
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| Lecture 18 |
5.5 Dynamical Systems
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| Lecture 19 |
5.5 Dynamical Systems (Continued)
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| Lecture 20 |
10.1 (from 9th Edition) Complex Numbers
10.2 (from 9th Edition) Division of Complex Numbers |
| Week 9: October 30-November 3 | |
| ASSIGNMENT #4: Due at 11:59PM on Friday Nov. 3 |
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| Lecture 21 |
10.2 (from 9th Edition) Division of Complex Numbers
10.3 (from 9th Edition) Polar Form of a Complex Number |
| Lecture 22 |
5.3 Complex Eigenvalues and Eigenvectors
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| Lecture 23 |
3.1 Vectors in 2-space, 3-space and n-space
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| Week 10: November 6-10 | |
| MIDTERM #2: Evening of Wednesday Nov. 8 |
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| Lecture 24 |
3.2 Norm, Dot product, and Distance in R^n
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| Lecture 25 |
3.3 Orthogonality 3.4 The Geometry of Linear Systems |
| Lecture 26 |
3.4 The Geometry of Linear Systems (Continued)
3.5 Cross Product
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| Week 11: November 113-17 | |
| LAB #4 (Matlab): Due at 11:59PM on Friday Nov. 17 NOTE: Matlab TA is available this week |
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| Lecture 27 |
4.1 Real Vector Spaces
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| Lecture 28 |
4.1 Real Vector Spaces (Continued) 4.2 Subspaces |
| Lecture 29 |
4.2 Subspaces (Continued)
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| Week 12: November 20-24 | |
| ASSIGNMENT #5: Due at 11:59PM on Friday Nov. 24 |
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| Lecture 30 |
4.3 Linear Independence
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| Lecture 31 |
4.3 Linear Independence (Continued) 4.4 Coordinates and Basis |
| Lecture 32 |
4.4 Coordinates and Basis (Continued)
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| Week 13: November 27-December 1 | |
| LAB #5 (Matlab): Due at 11:59PM on Friday Dec. 1 NOTE: Matlab TA is available this week |
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| Lecture 33 |
6.3 Gram-Schmidt Process
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| Lecture 34 |
6.3 Gram-Schmidt Process (Continued)
4.5 Dimension
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| Lecture 35 |
4.5 Dimension (Continued) 4.7 Row Space, Column Space, and Null Space |
| Week 14: December 4-6 | |
| Lecture 36 |
4.7 Row Space, Column Space, and Null Space (Continued)
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| Lecture 37 |
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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