MAT240F Algebra I
Classes: T11-1, R12;
Room: HS610. (Health Sciences, 155 College Street)
Midterm exam: T11-1 on October 18 , 2016, in EX 200
This course is an introduction to linear algebra, aimed at students in our specialist programs.
Text Book: Our text book will be Linear Algebra (fourth edition) by Friedberg, Insel and Spence,
Prentice Hall; it is a required reading.
Abstract (from Academic Calendar):
A theoretical approach to: vector spaces over arbitrary fields, including C and Z_p. Subspaces, bases and dimension. Linear transformations, matrices, change of basis, similarity, determinants. Polynomials over a field (including unique factorization, resultants). Eigenvalues, eigenvectors, characteristic polynomial, diagonalization. Minimal polynomial, Cayley-Hamilton theorem.
Prerequisite: High school level calculus
The required homework problems for this course will be sent online, via
Crowdmark. You will be asked to submit the solutions electronically, via
Crowdmark. (More information will be given later.)
Our late policy is as follows: No late assignments will be accepted.
You can certainly discuss homework with classmates, but you have to write up the solutions yourself, in your own words.
Otherwise it is considered unauthorized aid or assistance (working
too closely with another student on an individual assignment so that the
end result is too similar), which is an academic offence under the University's
Code of Behaviour on Academic Matters. If you find
the solutions in books or on the internet, you must quote your source (and
still write it up in your own words!) Otherwise, it may count as
plagiarism which again is an academic offense.
Here is a sample latex source file
and its pdf output for download, in case you want to type up your solutions in latex and need some hints.
Below, in the `Calendar', I will give a few additional problems
(not to be handed in), required readings, and additional references.
Week 1: September 11-15, 2016.
Week 2: September 18-22, 2016.
Week 3: September 25-29, 2016.
Week 4: October 3-7, 2016
Week 5: October 10-14, 2016.
Week 6: October 17-21, 2016
Week 7: October 24-28, 2016
Week 8: October 31- November 4
Week 12: November 30 - December 6
Required reading: Section 4.2-4.4. My approach to determinants is a bit different from the textbook, so you should also review
my notes (posted on Blackboard, under course materials).
Additional homework (do not hand in).
- Section 4.2, problems 1, 2, 5, 7, 9, 11. Also compute the last few determinants using the method explained on p. 234 (using that the determinant of an upper/lower triangular matrix is the product of diagonal entries).
- Section 4.3, problems 22. (We've encountered the Vandermonde matrix as the change-of-basis matrix from the standard basis of polynomials to the basis given by Lagrange polynomials. Now it's time to calculate its determinant.)
- Section 4.3, problem 28, Section 4.4, problem 1, Section 4.5, problems 3-10
Tuesday, December 6 is last day of classes. The tutorials will take place until that date.
The final exam is scheduled for Saturday, December 17. See
Exam Schedule for details. The exam can cover anything that was covered during this course. It will be a mix of computational and theoretical questions. To prepare, I recommend looking at MAT240 final exams from earlier years, e.g.
and so on. Some other things:
Don't forget to bring your student ID!!
- We will not be using Crowdmark for the final exam; the exam booklets are provided.
It's a `no tools are allowed' exam. Especially, no calculators, no electronic gadgets of any sort, no formula sheets.
- If anything is unclear on the exam, feel free to ask.
- The exam will include a T/F question, similar to what was on the
F2014 final exam. You only have to decide whether the answer is T or F; no explanation is required. None of these questions are meant as `trick questions'. Again, if you find a question ambiguous or unclear, feel free to ask. (You can also add a small written explanation -- but normally it shouldn't be required.)
The exam will also include a `proof' question. To prepare for this, I recommend going over the `proof-style' homework
problems, and make sure you really understand them.
- Our TA's will hold some office hours before the exam. Details to
be announced via blackboard.
If there are any other questions regarding the upcoming exam, feel free to email.