NEWS November 2021

Our final exam is scheduled for Wednesday 8:30am December 15 in LIFE 2302 (a nice room in the old Student Union Building, from the photos of the room it appears each of you may have your own desk). Our exam is a 3 hour exam. I have arranged MATH ANNEX 1110 for December 14 from 10-12. And I will be available at some other times Dec 13,14.

advice for final Some students ask about how to study. One recommendation is to create some summary notes from what we have covered. Then reading assignments and your midterms come next. Try to figure out what you do wrong. I wonÕt entertain regrading at this point. Then you have two practice exams. Symmetric matrices should play a role.

topics

linear transformations (representation as matrices, matrix multiplication as function composition)

Gaussian elimination including vector parametric form.

Determinants (how to calculate, product rule)

Vector Spaces (linear independence, linear dependence, basis, dimension, extending a set of vectors to a basis)

Row Space, Column Space, Rank, Nullspace, nullity thm (how multiplication on left or right affects row and column spaces)

Change of Basis

Eigenvectors/Eigenvalues (eigenspace for lambda is nullspace(A-lambda I), dimension of eigenspace is at most multiplicity as a root in det(A-lambda I), similarity e.g. A similar to B, then det(A-lambda I)=det(B-lambda I), matrix is diagonalizable if sum of dimensions of eigenspaces in equal to size of matrix or each eigenspace dimension is equal to multiplicity as a root, examples of non diagonalizable matrices, applications of diagonalizability to computing powers etc, dominant eigenvectors/eigenvalues )

Differential equations (diagonalization, exponentiation of matrices, complex numbers)

Vector geometry (length of vector, dot product and angle between vectors, projections, Gram Schmidt process, orthogonal vectors, orthonormal bases)

Orthogonal vector spaces (orthogonal complement, projection onto a vector space using an orthonormal basis for the space)

Symmetric matrices (are diagonalizable, have real eigenvalues, have an orthonormal basis of eigenvectors, Hermitian definition)

Matrices for various linear transformations including rotation about an axis in 3-space We also has lectures on applications which would not be directly testable (Proof of partial fractions idea, Smolensky proof of bound of Sauer, Perles and Shelah and Vapnik and Chervonenkis, equiangular lines, Fourier coefficients, Wronksian, Petersen graph)

Welcome. This is an Honours level course that both covers the material of MATH 221 and MATH 152 but goes at a faster pace and adds some theoretical material. The grading standards (for me) are roughly those of MATH 221 and so some judicious scaling will be used. It will be substantially more work than MATH 221 but hopefully much more interesting.

Please note that this course cannot be taken for credit if you have already taken MATH 221 or MATH 152.

Our Section 101 meets 10:00-10:50 in Math Annex 1100. My office is nearby, Math Annex 1114.

I will be available for office hours MWF 11-12 and 12-1 after class and often at 1 as well. I and also have booked MATH 102 for special office hour/tutorial 5-6 Thursdays before assignments are due. Thus the first session will be Sept. 16. While I will be available for questions, I hope you begin talking to each other in that venue (but keep your masks on!).

I hope that the class will be almost entirely in person but Covid issues may intervene. Masks will be mandatory in classrooms. As a student, you won`t be able to eat in the classroom but can take brief sips of water if needed. I do hope students will continue to answer and ask questions in class but they will have to speak up more than usual. While vaccinations are not currently mandated, you will be restricted from number of activities without full vaccination. Planes/Trains for example or indoor restaurants (it does rain in Vancouver).

The room Math Annex 1100 has decent ventilation (they have tested this) and there are windows that can open to provide additional ventilation. I expect the midterms to be in person. We will have more information as the term begins.

For those unable to attend a lecture in person (surely you don`t wish to miss a lecture! But for example if some symptoms require you to self isolate. . . ), I typically post decent lecture notes after the fact. Attending in person is valuable for you.

Midterm 1 is scheduled for Friday October 8 (before the thanksgiving holiday) and Midterm 2 is scheduled for Wednesday Nov 17 after the fall break (Wednesday Nov 10 through Friday Nov 12).

Other Materials (in a kind of reverse order, recently added material first)