Math 101: Graduate Linear Algebra

Fall 2017

 

Course Info:

 

Syllabus:

We follow the official Math 101 syllabus, but we will not cover group theory.

[PDF] Syllabus

Linear algebra
111 Sep(M)Introduction; Definitions and basic theoryDF section 11.1
FIS chapter 1
WS 1 [TeX] [PDF]
Daily HW 1 [TeX] [PDF]
212 Sep(T)Infinite-dimensional vector spacesDF appendix I.2
FIS section 1.7
313 Sep(W)The matrix of a linear transformationDF section 11.2Daily HW 3: DF 11.2.11
415 Sep(F)Dual vector spacesDF section 11.3
FIS section 2.6
Daily HW 4 [TeX] [PDF]
Weekly HW 1 [TeX] [PDF]
518 Sep(M)AnnihilatorsFIS section 2.6
Roman pp. 101-107
Daily HW 5 [TeX] [PDF]
620 Sep(W)Tensor products
722 Sep(F)Normal and self-adjoint operators
-25 Sep(M)No class: JV in Banff
-27 Sep(W)No class: JV in Banff
829 Sep(F)Unitary and orthogonal operators
92 Oct(M)Orthogonal projections and the spectral theorem
103 Oct(T)Singular value decomposition (SVD)
114 Oct(W)Bilinear and quadratic forms
Modules
126 Oct(F)Basic definitions and examplesDF section 10.1
139 Oct(M)Quotient modules and module homomorphismsDF section 10.2
1411 Oct(W)Generation of modules, direct sums, and free modulesDF section 10.3
-12 Oct(R)Midterm exam, covering linear algebra
(4:00-6:00 p.m.)
1513 Oct(F)Tensor products of modulesDF section 10.4
1616 Oct(M)Exact sequencesDF section 10.5
1717 Oct(T)Diagram chases
1818 Oct(W)Projective modulesDF section 10.5
1920 Oct(F)Projective modulesDF section 10.5
2023 Oct(M)Injective modulesDF section 10.5
2125 Oct(W)LocalizationDF sections 7.5, 15.4
Modules over PIDs, canonical forms
2227 Oct(F)The basic theoryDF section 12.1
2330 Oct(M)Examples and applications
241 Nov(W)Smith normal form
253 Nov(F)Rational canonical formDF section 12.2
266 Nov(M)Jordan canonical formDF section 12.3
277 Nov(T)TBD
Category theory
288 Nov(W)CategoriesDF Appendix II
2910 Nov(F)Functors
3013 Nov(M)Natural transformations, applications
Wrap-up
3114 Nov(T)Wrap-up
-17 Nov(F)Final exam, comprehensive
(8:00 a.m.-11:00 a.m.)

 

Homework:

The homework assignments will be assigned on a daily basis and weekly basis and will be posted above.

Daily homework is due the following class period: we will discuss the problem in class, and you will self-assess in red pen. At the end of the term, all daily homework will be collected, with a short concluding self-assessment.

Weekly homework is due as indicated, and will collected and graded in the usual manner.

Cooperation on homework is permitted (and encouraged), but if you work together, do not take any paper away with you--in other words, you can share your thoughts (say on a blackboard), but you have to walk away with only your understanding. In particular, you must write the solution up on your own. Please acknowledge any cooperative work at the end of each assignment.

Plagiarism, collusion, or other violations of the Academic Honor Principle, after consultation, will be referred to the The Committee on Standards.

[PDF] Homework Submission Guidelines