Math 101: Graduate Linear Algebra

Fall 2017


Course Info:



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]
Weekly HW 1 solutions [TeX] [PDF]
518 Sep(M)AnnihilatorsFIS section 2.6
Roman pp. 101-107
Daily HW 5 [TeX] [PDF]
620 Sep(W)Tensor productsRoman chapter 14Daily HW 6 [TeX] [PDF]
722 Sep(F)Tensor products and bilinear formsRoman chapter 14Weekly HW 2 [TeX] [PDF]
Weekly HW 2 solutions [TeX] [PDF]
-25 Sep(M)No class: JV in Banff
-27 Sep(W)No class: JV in Banff
829 Sep(F)Adjoints, self-adjoint operators, inner productsFIS sections 6.1-6.3Daily HW 8 [TeX] [PDF]
92 Oct(M)Orthogonal, normal, and unitary operatorsFIS sections 6.4-6.5Daily HW 9 [TeX] [PDF]
103 Oct(T)Singular value decomposition (SVD)FIS section 6.7
114 Oct(W)Orthogonal projections and the spectral theoremFIS section 6.6Daily HW 11 [TeX] [PDF]
Weekly HW 3 [TeX] [PDF]
Weekly HW 3 solutions [TeX] [PDF]
126 Oct(F)Basic definitions and examplesDF section 10.1Daily HW 12 [TeX] [PDF]
139 Oct(M)Quotient modules and module homomorphismsDF section 10.2Daily HW 13 [TeX] [PDF]
1411 Oct(W)Generation of modules, direct sums, and free modulesDF section 10.3
-12 Oct(R)Midterm exam, covering linear algebra
(4:30-6:30 p.m., Kemeny 343)
Midterm exam solutions [TeX] [PDF]
1513 Oct(F)Tensor products of modulesDF section 10.4
1616 Oct(M)Tensor products, exact sequencesDF section 10.5Daily HW 16 [TeX] [PDF]
Weekly HW 4 [TeX] [PDF]
Weekly HW 4 solutions [TeX] [PDF]
1718 Oct(W)Diagram chasesDF section 10.5Daily HW 17 [TeX] [PDF]
1820 Oct(F)Projective modulesDF section 10.5Daily HW 18 [TeX] [PDF]
1923 Oct(M)Injective modules; rings of fractionsDF section 10.5Daily HW 19 [TeX] [PDF]
2025 Oct(W)LocalizationDF sections 7.5, 15.4Daily HW 20 [TeX] [PDF]
Weekly HW 5 [TeX] [PDF]
Weekly HW 5 solutions [TeX] [PDF]
2127 Oct(F)Localization and locally free modulesDaily HW 21 [TeX] [PDF]
Modules over PIDs, canonical forms
2230 Oct(M)Euclidean domains and PIDsDF sections 8.1-8.2Daily HW 22 [TeX] [PDF]
2331 Oct(T)UFDs, FTFGMPIDDF sections 8.1-8.2
DF section 12.1
241 Nov(W)Basic theory (FTFGMPID)DF section 12.1
253 Nov(F)Smith normal formDaily HW 25 [TeX] [PDF]
Weekly HW 6 [TeX] [PDF]
Weekly HW 6 solutions [TeX] [PDF]
266 Nov(M)Rational canonical formDF section 12.2Daily HW 26 [TeX] [PDF]
277 Nov(T)Noetherian rings
288 Nov(W)Jordan canonical form, applicationsDF section 12.3
Category theory and wrap-up
2910 Nov(F)Categories and functorsDF Appendix IIDaily HW 29 [TeX] [PDF]
3013 Nov(M)Natural transformations, wrap-up
-17 Nov(F)Final exam, comprehensive
(8:00 a.m.-11:00 a.m.) in Kemeny 108
Final exam solutions [TeX] [PDF]



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