Math 101: Graduate Linear Algebra
Fall 2017
Course Info:
 Lectures: Monday, Wednesday, Friday, block 11 (11:30 a.m.  12:35 p.m.)
 xperiod: Tuesday, block 11X (12:151:05 p.m.)
 Dates: 11 September 2017  14 November 2017
 Room: Kemeny 201
 Instructor: John Voight
 Office: 341 Kemeny Hall
 Email: jvoight@gmail.com
 Office hours: Tuesdays, 1:152:15 p.m. or by appointment
 Course Web Page: http://www.math.dartmouth.edu/~m101f17/
 Prerequisites: A previous course in undergraduate algebra is strongly recommended.
 Required Text: David S. Dummit and Richard M. Foote, Abstract Algebra, 3rd ed., Wiley, 2003; see their errata.
 Recommended Texts:
 Stephen Friedberg, Arnold Insel, and Lawrence Spence, Linear algebra, 4th. ed., Pearson, 2002.
 Steven Roman, Advanced linear algebra, 3rd. ed., GTM vol. 135, 2007.
 Serge Lang, Algebra, 3rd. ed., GTM vol. 211, SpringerVerlag, 2005.
 Thomas Hungerford, Algebra, 8th ed., GTM vol. 73, SpringerVerlag, 2003.
 Paolo Aluffi, Algebra: Chapter 0, GSM, American Mathematical Society, 2009.
 Michael Artin, Algebra, 2nd. ed., Pearson, 2010.
 Grading: Grade will be based on daily homework (25%), weekly homework (25%), a midterm (25%), and a final exam (25%).
Syllabus:
We follow the official Math 101 syllabus, but we will not cover group theory.
[PDF] Syllabus
Linear algebra  
1  11 Sep  (M)  Introduction; Definitions and basic theory  DF section 11.1 FIS chapter 1  WS 1 [TeX] [PDF] Daily HW 1 [TeX] [PDF] 
2  12 Sep  (T)  Infinitedimensional vector spaces  DF appendix I.2 FIS section 1.7 

3  13 Sep  (W)  The matrix of a linear transformation  DF section 11.2  Daily HW 3: DF 11.2.11 
4  15 Sep  (F)  Dual vector spaces  DF section 11.3 FIS section 2.6  Daily HW 4 [TeX] [PDF] Weekly HW 1 [TeX] [PDF] Weekly HW 1 solutions [TeX] [PDF] 
5  18 Sep  (M)  Annihilators  FIS section 2.6 Roman pp. 101107  Daily HW 5 [TeX] [PDF] 
6  20 Sep  (W)  Tensor products  Roman chapter 14  Daily HW 6 [TeX] [PDF] 
7  22 Sep  (F)  Tensor products and bilinear forms  Roman chapter 14  Weekly 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  
8  29 Sep  (F)  Adjoints, selfadjoint operators, inner products  FIS sections 6.16.3  Daily HW 8 [TeX] [PDF] 
9  2 Oct  (M)  Orthogonal, normal, and unitary operators  FIS sections 6.46.5  Daily HW 9 [TeX] [PDF] 
10  3 Oct  (T)  Singular value decomposition (SVD)  FIS section 6.7  
11  4 Oct  (W)  Orthogonal projections and the spectral theorem  FIS section 6.6  Daily HW 11 [TeX] [PDF] Weekly HW 3 [TeX] [PDF] Weekly HW 3 solutions [TeX] [PDF] 
Modules  
12  6 Oct  (F)  Basic definitions and examples  DF section 10.1  Daily HW 12 [TeX] [PDF] 
13  9 Oct  (M)  Quotient modules and module homomorphisms  DF section 10.2  Daily HW 13 [TeX] [PDF] 
14  11 Oct  (W)  Generation of modules, direct sums, and free modules  DF section 10.3  
  12 Oct  (R)  Midterm exam, covering linear algebra (4:306:30 p.m., Kemeny 343)  Midterm exam solutions [TeX] [PDF]  
15  13 Oct  (F)  Tensor products of modules  DF section 10.4  
16  16 Oct  (M)  Tensor products, exact sequences  DF section 10.5  Daily HW 16 [TeX] [PDF] Weekly HW 4 [TeX] [PDF] Weekly HW 4 solutions [TeX] [PDF] 
17  18 Oct  (W)  Diagram chases  DF section 10.5  Daily HW 17 [TeX] [PDF] 
18  20 Oct  (F)  Projective modules  DF section 10.5  Daily HW 18 [TeX] [PDF] 
19  23 Oct  (M)  Injective modules; rings of fractions  DF section 10.5  Daily HW 19 [TeX] [PDF] 
20  25 Oct  (W)  Localization  DF sections 7.5, 15.4  Daily HW 20 [TeX] [PDF] Weekly HW 5 [TeX] [PDF] Weekly HW 5 solutions [TeX] [PDF] 
21  27 Oct  (F)  Localization and locally free modules  Daily HW 21 [TeX] [PDF]  
Modules over PIDs, canonical forms  
22  30 Oct  (M)  Euclidean domains and PIDs  DF sections 8.18.2  Daily HW 22 [TeX] [PDF] 
23  31 Oct  (T)  UFDs, FTFGMPID  DF sections 8.18.2 DF section 12.1 

24  1 Nov  (W)  Basic theory (FTFGMPID)  DF section 12.1  
25  3 Nov  (F)  Smith normal form  Daily HW 25 [TeX] [PDF] Weekly HW 6 [TeX] [PDF] Weekly HW 6 solutions [TeX] [PDF]  
26  6 Nov  (M)  Rational canonical form  DF section 12.2  Daily HW 26 [TeX] [PDF] 
27  7 Nov  (T)  Noetherian rings  
28  8 Nov  (W)  Jordan canonical form, applications  DF section 12.3  
Category theory and wrapup  
29  10 Nov  (F)  Categories and functors  DF Appendix II  Daily HW 29 [TeX] [PDF] 
30  13 Nov  (M)  Natural transformations, wrapup  
  17 Nov  (F)  Final exam, comprehensive (8:00 a.m.11:00 a.m.) in Kemeny 108  Final exam solutions [TeX] [PDF] 
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 selfassess in red pen. At the end of the term, all daily homework will be collected, with a short concluding selfassessment.
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 youin 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