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] 
5  18 Sep  (M)  Annihilators  FIS section 2.6 Roman pp. 101107  Daily HW 5 [TeX] [PDF] 
6  20 Sep  (W)  Tensor products  
7  22 Sep  (F)  Normal and selfadjoint operators  
  25 Sep  (M)  No class: JV in Banff  
  27 Sep  (W)  No class: JV in Banff  
8  29 Sep  (F)  Unitary and orthogonal operators  
9  2 Oct  (M)  Orthogonal projections and the spectral theorem  
10  3 Oct  (T)  Singular value decomposition (SVD)  
11  4 Oct  (W)  Bilinear and quadratic forms  
Modules  
12  6 Oct  (F)  Basic definitions and examples  DF section 10.1  
13  9 Oct  (M)  Quotient modules and module homomorphisms  DF section 10.2  
14  11 Oct  (W)  Generation of modules, direct sums, and free modules  DF section 10.3  
  12 Oct  (R)  Midterm exam, covering linear algebra (4:006:00 p.m.) 

15  13 Oct  (F)  Tensor products of modules  DF section 10.4  
16  16 Oct  (M)  Exact sequences  DF section 10.5  
17  17 Oct  (T)  Diagram chases  
18  18 Oct  (W)  Projective modules  DF section 10.5  
19  20 Oct  (F)  Projective modules  DF section 10.5  
20  23 Oct  (M)  Injective modules  DF section 10.5  
21  25 Oct  (W)  Localization  DF sections 7.5, 15.4  
Modules over PIDs, canonical forms  
22  27 Oct  (F)  The basic theory  DF section 12.1  
23  30 Oct  (M)  Examples and applications  
24  1 Nov  (W)  Smith normal form  
25  3 Nov  (F)  Rational canonical form  DF section 12.2  
26  6 Nov  (M)  Jordan canonical form  DF section 12.3  
27  7 Nov  (T)  TBD  
Category theory  
28  8 Nov  (W)  Categories  DF Appendix II  
29  10 Nov  (F)  Functors  
30  13 Nov  (M)  Natural transformations, applications  
Wrapup  
31  14 Nov  (T)  Wrapup  
  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 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