Math 212. Honors Linear Algebra - Fall 23 - Hans Lindblad

Linear algebra is a collection of methods and concepts related to solving systems of linear equations and it also provides a language for identitifying algebraic structures in a variety of situations. It has many applications to science/engineering.
The departmental Course Syllabus gives a list of topics and sections covered in the required text: Axler, 'Linear Algebra Done Right', 3rd ed. You should have access to the online version. It comes with a website, with videos and slides and errata

The lectures are MW 1.30-2.45 in Hodson 211. The sections are F 1.30-2.20 in Hodson 315.
Professor: Hans Lindblad, [email protected], office hour M 3-4 (and sometimes also W 3-4) in Krieger 406
TA: Jonathan Lin, [email protected], office hour Th 9.50-10.50 in Krieger 211, and Th 12-1, F 3-4 in helproom Krieger 213
There will be two midterms and a final. Midterm 1 on 10/2 covers chapters 1-3. Midterm 2 on 11/6 covers chapters 4-7. The final on 12/19, 6-9 pm, covers all chapters 1-10. There will be weekly homework due in section. The grade will be based on the larger of I) 33% homework(best 12), 17% each midterm, 33% final, or II) 33% homework, 17% best midterm, 50% final

Students are expected to make the transition to proving things in this course in addition to getting used to abstract concepts while the course is fast paced. It would be helpful to have had a computationally based linear algebra course already. If not you can e.g. look at the videos by Khan Academy or Gilbert Strang at MIT. If it is too much you may want to drop down to the regular linear algebra course. It is strongly suggested that you look at least at the bold words in the sections of the text before they will be covered in lectures to get used to the new concepts, see the schedule below. In the past we used another text Friedberg, Insel and Spence 'Linear Algebra'. Other universities have used Hoffman and Kunze 'Linear Algebra'. and Triel 'Linear Algebra done wrong'. Another book with a unique perspective is Lax 'Linear Algebra and its Applications'.

wk  date  Monday  Wednesday
  1  8/28  1.AB Real and Complex Scalars and Vector Spaces  1.BC Subspaces and Direct Sums
  2  9/4  Holiday  2.AB Span and linear independence.
  3  9/11  2.BC Basis and dimension.  3.AB Linear maps, Injectivity and Surjectivity
  4  9/18  3.BC The nullspace and the range.  3.CD Matrix multiplication and invertibility
  5  9/25  3.E Products and Quotients  3.F The Dual space
  6  10/2  Midterm 1  4. Polynomials
  7  10/9  5.AB Eingenvalues and eigenvectors  5.BC Upper triangular and diagonal matrices
  8  10/16  6.AB Inner Products and Orthonormal Bases  6.BC Orthogonal Complement and Minimization
  9  10/23  7.A Selfadjoint and Normal Operators  7.B The Complex and Real Spectral Theorem
10  10/30  7.C Positive Operators and Isometries  7.D Polar and Singular Value Decompositions
11  11/6  Midterm 2  8.A Generalized Eigenvectors
12  11/13  8.B Decomposition of operators.  8.C Characteristic and Minimal polynomials
13  11/20  Fall Recess  Fall Recess
14  11/27  9.A Complexification  9.B Operators on Real Inner products Spaces
15  12/4  10.A The Trace  10.B The Determinant

wk  section  Homework
  1  9/1  1.A: 1, 6, 8, 1.B: 3, 5, 1.C: 3, 8, 10, 19, 20, 23.
  2  9/8  2.A: 1, 3, 6, 10, 11, 13, 2.B: 3, 5
  3  9/15  2.B: 6, 8, 2.C: 1, 3, 5, 11, 13, 3.A: 3, 4, 11, 13, 14,
  4  9/22  3.B: 12, 14, 20, 21, 28, 3.C: 3, 9, 3.D: 3, 4, 5, 8, 14,
  5  9/29  3.E: 7, 12, 16, 17, 3.F: 3, 7, 9, 14, 25, 27
  6  10/6  3.E: 18, 3.F: 28, 34, 36, 37, 4: 4, 5, 8.
  7  10/13  5.A: 8, 14, 15, 16, 5.B: 1, 4, 9, 20, 5.C: 1, 5, 7, 12.
  8  10/20  Fall Break No Homework
  9  10/27  6.A: 6, 13, 24, 28, 6.B: 2, 5, 7, 15, 6.C: 4, 7, 11, 12.
10  11/3  7.A: 2, 4, 11, 20, 7.B: 4, 9, 7.C: 7, 8, 10, 11, 7.D: 5, 7, 14, 16
11  11/10  8.A: 1, 4, 5, 7, 12, 14.
12  11/17  8.B: 1, 3, 6, 11, 8.C: 4, 12, 13, 15.
13  11/24  Fall Recess No Homework
14  12/1  9.A: 2, 3, 16, 17, 9.B: 3, 4, 5, 8.
15  12/8  10.A: 18, 19, 10.B: 4, 6, 10, 12.