We meet in Maass 10 (Chemistry Building) MTR 10:35 AM - 11:25 AM.
(The first lecture is on Tuesday Sept. 2nd, the last one on Thursday Dec. 4th.)

Instructor: Mikael Pichot
Office: Burnside Hall 925
Office hours at 10am on Wednesdays

TA: Krista Reimer
Tutorial: 3:35 - 4:25 on Tuesdays in Burn 1205.
Office hours: 8:30 - 10:30 on Tuesdays in Burn 1030.

A detailled version of the syllabus follows. The text is Elementary Linear Algebra, Second Edition, by W. Keith Nicholson.
ISBN: 0-07-071980-2. ISBN13: 978-0-07-071980-4

(The assignments will be mostly taken from there.)

Grading scheme: Max(10% Assignments + 90% Final exam, 10% Assignments + 15% Midterm + 75% Final exam)

There will be an in-class midterm on October 14th (in Mass 10 at 10:35). Topics: 1 to 11 included.

The Final exam will take place on Dec. 12th at 2pm.

The first homework is due Sept. 29. (Exercises from 1 to 7 below, 7 is included.)
The second homework is due Oct. 28. (Exercises from 8 to 14 included, please hand in directly to the TA.)
The Last homework is due Dec. 2nd. (Exercise from 15 to 25 included, to be handed in directly to the TA.)

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Detailled syllabus and the topics that we covered in class:

1. Matrices (1.1)
   Topics: addition, scalar multiplication, transposition, graphs
   Assignment: Ex. 1 a), b), c), and d), on p. 9 (this will take longer to read than solve...)
2. Linear equations and their solutions (1.2.1, 1.2.2, 1.2.4)
   Topics: Linear equations, linear systems, geometric interpretation. The fundamental theorem of linear systems
   Assignment: Ex. 7 p. 21
3. Gaussian elimination (1.2.3)
   Topics: How to solve a linear system?
   Assignment: Ex. 3 a) on p. 20 and Ex. 4 g) p. 21
4. Homogeneous system, rank, kernel dimension (1.2.4, 1.3)
   Topics: The rank theorem
   Assignment: Ex. 1 g) on p. 25
5. Basic vector geometry (3.3.1,3.3.2,3.3.3,3.2.1,3.2.2)
   Topics: lines, planes, dot product. Angles and the law of cosine
   Assignment: Ex. 7 p 148 and Ex. 18 p. 149
6. Matrix multiplication (1.4)
   Topics: matrix multiplication, directed graph
   Assignment: Ex. 27 a) on p. 37
7. Matrix inverses (1.5)
   Topics: The inverse of a square matrix and how to compute it
   Assignment: Ex. 17 a) on p. 48
8. Elementary matrices (1.6)
   Topics: The 3 types. Applications to inverses and rank.
   Assignment: Ex. 13 a) on p. 55
9. Definition of the determinant (2.1.2, 2.2.1)
   Topics: Determinant, inverses, elementary matrices.
   Assignment: Ex. 8 a)b)c)d)e)f) on p. 81
10. Definition of the determinant (2.1.1,2.2.2)
    Topics: The cofactor expansion. The adjoint matrix.
    Assignment: Ex. 8 b) p. 88
11. Definition of the determinant (2.1.3,2.2.4,2.2.5)
    Topics: More on cofactors, some proofs. The Cramer rule.
    Assignment: Ex. 15 a) p. 89
12. Diagonalization and eigenvalues (2.3)
    Topics: Eigenvalues, eigenvectors. The characteristic polynomial. Finding the eigenvalues.
    Assignment: Ex. 2 c) p. 99
13. Diagonalization and eigenvalues (2.3)
    Topics: Diagonalization theorems (e.g. distinct eigenvalues). Conjugate matrices. Cayley Hamilton Theorem.
    Assignment: Ex. 16 b) p. 100, Ex. 21 p. 100
14. Linear dynamical systems (2.4)
    Topics: Predator-Prey models, dominant eigenvalues.
    Assignment: Ex. 5 a), b), c), d) p. 109
15. Complex numbers (2.5)
    Topics: Conjugate, modulus, argument. Polar form, Euler's formula. Roots, roots of unity.
    Assignment: Ex. 13 p. 119, Ex 20 a) p.120, 22 a) p. 120.
16. Linear transformations of $\mathbb{R}^2$ (3.4)
    Topics: Matrix of a linear transformation. Examples, rotations, projections. Effect on the unit sphere. Isometries.
    Assignment: 4b) p 173, 12 p. 174
17. Subspaces and spanning sets (4.1)
    Topics: Definitions, examples.
    Assignment: 7b) p 188, 24 a), b) p. 188
18. Linear independence (4.2)
    Topics: Independent sets, invertibiilty of matrices.
    Assignment: 2c) p 193, 3 b) p. 194
19. Basis (4.3)
    Topics: The fundamental theorem of basis, Steinitz exchange lemma.
    Assignment: 7c) p 201, 25 p. 202
20. Rank (4.4)
    Topics: The rank transpose theorem, the rank theorem revisited.
    Assignment: 12 p. 210, 15 a) p 210
21. Orthogonality (4.5)
    Topics: Cauchy's inequality, the Gram--Schmidt algorithm.
    Assignment: 7 p. 221, 12 p 222
22. Projections and approximations (4.6)
    Topics: Orthogonal complements, Approximation theorem, Least square approximation.
    Assignment: 5 a) p. 233, 19 a p 234
23. Orthogonal diagonalization (4.7)
    Topics: Orthogonal matrices, Principal axis, Diagonalization revisited.
    Assignment: 5 a) p. 243, 10 a) p 243, 13 a) p 243
24. Quadratic forms (4.8)
    Topics: Principal axis, positive definite matrices, Choleski factorization.
    Assignment: 3e p. 255, 8a) p. 256, 14 p. 256.
25. Singular value decomposition (4.11)
    Topics: singular values, SVD, Fundamental subspaces, Polar decomposition.
    Assignment: 4. p 290 and 17 p. 291
26. The last week is for review.