

Web page: http://www.math.ucla.edu/~cm/115ah.html
Prerequisites: Math 33A (basic linear alegbra) or equivalent. You should be able to manipulate matrices and determinants, and solve systems of linear equations. Familiarity with complex numbers is also required.
Course description:
This is an honors introductory course in abstract linear algebra.
Although we use the same textbook as the sections of Math 115A, we will
cover more material, and we will put more emphasis on doing rigorous
proofs. The course should provide a valuable introduction to mathematical
thought.
Topics to be covered are: vector spaces, subspaces, basis and
dimension, linear
transformations and
matrices, rank and nullity, change of basis and similarity of matrices,
dual spaces, direct sums, eigenvectors and eigenvalues, inner
product spaces, orthogonality and orthonormality, GramSchmidt process,
adjoints of linear transformations, quadratic forms and
symmetric matrices, orthogonal and unitary matrices, spectral theorem.
Textbook: S. H. Friedberg, A. J. Insel and L. E. Spence,
Linear Algebra, Custom UCLA Edition, Pearson Prentice Hall, 2003.
The plan is to cover Chapters 1, 2, 3, 4, 5.15.2, and 6.16.6 from the
textbook. Note that the
Custom UCLA Edition differs from the standard Fourth Edition (available at
various online bookstores) in that it contains an appendix about how to
write proofs.
Another recommended resource is the book by Peter Petersen, Linear
Algebra, available online.
Grading: 50% final, 25% best score of two midterms, 25% homework.
Exams: There will be two inclass midterms: one on Monday, October 19, and the other on Wednesday, November 18. The final exam is scheduled for Friday, December 11, 8:00 AM  11:00 AM.
No makeup exams will be given, except in case of a documented emergency. Homework: Homework will be assigned every week and will be due the
following Friday. There will be a total of eight problem sets. The lowest score
of the eight will be dropped, and the other seven will be added up to give
your total homework score.
The homework assignments will be handed out
in class and will also be posted on the web page. You must hand in the
homework in class each Friday. You are encouraged
to talk about the problems with other students, but you should write up the solutions individually. You should acknowledge the assistance of
any book, student or professor. No late homework will be accepted.
Problem Set 1 (due October 2)
Problem Set 2 (due October 9)
Problem Set 3 (due October 16)
Problem Set 4 (due October 30)
Problem Set 5 (due November 6)
Problem Set 6 (due Monday, November 16)
Problem Set 7 (due Wednesday, November 25)
Problem Set 8 (due December 4)