Algebra 1/Extended 104016

Syllabus
Algebra 1/Extended 104016
Spring 2016-17
(5 credits)
Prerequisites

Instructor
Dr. Naomi Shaked, nomi@tx.technion.ac.il
Meetings
4 weekly hours of lecture
2 weekly hours of TA
Description
The following main topics will be covered:
1. Polynomials, Complex numbers and Fields (~5 hours).
2. Matrices: Terminology and special matrices, algebraic operations on matrices (~4 hours).
3. Systems of linear equations, Gaussian elimination, rank of a matrix (~5 hours).
4. Vector spaces and subspaces (~5 hours).
5. Linear combinations, linear span, linear dependence/independence (~4 hours).
6. Basis and dimension, including row and column spaces and coordinate vectors (~7 hours).
7. Invertible matrices, definition and properties (~2 hours).
8. Determinants, definitions and properties (~4 hours).
9. Linear transformations, kernel, image, dimension theorem, matrix with respect to a basis (~6 hours).
10. Matrix similarity and change of basis (~2 hours).
11. Eigenvalues and diagonalization (~6 hours).