# Algebra 1

### Course topics

- General background: sets and operations on them, Complex numbers: definition (via ordered pairs), addition and multiplication, inverses, adjoint, absolute value. Real and complex polynomials and their roots.
- Fields: Definition, properties, examples: Rationals, reals, complex numbers, integers mod p.
- Linear equations over fields, matrices and elementary row operations, rank of a matrix, solutions of homogeneous and non homogeneous systems of linear equations and the connections between them.
- Vector spaces over fields, subspaces, bases and dimensions, coordinates change of coordinate matrix, row rank as rank of a subspace, sums, direct sums of subspaces and the dimension theorem.
- Matrices multiplication, the algebra of square matrices, inverse determinants: properties, Cramer’s rule, adjoint and its use for finding the inverse.
- Linerar transformationsbasic propertieskernel and image of a linear trasformationrepresentaion of linear transformations by matrices and the effect of change of bases.linear functionals, dual bases

### Course Information

- University course catalogue:
- 201.1.7011
- Level:
- First Year
- Credits:
- 5.0

##### Recently Given

- 2020–21–B ()
- 2020–21–A (Prof. Ido Efrat)
- 2019–20–B ()
- 2019–20–A (Dr. Inna Entova-Aizenbud)
- 2018–19–B (Dr. Stewart Smith)
- 2018–19–A ()
- 2017–18–B (Dr. Stewart Smith)
- 2017–18–A ()