0366.1102.03 INTRODUCTION TO ALGEBRA II

Lecturer:
Dany Leviatan
Winter Semester 2001.
Time and place:
Monday     8.00-10.00 in Melamed Hall
Thursdays 10.00-11.00 in Lev Hall

Grade: An examination at the end of the semester

The syllabus of the course

  1. THE RING OF POLYNOMIALS
    Examples of rings, the integers, the complex integers. Division, primes, factorization. The ring of polynomials and its properties, the algebra of polynomials. Ideals, greatest common denominator.
  2. MATRICES
    Characteristic (eigen) values and charateristic (eigen) vectors. Diagonal matrices and diagonalization. Characteristic polynomial.
  3. ORTHOGONALIZATION
    Scalar products. Orthogonal projections, Gram-Schmidt orthogonalization. Orthogonal matrices, symmetric matrices. Block matrices, positive definite matrices.
  4. GROUPS
    Groups of matrices. Groups and subgroups. Cyclic groups. Lagrange theorem.
Recommended bibliography:
  1. Kenneth Hoffman and Ray Kunze- Linear Algebra.
  2. Open University- Linear Algebra . (in Hebrew)