# Complements to linear algebra I, Math 80146

### Announcements:

- January 15. It was agreed on
the last class that the final quiz will be hold on the lecture on January 22.
It will be a multiple choice test on the topics we studied during the
semester.

**General Info:**

### Instructor:

· Michael Temkin

· E-mail: temkinmath.huji.ac.il

· Office: Ros 78A (tel. 02-6584575)

· Office Hours: Sundays 17-18 at Ros 78A.

· Seminars: Sundays 16-17at Shprintzak 102.

### Material:

### · This course is a companion of
the basic linear algebra course 80134. I will present various important
complementary material that is skipped in 80134 due to time restrictions. This
course is more challenging (and, hopefully, interesting) and the speed of
exposition will be substantially higher.

### Grading:

·
There is only a pass grade in the course. It will be assigned in the end on
base of a short exam on the last class.

### Lectures:

- November 13. Constructions
with sets: disjoint union, products, powers. Invertible maps of sets.
- November 20. Actions and
their properties: unit, inverse, associativity, commutativity. Groups and
groups of automorphisms (symmetries) of objects. S_n=Aut({1…n}). Also, you
can find here
notes of the lecture taken by Amit Novick.
- November 27. Cyclic groups
Z and Z/nZ, homomorphisms of groups, the kernel of a homomorphism. Also,
you can find here
notes of the lecture taken by Amit Novick.
- December 4. Examples of
vector spaces: the space of sequences and the subspaces of polynomials and
Fibonachi sequences, the space (F_3)^4 and the game "set". .
Also, you can find here
notes of the lecture taken by Amit Novick.
- December 11. Partial and
total orders, Zorn's lemma, and existence of a basis in an arbitrary
vector space. Also, you can find here
notes of the lecture taken by Amit Novick.
- December 18. Vector spaces
of polynomials and formal power series. Sums and products of vector
spaces. Also, you can find here
notes of the lecture taken by Amit Novick.
- January 1. Dual vector
spaces, continuation of functional, dual of the dual. Also, you can find here
notes of the lecture taken by Amit Novick.
- January 8. Duality for
finite-dimensional vector spaces. Dual bases. Dual linear maps between dual
spaces (going in the opposite direction). Also, you can find here
notes of the lecture taken by Amit Novick.
- January 15. Dual linear map
of a linear map.