Mivnim Algebrim

Syllabus: Groups (through Chapter 7 of ALGEBRA: Groups,Rings, and Fields) Algebra text
a bit of rings (Chapters 13 and 14), and a taste of fields (p.187), in order to develop finite algebraic structures for computer science.

A Hebrew summary of much of the material, prepared by Aviv Dror, is available on Sicum1
or Sicum2
NEWS: First quiz 18 Dec at 18.00. Some targilim in Hebrew are now available at the library.

Second quiz 29 January at 18.00

Format of final exam:

8 questions true-false with explanation (5 points each); 2 questions of examples (10 points each); 2 theorems to be proved (20 points each) from the following list of theorems:

A. Lagrange's Theorem (If H is a subgroup of G then |H| divides |G|.)

B. Equivalence of conditions for N to be a normal subgroup of G, and the construction of G/N and the natural homomorphism from G to N, with kernel N.

C. Noether's first isomorphism theorem

D. Noether's third isomorphism theorem (H+N)/N is isomorphic to H/(H\cap N)

E. Every finite integral domain is a field. (One should prove first that every finite monoid with cancellation is a group.)

F. The characteristic of any field is either 0 or a prime integer.