Course: 21236, Math Studies II (Algebra part)

Time and place: MWF 10:30-11:20 at Porter Hall A20 and

MWF 1:30-2:20 at Wean Hall 6423

Professor: Dhruv Mubayi

Office: 6307 Wean

Tel:
8-9865

E-mail: mubayi@math.cmu.edu

Course web page

Office Hours: 11:30-12:30 on W and F and by appointment

This semester we will study rings and inner product spaces.
If time permits we
will look at some applications of algebra to combinatorics.

Topics in Ring theory: definitions and examples, homomorphisms, ideals and
quotient rings, the field of quotients of an integral domain, Euclidean rings,
polynomial rings.

Topics in Inner product spaces: scalar products, orthogonal bases, rank,
bilinear maps, dual space, quadratic forms, Sylvester's theorem, symmetric,
hermitian and unitary operators, diagonalization

Further topics: I will introduce the linear algebra method in combinatorics by illustrating the dimension argument on various problems about set systems. If time permits we will discuss wedge products.

Grading Policies:

Your grade will be based on two mid-term tests, homework, problem seminar
presentation and writeups, and a final exam

Homework:

Homework 1, Due Wednesday January 30

Solutions to Homework 1

Homework 2, Due Wednesday Feb 13

Solutions to Homework 2

Homework 3, Due Wednesday Feb 27

Solutions to Homework 3

Solutions to Test 1

Homework 4, Due Wednesday March 26

Solutions to Homework 4

Homework 5, Due Wednesday April 9

Homework 6, Due Wednesday April 30

Solutions to Homework 6