General Information
Math 510 Seminars in Mathematics
      Place: Ross 3000, Thursdays 9:00-9:50;

Math-Phys & CS seminar
     Place: Ross 3000, Thursdays 10:00-10:50
     Topics from Math 510, discussed in more depth.

Math 510 - Syllabus

Topics covered

Math 510 - Seminars in Mathematics
(Mathematical-Physics & Computer Science)
Spring 2000 instructor: Lucian Ionescu.

Time & Place: Thusrdays 9:00-9:50, Ross 3000.

The goal of the course is the contact with modern and interesting applications of mathematical theories.

1. Wavelets
They are recently used in data compression technology (image processing, etc.):
“Applications of wavelet theory continues to grow rapidly. Engineers, working in everything from mathematics and physics to digital signal processing, image compression, and speech and pattern recognition, need to understand this exciting subject”.

2. Quantum physics
“Low and high energy phenomena” … (too many to list!).
      ( It is a different way of thinking about “reality” worth knowing!)

3. Quantum computing
The parallel computing is an old subject. The modern one is “infinitely many parallel computing paths”. It is a new emerging domain of CS, promising to give us a clue on how we think and what conscience is!

“Hilbert Spaces, Wavelets, Generalised Functions and Modern Quantum mechanics”, by Willi-Hans Steeb, Mathematics and Its Applications, 1998.

We will learn the mathematical tools needed to be able to address these applications: Hilbert space theory, Fourier transform and wavelets, linear operators, generalized functions and quantum mechanics, quantum bits, Q-gates and Q-copying.

Basic knowledge in linear algebra (matrices, determinants, vector spaces) and calculus is required. An intuitive understanding of Euclidean R3 will help with Hilbert spaces,  a calculus level understanding of differential equations would suffice and some real analysis would be helpful.
The approach will be rigorous, without being hindered by very technical issues of analysis, focusing on the conceptual part of the mathematics, physics or CS involved.
Optional exercises are included as a way to feel we understand the formalism, being meant to give a feed-back on the hidden difficulties involved.

I will start presenting the first couple of lectures. Meanwhile students will decide what to present and when, oriented on a subject, or a part of the textbook, or a solution to a problem.

Lucian Ionescu
Updated 12/13/01