guru dx

Can I have an internship?
I assume so, look up the company web site (use search term "The Aerospace Corp") - but they will all require US citizenship.

What advice would you have for a young person who's good at math and science, but doesn't know what they want to be when they grow up?
Take as many different subjects as possible - find one you really like (almost every science or technology area has a place for math).

What advice would you give to a young person looking to pursue an aerospace engineering career?
All the math you can stand and one typing course (saves time when using a computer) - different math leads to different ways of thinking - different ways of thinking allow more problems to be addressed.

From your experience, which math and science subjects are used the most in aerospace engineering?

more stable subjects:
• propulsion
• mechanics - stress and forces
• thermal - temperature management
• power - generation and distribution

less stable subjects:
• guidance, navigation, control
• sensors and communications - optics, antennas, ...

All depend heavily on computing models based on assumed physical properties. Models are continually evolving.

What's the coolest aerospace project you've ever worked on?

milstar fail fix - control engineering, filters (look up "failure of first milstar launch")

communication network analysis - linear programming

curve clustering - "thank you"

At what point did you realize that you wanted to pursue aerospace engineering?
I didn't - I moved to computing when there were no jobs in math in 1975 - pattern analysis and recognition corp, Rome, NY. I moved to aerospace when I was fired from a company in LA (they thought that what I was doing would interfere with what they wanted me to do; it hadn't and didn't, and I told them I intended to keep doing it) - aerospace engineering was just getting into modern computing in 1980, and I was a programming wizard (the person who hired me knew me from UCLA).

Could you give us a brutally honest review of CalTech?
I loved it - it was quite difficult and I would not have been ready for it from high school (I learned many years later that the person I was working for had been there the exact same 4 years, in adjacent buildings, and as near as we could tell, we never saw each other).

What's your favorite field or topic in math?

• combinatorics and number theory - these two subjects allow very simple and understandable problem statements, with very difficult solutions
• four color theorem
• Fermat's last theorem

I am also interested in new kinds of logics, especially ones that explicitly deal with:

• self-reference
• contradiction
• relevance and importance

and other qualities not normally studied in logic.

Could you tell us about your unusual path into admission at UCLA?
When I was in 11th grade (1964-5), my mother was a junior at UCLA (she dropped out of UC Berkeley when she got married) - I read the UCLA general catalog, cover to cover (1200pg or so, an inch thick anyway) - it said there were tests 8-) (I always score higher than what I know on multiple choice tests). I took the achievement tests (the hard math was not available the only time I could take them, and I knew I'd mess up the easy math one, so I took English, social studies, German).

What was the best/most favorite class you took in college?

• Chinese (you didn't say math class 8-))
• my very first college math class (2nd year calculus)
• non-standard analysis (logic-based approach to the real line and calculus that justifies the use of "infinitesimals")

What is the most difficult class you've taken?

• physics (you didn't say math class 8-))
• non-standard analysis

How did you approach learning new facets of mathematics, and their applications in your work?
Read until it makes no sense; do something else; read again and again - only had one class where I did not know what the content would be - non-standard analysis.

How often do you learn new math?
Every few months now, but with various long gaps.

If you had a favorite number, what would it be, and why?

17 - Fermat prime - Gauss showed that a regular polygon of n sides was constructable with straightedge and compass only the prime factors of n are Fermat primes or 2 (he did it by converting the construction to a polynomial problem, and showing what polynomial problems were solvable with straightedge and compass)

31 - Mersenne prime - all the largest primes have this form (2 ^ p - 1) for a prime p (but not all numbers of that form are primes 2047 = 2 ^ 11 - 1 = 23 * 89)

32 sort of (Sandy Koufax's uniform number) - I am ambi-sinistrous (sinister - Latin for left)

1729 - Ramanujan and Hardy (it is the smallest positive integer that is the sum of two cubes two different ways 1729 = 1^3 + 12^3 = 9^3 + 10^3)

How and when did you realize that you wanted to do a PhD?
I never thought about it until college, in my junior or so; school was SO much easier than the real world - I could have graduated in 3 years, but there was a draft rule change in 1968 (no longer any automatic draft deferments for gdraduate students), so I stayed a fourth - I ran out of math classes to take for credit; took many others:

half the udergraduate English major

Chinese, Russian, linguistics, psychology ("pig with a surfboard")

How was your experience with physics (mechanics, electromagnetism) and your unique approach to these subjects?
I never liked physics much 8-), except for relativity and quantum mechanics (which use math much more heavily than most other areas of physics)

Is there still a difference in "Old" vs "New" ways of doing math at the college level and beyond, or is it more standardized at that point?
There is much more computing, for mathematical and modeling experiments, but other areas are not much different - for example, I could teach a 1 year calculus class starting tomorrow - that has not changed much. There is a need for new kinds of mathematics for new kinds of subjects (most of the math we have derives from physics problems).

Got another question? Email Dr. Landauer and ask!