tychonoff

Nice overview of some IBM accomplishments. Really liked the part about their role in Apollo 13.

Metaphors!

Skip the chocolates. Instead, confirm their confidence in you by doing something useful as quickly as possible. Minimize cultural differences (ie. try to fit in without sacrificing anything important). Don't pander - you were hired for a reason.

I never forgot a quote attributed to Liebnitz in my high school trigonometry book, which went something like:

"Although the world may be a dream, I would call that dream real enough if, using reason well, I was never deceived by it"

Without reference to the formal notion of limits in real numbers (invented in the 19th century), the expression 1=0.999... is meaningless. So one shouldn't be surprised at the confusion and dumb arguments surrounding it.

Walter Rudin's book is a masterpiece. I read this book 35 years ago for my comps, and remember it as one of the best. Bear in mind there's no easy way to learn mathematics - it's going to be hard no matter what approach you take because that's the nature of the subject. My advice to undergrads is to skip computing completely because it's much easier to learn when you need it (unlike mathematics). You'll build your first computer program long before you prove your first theorem.

I left mathematics 20 years ago (PhD, logic) by way of Prolog (logic programming) and then drifted towards relational databases (with some side trips into scheduling using graph theory).

You are in a good position - mathematics is a powerful tool for programmers.

I would suggest finding a real problem to solve, and then choose the appropriate language to work on it. Microsoft's .NET languages are a good way to get into programing (VB and SQL Server are my preferred tools).

On page 25, the subscript for E in the second equation should be k, not m?

US population way out of date (ditto for Canada)

Free logic books: http://www.e-booksdirectory.com/listing.php?category=33

Free math books: http://www.e-booksdirectory.com/mathematics.php

I hope the G summiteers like insects.

I never forgot his wonderful book Principles of Mathematical Analysis, which I read from cover to cover as a grad student in the late 70s.

The subject is incredibly rich, and it will take time to master basic principles. The Chinese Remainder Theorem is a good example - it requires no previous math but the concepts used to prove it are fundamental to the subject. You will need to take several courses to get enough experience to do anything useful, because you're not just learning formulas.

Line up 60 boxes in order, each representing a time slot for one instruction. Selecting any 30 of them would represent one way the 60 instructions could be interleaved, if those 30 selections represent the first loop. A different selection of 30 boxes for the first loop would represent a different arrangement for the 60 instructions, and all arrangements may be obtained this way. So 60 choose 30 would be all possible arrangements.