Basic Topics in Mathematics

I will admit, I have always done reasonably well in math. I like the subject – it seems intuitive to me for the most part. One of the things that stuck with me for the longest time, though, was quality of instruction I got from once teacher in Highschool – my Calculus teacher. During the first day of class, he explained all pre-calculus math to us in about 30 minutes, and it made sense. I had the same experience listening to Richard Feynman’s lectures on Physics.

That is why I was so astounded to find this gold mine in a used book store. John Riner, the author, walks through mathematics the way it should be done – starting with set theory and gradually progressing through algebra, geometry and matrix theory up to calculus. This is a small book – only 297 pages including the index, but it teaches math in the way it was meant to be taught. This is not to say that this book is easy – it moves fast and it has none of the “new math” garbage word problems in it that contemporary students are probably used to. Instead, it focuses with laser precision on the actual mathematical concepts. For the serious student of mathematics, I cannot recommend this book enough.

One last note, this book was published in 1963 and is out of print. As of this writing, there are only 4 used copies left on Amazon. I would not expect those copies to remain available forever.

Basic topics in mathematics

Math/Physics Collaboration Sheds New Light

Math/Physics Collaboration Sheds New Light

Although not a significant advance in and of itself, this paper shows the significant advances that can be had by multi-domain collaboration. I find that frequently there are metaphors and abstractions that one can draw from one field of study and map onto another that, in the parent field would be considered trite, whereas in the adopted field are new and innovative. My guess is that this will happen more and more often (just look at economics, which is slowly but surely swallowing the entire field of social sciences).

As for the paper itself, it talks about computational hardness – something for you crypto-geeks out there.

Low Energy Transfer to the Moon

Low Energy Transfer to the Moon[pdf]

An intriguing paper about a method of low energy (estimated at 10% of current energy costs) movement from the earth to the moon taking into account all four bodies (sun, earth, moon, spaceship) involved instead of the typical two body method (earth, spaceship). This looks very, very interesting simply because it has the potential to dramatically decrease the launch cost of moon missions – making things like Google Lunar X Prize much more possible. Now, if only I could actually understand the specifics behind the math. Oh well, that’s what friends are for.

Fooled by Randomness

Fooled by Randomness

A mildly short-ish book that really should have been 4 times shorter. The interesting idea that is central to this book is that almost no one is good at understanding probability. The book is essentially example after example illustrating this principle.