Archive for July, 2006

Perfect Number

July 30, 2006 at 7:58 pm · Filed under numbers

Alex and Peter are my colleagues. On Friday, they were deeply engrossed in a conversation. As I was walking past them, I asked them what they were talking about. Alex replied that they are trying to find an algorithm for “perfect numbers”. I asked “What is a perfect number?”. Alex explained to me what it is. Since I am not as good at explaining things as Alex is, I decided to find a good link. I found a few, but this one from Wikipedia, is probably one of the better ones.

A Perfect Number is defined as an integer which is the sum of its proper positive divisors, that is, the sum of the positive divisors not including the number. Six (6) is the first perfect number, because 1, 2 and 3 are its proper positive divisors and 1 + 2 + 3 = 6. The next perfect number is 28 = 1 + 2 + 4 + 7 + 14. The next perfect numbers are 496 and 8128.

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Book: Letters to a Young Mathematician

July 30, 2006 at 6:54 pm · Filed under Books, Math, mathematics

This is a repost from my Learnlog.

I just finished it yesterday. I really enjoyed reading it. Here are some of my favorite chapters.

  • Why Do Math?
  • The Breadth of Mathematics
  • Surrounded by Math
  • How Mathematicians Think
  • How to Learn Math
  • Mathetmatical Story Telling
  • Pure or Applied?
  • Where Do You Get Those Crazy Ideas?
  • How to Teach Math
  • Is God a Mathematician?

The last chapter “Is God a Mathematician” is all about Symmetry. I really love this chapter. Here are a few quotes from it.

“God and mathematics both strike terror into the heart of the common humanity, but the connection must surely run deeper…. You needn’t subscribe to a personal deity to be awestruck by the astonishing patterns in the universe or to observe that they seem to be mathematical. Every spiral snail shell or circular ripple on a pond shouts that message at us.”

“What are the laws of nature? Are they deep truths about the world, or simplifications imposed on nature’s unutterable complexity by humanity’s limited brainpower?… Are mathematical patterns really present in nature, or do we invent them? Or, if real, are they merely a superficial aspect of nature that we fixate on because it’s what we comprehend?”

“Because we cannot experience the universe objectively, we sometimes see patterns that do not exist.”

“One of the simplest and most elegant sources of mathematical pattern in nature is symmetry. Symmetry is all around us. We ourselves are bilaterally symmetric…. There are symmetries in the structure of the atom and the swirl of galaxies.”

“Imagination is an activity of brains, which are made from the same kind of materials as the rest of the cosmos…”

“Symmetry is deep, elegant and general. It is also a geometric concept. So the geometer God is really a God of symmetry.”

This book, in my mind at least, raises more questions than it answers. But it provides lots of hints on where to look, and what to look for.

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Elementary Calculus

July 30, 2006 at 11:40 am · Filed under Calculus, Math, mathematics

elementary-calculus.png

This is something I missed when I was studying calculus, a few decades ago. Calculus was not difficult for me. I picked it up pretty fast and even applied some of it in other courses in engineering. But I never really grasped the essence. So I am back on a different quest. To understand the relevance of Calculus and applications.

A book like this helps. I think, if you know what it is used for, you can relate to the subject better.

This is from Elementary Calculus: An Infinitesimal Approach, a free e-book. Found it on del.icio.us.

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