Natural Blogarithms

The 100 Greatest Theorems

SplineGuy — Fri, 23 Mar 2007 03:49:16 +0000

In July, 1999, Paul and Jack Abad presented their list of “The Hundred Greatest Theorems.” I was intrigued and though it might be interesting to re-post.

Their ranking is based on the following criteria: “the place the theorem holds in the literature, the quality of the proof, and the unexpectedness of the result.”

The list is of course as arbitrary as the movie and book list, but the theorems here are all certainly worthy results.

1 The Irrationality of the Square Root of 2, Pythagoras and his school, 500 B.C.
2 Fundamental Theorem of Algebra, Karl Frederich Gauss, 1799
3 The Denumerability of the Rational Numbers, Georg Cantor, 1867
4 Pythagorean Theorem, Pythagoras and his school, 500 B.C.
5 Prime Number Theorem, Jacques Hadamard and Charles-Jean de la Vallee Poussin (separately), 1896
6 Godel’s Incompleteness Theorem, Kurt Godel, 1931
7 Law of Quadratic Reciprocity, Karl Frederich Gauss, 1801
8 The Impossibility of Trisecting the Angle and Doubling the Cube, Pierre Wantzel, 1837
9 The Area of a Circle, Archimedes, 225 B.C.
10 Euler’s Generalization of Fermat’s Little Theorem (Fermat’s Little Theorem), Leonhard Euler (Pierre de Fermat), 1760 (1640)
… (view the rest of the list)

What’s wrong with my computer?

SplineGuy — Fri, 23 Mar 2007 02:16:08 +0000

My Mathematical Genealogy

SplineGuy — Tue, 20 Mar 2007 15:27:58 +0000

For a long time I have been planning to work up my mathematical genealogy using “The Mathematical Genealogy Project” site. They have the aspirations of documenting the entirety of the genealogy of ALL the mathematicians of the world. I had not heard of the site until after I graduated with my doctorate but was surprised to find quite a few BIG names in my academic heritages. Names like Gauss, Euler, Leibniz, Weierstrass, Hilbert, Poisson, Fourier, Klein, as well as many others.

I have spent more time compiling my heritage than I probably have ought, but you can now download document with it all drawn out:

Dr. Franklin’s Mathematical Genealogy (pdf)

Friday Random 10

SplineGuy — Fri, 02 Mar 2007 04:32:28 +0000

“Walk On Your Knees” by Aaron & Jeoffrey (Aaron Jeoffrey)
“In The Light” by dc Talk (Jesus Freak)
“Thrive” by Newsboys (Thrive)
“Victory Chant” by Various (16 Biggest Praise and Worship Songs Volume 1)
“Semper Fidelis” by John Philip Sousa (Great American Marches I)
“The Pride Of The Wolverines” by John Philip Sousa (Great American Marches I)
“Lamb of God” by Rebecca St. James (Worship God)
“Please Mr. Postman” by The Marvelettes (20th Century Masters: The Millennium Collection: Best Of The Marvelettes)
“Unwritten” by Natasha Bedingfield (Unwritten)
“An Irish Party In Third Class” by Gaelic Storm (Back To Titanic)

Do you have more time to waste?

SplineGuy — Tue, 27 Feb 2007 16:20:48 +0000

Try this:

You swing from wires to try to go as far as you can. You fling them by click on the screen and the wire shoots towards the direction of the click. It will stick to the brightly colored regions for a few seconds but then release. Very Tarzan-like, AHH-ahh-ahha-haahhha! (FYI: That was my Tarzan voice)

UPDATE: My record is ~~70.46~~ ~~91.74~~ 137.36

HT: Tumbleo

Faith and Science: Historical Case Studies

SplineGuy — Mon, 26 Feb 2007 21:02:42 +0000

Class Date: Friday, February 16, 2007

Dr. Boyd was in charge for another day. This time he covered topics from the history of science as an illustration of how science progresses. Using specific case studies from the history of scientific endeavor, we learn some important principles that undergird how we understand science as it is today.

Below are some of the topics that we touched on in this class:

The UV Catastrophe: This serves as a good case study to see how scientific revolutions occur as well as a lesson about the dangers of extrapolation
Causality: the difficulty of assessing the cause from the effect. Wearing skirts causes an increased likelihood of breast cancer
Did Science arise in a Christian World? Did the Christian World help to create modern science? (see Eric Snow’s Paper)
Positivism vs. Realism
Galileo
Michael Faraday
Isaac Newton

Friday Random 10

SplineGuy — Fri, 23 Feb 2007 21:41:47 +0000

I almost missed it again, but I didn’t forget. Here’s another edition of the Friday Random 10:

“Sinking” by Jars of Clay (Jars of Clay)
“Blessed Be The Name” by Andy Park (25 Top Vineyard Worship Songs)
“I’ll Fly Away” by the Blackwood Brothers
“A Lover’s Concerto” by The Toys
“Bach’s Prelude and Fugue in E Flat Minor / D sharp Minor” by The Canadian Brass (The Essential Canadian Brass)
“Any Man of Mine” by Shania Twain (Greatest Hits)
“Great is Thy Faithfulness” by The Cathedrals
“Hold On” by Selah (The Best of America)
“In the Secret (I Want to Know You)” (Vineyard Music, Season of Renewal:The River is Here)
“Such a Groovy Guy” by Weird Al Yankovic (Weird Al Yankovic)

Also, I am sorry for the light posting this week. I have been fairly busy due to events on the job front and I will be posting regarding this in the near future.

Another dose of math humor

SplineGuy — Thu, 22 Feb 2007 15:52:56 +0000

I’ve posted a few like this before, but I was hit with a couple new ones today in my Inbox. Thanks LB and jonboy for sending them my way:

Friday Random 10 (late)

SplineGuy — Mon, 19 Feb 2007 05:40:04 +0000

Sorry I missed Friday’s Random 10. That makes this, technically, a Monday Random 10 but we’ll overlook it this once.

“Chevette” by Audio Adrenaline (Hit Parade)
“More Than the Watchmen” by Jeremy Casella/Rebecca St. James (Worship God)
“What If I Stumble?” by dc Talk (Jesus Freak) – One of my All-Time Favorites!!!
“I Thank You, Lord” by Alicia Williamson (New Orleans Homecoming)
“He Understands My Tears” by The Isaacs (New Orleans Homecoming)
“He Didn’t Have To But He Did” by Shiloh Quartet (Jesus Knows Who I Am)
“Sixteen Candles” by The Crests (Happy Days 50′s And 60′s)
“We Will Dance” by David Ruis (Refiner’s Fire: 25 Top Vinyard Worship Songs Disc 2)
“Quiet You With My Love” by Matt Bronleewe/Rebecca St. James (Worship God)
“Just to be with You” by Third Day – This makes two from the all-time favorites list making it onto the random 10

In light of a couple of results on this list, I am going to have to start keeping track of the Official All Time Favorites List as they appear on the Friday Random 10. Once this list reaches a significant number, it will become an official page on this blog.

Calculus IV: Directional Derivatives

SplineGuy — Mon, 19 Feb 2007 04:21:00 +0000

We finished the concept of directional derivatives, introducing the notation for the gradient of a function of several variables. We proved the formula of the maximum value of the directional derivative, as well as the direction for which it is maximized.

Next time we’ll begin basic optimization theory for functions of several variables.