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Simplicity | Derek Wise's blog on Mathematics, Physics, and other fun stuff.Derek Wise's blog on Mathematics, Physics, and other fun stuff.
http://dkwise.wordpress.com/
Derek Wise's blog on Mathematics, Physics, and other fun stuff.
http://dkwise.wordpress.com/
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Simplicity | Derek Wise's blog on Mathematics, Physics, and other fun stuff. | dkwise.wordpress.com Reviews
https://dkwise.wordpress.com
Derek Wise's blog on Mathematics, Physics, and other fun stuff.
dkwise.wordpress.com
George Hart’s “12-Card Star” and suit permutations. | Simplicity
https://dkwise.wordpress.com/2015/03/07/george-harts-12-card-star-and-suit-permutations
Derek Wise's blog on Mathematics, Physics, and other fun stuff. Laquo; From the Poincaré group to Heisenberg doubles. Torsor a la George Hart. George Hart’s “12-Card Star” and suit permutations. When I was at the JMM. In San Antonio in January, I was happy to catch a workshop by George Hart:. I went to some great talks at the JMM, but a hands-on, interactive workshop was a nice change of pace in the schedule. Having seen some of George’s artwork. Here’s what mine looked like:. Flipping that blue line fro...
Teleparallel gravity and Poincaré symmetry | Simplicity
https://dkwise.wordpress.com/2012/04/19/teleparallel-gravity-and-poincare-symmetry
Derek Wise's blog on Mathematics, Physics, and other fun stuff. Laquo; Workshop pictures from Bad Honnef. Observer Space: new paper and ILQGS talk. Teleparallel gravity and Poincaré symmetry. Lately John Baez and I have been thinking a bit about teleparallel gravity, from a somewhat esoteric point of view based on 2-groups. We’re just about to finish up a paper on that. Right now, though, I just have a few thoughts about one of the more usual ways of thinking about teleparallel gravity. From a certain po...
From the Poincaré group to Heisenberg doubles | Simplicity
https://dkwise.wordpress.com/2014/09/25/heisenberg-double
Derek Wise's blog on Mathematics, Physics, and other fun stuff. Laquo; Hopf algebroids and (quantum) groupoids (Part 2). George Hart’s “12-Card Star” and suit permutations. From the Poincaré group to Heisenberg doubles. First, consider the Poincaré group, the group of symmetries of Minkowski spacetime. Once we pick an origin of Minkowski spacetime, making it into a vector space. The Poincaré group becomes a semidirect product. And the action on. It should act on. In this construction. All I really ne...
Blog post on Observer Space by Jeffrey Morton | Simplicity
https://dkwise.wordpress.com/2012/10/17/968
Derek Wise's blog on Mathematics, Physics, and other fun stuff. Laquo; Observer Space: new paper and ILQGS talk. Hopf algebroids and (quantum) groupoids (Part 1). Blog post on Observer Space by Jeffrey Morton. This is a very nice blog post by Jeffrey Morton about observer space! This entry is a by-special-request blog, which Derek Wise invited me to write for the blog associated with the International Loop Quantum Gravity Seminar,. Formats, and the slides are here. 2,961 more words. From your own site.
The geometric role of symmetry breaking in gravity | Simplicity
https://dkwise.wordpress.com/2012/01/30/the-geometric-role-of-symmetry-breaking-in-gravity
Derek Wise's blog on Mathematics, Physics, and other fun stuff. Laquo; Explaining Cartan geometry. Göttingen talk on Cartan geometrodynamics. The geometric role of symmetry breaking in gravity. I suffered a blogging derailment at the end of 2011. Now I’m eager to get back on track, and I’ve got a bunch of stuff I want to write about. Right at the end of the year, I wrote a short conference proceedings article:. The geometric role of symmetry breaking in gravity. Much less famous is this: broken symmetry.
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L’Hopital’s Rule for Limits | My Math Blog
https://pqnelson.wordpress.com/2012/06/13/lhopitals-rule-for-limits
A topnotch WordPress.com site. Series Convergence: What Does It Mean? L’Hopital’s Rule for Limits. June 13, 2012. Now we are concerned about limits and we can have nightmarish limits. For example if. What can we do? We end up using derivatives to help evaluate such limits. We have L’Hopital’s rule state, if. 2 Sketch of Proof. We can use linear approximations. Use these approximations in (1a), then take the limit. So our limit becomes. We evaluate the inner limit first. So (4) simplifies to. You are comm...
[Index] Calculus in a Single Variable | My Math Blog
https://pqnelson.wordpress.com/2013/10/26/index-calculus-in-a-single-variable
A topnotch WordPress.com site. Index] Calculus in a Single Variable. October 26, 2013. Differential Calculus in a Single Variable. Using big O notation. Line Tangent to a Curve. Tangent Lines as Linear Approximations. Some Useful Trigonometric Limits. The inverse function to the exponential mapping. The First Derivative Test. An example optimizing a rectangle’s area. Curve Sketching (General Scheme). L’Hopital’s Rule for Limits. Differentiation Technique #1: Logarithmic Differentiation. You are commentin...
Inverse Function Theorem | My Math Blog
https://pqnelson.wordpress.com/2012/06/04/inverse-function-theorem
A topnotch WordPress.com site. Optimization (Motivation) →. June 4, 2012. So we have some function. The “Inverse Function”. Is another function denoted. Be a function of. So what happens if we differentiate both sides of Equation (1) with respect to. The right hand side is trivial. The left hand side is more interesting. We see, by the chain rule, it is. But we do not know how to differentiate an inverse function…what to do? Why not set Equations (2) and (3) equal? Be a function and. What do we do? Pingb...
Antidifferentiation (Part 1) | My Math Blog
https://pqnelson.wordpress.com/2012/06/06/antidifferentiation-part-1
A topnotch WordPress.com site. Endomorphisms of the Fano Plane. Antidifferentiation (Part 2: Indefinite Integration) →. June 6, 2012. 1 Derivatives Properties Review. Be given. We recall the derivative. We have several rules for differentiation:. We want to introduce an “inverse” of differentiation. We will use the notation. Is an “Antiderivative”. Usually it’s an open interval) iff. What is its antiderivative? Well, we see its of the form. We take its derivative. To be equal to. Is the antiderivative for.
Exponential Function | My Math Blog
https://pqnelson.wordpress.com/2012/06/03/exponential-function
A topnotch WordPress.com site. Line Tangent to a Curve. Tangent Lines as Linear Approximations →. June 3, 2012. So we threw down a challenge at the end of our discussion of Tangent Lines. Recall we wanted to find a curve. Such that for any. We have the line tangent to that point. Historical note: Debeaune asked Descartes this problem in a letter in 1638; Leibniz solved this problem in 1684 using “infinitesimals”. We will use modern calculus to solve the problem! We can rewrite this to be. We could do this.
Implicit Differentiation | My Math Blog
https://pqnelson.wordpress.com/2012/06/04/implicit-differentiation
A topnotch WordPress.com site. Future Directions (After Differential Calculus) →. June 4, 2012. Recall a circle consists of the points. Question: how do we construct the line tangent to a point on the circle? This problem really boils down to “How do we take the derivative of Equation (1)? 8221; Since this is the meat of the matter, lets study this problem. What we can try to do is differentiate everything in (1) with respect to. We could then use the chain rule. Then evaluate the derivative to obtain.
Alex Nelson | My Math Blog
https://pqnelson.wordpress.com/author/jbufordjr
A topnotch WordPress.com site. Author Archives: Alex Nelson. I like math. I like programming. Most of all, I love puzzles. Index] Calculus in a Single Variable. October 26, 2013. Just to keep readers in the loop: I have not forsaken you! I just have a job now… I got hired to program in Clojure, a peculiar member of the Java family and distant relation to the LISP clan. Nevertheless, … Continue reading →. September 22, 2012. Introduction to Double Integration. July 25, 2012. Notes on Mathematical Writing.
Optimization Example: Area of Rectangle | My Math Blog
https://pqnelson.wordpress.com/2012/06/04/optimization-example-area-of-rectangle
A topnotch WordPress.com site. First Derivative Test →. Optimization Example: Area of Rectangle. June 4, 2012. We have a string of length. It does not stretch. But we want to form a rectangle using this string as its boundary. Moreover we want this rectangle’s area is maximized. What to do? Spoiler alert: solution below! Well, if we form a rectangle, then it has sides. The perimiter is equal to the length of string). The area would be. This seems simple enough. We impose our constraint to write. Index] C...
Contents | My Math Blog
https://pqnelson.wordpress.com/contents
A topnotch WordPress.com site. I realize a blog format isn’t ideal for writing mathematical notes, especially if I need to recall something I wrote about ages ago. So this page just keeps track of the material I’ve written about. 11 Calculus in a Single Variable. Including elementary algebra and naive set theory. Analytical Table of Contents. Calculus in a Single Variable. Specifically their convergence or divergence. Series Convergence: What Does It Mean? The Definition of Convergence for Series. Fill i...
My Math Blog | "A topnotch WordPress.com site" | Page 2
https://pqnelson.wordpress.com/page/2
A topnotch WordPress.com site. Newer posts →. Directional Derivative, Gradient. July 3, 2012. Suppose we have a scalar function of several variables. Be some unit vector. How does. We can consider this quantity as a function. What does this look like? Continue reading →. Chain Rule for Partial Derivatives. July 3, 2012. We will need to use partial derivatives. 8230; Continue reading →. Curves, Velocity, “Classical Kinematics”. July 3, 2012. We are interested in describing the motion of my car. Well,.
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Simplicity | Derek Wise's blog on Mathematics, Physics, and other fun stuff.
Derek Wise's blog on Mathematics, Physics, and other fun stuff. Torsor a la George Hart. As a project with a certain 4-year-old relative of mine, we constructed the proof I described before that the outer vertices of George Hart’s 12-Card Star form a 4! Torsor. (I guess I didn’t say it that way before, but it’s true! Here’s our proof:. Last time I suggested using a deck of 12 cards like this:. You can get any permutation of these colors in our Star by. Rather than just a 4! When I was at the JMM. We each...
From Within Training for the 2012 Boston Marathon
From Within Training for the 2012 Boston Marathon. Tuesday, April 17, 2012. April 17 - - Running With Your Heart- - Boston 2012. A restless night of sleep had me waking up at 3:00 in the morning. It was hard to go back to bed with all that had happened and all the emotions that I had swirling about in my head and heart. After laying in bed and staring at the ceiling for what seemed forever, I managed to drift off again for a couple of hours. It seemed like the race was a lot longer than 26.2 miles...
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