We will be presenting several different magic tricks that are based on mathematical principals or "Mathemagic". Magic can be a powerful tool for mathematics teachers if used properly. Of course, since it is entertainment, it can be used to dazzle the students. Thus it makes a great hook into a particular lesson. Or of course, it could be used as another "5 minute fillers". However, used properly mathemagic can be used to teach concepts as a core part of a lesson. Such magic tricks can also be a basis for good questions for homework or projects. Magical Tricks will be presented that are appropriate for grades 3-12.

In the episode "The Prisoner of Benda" of the television show Futurama, Professor Farnsworth and Amy create a mind switching machine, only to afterwards realize that when two people have switched minds, they can never switch back with each other. Throughout the episode, the Professor, with the help of the Globetrotters, try to find a way to solve the problem using two or more additional bodies. The solution to this problem is now called the Futurama Theorem, and is a real-life mathematical theorem, invented by Futurama writer Ken Keeler, who holds a PhD in applied mathematics. In this talk, we will introduce the mathematics behind the Futurama Theorem and present its proof.

Discontinuous Galerkin (DG) methods have gained in popularity during the last fifteen years because of their ability to address problems having discontinuities, such as those that arise in hyperbolic problems. DG methods allow discontinuous bases, which simplify both h- refinement (mesh refinement and coarsening) and p-refinement (method order variation). However, for DG methods to be used in an adaptive framework one needs a posteriori error estimates to guide adaptivity and stop the refinement process. The solution space consists of piecewise continuous polynomial functions relative to a structured or unstructured mesh. As such, it can sharply capture solution discontinuities relative to the computational mesh. It maintains local conservation on an elemental basis. The success of the DG method is due to the following properties: (i) does not require continuity across element boundaries, (ii) is locally conservative, (iii) is well suited to solve problems on locally refined meshes with hanging nodes, (iv) exhibits strong superconvergence that can be used to estimate the discretization error, (v) has a simple communication pattern between elements with a common face that makes it useful for parallel computation and (vi) it can handle problems with complex geometries to high order.
The local discontinuous Galerkin (LDG) finite element method is an extension of the DG method aimed at solving ordinary and partial differential equations containing higher than first-order spatial derivatives. In this talk, we present new superconvergence results for the LDG method applied to the second-order scalar wave equation in one space dimension. We show that the leading terms of the spatial discretization errors for the p-degree LDG solution and its spatial derivative are proportional to the (p + 1)-degree right Radau and (p + 1)-degree left Radau polynomials, respectively. More precisely, we prove that the global discretization error for the LDG solution is O(hp+3/2) superconvergent at the roots of the right Radau polynomial of degree p + 1 and the solution’s derivative converges as O(hp+3/2) at the roots of the (p + 1)-degree left Radau polynomial while a local error analysis and computational results and show higher O(hp+2) convergence rates at the roots of Radau polynomials of degree p + 1 on each element for both the solution and its derivative. These results are used to construct asymptotically correct a posteriori error estimates. We further show that the LDG discretization error estimates converge to the true spatial errors under mesh refinement. Finally, we prove that the global effectivity indices, for both the solution and its derivative, in the L2-norm converge to unity at O(h1/2) rates. Several numerical simulations are performed to validate the theory.

Located at Offutt Air Force Base near Omaha, Neb., U.S. Strategic Command (USSTRATCOM) is one of nine unified commands in the Department of Defense. USSTRATCOM integrates and coordinates the necessary command and control capability to provide accurate and timely information for the President, the Secretary of Defense, other National Leadership and regional combatant commanders.
Its responsibilities include space operations; Defense Department information operations; global missile defense; and combating weapons of mass destruction.
This presentation will include information on operations research and general mathematical applications at USSTRATCOM. Specific focus will be on reliability testing and the use of Mann Grubbs in confidence interval determinations. Also presented will be information on mathematical programs and careers at USSTRATCOM and the US Department of Defense.