### RESOURCES

Come savor cookies (and brownies!) and enjoy an introductory math talk! After the presentation there will be time to socialize with fellow students and faculty members.
Math & Cookies take place in FOBS12 (unless otherwise noted).

Upcoming Events:

Math & Cookies: Friday, Dec. 9, noon - 1:00 p.m.
Location: REH 109
Speaker: Gerald A. Golding, Rutgers University
Title: Electromagnetic Waves and the Quantum Wave Function: Linear or Nonlinear?

Wave motion is everywhere in nature - water waves, vibrations in strings and surfaces, sound waves, electromagnetic waves and at the submicroscopic level, the still-mysterious wave functions that describe the behavior of quantum particles. Mathematically, wave motion is described by solutions to a class of partial differential equations called wave equations. Many wave equations are linear, which means that the superposition of two solutions is again a solution. But in almost all real physical situations, linearity is an approximation that eventually breaks down. Sometimes nonlinear wave equations provide better descriptions, describing or predicting new phenomena. The exception to this is quantum mechanics, with wave functions obeying Schrödinger’s famous equation. Here linearity is taken to be absolutely exact - indeed, a basic axiom of the theory. In this non-technical seminar, I will explore briefly some aspects of linearity and nonlinearity in electromagnetism and quantum theory. These are domain of my ongoing research - including the question of whether linearity in quantum mechanics should remain a fundamental assumption.

PAST EVENTS:

Math & Cookies:  Wednesday Nov. 2, 3:30-4:30 p.m.
Speaker:  Hyunchul Park
Title:  Absolutely Convergent Sequence, a Measure of Finite Variation, and Hardy Space

Abstract:  In Mat252 (Calculus 2) students are first exposed to a notion of absolutely convergence of real numbers, which describes a strong convergence of series compared to a weak notion of convergence of series, conditional convergence. Conditional convergent series can be rearranged to converge to any numbers including $\pm\infty$ while the absolutely convergent series converges to the same limit under any rearrangement and can be written as difference of two convergent nonnegative series. In mathematics, there are other cases that are similar to the notion of absolute convergence of series of numbers. We will introduce measure, which is a generalization of length or area and introduce a notion of measure of finite variation. Measures of finite variation can be decomposed into positive and negative parts (Hahn-Jordan decomposition). We also discuss Harmonic functions and Hardy space. For Harmonic function which is in the Hardy space, it can be written as a difference of two nonnegative harmonic functions.

Math Seminar:  Wednesday Oct. 12, 3:30-4:30 p.m.
Speaker:  Natalie Cartwright
Title:  Electromagnetic Pulse Propagation and Asymptotic Expansions:  The basics, applications, and the yet unknown
Abstract:  Asymptotic expansions of integrals have been used to provide insight into electromagnetic pulse propagation since the early 1900’s.  Theoretical advances in asymptotic techniques through the 20th century have enabled more studies, and led to some surprising results.   Of considerable interest is the so-called Brillouin precursor whose peak amplitude experiences algebraic, rather than exponential, decay with propagation distance.  It has been speculated that this slowly-decaying precursor may be used for improved detection and imaging.  Here, we will discuss its use in a synthetic aperture radar application.

Speaker: Laura Turner
Title: To infinity ... and beyond!
Subtitle: Some Paradoxes of the Infinite Throughout History

Abstract: Zeno's dichotomy paradox states (roughly) that to reach the fi nish line in a race, a runner must fi rst get halfway there. Before he can get halfway there, he must get a quarter of the way there. Before traveling a quarter, he must travel one-eighth; before an eighth, one-sixteenth; and so on. Since this sequence continues forever, how can the runner reach the finish? How can he even take a single step?
The infi nite and the in finitely small | confounded mathematicians from antiquity. In this talk, I'll touch upon a few interesting discussions related to the infi nite, focusing on known paradoxes throughout history related to physics and calculus.

Location: FOB S14
Time: 11 a.m. - 12 p.m.
Date: Wednesday April 9, 2014

Speaker: Stanley R. Huddy

Title: Chaos and Butterflies

Abstract: If a butterfly flaps its wings in Brazil does this set off a tornado in Texas? Why are weather reports often incorrect? Join me as we answer these questions and more through a visually interactive introduction to chaos theory.

Location: FOB S14
Time: 11 a.m. - 12 p.m.
Date: Wednesday February 19, 2014

The Pythagorean Theorem

By Francis Valiquette

Abstract: Given a right triangle, the Pythagorean Theorem says that c2 = a2 + b2. How many proofs of this theorem do you know?
In the book, The Pythagorean Proposition, Elisha Scoot Loomis gives 256 proofs! At our next Math & Cookies get together I will show 2 of these proofs. If you have had Axiomatic Geometry, you'll be able to help derive the two proofs.

11 a.m.-12 p.m. Wednesday, Nov. 13, 2013

FOB S-12
MATHEMATICS CONFERENCE ROOM