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Date: 2014-09-29 09:54:41 Partial differential equation Complex number Representation theory Operator theory Integral transforms Oscillator semigroup Fourier transform Mathematical analysis Fourier analysis Functional analysis		Matthew Rosenzweig Contact Information [removed] matthewhr.wordpress.com Add to Reading List Source URL: matthewhr.files.wordpress.com Download Document from Source Website File Size: 145,24 KB Share Document on Facebook

	QUATERNION ALGEBRAS KEITH CONRAD 1. Introduction A complex number is a sum a+bi with a, b ∈ R and i2 = −1. Addition and multiplication are given by the rules DocID: 1v0QV - View Document
	COMPLEX NUMBERS 5 minute review. Remind students what a complex number is, how to add and multiply them, what the complex conjugate is, and how to do division. They will also need to know that a root of a polynomial f (x DocID: 1tMHT - View Document
	EULER’S RELATION 5 minute review. Review Euler’s relation, eiθ = cos θ + i sin θ, commenting briefly on how it follows from the Maclaurin series of exp, sin and cos. Discuss how this means that any complex number DocID: 1tFGt - View Document
	THE ARGAND DIAGRAM 5 minute review. Review the argand diagram (aka argand plane, aka complex plane), the modulus and argument and the polar form of a complex number as z = r(cos θ + i sin θ). Also cover the geometric DocID: 1tB8n - View Document
	Is The Response in Liberia Succeeding? Positive indications Yaneer Bar-Yam New England Complex Systems institute October 17, 2014 The number of cases of Ebola in West Africa has been growing exponentially, and projection DocID: 1tqhz - View Document