Theorem

roots. Thus, a standard encryption procedure can be efficiently included in the process. This section lays out Dr. Johnston’s work and provides a simple worked example. 3.1 The Chinese Remainder Theorem Recall the standard statement of the Chinese Remainder Theorem [1]: Theorem 3.1 (Chinese Remainder Theorem). Let n1, n2, . . . , nk ∈ Z with every ni pairwise coprime and ni > 1. Let N = n1n2 . . . nk. Then there exists a unique x ∈ Z with 0 ≤ x < N such that x ≡ a1 mod n1 x ≡ a2 mod n2 . .…

If R and r is the Circumradius and Inradius of a non-degenerate triangle then due to Euler we have an Inequality stated as and the equality holds when the triangle is equilateral. This ubiquitous inequality occurs in the literature in many different equivalent forms [4] and also Many other different simple approaches for proving this inequality are known. (some of them can be found in [2], [3], [5], [17], and [18] ). In this article we present a proof for this Inequality based on two basic…

In this essay, we present a discussion about Bayesian methods in Spatial Statistics. Bayesian methods are approaches to statistical inferences which have been around for several decades and are also used in Geographic Information Systems. The application of these methods in practical problems has increased significantly within the last few years due to recent advances in tools for computation and simulation [1]. At the heart of any Bayesian data analysis method are the likelihood function, which…

Is Algebra Necessary? By The New York Times Algebra is necessary because it is the branch of mathematics that studies l combining elements of abstract structures according to certain rules . Originally these elements would put be interpreted as numbers or quantities, so that the algebra somewhat originally was a generalization . The adjective " algebraic " usually denotes a relationship with algebra , such as in algebraic structure . For historical reasons, it may also indicate a relationship…

Marie-Sophie Germain Although she is not well known, Marie-Sophie Germain contributed much to the fields of mathematics, philosophy, and physics and proved to be an exceptional physicist, mathematician, and philosopher throughout her lifetime. Overcoming all obstacles thrown her way, Germain fought relentlessly for her education and proved to not only her parents, but the whole mathematic and scientific community that women could be successful. From the start of her life, Germain was blessed…

Sophie Germain is one of France’s greatest female mathematician prior to revolutionary war, she was the daughter of Ambroise-François Germain and Marie-Madeleine Gruguelu. Her father worked as a part time deputy to the State-General. In his speeches he gave he referred to himself as a merchant and ardently defended the rights of the Third Estate, which he was there to represent. Somewhat later in his life time he became one of the directors of the Banque de France or in English the Bank of…

“Sophie Germain’s Theorem can be applied for many prime exponents, by producing a valid auxiliary prime, to eliminate the existence of solutions to the Fermat equation involving numbers not divisible by the exponent p” (Laubenbacher and Pengelley, 9). Legendre later used Germain’s findings in a supplement to the second edition of his book, Essai sur le Théorie des Nombres (O’Connor and Robertson). The Institut de France awarded Germain a medal for her work on Fermat’s Last Theorem and Germain…

Kenneth Arrow Kenneth J. Arrow was born in New York city August 23, 1921. Growing up in the Great Depression he was very partial to the thought of socialism. This factor was a huge part in his life because it would keep his views toward left sensibility.He received his undergraduate at the City College of New York. He would graduate from there with a degree in Science in Social Sciences, but a major in mathematics. From here kenneth was able to really begin his journey into the…

Discuss the Malthus theorem and the likelihood that it will result in world crisis as predicted. Please also include both New Malthusian and Anti-Malthusian points of view. The Malthus Theorem is a prediction that was created by an English economist named Thomas Malthus. He is known for his world acclaimed book, “An Essay on the Principle of Population”. He believed that population is geometrically doubling as it grows, while the food supply is increasing arithmetically. This eerie thought…

cool down sheet for the week. The second packet is a chapter 10 packet. There are a lot of terms and theorems in this chapter so she typed them up for…