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Math 453 HW 1
Math 453 HW 1 (with solutions)
munh1
Prime Algorithms
Primality Tests and Factoring Algorithms
The Arzela-Ascoli Theorem
We will form a proof of the Arzela-Ascoli Theorem through use of the Heine-Borel theorem. We will also be considering some notions of compactness on metric spaces. The Arzela-Ascoli Theorem then allows us to show compactness, letting us state and prove Peano's existence theorem, pertaining to the existence of the solutions of a type of ODE. Then we will state the Kolmogorov-Riesz compactness theorem, allowing us to show compactness in $L^p$ spaces, building from the Arzela-Ascoli Theorem.
Oliver Williamson
Kesir Türevde Son Yaklaşımlar
Fractional Tufteffect Final Gates
Kübra Değerli
Series Representation of Power Function
In this paper, we derive and prove, by means of Binomial theorem and Faulhaber's formula, the following identity between $m$-order polynomials in $$T$$ $$\sum_{k=1}^{\ell}\sum_{j=0}^m A_{m,j}k^j(T-k)^j=\sum_{k=0}^{m}(-1)^{m-k}U_m(\ell,k)\cdot T^k=T^{2m+1}, \ \ell=T\in\mathbb{N}.$$
Kolosov Petro
The Hopf Fibration: Homotopy Groups of Spheres
Created for Stanford Mathematics Camp 2016. A brief introduction to the Hopf Fibration for introductory topology students.
Trey Connelly
Is e + $\pi$ irrational?
In mathematics, a rational number is any number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Since q may be equal to 1, every integer is a rational number. The set of all rational numbers, often referred to as ”the rationals”, is usually denoted by a boldface Q (or blackboard bold , Unicode ); it was thus denoted in 1895 by Giuseppe Peano after quoziente, Italian for ”quotient”. The decimal expansion of a rational number always either terminates after a finite number of digits or begins to repeat the same finite sequence of digits over and over. Moreover, any repeating or terminating decimal represents a rational number. These statements hold true not just for base 10, but also for any other integer base (e.g. binary, hexadecimal). A real number that is not rational is called irrational. Irrational numbers include √2, , e, and . The decimal expansion of an irrational number continues without repeating. Since the set of rational numbers is countable, and the set of real numbers is uncountable, almost allreal numbers are irrational.
jackson
Si $$AB=I$$ entonces $$A$$ es invertible y $$A^{-1}=B$$
Vamos a demostrar el notable teorema que dice que, dadas dos matrices cuadradras $$A$$ y $$B$$ del mismo tamaño, si $$AB=I$$, donde $$I$$ es la matriz identidad del mismo tamaño que la matrices $$A$$ y $$B$$, entonces $$A$$ es invertible y $$B^{-1}=A$$. La prueba será directa y sólo usaremos el hecho de que si $$|A|\ne0$$ entonces $$A$$ es invertible. La pregunta es si puedes tú, estimado estudiante, ofrecer otra prueba de la que aquí se sugiere. Sirva además este texto como un ejemplo de escritura con LaTeX.
Memo Garro
Template for submission to Société Mathématique de France
This is a template for the class to be used when publishing in a review from the Société Mathématique de France. The repository can be found at this address.
Filippo Alberto Edoardo Nuccio