Would you please suggest a good, readable introductory probability book for graduate level ? I have Shiryaev ‘s Probability with me, however i want to find another one. Preferably with solution manual for self study.

This question already has an answer here: A continuously differentiable map is locally Lipschitz 3 answers

This question already has an answer here: What are the recommended textbooks for introductory calculus? 8 answers Which calculus text should I use for self-study? 6 answers

What is a good reference to learn about differentials and related topics. Some of my questions are: Why is it possible to split $dy/dx$ into individual terms $dx$ and $dy$? In a separated differential equation such as $F(x)dx + G(y)dy = 0$, what is the physical intuition behind “$F(x)dx$”? When integrating the latter equation, what […]

Gödel’s Second Incompleteness Theorem says that if $ \mathsf{ZFC} $ is consistent, then $ \mathsf{ZFC} \nvdash \text{Con}(\mathsf{ZFC}) $, i.e., $ \text{Con}(\mathsf{ZFC}) $ is not provable in $ \mathsf{ZFC} $. Does anyone know of an authoritative reference that contains the claim that $ \neg \text{Con}(\mathsf{ZFC}) $ is also not provable in $ \mathsf{ZFC} $ if $ […]

My field is Coding Theory and my background is Algebraic, there are many applications of Genetic Algorithm in Coding Theory, I would to know the easiest and the most elementary and introductory note about “Genetic Algorithm in Coding Theory”, also is this algorithm using in Crypto too?

Based in many questions and answers like [1, 2, 3 ] and a comment a good comment here [4]. I would like to know that the space $H=H_0^1(\Omega)\cap H^2(\Omega)$ can be equiped with this norm $$\tag{1}\|\cdot\|_H=||\Delta\cdot||_{L^2}+||\nabla\cdot||_{L^2}+||\cdot||_{L^2},$$ this is the $H^2$-norm. Or, is it equipped with this one $$\tag{2}\|\cdot\|_H=||\Delta\cdot||_{L^2}+||\cdot||_{L^2}.$$ Can I say that if $H$ is […]

I am wondering if any of you could point me to any books and/or lecture notes that explain the Weierstrass $\wp$ function for a self-studying student of elliptic curves and functions. I am interested in any resources that may give the history of the Weierstrass function and its derivation. I do understand the basics of […]

I am starting to read about the Kronecker-Weber Theorem. It says that any abelian extension of $\mathbb{Q}$ is contained in a cyclotomic extension. I read somewhere that for quadratic extensions the proof is not very difficult. Can anyone tell me any reference material for the proof of the kronecker weber theorem for quadratic extensions ?

I read somewhere that there is a classical (due to Philip Hall?) construction of a Lie algebra associated to any discrete group $\pi$ which is obtained from filtration quotients of the descending central series of $\pi$. Can anyone recommend some introductory material on this construction?

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