相关论文: Foundations of algebraic surgery

These informal notes discuss a few basic notions and examples, with emphasis on constructions that may be relevant for analysis on metric spaces.

An algebraic deformation theory of algebras over the Landweber-Novikov algebra is obtained.

This is an overview of higher structural constructions in physics. The main motivations of our current attempt are as follows: (i) to provide a brief introduction to derived algebraic geometry, (ii) to understand how derived objects…

I give an introduction to algorithmic uses of the principle of inclusion-exclusion. The presentation is intended to be be concrete and accessible, at the expense of generality and comprehensiveness.

In this paper, for a given finitely generated algebra (an algebraic structure with arbitrary operations and no predicates) A we study finitely generated limit algebras of A, approaching them via model theory and algebraic geometry. Along…

This article provides a simple geometric interpretation of the quadratic formula. The geometry helps to demystify the formula's complex appearance and casts it into a much simpler existence, thus potentially benefits early algebra students.

We give a new proof of the fundamental theorem of algebra. It is entirely elementary, focused on using long division to its fullest extent. Further, the method quickly recovers a more general version of the theorem recently obtained by…

Lecture notes for an introductory course in elementary particles.

We show how one can do algebraic geometry with respect to the category of simplicial objects in an exact category. As a biproduct, we get a theory of derived analytic geometry.

This paper establishes a uniform procedure to split the operations in any algebraic operad, generalizing previous known notions of splitting algebraic structures from the dendriform algebra of Loday that splits the associative operation to…

In this Master of Science Thesis I introduce geometric algebra both from the traditional geometric setting of vector spaces, and also from a more combinatorial view which simplifies common relations and operations. This view enables us to…

Evaluation of basic integrals over Gaussian functions, traditionally utilized for electronic structure computations on molecules and solids, is discussed in a pedagogical form.

A brief survey of real algebraic structures on topological spaces is given. This article is written for the Gokova Gemetry/Topology Conference proceedings.

Passing from arithmetic schemes to algebraic schemes, in a similar manner we will have the computation of the \'etale fundamental group of an algebraic scheme and then will define and discuss the qc fundamental group of an algebraic scheme…

Several open problems in algebraic logic are solved.

In this survey, we describe the fundamental differential-geometric structures of information manifolds, state the fundamental theorem of information geometry, and illustrate some use cases of these information manifolds in information…

The author has recently introduced abstract algebraic frameworks of analogical proportions and similarity within the general setting of universal algebra. The purpose of this paper is to build a bridge from similarity to analogical…

We show that the symmetrization of a brace algebra structure yields the structure of a symmetric brace algebra.

The present text surveys some relevant situations and results where basic Module Theory interacts with computational aspects of operator algebras. We tried to keep a balance between constructive and algebraic aspects.

We discuss a version of the fundamental theorem of calculus in several variables and some applications, of potential interest as a teaching material in undergraduate courses.