Artificial intelligence has recently experienced remarkable advances, fueled by large
models, vast datasets, accelerated hardware, and, last but not least, the transformative …

In Chapter 1, we have seen how the algebra of the polynomial rings k [x1,..., xn] and the
geometry of affine algebraic varieties are linked. In this chapter, we will study the method of …

" This book is designed as a text for the first year of graduate algebra, but it can also serve as
a reference since it contains more advanced topics as well. This second edition has a …

Since 1973, Galois theory has been educating undergraduate students on Galois groups
and classical Galois theory. In Galois Theory, Fifth Edition, mathematician and popular …

The new sixth edition of Modern Algebra has two main goals: to introduce the most important
kinds of algebraic structures, and to help students improve their ability to understand and …

This paper presents a method that enables automated morphology analysis of partially
overlapping nanoparticles in electron micrographs. In the undertaking of morphology …

In this paper, an efficient statistical model, called generalized Gamma distribution (GΓD), for
the empirical modeling of synthetic aperture radar (SAR) images is proposed. The GΓD …

With the continued advance of computing power and accessibility, the view that" real
mathematicians don't compute" no longer has any traction for a newer generation of …

Galois theory is the interplay between polynomials, fields, and groups. The quadratic
formula giving the roots of a quadratic polynomial was essentially known by the …

Hidden in the heart of the theory of relativity, quantum mechanics, string theory, and modern
cosmology lies one concept: symmetry."" Symmetry has been a key idea for artists, architects …