This textbook describes both the conventional and less common uses of linear regression in the practical context of today's mathematical and scientific research. It blends both theory and application to equip the reader with an understanding of the basic principles necessary to …
This book provides an introduction to fundamental methods and techniques of algebra over ordered fields. It is a revised and updated translation of the classic textbook Einführung in die reelle Algebra. Beginning with the basics of ordered fields and their real closures, the boo…
Intended for graduate courses or for independent study, this book presents the basic theory of fields. The first part begins with a discussion of polynomials over a ring, the division algorithm, irreducibility, field extensions, and embeddings. The second part is devoted to Galo…
"The past decade has seen numerous major mathematical breakthroughs for topics such as the finite field Kakeya conjecture, the cap set conjecture, Erdös's distinct distances problem, the joints problem, as well as others, thanks to the introduction of new polynomial methods. The…
"The past decade has seen numerous major mathematical breakthroughs for topics such as the finite field Kakeya conjecture, the cap set conjecture, Erdös's distinct distances problem, the joints problem, as well as others, thanks to the introduction of new polynomial methods. The…
The past decade has seen numerous major mathematical breakthroughs for topics such as the finite field Kakeya conjecture, the cap set conjecture, Erdös's distinct distances problem, the joints problem, as well as others, thanks to the introduction of new polynomial methods. Ther…
Incidences and classical discrete geometry -- Basic real algebraic geometry in R² -- Polynomial partitioning -- Basic real algebraic geometry in Rd -- The joints problem and degree reduction -- Polynomial methods in finite fields -- The Elekes-Sharir-Guth-Katz framework -- Const…