相关论文: Plane Geometry: An Elementary School Textbook (ca.…

An essay on Horndeski gravity, how it was formulated in the early 1970s and how it was 're-discovered' and widely adopted by Cosmologists more than thirty years later.

An introduction to applied mathematics written for students in engineering and science. Focus is on a rigorous presentation that also builds understanding by discussion, analogy, and examples. Discussion of concepts involved in modeling…

From antiquity the conceptual perception of space changed painfully and at a relatively slow pace. It went through mythological descriptions, religious beliefs, metaphysical worldviews and cosmological models with a mechanistic structure,…

This book is devoted to an informal discussion of patterns constructed for treating physical problems. Such patterns, when sufficiently formalized, are usually referred as "models", and tents to be applied not only in physics, but conquer…

These notes are loosely based on an introductory course in algebraic geometry given at Rutgers University in Spring of 2024. We introduce some relatively advanced topics at the expense of the technical details.

Present day mathematics is a human construct, where computers are used more and more but do not play a creative role. This situation may change however: computers may become creative, and since they function very differently from the human…

In the next 30 years, a new generation of space and ground-based telescopes will permit to obtain multi-frequency observations of faint sources and, for the first time in human history, to achieve a deep, almost synoptical monitoring of the…

In point of fact the Indian tradition in mathematics is long and glorious. It dates back to earliest times, and indeed many of the Indian discoveries from 5000 years ago correspond rather naturally to modern mathematical results.

We discuss Einstein's knowledge of projective geometry. We show that two pages of Einstein's Scratch Notebook from around 1912 with geometrical sketches can directly be associated with similar sketches in manuscript pages dating from his…

The addendum updates the results presented in the paper `Fake Projective Plane, Invent Math 168, 321-370 (2007)' and makes some additions and corrections. The fake projective planes are classified into twenty six classes. Together with a…

This is an essay that considering the knowledge structure and language of a different nature, attempts to build on an explanation of the object of study and characteristics of the mathematical science. We end up with a learning cycle of…

Implementation of a STEAM Makerspace to dynamize the teaching and learning processes of mathematics (with emphasis on geometry) of second-year students in the upper secondary level.

064<p type="texpara" tag="Body Text" et="abstract" bin="clone" >There are two schools, or lines of thought, that try to unify the apparently divergent laws of dynamics and thermodynamics and to explain the observed time-asymmetry of the…

These lectures were a part of the geometry course held during the Fall 2011 Mathematics Advanced Study Semesters (MASS) Program at Penn State (\url{http://www.math.psu.edu/mass/}). The lectures are meant to be accessible to advanced…

This text is reproduced with the kind permission of Fran\c{c}ois Ap\'ery. It was originally edited by Fran\c{c}ois Gu\'enard and Gilbert Leli\`evre for the book "Penser les math\'ematiques". It is the modified and abridged version of a text…

This book is an introductory course to basic commutative algebra with a particular emphasis on finitely generated projective modules, which constitutes the algebraic version of the vector bundles in differential geometry. We adopt the…

Astronomical observations were used as a marker for time and the Calendar from ancient times. A more subtle calibration of epochs is thrown up by an observation of the position of the solstices and equinoxes, because these points shift in…

All existing experimental results are currently interpreted using classical geometry. However, there are theoretical reasons to suspect that at a deeper level, geometry emerges as an approximate macroscopic behavior of a quantum system at…

A class of photoacoustic acquisition geometries in n-space is considered such that the spherical mean transform admits an exact filtered back projection reconstruction formula. The reconstruction is interpreted as a time reversion mirror…

This is a study of a problem in geodesy with methods from complex algebraic geometry: for a fixed number of measure points and target points at unknown position in the Euclidean plane, we study the problem of determining their relative…