Polymorphism-homogeneity and universal algebraic geometry

2 00 2 . Seven Lectures on the Universal Algebraic Geometry

Introductory Geometry: Algebraic Geometry

Poincaré and Algebraic Geometry

A few of the contributions of Poincaré to algebraic geometry are described, with emphasis on his late work on normal functions. A very brief description of some recent works is also given. Although the subject of algebraic geometry was not one of Poincaré's major preoccupations, his work in the field showed characteristic insight and brilliance and certainly has had a lasting effect. I shall br...

Euler and algebraic geometry

Euler’s work on elliptic integrals is a milestone in the history of algebraic geometry. The founders of calculus understood that some algebraic functions could be integrated using elementary functions (logarithms and inverse trigonometric functions). Euler realized that integrating other algebraic functions leads to genuinely different functions, elliptic integrals. These functions are not some...

Algebraic Geometry

Physical objects and constraints may be modeled by polynomial equations and inequalities. For this reason algebraic geometry, the study of solutions to systems of polynomial equations, is a tool for scientists and engineers. Moreover, relations between concepts arising in science and engineering are often described by polynomials. Whatever their source, once polynomials enter the picture, notio...