Introduction to tropical geometry
Tropical geometry is a combinatorial shadow of algebraic geometry, offering new polyhedral tools to compute invariants of algebraic varieties. It is based on tropical algebra, where the sum of two numbers is their minimum and the product is their sum. This turns polynomials into piecewise-linear functions, and their zero sets into polyhedral complexes. These tropical varieties retain a surprising amount of information about their classical counterparts. Tropical geometry is a young subject that…
Read More ↓Title Statements
- Full title :Introduction to tropical geometry / Diane Maclagan, Bernd Sturmfels.
Summary
Tropical geometry is a combinatorial shadow of algebraic geometry, offering new polyhedral tools to compute invariants of algebraic varieties. It is based on tropical algebra, where the sum of two numbers is their minimum and the product is their sum. This turns polynomials into piecewise-linear functions, and their zero sets into polyhedral complexes. These tropical varieties retain a surprising amount of information about their classical counterparts. Tropical geometry is a young subject that has undergone a rapid development since the beginning of the 21st century. While establishing itself as an area in its own right, deep connections have been made to many branches of pure and applied mathematics. This book offers a self-contained introduction to tropical geometry, suitable as a course text for beginning graduate students. Proofs are provided for the main results, such as the Fundamental Theorem and the Structure Theorem. Numerous examples and explicit computations illustrate the main concepts. Each of the six chapters concludes with problems that will help the readers to practice their tropical skills, and to gain access to the research literature. --Provided by publisher.
Read More ↓Edition Statements
- Publication Date:©2015
Publication Statements
- Publisher(s):American mathematical Society
- Place of Publication:Providence, Rhode Island
- Language:eng
- Publication Date:©2015
The Physical Object
- Description:xii, 363 pages : : illustrations ; : 27 cm.
Edition Identifiers
- ISBN:9780821851982, 0821851985
- oclc:ocn891135672
- LC Classification:QA582
- Dewey Decimal:516.3/5
Table of Contents
1. Tropical Islands -- 2. Building Blocks -- 3. Tropical Varieties -- 4. Tropical Rain Forest -- 5. Tropical Garden -- 6. Tropic Connections.
Read More ↓Subjects
Writers
More from this Series
No reviews yet. Be the first to rate this work.
Related Works
more →
Real solutions to equations from geometry
Gröbner bases in commutative algebra
Cluster algebras and Poisson geometry
Algebraic design theory
Toric topology
Algebraic topology: applications and new directions : Stanf…
Algebraic topology: applications and new directions : Stanf…
Stanford Symposium on Algebraic Topology: Applications and New Directions, Stanford, Calif.)
Files & Downloads
-
Introduction to Tropical Geometry -- (.djvu)
DJVU · 4.2 MB · updated -
Introduction to Tropical Geometry -- (.pdf)
PDF · 14.7 MB · updated -
Introduction to tropical geometry -- (.djvu)
DJVU · 2.9 MB · updated -
Notices of the American Mathematical Society -- (…
PDF · 79.3 MB · updated -
Introduction to Tropical Geometry [second printin…
PDF · 5.6 MB · updated -
Introduction to Tropical Geometry -- (.pdf)
PDF · 3.9 MB · updated
Rate & Review