Popescu-Pampu, Patrick.
What is the Genus? [electronic resource] / by Patrick Popescu-Pampu. - 1st ed. 2016. - XVII, 184 p. 20 illus. online resource. - History of Mathematics Subseries, 2162 2193-1771 ; . - History of Mathematics Subseries, 2162 .
Exploring several of the evolutionary branches of the mathematical notion of genus, this book traces the idea from its prehistory in problems of integration, through algebraic curves and their associated Riemann surfaces, into algebraic surfaces, and finally into higher dimensions. Its importance in analysis, algebraic geometry, number theory and topology is emphasized through many theorems. Almost every chapter is organized around excerpts from a research paper in which a new perspective was brought on the genus or on one of the objects to which this notion applies. The author was motivated by the belief that a subject may best be understood and communicated by studying its broad lines of development, feeling the way one arrives at the definitions of its fundamental notions, and appreciating the amount of effort spent in order to explore its phenomena.
9783319423128
10.1007/978-3-319-42312-8 doi
Mathematics.
History.
Algebraic geometry.
Algebraic topology.
Mathematics—Study and teaching .
History of Mathematical Sciences.
Algebraic Geometry.
Algebraic Topology.
Mathematics Education.
QA21-27
510.9
What is the Genus? [electronic resource] / by Patrick Popescu-Pampu. - 1st ed. 2016. - XVII, 184 p. 20 illus. online resource. - History of Mathematics Subseries, 2162 2193-1771 ; . - History of Mathematics Subseries, 2162 .
Exploring several of the evolutionary branches of the mathematical notion of genus, this book traces the idea from its prehistory in problems of integration, through algebraic curves and their associated Riemann surfaces, into algebraic surfaces, and finally into higher dimensions. Its importance in analysis, algebraic geometry, number theory and topology is emphasized through many theorems. Almost every chapter is organized around excerpts from a research paper in which a new perspective was brought on the genus or on one of the objects to which this notion applies. The author was motivated by the belief that a subject may best be understood and communicated by studying its broad lines of development, feeling the way one arrives at the definitions of its fundamental notions, and appreciating the amount of effort spent in order to explore its phenomena.
9783319423128
10.1007/978-3-319-42312-8 doi
Mathematics.
History.
Algebraic geometry.
Algebraic topology.
Mathematics—Study and teaching .
History of Mathematical Sciences.
Algebraic Geometry.
Algebraic Topology.
Mathematics Education.
QA21-27
510.9