Gu J. Geometry Problems For Math Competitions 2021 torrent

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This book builds upon the earlier volume "Problems in Analysis", more than doubling it with a new section of problems on complex analysis. The problems on real analysis from the earlier book have all been checked, and stylistic, typographical, and mathematical errors have been corrected. The problems in complex analysis cover most of the principal topics in the theory of functions of a complex variable. The problems in the book cover, in real analysis: set algebra, measure and topology, real- and complex-valued functions, and topological vector spaces; in complex analysis: polynomials and power series, functions holomorphic in a region, entire functions, analytic continuation, singularities, harmonic functions, families of functions, and convexity theorems.
Preface
Real Analysis
Set Algebra and Function Lattices
Topology, Limits, and Continuity
Real- and Complex-valued Functions
Measure and Topology
Measure Theory
Topological Vector Spaces
Complex Analysis
Elementary Theory
Functions Holomorphic in a Disc
Functions Holomorphic in a Region
Entire Functions
Analytic Continuation
Singularities
Harmonic Functions
Families of Functions
Convexity Theorems
Solutions
Real Analysis
Complex Analysis
Bibliography
Symbol List
Glossary / Index