Landscape of 21st Century Mathematics by Bogdan Grechuk

Book Details






Landscape of 21st Century Mathematics

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Contents of Landscape of 21st Century Mathematics eBook

  • Number Theory
  • Gaps Between Primes
  • Prime Values of Polynomials
  • Primes in Sets of Integers
  • Finding Integer Solutions to Equations and Systems
  • Counting Solutions to Equations and Inequalities
  • Special Integer Sequences
  • Multiplicative Functions
  • Diophantine Approximation
  • Elliptic Curves
  • Other Topics in Number Theory
  • Combinatorics
  • Ramsey Theory on the Integers
  • Patterns in Sets of Integers
  • Patterns in Lattices
  • Sum-Product Phenomena
  • Other topics in Combinatorial Number Theory
  • Colouring of Graphs
  • The Ramsey Theory of Graphs
  • Expander Graphs
  • Other Topics in Graph Theory
  • Counting Problems
  • Topological Combinatorics
  • Design Theory
  • Analysis
  • Discrete Time Dynamical Systems
  • Continuous Time Dynamical Systems
  • Functions of Complex Variables and Generalizations
  • Properties of Polynomials
  • The Riemann Zeta Function and Other Special Functions
  • Inequalities in Analysis
  • Differentiability
  • Differential and Integral Equations
  • Transformations of Functions, Operators
  • Harmonic Analysis
  • Banach Spaces
  • The Embedding Theory of Metric Spaces
  • The Kakeya Conjecture
  • Approximation of Functions
  • Other Topics in Analysis
  • Algebra
  • Linear Algebra
  • Growth in Groups
  • Simple Groups
  • Existence of Groups with Special Properties
  • Other Topics in Group Theory
  • Rings
  • Fields
  • Geometry and Topology
  • Packing Problems
  • Combinatorial Geometry
  • The Isoperimetric Inequality and Beyond
  • Topics in Plane Geometry
  • Topics in Space Geometry
  • Knot Theory
  • Minimal Surfaces
  • General Surfaces
  • Topology in Higher Dimensions
  • Probability and Statistics
  • Random Graphs
  • Random Matrices
  • From Independence to Convex Sets
  • Discrete Time Stochastic Processes, Random Walks
  • Continuous Time Stochastic Processes
  • Bernoulli Convolutions
  • Percolation Theory
  • Compressed Sensing and Related Problems
  • Other Theorems Related to Probability
  • Algorithms and Complexity
  • Exact Algorithms
  • Approximation Algorithms and Complexity
  • Linear Programming and Polytopes
  • Numerical Algorithms
  • Average-Case Algorithms and Complexity
  • The Complexity Zoo
  • Decidable and Undecidable Problems
  • Logic and Set Theory
  • Squaring the Circle with and Without the Axiom of Choice
  • Defining Z in Q
  • Comparing Cardinalities of Sets
  • Characterization of Random Real Numbers

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