**PDF Free Download | Landscape of 21st Century Mathematics by Bogdan Grechuk**

## 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