Number Theory

  1. Advanced Topics and Connections
    1. Algebraic Number Theory
      1. Algebraic Numbers
        1. Algebraic Integers
          1. Number Fields
            1. Rings of Integers
              1. Unique Factorization
              2. Elliptic Curves
                1. Basic Definitions
                  1. Group Law
                    1. Rational Points
                      1. Elliptic Curve Cryptography
                        1. Connection to Diophantine Equations
                        2. Computational Number Theory
                          1. Algorithms and Complexity
                            1. Computer Algebra Systems
                              1. Large Number Arithmetic
                                1. Parallel Algorithms
                                2. Applications to Other Areas
                                  1. Coding Theory
                                    1. Combinatorics
                                      1. Geometry
                                        1. Physics

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                                      13. Cryptographic Applications

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                                      1. Foundations of Number Theory