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Algebra and number
1) Modular arithmetic – This technique is used throughout Number Theory. For example, Mod 3 means the remainder when dividing by 3.
2) Goldbach’s conjecture: “Every even number greater than 2 can be expressed as the sum of two primes.” One of the great unsolved problems in mathematics.
3) Probabilistic number theory
4) Applications of complex numbers: The stunning graphics of Mandelbrot and Julia Sets are generated by complex numbers.
5) Diophantine equations: These are polynomials which have integer solutions. Fermat’s Last Theorem is one of the most famous such equations.
6) Continued fractions: These are fractions which continue to infinity. The great Indian mathematician Ramanujan discovered some amazing examples of these.
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