Algebra and number 1) Modular arithmetic – This technique is used throughout Number Theory.For example, Mod 3 means the remainder when dividing by 3.Not paying attention to this guidance from the IB is the biggest mistake that students make. Code Breaking You may also enjoy taking part in our school’s code breaking website. 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.

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7) Patterns in Pascal’s triangle: There are a large number of patterns to discover – including the Fibonacci sequence.

8) Finding prime numbers: The search for prime numbers and the twin prime conjecture are some of the most important problems in mathematics.6) Continued fractions: These are fractions which continue to infinity.The great Indian mathematician Ramanujan discovered some amazing examples of these.19) Natural logarithms of complex numbers 20) Twin primes problem: The question as to whether there are patterns in the primes has fascinated mathematicians for centuries.The twin prime conjecture states that there are infinitely many consecutive primes ( eg. There has been a recent breakthrough in this problem.27) Prime number sieves 28) Recurrence expressions for phi (golden ratio): Phi appears with remarkable consistency in nature and appears to shape our understanding of beauty and symmetry.

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