*This is the British International School Phuket’s IB maths exploration (IA) page.*This list is for SL and HL students (exam 2020) and for Applications and Analysis students (exam 2021).Use this resource as a starting point and inspiration for your own personal investigation.

*This is the British International School Phuket’s IB maths exploration (IA) page.*This list is for SL and HL students (exam 2020) and for Applications and Analysis students (exam 2021).Use this resource as a starting point and inspiration for your own personal investigation.

Investigate what makes a number happy or sad, or sociable! 39) Zeno’s Paradox – Achilles and the Tortoise – A look at the classic paradox from ancient Greece – the philosopher “proved” a runner could never catch a tortoise – no matter how fast he ran.

40) Stellar Numbers – This is an excellent example of a pattern sequence investigation.

The great Indian mathematician Ramanujan discovered some amazing examples of these.

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

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.This also has some harder exams for those students aiming for 6s and 7s.The Past IB Exams section takes you to full video worked solutions to every question on every past paper – and you can also get a prediction exam for the upcoming year.33) The Chinese Remainder Theorem: This is a method developed by a Chinese mathematician Sun Zi over 1500 years ago to solve a numerical puzzle. 35) Fermat’s Theorem on the sum of 2 squares – An example of how to use mathematical proof to solve problems in number theory. 37) Mathematical proof and paradox – a good opportunity to explore some methods of proof and to show how logical errors occur.An interesting insight into the mathematical field of Number Theory. 38) Friendly numbers, Solitary numbers, perfect numbers.32) RSA code – the most important code in the world?How all our digital communications are kept safe through the properties of primes. A post which looks at the maths behind this particularly troublesome series. How strange things happen when we start to manipulate divergent series.29) The Riemann Hypothesis – one of the greatest unsolved problems in mathematics – worth

5) Diophantine equations: These are polynomials which have integer solutions.

This also has some harder exams for those students aiming for 6s and 7s.

The Past IB Exams section takes you to full video worked solutions to every question on every past paper – and you can also get a prediction exam for the upcoming year.

33) The Chinese Remainder Theorem: This is a method developed by a Chinese mathematician Sun Zi over 1500 years ago to solve a numerical puzzle. 35) Fermat’s Theorem on the sum of 2 squares – An example of how to use mathematical proof to solve problems in number theory. 37) Mathematical proof and paradox – a good opportunity to explore some methods of proof and to show how logical errors occur.

An interesting insight into the mathematical field of Number Theory. 38) Friendly numbers, Solitary numbers, perfect numbers.

||5) Diophantine equations: These are polynomials which have integer solutions.This also has some harder exams for those students aiming for 6s and 7s.The Past IB Exams section takes you to full video worked solutions to every question on every past paper – and you can also get a prediction exam for the upcoming year.33) The Chinese Remainder Theorem: This is a method developed by a Chinese mathematician Sun Zi over 1500 years ago to solve a numerical puzzle. 35) Fermat’s Theorem on the sum of 2 squares – An example of how to use mathematical proof to solve problems in number theory. 37) Mathematical proof and paradox – a good opportunity to explore some methods of proof and to show how logical errors occur.An interesting insight into the mathematical field of Number Theory. 38) Friendly numbers, Solitary numbers, perfect numbers.32) RSA code – the most important code in the world?How all our digital communications are kept safe through the properties of primes. A post which looks at the maths behind this particularly troublesome series. How strange things happen when we start to manipulate divergent series.29) The Riemann Hypothesis – one of the greatest unsolved problems in mathematics – worth $1million to anyone who solves it (not for the faint hearted!) 30) Time travel to the future: Investigate how traveling close to the speed of light allows people to travel “forward” in time relative to someone on Earth. 31) Graham’s Number – a number so big that thinking about it could literally collapse your brain into a black hole.9) Random numbers 10) Pythagorean triples: A great introduction into number theory – investigating the solutions of Pythagoras’ Theorem which are integers (eg. 11) Mersenne primes: These are primes that can be written as 2^n -1.12) Magic squares and cubes: Investigate magic tricks that use mathematics. 13) Loci and complex numbers 14) Egyptian fractions: Egyptian fractions can only have a numerator of 1 – which leads to some interesting patterns. Can all fractions with a numerator of 2 be written as 2 Egyptian fractions?

million to anyone who solves it (not for the faint hearted!) 30) Time travel to the future: Investigate how traveling close to the speed of light allows people to travel “forward” in time relative to someone on Earth. 31) Graham’s Number – a number so big that thinking about it could literally collapse your brain into a black hole.9) Random numbers 10) Pythagorean triples: A great introduction into number theory – investigating the solutions of Pythagoras’ Theorem which are integers (eg. 11) Mersenne primes: These are primes that can be written as 2^n -1.12) Magic squares and cubes: Investigate magic tricks that use mathematics. 13) Loci and complex numbers 14) Egyptian fractions: Egyptian fractions can only have a numerator of 1 – which leads to some interesting patterns. Can all fractions with a numerator of 2 be written as 2 Egyptian fractions?

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