# STEP nrich course

March 24, 2017

The assignments are designed to develop your problem solving skills and provide an introduction to solving STEP (and STEP-like) problems. Most of the questions are taken from STEP I papers, with some STEP II questions appearing in later modules. The assignments also introduce mathematical ideas beyond the syllabus with lots of opportunities for extra reading. Hints and partial solutions are included.

Further reading for relevant maths topics:

https://plus.maths.org/content/ringing-changes

http://nrich.maths.org/10209

http://mathworld.wolfram.com/HolditchsTheorem.html

https://en.wikipedia.org/wiki/Holditch's_theorem

https://plus.maths.org/content/why-world-needs-pi

https://plus.maths.org/content/circles-rolling-circles

https://plus.maths.org/content/indeterminate-problems

https://en.wikipedia.org/wiki/Diophantine_equation

https://plus.maths.org/content/os/issue54/features/sangwin/index

https://nrich.maths.org/5480

http://nrich.maths.org/10595

https://plus.maths.org/content/os/issue55/package/index

https://en.wikipedia.org/wiki/Prosecutor%27s_fallacy

https://plus.maths.org/content/maths-minute-prosecutor-s-fallacy

https://plus.maths.org/content/os/issue55/features/dnacourt/index

https://plus.maths.org/content/understanding-uncertainty-breast-screening-statistical-controversy

https://plus.maths.org/content/understanding-uncertainty-visualising-probabilities

https://nrich.maths.org/10783

https://www.desmos.com/

http://nrich.maths.org/2199

https://en.wikipedia.org/wiki/Ternary_numeral_system

http://nrich.maths.org/1402

https://en.wikipedia.org/wiki/Inequality_of_arithmetic_and_geometric_means

https://plus.maths.org/content/conic-section-hide-seek

http://nrich.maths.org/10937

https://en.wikipedia.org/wiki/Euclid

https://plus.maths.org/content/how-euclid-once-rules-world

https://plus.maths.org/content/origins-proof

http://nrich.maths.org/1434

https://plus.maths.org/content/maths-minute-triangle-central

http://nrich.maths.org/10279

https://en.wikipedia.org/wiki/Euler%27s_totient_function

http://mathworld.wolfram.com/TotientFunction.html

https://nrich.maths.org/content/id/11472/CompoundAngles.pdf

http://nrich.maths.org/10981

https://en.wikipedia.org/wiki/Bertrand%27s_ballot_theorem

https://nrich.maths.org/10352

http://www.wikihow.com/Solve-a-Linear-Diophantine-Equation

https://plus.maths.org/content/life-and-numbers-fibonacci

https://plus.maths.org/content/maths-minute-take-it-limit

https://en.wikipedia.org/wiki/Logistic_map

https://plus.maths.org/content/alls-fair-love-and-maths

https://plus.maths.org/content/maths-minute-modular-arithmetic

http://nrich.maths.org/4350

https://artofproblemsolving.com/wiki/index.php/Modular_arithmetic/Introduction

https://plus.maths.org/content/modelling-nature-fractals

http://fractalfoundation.org/OFC/OFC-10-4.html

https://betterexplained.com/articles/understanding-the-monty-hall-problem/

https://plus.maths.org/content/maths-minute-bayes-theorem

https://plus.maths.org/content/meet-hyperbola

https://plus.maths.org/content/eulers-polyhedron-formula

https://nrich.maths.org/10448

https://xkcd.com/blue_eyes.html

https://xkcd.com/solution.html

https://en.wikipedia.org/wiki/Pathological_(mathematics)

https://plus.maths.org/content/basel-problem

https://plus.maths.org/content/infinite-series-surprises

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