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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