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

http://nrich.maths.org/10329

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/10474

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

http://nrich.maths.org/10628

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

https://nrich.maths.org/10693



Attachments



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