Carr’s Synopsis – 19th century text for self taught geniuses – marks out this A-star topic for I/GCSE maths hopefuls.
I think that mathematically interested sixth formers, wanting to study the subject at University, should have some background knowledge. Many would have heard about the Riemann Hypothesis and a link to prime numbers; this subject is beyond the scope of this blog but school pupils, with knowledge of prime numbers and geometric progressions, can see how the Zeta Function relates to prime numbers in the above bit of mathematics. I like it anyway.
Transformations for IGCSE summary – too late for this year. Year 10?? Nice colours though.
Transformations for IGCSE maths – if any of my students don’t know them (and recent work suggest some don’t) then learn them now.
Prime numbers hang like beads on a necklace (except that would be cosh …) on this quadratic.
Counting to infinity to enumerate the fractions in efficient and inefficient ways.
Ancient Greek, geometric view of prime numbers.
Area sandwich proves that finding areas is opposite to differentiation – The Fundamental Theorem of Calculus
Geometric Progressions, essential for Core AS mathematicians, appear in Victorian textbook, Synopsis of Elementary Results. In the case where the sum to infinity exists, there is a nice proof by similar triangles.
Big integrals, lines and planes and whoever thought that one hundred and thirty one thousand and seventy two divided by one hundred and five would be an answer to and A level question? It must be Further Pure 3 – write out now available at http://jped.co.uk/ExamBucket/examfiles/FP3Sum13W.pdf.