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Algebraic generalisation

Algebraic generalisation. Unlock stories by generalising number properties. Why is this man so famous?. ANDREW WILES. Fermat’s last theorem. No positive integers satisfy the equation: n > 2. On doing mathematics….

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Algebraic generalisation

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  1. Algebraic generalisation Unlock stories by generalising number properties

  2. Why is this man so famous? ANDREW WILES

  3. Fermat’s last theorem No positive integers satisfy the equation: n > 2

  4. On doing mathematics… Perhaps I can best describe my experience of doing mathematics in terms of a journey through a dark unexplored mansion.

  5. Finding the furniture… You enter the first room of the mansion and it's completely dark. You stumble around bumping into the furniture, but gradually you learn where each piece of furniture is.

  6. The light goes on Finally, after six months or so, you find the light switch, you turn it on, and suddenly it's all illuminated. You can see exactly where you were. Then you move into the next room and spend another six months in the dark.

  7. After 7 years Wiles proved Fermat’s Last theorem So each of these breakthroughs, while sometimes they're momentary, sometimes over a period of a day or two, they are the culmination of -- and couldn't exist without -- the many months of stumbling around in the dark that proceed them.

  8. Algebraic generalisation Aim: • To explore algebraic generalisations of number strategies Success Criteria: • I can generalise from a number strategy • I can explain why an algebraic identity is always true • I can use identities to manipulate algebraic expressions • I know key algebra vocabulary and recording conventions

  9. EGG TECHNIQUE E – Explain the strategy or method used to solve the problem. G – Give other examples that use the same strategy or method. G – Generalise – use algebra to show the underlying structure.

  10. Proofs • Show that the sum of consecutive numbers is always odd • Show that the sum of three consecutive numbers is always divisible by three

  11. Sophie germain

  12. Other Facts • Took 358 years before it was proved • It took 7 years for Andrew Wiles to prove it • The proof is 150 pages long

  13. Who is New Zealand’s most famous mathematician? • Vaughan Jones • Only winner of Fields medal (the mathematics equivalent of the Nobel Prize)

  14. How did he win it? Vaughan Jones was attending a conference in Mexico…

  15. What do mathematicians do? His car broke down…

  16. What do mathematicians do? He started looking at a dot pattern on the cover of a maths textbook…

  17. What do mathematicians do? He began experimenting with the mathematics that he saw in the dot pattern…

  18. What do mathematicians do? And noticed a link between the dots and knots…

  19. What do mathematicians do? This lead to him developing a formula for describing knots: V(T) = (1/t) (t – 1 – t – 3 – t – 1 + t – 2 + 1) = t – 4 + t – 3 + t – 1 Which is now called the Jones’ polynomial

  20. WOW! What do mathematicians do? And he won the Fields Medal.

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