Maths at Bondi Beach

Downloads

The downloads are in pdf form with approximate sizes shown.  I have also included versions in Mathematica notebooks which will require Wolfram CDF player from Wolfram to view.  Here is the link for downloading a free version of  CDF Player

Note: make sure the downloaded Mathematica file only has the ".nb" file extension - your browser may add ".txt" to it as well and CDF Player may not be able to render it.

  

Keywords:

  

Pascal's Theorem, Binomial Theorem, backward induction, weak induction,strong induction,well ordering principle, pigeonhole principle,wave equation, integral equation, recursive equation, characteristic function,generating function, combinatorial identities,calculus of variations,least time principle,Hamiltonian, Lagrangian, Fast Fourier Transform, De Morgan's Laws, contrapositive, epsilon delta proof, Bressoud,Erdos,Scholes,Euler,Feller,Feynman,Fibonacci. Fomin,Fourier, Gelfand,Ito, Kac,Lebesgue,Merton,Newton,Noether,Riemann,Stein,Taleb,Taylor,Vinogradov,von Neumann,Wiener, Sister Mary Celine Fasenmyer, de Finetti

  

  

  1. Mathematical Induction - Part 1  

    Background, types of induction, set theory, proof concepts, basic limit theory
    PDF (6 meg)   Mathematica notebook (2 meg)

  2. Mathematical Induction - Part 2  
     
    Induction applied in the context of Taylor's Theorem and Feynman path integrals
    PDF(8 meg)   Mathematica notebook  (2 meg)  For a link to the double slit experiment go here:  double slit video

       
  3. Mathematical Induction - Part 3
     
    Induction in the context of probability, "derangements" and the Mobius function 

    PDF (3 meg)  Mathematica notebook (1 meg)

  4. Mathematical Induction - Part 4  

    Induction in the context of recursive functions, the Fundamental Theorem of Arithmetic and Godel's Undecidability Theorem

    PDF (1 meg) Mathematica notebook (1 meg)

  5. Induction Problem Set
     
    PDF (5 meg) 

  6. Induction Solution Set
     
    PDF  (5 meg)     Mathematica notebook (5 meg)

  7. Why Ramsey's Theorem makes sense 

    PDF ( 0.2 meg)
  8.