Examples With Comments

//fibonacci as recurisve problem 
function fibonacciRecursion(n) {
    if (n = 0) {
        n = 1;
        fibonacciRecursion(n)
    } else {
        var fibParam1 = n - 1;
        var fib2Parm2 = n - 2;
        var fib1 = fibonacciRecursion(fibParam1) + fibonacciRecursion(fibParam2);
        console.log(fib1);
    }
}

//fibonacci as iterative problem
var count = 0;

function fibonacciIteration(a, b, count) {
    if (a = 0) {
        count++;
        return b;
    } else {
        var fib1 = a + b;
        a = count - 1;
        count++;
        console.log(a, fib1, count);
        fibonacciIteration(a, fib1, count);
    }
}

//1.2.6: Fermats Little Theorem Example
function square(x) { return x * x; }
                
function is_even(n) {
   return n % 2 === 0;
}
          
function square(x) { return x * x; }
                
function expmod(base,exp,m) {//base is our random number, others are our potential prime number 
   if (exp === 0) 
        return 1;
   else if (is_even(exp))//if the number is even use successive squaring 
        return square(expmod(base,exp/2,m)) % m;//recursive, random number smaller than n compute remaider of a to power of n modulo n
   else return (base * expmod(base,exp - 1,m)) % m;
}
          
function random(n) {
   return Math.floor(Math.random() * n);
}
          
function fermat_test(n) {
   function try_it(a) {//try the random number in expmod
      return expmod(a,n,n) === a;
   }
   return try_it(1 + random(n - 1));//generate a as a random number
}
          
function fast_is_prime(n,times) {//determines number of checks to run 
   if (times === 0)
        return true;
   else if (fermat_test(n))
        return fast_is_prime(n, times - 1);
   else return false;
}

fast_is_prime(91,3);


//1.3.1 Functions As Arguments 
//Creating a function that can take other functions within, functions passed in as parameters to be interchanged
function sum(term,a,next,b) {
   if (a > b)
        return 0;
   else return term(a) + 
               sum(term,next(a),next,b);
}