Section 1: done

I certainly set a high bar for the first week and barely scraped through.

I also cheated slightly by skipping a couple of exercises (1.45 which I was just too tired to experiment with, and one of the math proofs)

Here's my programs for the final exercise

1.46:
(define (iterative-improve good-enough improve)
    (lambda (guess)
      (define (iter new-guess)
        (if (good-enough new-guess)
            new-guess
            (iter (improve new-guess))))
      (iter guess)))

(define (sqrt x)
    (define (good-enough guess)
      (display guess)
      (newline)
      (if (< (abs (- (square guess) x))
             0.001)
          true
          false))
    (define (improve guess)
      (average guess (/ x guess)))
    ((iterative-improve good-enough improve) x))

for fixed point:

(define (fixed-point f)
    (define tolerance 0.00001)
    (define (good-enough guess)
      (let ((new-guess (f guess)))
        (if (< (abs (- new-guess guess)) tolerance)
            true
            false)))
    (define (improve guess)
      ((average-damp f) guess))
    (iterative-improve good-enough improve))

(define (average-damp f)
    (lambda (x) (average x (f x))))

> ((fixed-point cos) 1.0)
0.7390885809390573
> (define (fixed-sqrt x)
    ((fixed-point (lambda (y) (/ x y)))
                  1.0))
> (fixed-sqrt 10)
3.162277665175675

It's been enjoyable, but considering the quantity of exercises, I really had to barge through it. I'm going to take the next week easier so I can review some of the lectures.

Posting next sundays target tomorrow.