Write chapter 1 summary

README.md

@@ -12,3 +12,60 @@ execute `pacman -S mit-scheme` to install it. Then run the scripts via
 
 **This is currently (2020/12/16) work in progress.**
 
+
+# Chapter 1
+
+The first chapter of SICP starts by explaining the Scheme syntax. The first
+couple of exercises are simple enough. However, already at 1.5, the book
+foreshadows some of the difficulty that is about to come.
+
+```scheme
+(define (p) (p))
+(define (test x y)
+  (if (= x 0) 0 y))
+```
+
+The goal is to decide whether Scheme uses applicative-order-evaluation or
+normal-order-evaluation based on the above code. I have initially found the
+exercise confusing, but the code triggering an infinite loop is a clear
+indication of Scheme (or at least my version of Scheme, MIT Scheme) using
+applicative-order-evaluation.
+
+After this exercise, things get more comfortable again. The book proceeds to
+introduce if-else clauses, conditionals, as well as recursion. The book uses
+these primitives to compare iterative and recursive procedures based on a couple
+of typical CS example functions such as computing Fibonacci numbers, greatest
+common divisor, and fast exponentiation.
+
+Two new insights I had how using modulo instead of subtracting the divisor
+speeds up the GCD algorithm I learned in middle school and how exponentiation
+can run in O(log n) by halving even exponents.
+
+I wasn't able to prove the Golden Ration exercise at the time of working through
+this chapter. My knowledge of induction and proofs was too limited. I found that
+depressing at the time, and I wish they hadn't included that exercise.
+
+Nevertheless, the book moves on to further essential CS concepts such as Prime
+numbers and the Fermat primality test. Funnily enough, I used that probabilistic
+Prime test for a Project Euler exercise, wondering why I wasn't able to get the
+correct results. It turns out that this test detects probable primes (the book
+mentions that a little later and introduces the Miller-Rabin test that
+pseudoprimes cannot fool). On the one hand, it was cool to use an algorithm from
+a book directly. On the other hand, I was undoubtedly a bit annoyed by that
+story.
+
+The book moves on to discuss the runtime of some of the algorithms discussed to
+this point. It introduces some other mathematical concepts, such as calculating
+roots via the fixed-point method, Euler expansions, and the Newton method for
+finding minima/maxima. It was cool to see how the fixed-point method can be used
+to implement the Newton method if you plug the derivate of a function into it. I
+did my project presentation for math in high school about the Newton method. So
+this brought up cool memories. I wish I still had that presentation.
+
+Finally, SICP introduces the evaluation model for stateless functions and
+concludes with some exercises that require second-order procedures: procedures
+that take other procedures as arguments. 
+
+# Chapter 2
+
+