Write summary chapter 2

README.md

@@ -69,8 +69,49 @@ that take other procedures as arguments.
 
 # Chapter 2
 
+Chapter 2 starts by introducing compound data structures to represent pairs and
+rational numbers.  Abstraction barriers allow implementing procedures on data
+types independent of the underlying representation. For example, we could reduce
+a rational-number to its lowest denominator at creation or display time. The
+book introduces interval arithmetic to deepen the understanding of data
+abstractions.
+
+Next, the book shows how to create more complex data structures such as lists
+and trees from cons. Higher-order procedures such as map and fold operate on
+these structures, for example, to update each element or to aggregate data.
+
+The book then expands on the idea of higher-order procedures by introducing a
+picture language as shown in the following image. We can manipulate a painter
+with different transformations to create more complex images. The book does not
+present a way to paint to the screen, so I have implemented the painter to
+create a Python script that can then draw the images via the PIL library.
+
 ![Corner Split](misc/corner-split-3.png)
 
+The next section introduces symbolic data that we utilize to implement a system
+for symbolic differentiation. One of my favorite things about the book is that
+it references concepts from other disciplines, such as calculus. I am happy that
+my high school knowledge of these topics is still present enough for me to work
+through the exercises.
+
+Next, we explore sets and different ways to present them. The section finishes
+with the implementation of Huffman Encoding trees.
+
+The rest of this chapter shows how to implement an algebra system utilizing a
+data-directed programming style. We create packages for different types of
+numbers, such as rational, complex, and imaginary numbers. We install methods
+for all basic algebraic operations, and the functions dispatch the correct
+procedure depending on the data type.
+
+Over the next sections and many exercises, we expand the system to automatically
+simplify the numbers by creating a hierarchy of data types. Eventually, we
+extend the system to support polynomials and even rational polynomials by
+extending our previous rational numbers implementation.
+
+I found these exercises challenging but incredibly rewarding. The algebra system
+was the point where I gave up when I worked through the book initially, so I
+felt a sense of accomplishment when I finished it on my second attempt.
+
 
 # Chapter 3