here are some reading exercises for kevin houston's how to think like a mathematician

Chapter 2

1. What are Houston's 5 points for a systematic reading method?
2. Among techniques that Houston suggests, which have you been using when reading Hammack? Which haven't you been using?
3. Are there any pieces of advice that sound especially helpful for you?

Chapter 3

1. Why is it important to write solutions (or proofs) in complete sentences?
2. Exercise 3.1

Chapter 4

1. Critique the sentence: "For x > 0, f(x) > 0, g(x) > 0." (You may assume f and g are defined in advance.)
   Rewrite it more clearly.
2. Critique the following solution to the problem: Find the minimum of x²-x.
   Bad solution: f'=2x-1=0. x=1/2.
   Then write a good solution keeping in mind the advice in Chapters 3 and 4.

Chapter 5

1. Consider the following problem: Determine if x² + y² = z⁴ has infinitely many solutions in positive integers.
   Spend about 5-10 minutes thinking about how to solve it with Polya's 4-step method. Write down your ideas/plan and what you tried. (I don't care if you solve it, but if you did come to a conclusion, write that down as well.)