Math 347 Test 3, Spring 2009

Wednesday 29 April, in class, worth 15%.
You may not use books, notes, or written materials, or electronic devices.
Practice Test 3 and Solutions.

Study Session
Monday 27 April, 6:00--7:30pm, in Altgeld 347.

Material
Chapter 7 (from the Chinese Remainder Theorem onwards), Chapter 8, Chapter 13, and Homeworks 8, 9, 10.

How to study

• First make summary notes of the important definitions, theorems, ideas and methods from each section. (This effort helps you mentally organize the material.) Learn the definitions, and the statements of the major theorems.
• Memorize the following definitions and proofs:
  • Theorem 7.30 (Chinese Remainder Theorem). Note: the first paragraph of the proof in the text proves uniqueness of solutions modulo N, and the second paragraph proves existence of a solution.
  • Theorem 8.16 (Rational Zeros Theorem)
  • Definition 13.10 (limit/convergence of a sequence)
  • Examples 13.11 as covered in class, including that lim(a_n +b_n)=lim a_n + lim b_n, assuming the limits of a_n and b_n exist
  • Proposition 13.12
  • Theorem 13.16 (Monotone Convergence)
• Go through your summary notes and proofs slowly, at least twice. As you do so, ask yourself questions about what the definitions and theorems mean, and how to use them. Write down your questions and your answers - you get better at writing mathematics by practicing writing mathematics!
• Re-work all homework problems. Some test questions will build directly on the homework.
• Work through Practice Test 3 (see Solutions), except ignore Problems 2 and 3. In Problem 5, "nondecreasing" means "increasing".