Math 347 Test 3, Spring 2009
Wednesday 29 April, in class, worth 15%.
You may not use books, notes, or written materials, or electronic
Practice Test 3
Monday 27 April, 6:00--7:30pm, in Altgeld 347.
Chapter 7 (from the Chinese Remainder Theorem onwards), Chapter 8,
Chapter 13, and Homeworks 8, 9, 10.
How to study
Start studying TODAY.
- 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(an
+bn)=lim an + lim bn, assuming the limits
of an and bn 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".