MATH2003 Question List

After the review, you are anticipated to be able to answer these questions, for self-check:

Chapter 1 (Page 1-22)

1. What is Cartesian Product?
2. Describe the def of a function from $A$ to $B$.
3. How to prove that a function $f$ is injective? (page 8)
4. How to prove that a function $f$ is surjective? (page 8)
5. Define what is composite function $g\circ f$ ?(page 10)
6. How to prove Theorem 1.1.4

Chapter 2 (Page 23-54)

1. What is Archimedean Property?
2. What is Triangle Inequality?
3. What is $ϵ$ - neighborhood?

Chapter 3 (Page 55-101)

• What is Bernoulli’s Inequality?

Chapter 4

• What is Cluster Point?

Some tools for proving

• Mathematical Induction
• Contradiction

Chapter 6

• Chain rule:
• Cara thm
• 洛必达