1. Math Bridging Course Tutorial 1 Chris TC Wong 16/8/2012 19:00 – 20:00 19/8/2012 16:30 – 17:30

2. What have we learnt after this two lectures Hard Skills – Definition of Limits – Problem Solving Idea : Divide and Conquer – Necessary and Sufficient Condition – Using Maxima as a mathematical tools Soft Skills – How to collaborate with others – How to stay awake in long lectures – How to express abstract idea into mathematical statements

3. Definition of Limit of Sequence

4. Definition of Limit of function

5. Comparison of two definitions

6. Demonstration to Exercises in Lecture

8. Necessary and Sufficient Condition If A is required to make B happen (no guarantee), then A is a necessary condition of B E.g. – You must be registered before being a student in university. Registering is a necessary condition for being a student in university. Well, you probably need to pay for the registration fee, too. If A happen alone can make B happen with guarantee, then A is an sufficient condition of B E.g. – You must pass AL and scored better than the cut-off score to be an IE student. ‘pass AL and scored better than the cut-off score’ is a sufficient condition for being an IE student But being an IE student do not necessary means that you have passed AL. You can be a DSE student.

9. Necessary and Sufficient Condition (Cont.) If A is necessary and sufficient to make B happens, A is a necessary and sufficient condition for B. – E.g. Under normal circumstance, completing circuit between power button and power supply of a computer can turn it on. – E.g. You get a scholarship if and only if you have very high GPA and is truly outstanding. – E.g. Love between a couple brings them to marriage. (?)

10. If and only if If A happens implies B happens, and B happens implies A happens, then we say A happens if and only if B happens. We says that two things are equivalent under this condition. Some lazy people just write this as “iff” – E.g. A number can be divided by 9 if and only if the sum of its digits can be divided by 9.

11. End