Math Bridging Course Tutorial 1 Chris TC Wong

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

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

Definition of Limit of Sequence •

Definition of Limit of function •

Comparison of two definitions •

Demonstration to Exercises in Lecture •

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.

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. (? )

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.

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