CHAI MING YUNG(KEW080004)

1.) What do understand by
i.) Thinking
The ability to analyze problem and hence solve the particular problem.

ii.) Critical Thinking
Skilled, active, interpretation and evaluation of observations, communications, information, and argumentation; careful, deliberate determination of whether one should accept, reject, or suspend judgment about a claim and the degree of confidence with which one accepts or rejects it

iii.) Creative Thinking
The ability to create new things, and solve problem using new methods.

iv.) Mathematical Thinking
A cognitive approach to a problem that is both logical and mathematically sound.

v.) Lateral Thinking
A heuristic for solving problems; try to look at the problem from many angles instead of tackling it head-on.

2.) Have you ever being taught critical thinking in school or before entering the faculty of engineering?
No, I think I do not learn critical thinking as a specific subject though I may learn it indirectly through problem solving and experiments.

3.) What do you understand by “analysis”?
Analysis is an investigation of the component parts of a whole and their relations in making up the whole before we proceed to the answers of the problems.

What do you do when you analyze
i.) Argument?
Argument is a fact or assertion offered as evidence that something is true; a course of reasoning aimed at demonstrating a truth or falsehood; the methodical process of logical reasoning. Hence, we should find out whether it is true or not.

ii.) Reasoning?
Reasoning is draw or come to a conclusion when we think logically. We need to have certain knowledge in the particular topic before giving out reasons.

iii.) Claims?
Claim is an assertion that something is true or factual. We need to investigate and find out more during the process of analysis.

Could you analyze this problem
Solve the equation 4x3 – x4 = 30. If there is no solution give reason(s).

There is no solution to this equation. This can be easily showed by finding the turning point of the equation 4x3-x4. The turning point of the equation is at x=0 and x=3. X=3 is the maximum point of the equation which is equal to 27. Therefore it is impossible that the equation can be equal to 30. Furthermore, if we sketch it out we can see that the graft does not cut x- axis. Hence, there is no solution.

4.) What do you understand by

i.) Inductive reasoning in mathematics. Why is it useful to reason inductively in mathematics?
Inductive reasoning is reasoning from detailed facts to general principles. It is very useful to reason inductively in mathematics because almost all theorems in mathematics are found inductively.

ii.) Inductive argument. Give example.
Inductive argument is when the premises are supposed to support the conclusion, if the premises are true, it is not possible that the conclusion would be false. Thus, the conclusion follows the premises and inferences.

Example:
1. Alvin is Chinese. (Premise)
2. Most Chinese drink tea. (Premise)
3. Alvin drinks tea. (Conclusion)
In this example, even if both premises are true, it is still possible for the conclusion to be false.

iii.) Deductive argument. Give example.
Deductive argument is when it is impossible for the premises to be true, but actually the conclusion false. Thus, the conclusion follows the premises and inferences. Therefore, it is supposed to be a definitive proof of the truth of the claim (conclusion).

Example:
1. All men have 2 eyes. (Premise)
2. Alvin was a man. (Premise)
3. Alvin has 2 eyes. (Conclusion)
In this example, if the premises are true, then it simply isn't possible for the conclusion to be false.

5.) What do you notice in common about inductive reasoning in mathematics and inductive argument in real life situation?
Both of them are used to solve problem faced either in mathematics or real life.

6.) Where do you find similarities in application of mathematical thinking in mathematics and in real life situation?
There is no specific solution for a problem, it can be solved in many ways.

7.) Have you being taught how to think mathematically in school or in your engineering mathematics courses?
No, we learn the skills needed to solve the problem but not the skills to think mathematically.

8.) Do you think a more in depth knowledge of mathematical thinking will help you in your engineering mathematics courses? In what way do you think?
Yes, it is because engineering is all about problems solving. A more in depth knowledge of mathematical thinking will definitely help us to solve mathematical problems in better ways.

9.) What do you understand by problem solving in mathematics?
To solve problem using logically deduced methods, in inductive and deductive ways.

10.) a.) Do you think critical thinking skills should be learned by all engineering students or a combination of critical thinking and mathematical thinking and why?
Both of them should be learned by all engineering students. It is because critical thinking enables an engineer to solve a problem more effectively. Besides, mathematical thinking enables an engineer to solve mathematic related problems more effectively.

b.) Can you find a tangent parallel to x-axis on the curve y = ln x? Explain your solution.
No, there is no solution because by having differential of y to be 0, the answer is infinity, which are not defined in mathematic.