CHAN XING KHUAN KEW080005

1.) What do understand by
i.) Thinking
The ability to judge and consider something carefully.

ii.) Critical Thinking
Skilled, active, interpretation and evaluation of observations, communications, information, and argumentation.

iii.) Creative Thinking
The ability to create solution to a problem but in a new and better way.

iv.) Mathematical Thinking
An approach to a problem which is mathematically and logically sound. In short, it gives us the knowledge of the varieties of solutions to a problem and not just one concrete solution.

v.) Lateral Thinking
A way of solving problems by rejecting traditional methods and employing unorthodox and apparently illogical means



2.) Have you ever being taught critical thinking in school or before entering the faculty of engineering?
No. But I believe I had been practicing elements of critical thinking myself before entering the faculty of engineering.



3.) What do you understand by “analysis”?
An investigation of the component parts of a whole and their relations in making up the whole.

What do you do when you analyze
i.) Argument?
Since argument is defined as “a fact or assertion offered as evidence that something is true”, when analyzing an argument, the validity, suitability use of facts used in the argument must be analyzed.

ii.) Reasoning?
Since reasoning is defined as “the use of reason, especially to form conclusions, inferences, or judgments”, when analyzing reasoning, the use of reasons must be analyzed in term of its suitability and validity.

iii.) Claims?
Since claims is formed by a groups of arguments, when analyzing claims, the arguments used to support the claims must be analyzed whether it is true or false.

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.



4.) What do you understand by
i.) Inductive reasoning in mathematics. Why is it useful to reason inductively in mathematics?
An inductive reasoning is when you move from a set of examples to a theory that you think explains all the examples, as well as examples that will appear in the future. In mathematics, inductive reasoning is often used to make a guess at a property, and then deductive reasoning is used to prove that the property must hold for all cases, or for some delimited set of cases. Therefore it is very useful to reason inductively in mathematics because almost all theorem in mathematics are found inductively.


ii.) Inductive argument. Give example.
An inductive argument is one in which the premises are supposed to support the conclusion in such a way that if the premises are true, it is improbable that the conclusion would be false. Thus, the conclusion follows probably from the premises and inferences.
Example:
1. Socrates was Greek. (premise)
2. Most Greeks eat fish. (premise)
3. Socrates ate fish. (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.
A deductive argument is one in which it is impossible for the premises to be true but the conclusion false. Thus, the conclusion follows necessarily from the premises and inferences. In this way, it is supposed to be a definitive proof of the truth of the claim (conclusion).
Example:
1. All men are mortal. (premise)
2. Socrates was a man. (premise)
3. Socrates was mortal. (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?
In both situations, inductive argument is used to solve problem. Moreover, in both situations, almost all theorem or facts are acquired through inductive approach.



6.) Where do you find similarities in application of mathematical thinking in mathematics and in real life situation?
There are more than one solution to a problem.



7.) Have you being taught how to think mathematically in school or in your engineering mathematics courses?
No. We were gave a lot of mathematic questions to solve but were not taught how to think mathematically to approach a question.



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. Engineering is all about solving problems and a more in depth knowledge of mathematical thinking will help engineer to be able to solve mathematical problems better.



9.) What do you understand by problem solving in mathematics?
To be able to solve a mathematical problems with critical, mathematical and inductive approach.



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 critical thinking and mathematical thinking skills should be learned by all engineers. This is because critical thinking allows an engineer to be able to find a solution to a problem in a more effective way and the solution provided can solve the problem critically. Mathematical thinking allows an engineer to be able to solve mathematic related problems more effectively. These two skills are the two most important skills that an engineer must have.

b.) Can you find a tangent parallel to x-axis on the curve y = ln x? Explain your solution.
The tangent parallel to x-axis does not exist because if we take the differential of y to be 0, the answer that we will get is infinity, which are not defined in mathematic.