CHIA LI-YAN KEW080007

1. i) Thinking
The process of using mind to consider something carefully.

ii) Critical Thinking
An intellectual process which involves synthesizing, applying, analyzing, evaluating and conceptualizing information.

iii) Creative Thinking
The ability to invent something new.

iv) Mathematical Thinking
A cognitive approach to a problem that is both logical and mathematically sound. It allow us to solve problem and not
restrict us to saying that there is only one correct solution.

v) Lateral Thinking
Solving problem through an indirect and creative approach. It is about reasoning that is not immediately obvious and
about ideas that may not be obtainable by using only traditional step-by-step logic.

2. I have never been taught critical thinking until I take this subject.

3. Analysis – The examination and evaluation of the relevant information to select the best course of action from
among various alternatives.

i) Argument
Analyze premises in order to find out whether the argument is valid or invalid. If conclusion logically follows the
premises, the argument is valid.

ii) Reasoning
Analyze base on logic, facts and evidence.

iii) Claims
Use reasoning. Argument is valid if reasons justify claims.

4x^3 - x^4 = 30
x^4 - 4x^3 + 30 = 0
Because 4x^3 - x^4 equals a positive integer, x cannot be a negative integer since ‘negative integer power 3’ will get
negative answer. Substituting x=0 or x=4 will get 4x^3 - x^4 = 0. The above equation do not have solution because
the graph y_1 = x^4 , y_2 = - 4x^3 and y_3 = 30 do not intersect each other.

4. i) Inductive reasoning in mathematics
Process of reasoning that a general principle is true because the special cases that we’ve seen is true. For example
after seeing that all triangle angle’s sums are 180 degrees even for different shapes of triangle, a conclusion can be
made that triangles has angle sum of 180 degrees.

It is useful to reason inductively in mathematics because it plays a part in discovery of mathematical truth.

ii) Inductive argument. Give example.
Most fish lay eggs.
Salmon are fish.
Therefore, salmon probably lay eggs.
It is possible for premises to be true and for conclusion to be false. Substitue Mako shark for salmon, and this would
be the case.

iii) Deductive argument. Give example.
All fish lay eggs.
Whale is a fish.
Therefore, whales lay egg.
Both premises are factually incorrect, so the conclusion though valid, is nonsense.

5. A conclusion made base on what we’ve seen to be true.

6. There are lot of solution to a problem. We are no restricted to only one solution. All solution have their pro and cons.

7. I have never been taught how to think mathematically in school or engineering mathematics courses.

8. Yes because I will then be able to solve any kinds of mathematical problem with different solution available.

9. Analyzing the problem from different perspective. Apply deductive, inductive thinking and mathematical thinking.

10. i) Yes, all students should learn both mathematical thinking and critical thinking so that we’ll be able to solve any
problem at ease, think out of the box, be able to not just look at something the way it is, and able to apply our
knowledge in engineering field effectively.

ii) Mathematically, the tangent can be obtained to be at infinity by taking the differential of y to be 0. Therefore, the
tangent parallel to x-axis does not exist.