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@zareen said in MTH633 Assignment 1 Solution and Discussion:

Write down the elements of group under composition

Test 0: Is the operation associative? If not, then you’re done. 𝑇(𝑆)

is not a group. If the operation is associative, then proceed to…

Test 1: Does the set 𝑇(𝑆)
contains an identity? If you have a candidate function in 𝑇(𝑆), then what equations must it satisfy? Does it? If not, then 𝑇(𝑆)

is not a group. If you do have an identity, then proceed to…

Test 2: Does every element of 𝑇(𝑆)
have an inverse? Given an arbitrary function in 𝑓∈𝑇(𝑆), can you write down its inverse 𝑓−1∈𝑇(𝑆)? What equation must 𝑓 and 𝑓−1 satisfy? (Hint: you need the identity function.) If any function fails to have an inverse, then 𝑇(𝑆)

is not a group. If every function does have an inverse, then…

Congratulations! Your set 𝑇(𝑆)
is a group.
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Seven important keys for this are as follow.
1.Understand what forecasting is and is not
As a result of this a better environment will established for business activities. Accuracy and remove the game plan is also can be achieved.
2. Forecast demand and plan supply
In this way you can improve capital planning and customer service.
3. Communicate, corporate and collaborate
It is very helpful to get all important information for to forecast and it is trustable for user. More accurate and relevant forecast can be got.
4. Eliminate island of analysis
With this key more reliable and accurate forecast can be achieved.
5. Use tools wisely
With the help of this efficiency and effectiveness will be get.
6. Make it important
With the help of this forecasting key developers can take serious the issue that are under discussion. Accuracy and credibility can also be achieved.
7. Measure
Forecast performance can be including in the individual performance plans. Errors can be removed and improvement can be also achieved. Confidence of the forecasting can also be increased.

Heuristics are the strategies derived from previous experiences with similar problems. These strategies depend on using readily accessible, though loosely applicable, information to control problem solving in human beings, machines and abstract issues.[3][4]

The most fundamental heuristic is trial and error, which can be used in everything from matching nuts and bolts to finding the values of variables in algebra problems. In mathematics, some common heuristics involve the use of visual representations, additional assumptions, forward/backward reasoning and simplification.[5] Here are a few commonly used heuristics from George Pólya’s 1945 book, How to Solve It:[6]

If you are having difficulty understanding a problem, try drawing a picture. If you can't find a solution, try assuming that you have a solution and seeing what you can derive from that ("working backward"). If the problem is abstract, try examining a concrete example. Try solving a more general problem first (the "inventor's paradox": the more ambitious plan may have more chances of success).

Reff