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Solving Math Problems

Solving a math problem can be as easy as adding two plus five equals seven or as difficult as describing the geometry of a shape. So is there any method that applies to any problem in general? Here are some basic tips that will lead to some mathematical solutions.

Reading a math book is sort of like reading a drawing book, because you should read it with a pencil. You should read the theory and then examine the proofs of how it is formed. If the book is divided into chapters then read the entire chapter. Then if the book has a problem section (as math books often do) do as many problems as possible until you fill comfortable with your understanding of the subject.

This is simple advice, but now is the important part: the challenging word problems. These usually deal with the application of the math theory. This part can actually be fun. Yes that it: fun. It is fun because you don’t know the answer to the problem and have to use your mind to come up with a solution. It is a test of imagination and knowledge. Can the knowledge of the theories you learned be applied to a real word application?

Now read the question a couple of times. Try to see what kind of variables are given and determine what the problem is that needs solved. Do not look at any examples or math references yet. Try to find your own solution to the problem in your head. Then look back at the examples where you reached a problem that your own theories didn’t seem to solve. This is a simple method, but it helps you to better understand the problem, test your own ideas, and better understand the solutions that solve the problem.

After the first inspection of the problem, determine if it is purely mathematical or contains some graphical elements. It is very common for a math problem to have a graph or a shape. Which is seen in trigonometry and geometry and even calculus. If the problem is graphical, draw a picture. If it isn’t you are going to have to master “the art of the equation.” Restated, you may have an abstract math concept. Changing the equation might cause changes that your mind can’t exactly follow.

But dealing with the graphical first, it helps to draw a picture. It may be useful to use a Cad program. But just because you are using the computer doesn’t mean that you don’t have to plan your work. In the cad program draw the information that the problem gives. Then try to draw the answer or the representation of what is occurring in the problem. This gives you something tangible to picture in your mind. Pictures tell thousands of words, and you just drew your math problem. You are on the steps it takes to solve the problem.

Computers may also be used to crunch numbers. In general, there has to be a general understanding of the equation. Computers can crunch numbers, but the user has to have the proper input. The computer is useful for testing the results of several equations or graphing input, but the computer operator must solve the equation.

Now for the most rewarding part. The reason your mathematical quest began. It is the solution. But just as important as the solution is the way it is achieved. Are the steps logical and easy to follow? And is the solution correct? Test it. See if the solution is in the same range the answer is expected to be. Review the steps and check your solution.

Now is the moment when you test your knowledge and hard work. The solution either works or it doesn’t. But just because the answer is wrong doesn’t mean nothing was learned. And if this is a problem that is asking for a new solution. That is an answer or solution that hasn’t been tried before. If it is a new method or a problem that will take time or a life time to solve, such as a “Theory of Everything” the effort spent in trying to reach a solution may be a step towards or a “building block” to continue research.

In conclusion there is just those problems that intrigue the mind. And they appear when studying math or uncovered through real world situations. Solving these problems is similar to solving any problem rather it be on a test or in our studies. These problems can be fun and something that was undiscovered may be found. Math explains and is defined by the world we live in. Let’s just have some fun and see what discoveries we can make.

In math there are all kind of little discoveries to be found. You just need to find something interesting or see something that can be done in a different way. Maybe it is a challenging problem or that section of application of the theory. But don’t misjudge the value of your solution. Little discoveries add up to more and more discoveries. Maybe even a major discovery lies hidden in plain sight.

Here is an example of a problem that finally worked for me.

It took some time working off and on. Finally before I solved it was a period of trial and error. I knew the problem could be solved, but I was unsure you could solve it just using elementary mathematics. I learned a lot and think more work can be done with this problem.

Here is an example of another problem that I can’t solve without using the instructors and books solution.

I thought that you could just have one integral to solve the entire problem. This problem has led me to review calculus. I rediscovered “e” and now better understand the books solution. But I still believe there is a discovery to made here. I believe there is a simple integral that describes the problem. I have spent hours trying to find the simplest or even a different solution. Not all my work is shown here. Half of that work turned out to be mathematically untrue. But as mentioned before I didn’t stop the problem before I learned something. You will always learn something while trying to solve a challenging problem or any math problem you face.



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