The Power of Math: How It Shapes Our World

[Satonam]

This is a question many students ask their teachers from the beginning of time; however, I feel like a solid answer has never been offered. We learn all these rules, concepts, and tests, but we have no idea of how they relate to the real world. I think if we could -not just answer, but demonstrate to students the power of math, then their interest in the STEM field would increase tenfold!

For example:

Why do we learn how to count, add, subtract, multiply and divide? It's the first thing we learn! The answer is, (one of many) we use those fundamental tools in the real world to keep track of money, as well as objects. For example, let's assume there are an assortment of chairs in an auditorium. We will also assume the chairs are arranged in a rectangular shape. Your boss tells you to count those chairs and make sure there are at least 100. However, because you know geometry and you know that the width and length of a rectangle equals its area, you also know that there are 100 chairs in the auditorium only if the width and length of the arranged chairs are factors of 100; like 5 and 20, or 4 and 25 respectively.

I recently finished taking Calculus II during the Summer. I earned an A, however, that grade represents my ability to solve problems in a mathematics course, not apply it to the real world. I learned new tools and techniques, including the various tests used to determine whether a series converges or diverges. In spite of it all, I have no idea how I am going to apply these techniques when I get a job. When is it relevant?

I would like for everyone to post below about any concepts or techniques you learned and somehow relate it to something in the real world.

 

[symbolipoint]

The people who will use mathematics in the real world are the natural scientists, computer scientists, physical scientist, and the engineers - mostly. Most people do not become such scientists nor engineers. Another area using significant mathematics beyond just Basic Math are some of those in finance. Exponential growth and decay Mathematics is important for finance work (logarithms, functions for exponentiation, log functions, growth rates, interest rates, complicated situations in cost, price, revenue, profit).

Health-care and nursing rely on some mostly basic arithmetic, maybe basic algebra. Administrative or research might use statistics or probability knowledge (?)

Only a guess, carpenters and electricians may need some algebra and trigonometry.

Not really the pleasant optimistic answer you wanted.

 

[mathwonk]

ive always wanted to know this answer. maybe if more people knew what quasi coherent sheaves are they could chat socially with their math friends?

 

[HallsofIvy]

This is a question many students ask their teachers from the beginning of time; however, I feel like a solid answer has never been offered.

I presume you mean that you have never been given an answer that you understood.

We learn all these rules, concepts, and tests, but we have no idea of how they relate to the real world. I think if we could -not just answer, but demonstrate to students the power of math, then their interest in the STEM field would increase tenfold!

For example:

Why do we learn how to count, add, subtract, multiply and divide? It's the first thing we learn! The answer is, (one of many) we use those fundamental tools in the real world to keep track of money, as well as objects. For example, let's assume there are an assortment of chairs in an auditorium. We will also assume the chairs are arranged in a rectangular shape. Your boss tells you to count those chairs and make sure there are at least 100. However, because you know geometry and you know that the width and length of a rectangle equals its area, you also know that there are 100 chairs in the auditorium only if the width and length of the arranged chairs are factors of 100; like 5 and 20, or 4 and 25 respectively.

Are you giving this as an example of an application of math to the real world? I have seen effectively this same example in a number of basic arithmetic texts so your statement that students are not given such examples is false.

I recently finished taking Calculus II during the Summer. I earned an A, however, that grade represents my ability to solve problems in a mathematics course, not apply it to the real world. I learned new tools and techniques, including the various tests used to determine whether a series converges or diverges. In spite of it all, I have no idea how I am going to apply these techniques when I get a job. When is it relevant?

What text did you use? Every Calculus text I have seen has many examples of applications of Calculus. Of course, they have to be simplified because the author cannot assume that every student has experience with the particular application. You really learn to apply math to, say, engineering in an engineering class. You learn to apply math to business administration in a business administration class. That is the way it should be!

I would like for everyone to post below about any concepts or techniques you learned and somehow relate it to something in the real world.

I think everyone has experience using, say, addition to find the total cost of a grocery list or division to determine how many miles per gallon they are getting- things they learned in a math class. If you want examples of more advanced math, then you want engineers, physicists, etc. to give their experiences.

 

[mathwonk]

one of my favorite books is the differential equations book by martin braun. he starts off with a fascinating story of how scientists using differential equations proved conclusively that the famous painting "Disciples at Emaus" attributed perhaps to Vermeer and bought for $170,000 by the Rembrandt society, was in fact a modern forgery, based on the radioactive decay rates of the materials in the paint. He also discusses the collapse of the Tacoma narrows bridge, which you can google as "galloping gertie", because engineers failed to correctly estimate the forces due to wind and the effect on the bridge as it was built, or perhaps in this case their superiors failed to heed their warnings. There are also interesting analyses of "predator-prey" models which help explain the variation in certain interlinked populations such as sharks and food fish. For example, he gives a case where people introduced a predator insect to help control an insect infestation, and then upped the ante by also adding chemical poisons, only to find the infestation increased, because they were also killing off the predator who helped control the unwelcome insects. In a similar unintuitive situation, I believe they found that fishing increased the food fish population, due perhaps to reducing the food fish population to a point where the sharks died off and then the food fish could recover. The whole book is well written and interesting both in its discussion of theory and applications. used copies are available at this link:

http://www.abebooks.com/servlet/SearchResults?an=martin+braun&sts=t&tn=differential+equations

 

[aikismos]

This is a question many students ask their teachers from the beginning of time; however, I feel like a solid answer has never been offered. We learn all these rules, concepts, and tests, but we have no idea of how they relate to the real world. I think if we could -not just answer, but demonstrate to students the power of math, then their interest in the STEM field would increase tenfold!

I would like for everyone to post below about any concepts or techniques you learned and somehow relate it to something in the real world.

 

[symbolipoint]

I presume you mean that you have never been given an answer that you understood. Are you giving this as an example of an application of math to the real world? I have seen effectively this same example in a number of basic arithmetic texts so your statement that students are not given such examples is false. What text did you use? Every Calculus text I have seen has many examples of applications of Calculus. Of course, they have to be simplified because the author cannot assume that every student has experience with the particular application. You really learn to apply math to, say, engineering in an engineering class. You learn to apply math to business administration in a business administration class. That is the way it should be!I think everyone has experience using, say, addition to find the total cost of a grocery list or division to determine how many miles per gallon they are getting- things they learned in a math class. If you want examples of more advanced math, then you want engineers, physicists, etc. to give their experiences.

Very blunt, and maybe goes with other characterizations, but mostly correct. Who usually becomes good at Math? The engineers and scientists. Guess why!

 

[aikismos]

I think the question of the usefulness of mathematics is one loaded with much ambiguity. The REAL WORLD is almost a useless phrase. Certainly, the daily existence of an immigrant farm worker in the state of California, USA is a very different "real world" than that of the economist working for the US Federal Reserve. Unfortunately, the question of the practical uses of mathematics is largely subjective depending on your worldview.

Tradespeople certainly need to know their fractions and some of the basics of algebra, geometry, and trig, but I spoke with a civil engineer who said in her 35 year career, the number of times she used trigonometry could be counted on one hand. Ultimately, in the real world, Mathematics the Calculation has been relatively well automated, much like the automation of factory jobs in the prior centuries. The real value of mathematics these days in the "real world" which I tend to take as the day-to-day experience of the working stiff is not so much in practice, but in understanding. The true value of mathematical methods are not the utility of the calculation, but the philosophy and methodologies they teach. Axiomatic reasoning is something applicable in a much broader fashion than theorems of geometry, but rather to knowledge discrimination and retention. Math is important because it separates the educated ruling class (even those who are ignorant at the top rely on cadres of technical workers to maintain their status) from those who are socially stuck in the "real world".

I would have to insist the prime example of this to be the private capital global economic system whereby fiscal growth which occurs exponentially has the potential to destroy countries. Austerity measures in Greece are essentially a mathematical system to keep poor Greeks working for wealthy bankers all over Europe. The modern society is built on mathematical technique either directly like mathematics and economics or indirectly through science, technology, and engineering, however, one doesn't have to know almost any of it to enjoy the fruits of society. But those who understand it tend to take advantage of those who don't, sometimes wherein the latter have no choice. The typical home mortgaged in the US will ultimately results in an interest payment cost of 150% of the principal being paid out over the amortization.

Day in and day out, lives in the "real world" are affected by choices that are affected by statistical considerations. Here is where math is I believe the most utilitarian. Take this article that has to do with Ashley Madison and billions of dollars of payment and productivity of people. "It’s like a science fictional future where every woman on Earth is dead, and some Dilbert-like engineer has replaced them with badly-designed robots." As the "real world" continues to become wired and programmable, what is real and what is not real is increasingly a question of mathematical analysis.