How can classes like real analysis be applied in real life?
How can classes like real analysis be applied outside of academia? What fields are those skills useful in?
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Answers ( 2 )
Real Analysis takes algebraic equations, functions and their analysis up to the point of linear calculous but stops short of working with complex and imaginary numbers. It deals with how real numbers behave in a series or sequence and real functions. Math is imbedded in the behavior of everything in the physical world. You can apply the techniques you learn in Algebra 2 class to business, but it tends to model idealized cases and general trends better than more complex real world phenomena.
Any industry that requires you to understand trends, where data converges, differentiates, is smooth, or integrates will need to have people on staff who can do this to varying degrees. There are businesses who try to do this by “gut feeling”, but they are playing with fire and frequently have major setbacks, they may even end in complete failure. If someone doesn’t understand outliers and regression to the mean, they’ll look at data sets that are too small and become convinced that patterns exist which do not. They’ll believe that an action that they took was effective and then be baffled when it quickly stops working.
A business may not need a full fledged statistician or engineer to function effectively, but many jobs require that you collect data and analyze it to varying degrees. The more money and people that you wish to be responsible for, the better you’ll have to handle data. You’ll be hired over other candidates for better paying jobs at larger companies and the faster you’ll be promoted to higher positions the less afraid you are of using math daily.
Managers of many stripes often need to analyze data, such as those in charge of:
• Medical and health care systems
• Purchasing
• Commercial property and real estate
• Computer and information systems
• Natural science workers and engineers
Other occupations include actuaries, statisticians, forest conservationists, economists and computer programmers. I learned how to define and use functions writing programs in BASIC before I was introduced to them in math class.
My father was a machinist, a tool and die grinder for General Motors. He worked in a noisy auto factory but he used trig on a daily basis!
This math also sets the stage for working with complex and imaginary numbers. Real analysis isn’t going to cut it you want to be any type of electrical engineer, many jobs in science, and obviously being a mathematician.
Jeffrey Ferreri's answer is bang on. "Real Analysis" is a peculiar neologism for Calculus, which for some reason emphasizes restriction to the real numbers; it gets a lot more interesting when extended to the complex numbers! If you want a "refresher course" intended for seniors, have a peek at https://jick.net/maths/