Math and You

 

How is math used in everyday life? This is a big question requiring a big answer.  It is amazing at just how many uses are significant.  Math is everywhere, all the time, and constant as we move on.  Yet, few of us actually need to do any calculations beyond the basics. Knowing is has invaded almost everything is important to know. 

A. Medicine. CAT scans and MRI scans require deep math at their basis. Modeling of DNA and sequencing of genes use much math. The origin was with SONAR, where the computer was the human brain, i.e. operator. It is well past that now. The mathematics is called tomography. It takes the scans and uses them to reconstruct the complex images within the brain or body.

B. Transportation. Routing of vehicles (trucks and aircraft, etc) to maximize efficiency of costs use deep math. Involves one of the most difficult math problems called “The Traveling Salesman Problem.” It is still open, i.e. unsolved.

C. Electronics. Use the math of all of electromagnetic theory. Electronics is a huge application with probably none larger.

D. AI and Machine learning. The use of Bayesian methods is at the foundations.

E. Understanding the universe. i.e. cosmology. Most models of the universe are mathematical including operator algebras and functional analysis. String theory is all mathematical.

F. Population studies. For growth clever math models are used. For measures of poverty, etc, integral calculus is used, e.g. GINI index. Included here are prey-predator models - all math.

G. Climate studies. Based on varied mathematical and statistical models - guided by data. Wind turbine theory is very mathematical.

H. Psychology. Many models of types of behavior have a mathematical basis. These are relatively recent.

I. Voting. Many models are used for prediction and application. For example, Maine currently used one of them. Well beyond simple plurality.

J. Strength of materials is heavily based on mathematical methods. Industries: automotive, metallurgical, glass, …

K. Chemistry. Mathematical modeling of molecules is now a full area of chemistry.

M. Nuclear industry. The mathematically complex area of ray-tracing is at the basis of nuclear energy and nuclear reactors.

N. Traffic. Yes, models of traffic as partial differential equations are examined to understand the nature of traffic and traffic jams. Automata models are also used.

O. Ballistics. All aspects of rocketry use much mathematics. Just try for a soft lunar landing without math. Big users of control theory - very mathematical and difficult. Galileo was one of the first by developing ranging tables for canons.

P. Data analysis. This is all mathematical brought to applications by algorithms. Combines with artificial intelligence.

Q. The weather. The mathematics of weather is extremely complicated involving massive data and systems of partial differential equations. Basically, it is all math fueled by massive input of data. It works! Anecdotally, one of the first models was developed by Richardson, whose first models required three weeks of computation to predict the next day’s weather. Now we have computers, thankfully.

R. Epidemics. Mathematical models for the spread of disease is important to all medical forecasters. In fact, it is the varied models used by “experts” that give the wildly different outcomes for COVID-19. Many use tempered exponential models.

S. Oil exploration, including drilling, fracking, and reclamation all use very heavy math in varied ways. They are big users of finite element methods to solve complex partial differential equations. What this means is the range of interest is divided into tiny patchers, and then the solution is made for each piece with provision for linking them together – like a quilt. 

And this is just the short list.