Book pulls appplications from abstract mathematics

Jan 22, 2014

Mathematics can explain how light waves propagate in a fiber optic cable or that a linear flow of air over a plane's wings gives passengers a smooth ride, while nonlinear flow causes turbulence.

But pulling such real-world applications from traditional math textbooks is often a challenge.

"A lot of mathematics books are so theoretical that when we are working with engineers or physical scientists, they have trouble getting through this 'abstract nonsense'," said Wojbor Woyczynski, a professor of mathematics at Case Western Reserve University. "Abstract theory is essential to make math foolproof. But it distracts engineers and scientists from the essence of their projects."

So, Woyczynski, who earned his bachelor's and master's degrees in electrical and computer engineering, and Alex Saichev, a former professor of management, technology and economics at the Federal Institute of Technology, Zurich, embarked on a trilogy of texts to make certain abstract mathematical objects—called distributions, or generalized functions—more accessible to scientists and engineers.

Their second book, Distributions in the Physical and Engineering Sciences, Volume 2: Linear and Nonlinear Dynamics in Continuous Media, is now available. The volume is geared toward graduate students, researchers and advanced undergraduates, and is written in comparatively lighthearted prose for a math book.

Distributions are based largely on the work of Nobel Prize-winning physicist Paul Dirac and Fields Medal-winner Laurent Schwartz. In the book they are used to understand how:

  • materials spread in a hydrogen bomb explosion;
  • plankton develops, evolves and affects marine life;
  • temperature is distributed in a lit detonator fuse;
  • pesticides sprayed in a forest are spread when the forest is clear-cut;
  • vapor condenses on a surface—essential to controlling the process used to make such things as computer chips, optical fibers or the smooth diamond-film coating some razor blades.

"Every day we benefit from abstract math without realizing it," Woyczynski said. "But engineers and physical scientists don't have to spend years learning to live in this mathematical universe in order to operate in it."

Woyczynski's has written several textbooks about his specialties, probability and randomness. He calls this series a labor of love.

He and Saichev published the first volume in 1997, and planned the second and third volumes a decade ago. When Saichev visited Ohio four years ago, he said it was time to write the second.

Woyczynski went on sabbatical last spring and spent most of it in Switzerland, finishing the book and hiking with Saichev in the mountains.

Two weeks after the manuscript was finished and Woyczynski had returned home, he received a call that Saichev had suddenly become ill and died from blood clots in his lungs. Woyczynski added a memorial to the book.

Woyczynski said he'll finish the third volume, with Saichev as coauthor. "We thought about the book and planned it together," he said. "It's a joint production."

Explore further: How were fossil tracks made by Early Triassic swimming reptiles so well preserved?

add to favorites email to friend print save as pdf

Related Stories

Understanding disease states through math

Jan 13, 2014

Angela Reynolds, Ph.D., is in the business of translating math to biology and biology back to math. As an applied mathematician, she can turn chemical reactions into equations.

Is mathematics an effective way to describe the world?

Sep 03, 2013

Mathematics has been called the language of the universe. Scientists and engineers often speak of the elegance of mathematics when describing physical reality, citing examples such as π, E=mc2, and even s ...

Belgian wins Norway's $1 million Abel math prize

Mar 20, 2013

Belgian-born Pierre Deligne has won this year's $1-million Abel Prize in mathematics for his contributions to algebraic geometry and their "transformative impact on number theory, representation theory and ...

New Lincoln math pages suggest more education

Jun 08, 2013

Two math-notebook pages recently authenticated as belonging to Abraham Lincoln suggest the 16th president, who was known to downplay his formal education, may have spent more time in school than usually thought.

Recommended for you

Predicting human crowds with statistical physics

Feb 27, 2015

For the first time researchers have directly measured a general law of how pedestrians interact in a crowd. This law can be used to create realistic crowds in virtual reality games and to make public spaces safer.

Bribery 'hits 1.6 billion people a year'

Feb 27, 2015

A total of 1.6 billion people worldwide – nearly a quarter of the global population – are forced to pay bribes to gain access to everyday public services, according to a new book by academics at the Universities of Birmingham ...

Broken windows thesis springs a leak

Feb 27, 2015

The broken windows theory posits that minor misdemeanors, like littering or graffiti spraying, stimulate more serious anti-social behavior. LMU sociologists now argue that the idea is flawed and does not ...

User comments : 0

Please sign in to add a comment. Registration is free, and takes less than a minute. Read more

Click here to reset your password.
Sign in to get notified via email when new comments are made.