Wilfred Kaplan

Wilfred Kaplan (November 28, 1915 – December 26, 2007) was a professor of mathematics at the University of Michigan for 46 years, from 1940 through 1986.

His research focused on dynamical systems, the topology of curve families, complex function theory, and differential equations.

In total, he authored over 30 research papers and 11 textbooks.

He attended Boston Latin School and furthered his education at Harvard University, where he was granted his A.B. in mathematics in 1936 and graduated summa cum laude.

Later that same year he received his master's degree at Harvard.

Kaplan received a Rogers Fellow scholarship to study in Europe from 1936-1937, during his second year of graduate school.

He was based out of Zürich, Switzerland where many of the mathematicians working on the applications of topology to differential equations were located.

He also spent a month in Rome to work with famous mathematician Tullio Levi-Civita.

Upon returning to the United States, Kaplan accepted a yearlong teaching fellowship at Rice Institute for the 1938-1939 school year, thus completing his graduate program.

While attending lectures at the Eidgenössische Technische Hochschule (ETH) Zürich he met a fellow mathematician, Ida Roetting, whom he nicknamed Heidi and would eventually marry in 1938.

The couple lived in Houston for a year after their wedding while Kaplan taught at the Rice Institute.

The Kaplans had two children, Roland and Muriel.

Wilfred Kaplan died at the age of 92 after a short illness.

After Kaplan's short teaching position at Rice Institute, he went on to teach at the College of William and Mary in Virginia for one year.

He received his Ph.D. from Harvard in 1939 under the advisement of Hassler Whitney.

His dissertation covered regular curve families filling the plane.

In 1940 he was invited by T. H. Hildebrandt to join the faculty at the University of Michigan, after he had previously attended the Topology Congress.

The mathematics department at this time was diminishing due to the effects of World War II.

Enrollment was down and some of the faculty had been granted leaves to do military research.

When asked to record his contribution to the war effort, Kaplan mentioned teaching math exclusively to Air Force pre-meteorology students in the spring and summer of 1943, as well as teaching Navy V-12 and Army ASTP students for the majority of the academic year 1943-44.

In June 1944, Kaplan worked at Brown University as a researcher in an Applied Mathematics Group for the Taylor Model Basin, the Watertown Arsenal and the Bureau of Ordnance of the Navy Department.

He continued his research at Brown for 17 months.

Kaplan was named assistant professor in 1944, associate professor in 1950 and full professor in 1956.

His lectures were characterized by clarity and directness, a skill which allowed him to write several popular mathematics textbooks.

An updated version of his Advanced Calculus textbook is still used widely today.

A selection of Kaplan's books can be found in the bibliography.

Kaplan taught a variety of undergraduate and graduate courses during his time at Michigan, and further advised eight doctoral students.

Kaplan's skillful teaching won him respect among students and coworkers.

Donald Lewis, chair of the mathematics department and co-author said, "First and foremost, Wilfred Kaplan was a teacher. He enjoyed conveying the beauty and usefulness of mathematics, and his students responded enthusiastically. He was a superb expositor, and his ability to elegantly convey mathematical ideas explains the enormous impact of his textbooks. When we were writing our joint texts, he never came to a meeting without a new idea to be incorporated."

One of Kaplan's primary goals as an educator was bridging the gap between pure and applied mathematics.

He sympathized with the plight of engineers who felt the pressure to master more and more math concepts and then master the additional skill of applying it to their field.

In May 1947 he outlined a curriculum for a new Lectures on Mathematics Project sponsored by the Office of Naval Research.

His early research focused primarily on dynamical systems, and the topology of curve families.

In 1955, he became especially interested in complex function theory and made a significant contribution to mathematics in his study of a special class of Schlicht functions, for which he showed that the Bieberbach Conjecture held.

His later research took on a more applied approach as he returned once more to differential equations, this time engaging in a more global analysis.

In total, Wilfred Kaplan authored about 30 research papers.

For over thirty years Kaplan was an active member of the American Association of University Professors (AAUP) and served as president of the University of Michigan chapter from 1978 to 1985.

Wilfred Kaplan was born in Boston, Massachusetts to Jacob and Anne Kaplan.

Kaplan wrote math textbooks specifically for engineers, such as Advanced Mathematics for Engineers (1981), because he believed teachers needed to work on presenting mathematical knowledge more efficiently to this group.

Furthermore, he argued that science students in general, but specifically engineers, needed to be given other resources such as textbooks and articles to further their study outside of lectures along with the tools to employ those resources appropriately.