Carl B. Allendoerfer
Encyclopedia
Carl Barnett Allendoerfer (1911 – 1974) was a prominent American mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

 in the mid-twentieth century, known for his work in topology
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...

 and mathematics education.

Background

Allendoerfer was born in Kansas City
Kansas City, Missouri
Kansas City, Missouri is the largest city in the U.S. state of Missouri and is the anchor city of the Kansas City Metropolitan Area, the second largest metropolitan area in Missouri. It encompasses in parts of Jackson, Clay, Cass, and Platte counties...

, the son of a prominent banker. He graduated from Haverford College
Haverford College
Haverford College is a private, coeducational liberal arts college located in Haverford, Pennsylvania, United States, a suburb of Philadelphia...

 in 1932 and attended New College, Oxford
New College, Oxford
New College is one of the constituent colleges of the University of Oxford in the United Kingdom.- Overview :The College's official name, College of St Mary, is the same as that of the older Oriel College; hence, it has been referred to as the "New College of St Mary", and is now almost always...

 as a Rhodes Scholar, 1932-1934. He received his Ph.D. in mathematics from Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....

 in 1937.

Research & Teaching

Allendoerfer taught at Haverford College in the mid-1940s where he became known for work with André Weil
André Weil
André Weil was an influential mathematician of the 20th century, renowned for the breadth and quality of his research output, its influence on future work, and the elegance of his exposition. He is especially known for his foundational work in number theory and algebraic geometry...

 on the Gauss–Bonnet theorem
Gauss–Bonnet theorem
The Gauss–Bonnet theorem or Gauss–Bonnet formula in differential geometry is an important statement about surfaces which connects their geometry to their topology...

, an important theorem in differential geometry. He continued his studies of differential geometry at the Institute for Advanced Study
Institute for Advanced Study
The Institute for Advanced Study, located in Princeton, New Jersey, United States, is an independent postgraduate center for theoretical research and intellectual inquiry. It was founded in 1930 by Abraham Flexner...

 (1948-1949).

In 1951, he became professor and later chair of the Mathematics Department at the University of Washington
University of Washington
University of Washington is a public research university, founded in 1861 in Seattle, Washington, United States. The UW is the largest university in the Northwest and the oldest public university on the West Coast. The university has three campuses, with its largest campus in the University...

, where he is known for establishing the Summer Mathematics Institute for High School Teachers. Allendoerfer was president of the Mathematical Association of America
Mathematical Association of America
The Mathematical Association of America is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university, college, and high school teachers; graduate and undergraduate students; pure and applied mathematicians; computer scientists;...

 (1959-60) and editor of its monthly journal. In 1972, he received the MAA's Award for Distinguished Service to Mathematics. After his death, the MAA established the Carl B. Allendoerfer Award, which is given each year for "expository excellence published in Mathematics Magazine."

Allendoerfer is also known as a proponent of the New Math
New math
New Mathematics or New Math was a brief, dramatic change in the way mathematics was taught in American grade schools, and to a lesser extent in European countries, during the 1960s. The name is commonly given to a set of teaching practices introduced in the U.S...

 movement in the 1950s and 1960s, which sought to improve American primary and secondary mathematics education by teaching abstract concepts like set theory
Set theory
Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...

 early in the curriculum. Allendoerfer was a member of Commission on Mathematics of the College Entrance Examination Board whose 1959 report Program for College Preparatory Mathematics outlined many concepts of the New Math. The commission and report were criticized by some for emphasizing pure mathematics in place of more traditional and practical considerations like arithmetic.

Allendoerfer was the author, with Cletus Oakley, of several prominent mathematics textbooks used in the 1950s and 1960s. He was also author of a series of math films.

Books

  • Allendoerfer, Carl B., & Oakley, Cletus O. (1955). Principles of Mathematics. McGraw-Hill. (ISBN 0-07-001390-X)
  • Allendoerfer, Carl B., & Oakley, Cletus O. (1959). Fundamentals of Freshman Mathematics. McGraw-Hill. (ISBN 0-07-001366-7)
  • Allendoerfer, Carl B. (1965). Mathematics for Parents. MacMillan.
  • Allendoerfer, Carl B., & Oakely, Cletus O. (1967). Fundamentals of College Algebra. McGraw-Hill.
  • Allendoerfer, Carl B. (1971). Principles of Arithmetic and Geometry for Elementary School Teachers. MacMillan.
  • Allendoerfer, Carl B. (1974). Calculus of Several Variables and Differentiable Manifolds. Macmillan. (ISBN 0-02-301840-2)
  • Allendoerfer, Carl B., Oakley, Cletus O., & Kerr, Donald R. (1977). Elementary Functions. McGraw-Hill. (ISBN 0-07-001371-3)

Films

  • Cycloidal Curves or Tales from Wanklenberg Woods. Produced by Ward's Natural Science Establishment, Rochester, NY.
  • The Gauss-Bonnet Theorem. Ibid.
  • Geometric Concepts or How to Get Somewhere with Rigid Motion and Uniform Stretches. Ibid.
  • Area and Pi or How to Measure What There Is. Ibid.
  • Geometric Transformations. Ibid.
  • Equivalent Sets. Ibid.

External links

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