Lectures on Analytic and Projective Geometry

by Dirk Jan Struik

Based on a historic approach taken by instructors at MIT, this text is geared toward junior and senior undergraduate courses in analytic and projective geometry. Starting with concepts concerning points on a line and lines through a point, it proceeds to the geometry of plane and space, leading up to conics and quadrics developed within the context of metrical, affine, and projective transformations. The algebraic treatment is occasionally exchanged for a synthetic approach, and the connection of the geometrical material with other fields is frequently noted.
Prerequisites for this treatment include three semesters of calculus and analytic geometry. Special exercises at the end of the book introduce students to interesting peripheral problems, and solutions are provided.

306 pages, Kindle Edition

First published November 17, 2011

About the author

Dirk Jan Struik (September 30, 1894 – October 21, 2000) was a Dutch mathematician and Marxian theoretician who spent most of his life in the United States.

Dirk Jan Struik was born in 1894 in Rotterdam, Netherlands, as a teacher's son, Struik attended the Hogere Burgerschool (HBS) in The Hague. It was in this school that he was first introduced to left-wing politics by some of his teachers. In 1912 Struik entered University of Leiden, where he showed great interest in mathematics and physics, influenced by the eminent professors Paul Ehrenfest and Hendrik Lorentz. In 1917 he worked as a high school mathematics teacher for a while, after which he worked as a research assistant for J.A. Schouten. It was during this period that he developed his doctoral dissertation, "The Application of Tensor Methods to Riemannian Manifolds." In 1922 Struik obtained his doctorate in mathematics from University of Leiden. He was appointed to a teaching position at University of Utrecht in 1923. The same year he married Ruth Ramler, a Czech mathematician with a doctorate from the Charles University of Prague. In 1924, funded by a Rockefeller fellowship, Struik traveled to Rome to collaborate with the Italian mathematician Tullio Levi-Civita. It was in Rome that Struik first developed a keen interest in the history of mathematics. In 1925, thanks to an extension of his fellowship, Struik went to Göttingen to work with Richard Courant compiling Felix Klein's lectures on the history of 19th-century mathematics. He also started researching Renaissance mathematics at this time. In 1926 Struik was offered positions both at the Moscow State University and the Massachusetts Institute of Technology. He decided to accept the latter, where he spent the rest of his academic career. He collaborated with Norbert Wiener on differential geometry, while continuing his research on the history of mathematics. He was made full professor at MIT in 1940.

Struik was a steadfast Marxist. Having joined the Communist Party of the Netherlands in 1919, he remained a Party member his entire life. When asked, upon the occasion of his 100th birthday, how he managed to pen peer-reviewed journal articles at such an advanced age, Struik replied blithely that he had the "3Ms" a man needs to sustain himself: Marriage (his wife, Saly Ruth Ramler, was not alive when he turned one hundred in 1994), Mathematics, and Marxism. It is therefore not surprising that Dirk suffered persecution during the McCarthyite era. He was accused of being a Soviet spy, a charge he vehemently denied. Invoking the First and Fifth Amendments of the U.S. Constitution, he refused to answer any of the 200 questions put forward to him during the HUAC hearing. He was suspended from teaching for five years (with full salary) by MIT in the 1950s. Struik was re-instated in 1956. He retired from MIT in 1960 as Professor Emeritus of Mathematics. Aside from purely academic work, Struik also helped found the Journal of Science and Society, a Marxian journal on the history, sociology and development of science.

In 1950 Stuik published his Lectures on Classical Differential Geometry, which gained praise from Ian R. Porteous:

"Of all the textbooks on elementary differential geometry published in the last fifty years the most readable is one of the earliest, namely that by D.J. Stuik (1950). He is the only one to mention Allvar Gullstrand."

Struik's other major works include such classics as A Concise History of Mathematics, Yankee Science in the Making, The Birth of the Communist Manifesto, and A Source Book in Mathematics, 1200-1800, all of which are considered standard textbooks or references.

Struik died October 21, 2000, 21 days after celebrating his 106th birthday.

Source: http://en.wikipedia.org/wiki/Dirk_Jan...