Background
Hans Adolph Rademacher was born on April 3, 1892 in Wandsbeck, near Hamburg, Germany, the son of Adolph H. Rademacher, a merchant, and Emma Weinhever.
(Using a background of analysis and algebra, the reader is...)
Using a background of analysis and algebra, the reader is led to the fundamental theorems of number theory; the uniqueness of prime number factorization and the reciprocity law of quadratic residues. Cyclotomy is treated in some detail because of its own significance and as a framework for the elegant theorems on Gaussian sums. Asymptotic laws are discussed as a foretaste of analytic number theory; also, Dirichlet's theorem about primes in an arithmetic progression and V. Brun's theorem on twin primes.
https://www.amazon.com/elementary-Blaisdell-sciences-Introduction-mathematics/dp/B0006BLS5Y?SubscriptionId=AKIAJRRWTH346WSPOAFQ&tag=prabook-20&linkCode=sp1&camp=2025&creative=165953&creativeASIN=B0006BLS5Y
( What is so special about the number 30? How many colors...)
What is so special about the number 30? How many colors are needed to color a map? Do the prime numbers go on forever? Are there more whole numbers than even numbers? These and other mathematical puzzles are explored in this delightful book by two eminent mathematicians. Requiring no more background than plane geometry and elementary algebra, this book leads the reader into some of the most fundamental ideas of mathematics, the ideas that make the subject exciting and interesting. Explaining clearly how each problem has arisen and, in some cases, resolved, Hans Rademacher and Otto Toeplitz's deep curiosity for the subject and their outstanding pedagogical talents shine through. Originally published in 1957. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
https://www.amazon.com/Enjoyment-Mathematics-Selections-Amateur-Princeton/dp/0691626766?SubscriptionId=AKIAJRRWTH346WSPOAFQ&tag=prabook-20&linkCode=sp1&camp=2025&creative=165953&creativeASIN=0691626766
(Hans Adolph Rademacher (3 April 1892 to 7 February 1969) ...)
Hans Adolph Rademacher (3 April 1892 to 7 February 1969) was a German mathematician, known for work in mathematical analysis and number theory. This book was published in 1983 based on a series of lectures he delivered at Stanford University in 1947.
https://www.amazon.com/Higher-Mathematics-Elementary-Point-View/dp/3764330643?SubscriptionId=AKIAJRRWTH346WSPOAFQ&tag=prabook-20&linkCode=sp1&camp=2025&creative=165953&creativeASIN=3764330643
( What is so special about the number 30? How many colors...)
What is so special about the number 30? How many colors are needed to color a map? Do the prime numbers go on forever? Are there more whole numbers than even numbers? These and other mathematical puzzles are explored in this delightful book by two eminent mathematicians. Requiring no more background than plane geometry and elementary algebra, this book leads the reader into some of the most fundamental ideas of mathematics, the ideas that make the subject exciting and interesting. Explaining clearly how each problem has arisen and, in some cases, resolved, Hans Rademacher and Otto Toeplitz's deep curiosity for the subject and their outstanding pedagogical talents shine through.
https://www.amazon.com/Enjoyment-Math-Hans-Rademacher/dp/0691023514?SubscriptionId=AKIAJRRWTH346WSPOAFQ&tag=prabook-20&linkCode=sp1&camp=2025&creative=165953&creativeASIN=0691023514
Hans Adolph Rademacher was born on April 3, 1892 in Wandsbeck, near Hamburg, Germany, the son of Adolph H. Rademacher, a merchant, and Emma Weinhever.
He attended the Hamburger Volksschule, the Eilbecker Realschule, and the Uhlenhorst Oberrealschule, completing his schooling by Easter 1911. He then entered the University of Göttingen, where he spent nine semesters studying mathematics, physics, and philosophy. Because his interests were broad and the lectures of the famous but aging Felix Klein were disappointing, Rademacher temporarily abandoned his mathematical pursuits in order to study philosophy with Leonhard Nelson. The influence of Richard Courant brought him back to mathematics, however, and Rademacher completed a dissertation on single-valued mappings and mensurability under Constantin Carathéodory, obtaining his doctorate in 1917. His studies were temporarily interrupted by military service in the German army during World War I.
Upon graduation from Göttingen, Rademacher obtained a position as mathematics teacher at a school with rather modern educational ideas in the idyllic hamlet of Wickersdorf, near Saalfeld. During his two years there he published five papers that extended his work on mapping and differentiability, including a long two-part paper that introduced the term "total differentiability, " now in common use.
In 1919 he left Wickersdorf for Berlin, becoming privatdocent under Carathéodory, who had left Göttingen and relocated at the University of Berlin. There he continued publishing in the areas of mensurability, real variables, convergence factors, and Euler summability of series, culminating his work in 1922 with a paper that introduced a type of orthogonal functions now generally known as Rademacher functions.
In 1922, Rademacher was appointed assistant professor of mathematics at the recently created University of Hamburg. There, under the influence of Erich Hecke, Rademacher turned his attention to number theory, a subject that was to occupy much of his energy for the rest of his life and in which he made his most-outstanding contributions.
In 1925, after writing two long papers extending Viggo Brun's methods in number theory, he was offered, and accepted, a position as full professor at the University of Breslau. During his nine-year career at Breslau, Rademacher produced numerous studies in analytic number theory (particularly additive problems), functions of complex variables, Goldbach's problem, the Riemann zeta function, modular functions, and Dedekind sums. He also entered briefly the fields of theoretical physics and biology, writing two papers on Schr"dinger's wave mechanics and one on certain mathematical aspects of genetics. He also produced, in collaboration with Otto Toeplitz of the University of Bonn, a book on number theory addressed to a wide, nonspecialized audience.
This book, Von Zahlen und Figuren (1930), was eventually translated into nine languages and enjoyed numerous editions; in English it was known as The Enjoyment of Mathematics (1957). Rademacher's final work at Breslau was an excursion into geometry: he edited the posthumous manuscript of Ernst Steinitz on the theory of polyhedra, which was published as Vorlesungen über die Theorie der Polyeder, unter Einschluss der Elemente der Topologie (1934). Rademacher's stay at Breslau ended in 1934 when he was forced out of his position by the Nazis for having participated in the International League for the Rights of Man and having served as chairman of the Breslau chapter of the Deutsche Friedensgesellschaft (German Society for Peace).
He relocated to the small town of Nienhagen in Mecklenburg, on the Baltic coast. While there under less-than-ideal circumstances, he managed to write two mathematical papers on prime numbers in a real quadratic field.
In late 1934, Rademacher accepted an invitation to spend two years at the University of Pennsylvania in Philadelphia as a Rockefeller Fellow. He returned to Germany briefly in the summer of 1935 but then resumed his association with the University of Pennsylvania. In spite of his full professorship in Germany and his international reputation, the university instated him as an assistant professor, a situation that was not remedied until 1939, when he was again made full professor.
Despite the disappointment at his initial demotion, Rademacher's work flourished in his new surroundings and his new language. He found professional stimulation from colleagues such as Antoni Zygmund and Isaac Jacob Schoenberg of the University of Pennsylvania, Arnold Dresden of nearby Swarthmore College, and his numerous graduate students, many of whom soon became productive mathematicians in their own right.
In 1943, Rademacher became a naturalized citizen.
The Rademacher home served as a meeting place for mathematicians, musicians, and other interesting personalities. Rademacher's interest in peace issues found an outlet in his association with the Society of Friends, with whom he remained active to the end of his life. Rademacher enjoyed several leaves during his later years at institutions such as Haverford College, the Institute for Advanced Study in Princeton, the University of Oregon, the Tata Institute in Bombay, and his alma mater in Göttingen; numerous papers and four monographs resulted from these leaves. To honor him upon his retirement in 1962, the University of Pennsylvania organized the year-long Institute in the Theory of Numbers. After his retirement, Rademacher taught for two years at New York University and then at the Rockefeller Institute until a cerebral hemorrhage left him paralyzed from 1967 to the end of his life.
He died in Haverford, Pennsylvania.
( What is so special about the number 30? How many colors...)
( What is so special about the number 30? How many colors...)
(Using a background of analysis and algebra, the reader is...)
(Hans Adolph Rademacher (3 April 1892 to 7 February 1969) ...)
In Berlin he married Suzanne Gaspary in 1921; they had one child before their divorce in 1929. He met and married Olga Frey; they had one child. His second marriage ended in divorce in 1947, and two years later he married Irma Wolpe, the sister of his colleague Schoenberg and an accomplished pianist.