Background
Ezra Miller was born on May 12, 1812, near Pleasant Valley, Bergen County, New Jersey. He was the son of Ezra Wilson Miller, a native of Westchester County, New York, and Hannah (Ryerson) Miller of Pompton, New Jersey.
(Geometric combinatorics describes a wide area of mathemat...)
Geometric combinatorics describes a wide area of mathematics that is primarily the study of geometric objects and their combinatorial structure. Perhaps the most familiar examples are polytopes and simplicial complexes, but the subject is much broader. This volume is a compilation of expository articles at the interface between combinatorics and geometry, based on a three-week program of lectures at the Institute for Advanced Study/Park City Math Institute (IAS/PCMI) summer program on Geometric Combinatorics. The topics covered include posets, graphs, hyperplane arrangements, discrete Morse theory, and more. These objects are considered from multiple perspectives, such as in enumerative or topological contexts, or in the presence of discrete or continuous group actions. Most of the exposition is aimed at graduate students or researchers learning the material for the first time. Many of the articles include substantial numbers of exercises, and all include numerous examples. The reader is led quickly to the state of the art and current active research by worldwide authorities on their respective subjects. Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.
https://www.amazon.com/Geometric-Combinatorics-Park-City-Mathematics/dp/0821837362?SubscriptionId=AKIAJRRWTH346WSPOAFQ&tag=prabook-20&linkCode=sp1&camp=2025&creative=165953&creativeASIN=0821837362
( Recent developments are covered Contains over 100 figu...)
Recent developments are covered Contains over 100 figures and 250 exercises Includes complete proofs
https://www.amazon.com/Combinatorial-Commutative-Algebra-Graduate-Mathematics/dp/0387237070?SubscriptionId=AKIAJRRWTH346WSPOAFQ&tag=prabook-20&linkCode=sp1&camp=2025&creative=165953&creativeASIN=0387237070
Ezra Miller was born on May 12, 1812, near Pleasant Valley, Bergen County, New Jersey. He was the son of Ezra Wilson Miller, a native of Westchester County, New York, and Hannah (Ryerson) Miller of Pompton, New Jersey.
During his boyhood, the family moved to New York City, then to Rhinebeck, and finally to Flushing, L. I. , where he received his preparatory school education. His parents wished him to study medicine but Ezra preferred to take up topographical, mechanical, and hydraulic engineering, and became a civil engineer.
For upwards of ten years, Miller practiced his profession in and about New York. As an avocation, he engaged in military studies and was active in the state militia. In 1833, he enlisted in a company of artillery belonging to the 2nd New York Militia and became, by promotion, adjutant in 1839, lieutenant-colonel in 1840, and colonel in 1842. In May 1841, he settled at Fort Hamilton, New York, where he continued the practice of his profession until 1848, when he removed to Rock County, Wisconsin, to take part in the survey of public lands. After a period with the State Survey, he engaged in railway survey and construction work. While so employed in 1853, he became interested in the improvement of existing methods of coupling railway cars, and for some ten years studied and experimented quietly with the problem. His work resulted in the perfection of a car coupler. Continuing his experiments, he improved his basic idea. In 1867, Miller returned to the East and lived for three years in Brooklyn, New York, then purchased a farm near Mahwah, New Jersey, where he spent the rest of his life, devoting his time mainly to raising prize livestock. He was commissioned colonel in the Wisconsin militia in 1851, and in 1852, was elected to the Wisconsin Senate, serving one term. Under President Buchanan, he was deputy postmaster of Janesville, Wisconsin, for two years, and at another time was a justice of the peace in Magnolia, Wisconsin. After taking up his residence in New Jersey, he was elected to the state Senate in 1883 and held his seat at the time of his death. He was several times a candidate for Congress. He died in Mahwah.
Miller is known for the perfection of a car coupler for which he obtained patent No. 38, 057 on March 31, 1863. Then, he improved his idea and on January 31, 1865, secured patent No. 46, 126 for his combined railroad-car platform, coupler, and buffer. Two years later, he succeeded in placing his coupler arrangement on three cars being built in the railroad shops at Adrian, Michigan. It proved an immediate success and soon replaced the dangerous old railroad car platform with its loose link coupling throughout the United States and was widely adopted in Europe. The Miller coupler continued in favor for about twenty years before it was superseded by the Janney coupler, and provided its inventor with a large income.
(Geometric combinatorics describes a wide area of mathemat...)
( Recent developments are covered Contains over 100 figu...)
Miller was a member of the Wisconsin State Senate from the 17th district from 1853 to 1854. Additionally, he was a justice of the peace in Magnolia and Postmaster of Janesville, Wisconsin. Miller joined the New Jersey Senate in 1863. He was a Democrat.
a member of the Wisconsin State Senate
Miller had a natural capacity for making friends which led to his election to public office both in Wisconsin and in New Jersey. He was the most affable of men, and his genial good nature and ready wit make him a welcome guest at many firesides. He indulged in a European tour, where he studied the styles of architecture and other improvements of the Old World.
In May 1841, Miller married Amanda J. Miller of New York. They had five children.
