| 词条 | Robert Berger (mathematician) |
| 释义 |
Robert Berger (born 1938) is an applied mathematician, known for inventing the first aperiodic tiling[1] using a set of 20,426 distinct tile shapes. Contributions to tiling theoryThe unexpected existence of aperiodic tilings, although not Berger's explicit construction of them, follows from another result proved by Berger: that the so-called domino problem is undecidable, disproving a conjecture of Hao Wang, Berger's advisor. The result is analogous to a 1962 construction used by Kahr, Moore, and Wang, to show that a more constrained version of the domino problem was undecidable.[2] Education and careerBerger did his undergraduate studies at Rensselaer Polytechnic Institute, and studied applied physics at Harvard, earning a master's degree, before shifting to applied mathematics for his doctorate. Along with Hao Wang, Berger's other two doctoral committee members were Patrick Carl Fischer and Marvin Minsky. Later, he has worked in the Digital Integrated Circuits Group of the Lincoln Laboratory.[3] PublicationsBerger's work on tiling was published as "The Undecidability of the Domino Problem" in the Memoirs of the AMS in 1966.[4] This paper is essentially a reprint of Berger's 1964 dissertation at Harvard University.[5] In 2009, a paper by Berger and other Lincoln Laboratories researchers, "Wafer-scale 3D integration of InGaAs image sensors with Si readout circuits", won the best paper award at the IEEE International 3D System Integration Conference (3DIC).[6] In 2010, a CMOS infrared imaging device with an analog-to-digital converter in each pixel, coinvented by Berger, was one of R&D Magazines R&D 100 Award recipients.[7] References1. ^{{cite book|last=Darling|first=David J.|authorlink=David J. Darling|title=The universal book of mathematics: from Abracadabra to Zeno's paradoxes|url=https://books.google.com/books?id=0YiXM-x--4wC&pg=PA18|accessdate=29 September 2011|year=2004|publisher=John Wiley and Sons|isbn=978-0-471-27047-8|pages=18–}} {{Authority control}}{{DEFAULTSORT:Berger, Robert}}2. ^{{cite journal|journal = Mathematical Reviews | volume = 36 | number = 49 | last = Büchi | first = J. R. | authorlink = Julius Richard Büchi | title = The undecidability of the domino problem | mr = 0216954 }} 3. ^Author biography from {{citation|url=http://www.ll.mit.edu/publications/journal/pdf/vol02_no1/2.1.5.neuromorphicsystems.pdf|title=A generic architecture for wafer-scale neuromorphic systems|first1=J. I.|last1=Raffel|first2=J. R.|last2=Mann|first3=R.|last3=Berger|first4=A. M.|last4=Soares|first5=S.|last5=Gilbert|journal=The Lincoln Laboratory Journal|volume=2|issue=1|year=1989|pages=63–76}}. 4. ^{{citation |last=Berger |first=Robert |title=The Undecidability of the Domino Problem |journal=Memoirs of the American Mathematical Society |volume=66 |year=1966 |page=72 pp.|doi=10.1090/memo/0066|url=https://books.google.com/books?hl=en&lr=&id=8AmiHD0Lbu8C&oi=fnd&pg=PA1&dq=%22Robert+Berger%22+%22The+undecidability+of+the+domino+problem%22&q&f=false#v=onepage&q&f=false}}. 5. ^{{mathgenealogy|name=Robert Berger|id=114475}}. 6. ^Awards and Recognition, Lincoln Laboratory Annual Report 2010, p. 50, retrieved 2011-09-30. 7. ^MIT Lincoln Laboratory receives five R&D 100 Awards, Lincoln Laboratory, retrieved 2011-09-30. 7 : Living people|20th-century American mathematicians|21st-century American mathematicians|Rensselaer Polytechnic Institute alumni|Harvard School of Engineering and Applied Sciences alumni|1938 births|MIT Lincoln Laboratory people |
| 随便看 |
|
开放百科全书收录14589846条英语、德语、日语等多语种百科知识，基本涵盖了大多数领域的百科知识，是一部内容自由、开放的电子版国际百科全书。