Zinovy Reichstein is a Russian-born American mathematician. He is a professor at the University of British Columbia in Vancouver, he studies algebra, algebraic geometry and algebraic groups. He introduced the concept of essential dimension. Reichstein received his PhD degree in 1988 from Harvard University under the supervision of Michael Artin. Parts of his thesis entitled "The Behavior of Stability under Equivariant Maps" were published in the journal Inventiones Mathematicae; as of 2011, he is on the editorial board of the mathematics journal Transformation groups. In high school, Reichstein participated in the national mathematics Olympiad in Russia and was the third highest scorer in 1977 and second highest scorer in 1978; because of the Antisemitism in the Soviet Union at the time, Reichstein was not accepted to Moscow University though he had passed the special math entrance exams. He attended a semester of college at Russian University of Transport instead, his family decided to emigrate, arriving in Vienna, Austria, in August 1979 and New York, United States in the fall of 1980.
Reichstein worked as a delivery boy for a short period of time in New York. He was accepted to and attended California Institute of Technology for his undergraduate studies. Winner of the 2013 Jeffery-Williams Prize awarded by the Canadian Mathematical Society Fellow of the American Mathematical Society, 2012 Invited Speaker to the International Congress of Mathematicians Official website Zinovy Reichstein at the Mathematics Genealogy Project
Shimshon Avraham Amitsur was an Israeli mathematician. He is best known for his work in particular PI rings, an area of abstract algebra. Amitsur was born in Jerusalem and studied at the Hebrew University under the supervision of Jacob Levitzki, his studies were interrupted, first by World War II and by the Israel's War of Independence. He received his M. Sc. degree in 1946, his Ph. D. in 1950. For his joint work with Levitzki, he received the first Israel Prize in Exact Sciences, he worked at the Hebrew University until his retirement in 1989. Amitsur was a visiting scholar at the Institute for Advanced Study from 1952 to 1954, he was an Invited Speaker at the ICM in 1970 in Nice. He was a member of the Israel Academy of Sciences, where he was the Head for Experimental Science Section, he was one of the founding editors of the Israel Journal of Mathematics, the mathematical editor of the Hebrew Encyclopedia. Amitsur received a number of awards, including the honorary doctorate from Ben-Gurion University in 1990.
His students included Amitai Regev, Eliyahu Rips and Aner Shalev. Amitsur and Jacob Levitzki were each awarded the Israel Prize in exact sciences, in 1953, its inaugural year. Amitsur–Levitzki theorem List of Israel Prize recipients Amitsur, A. S.. Selected papers of S. A. Amitsur with commentary. Part 1, Providence, R. I.: American Mathematical Society, ISBN 978-0-8218-2924-0, MR 1866636 Amitsur, S. A. Mann, Avinoam. Selected papers of S. A. Amitsur with commentary. Part 2, Providence, R. I.: American Mathematical Society, ISBN 978-0-8218-2925-7, MR 1866637 "Shimshon Avraham Amitsur", by A. Mann, Israel Journal of Mathematics, Vol. 96, ix - xxvii. Formanek, Edward, "Review of Selected papers of S. A. Amitsur", Bulletin of the American Mathematical Society, 40: 131–135, doi:10.1090/s0273-0979-02-00960-6, ISSN 0002-9904 Shimshon Amitsur at the Mathematics Genealogy Project O'Connor, John J..
Princeton University is a private Ivy League research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the nine colonial colleges chartered before the American Revolution; the institution moved to Newark in 1747 to the current site nine years and renamed itself Princeton University in 1896. Princeton provides undergraduate and graduate instruction in the humanities, social sciences, natural sciences, engineering, it offers professional degrees through the Woodrow Wilson School of Public and International Affairs, the School of Engineering and Applied Science, the School of Architecture and the Bendheim Center for Finance. The university has ties with the Institute for Advanced Study, Princeton Theological Seminary and the Westminster Choir College of Rider University. Princeton has the largest endowment per student in the United States. From 2001 to 2018, Princeton University was ranked either first or second among national universities by U.
S. News & World Report, holding the top spot for 16 of those 18 years; as of October 2018, 65 Nobel laureates, 15 Fields Medalists and 13 Turing Award laureates have been affiliated with Princeton University as alumni, faculty members or researchers. In addition, Princeton has been associated with 21 National Medal of Science winners, 5 Abel Prize winners, 5 National Humanities Medal recipients, 209 Rhodes Scholars, 139 Gates Cambridge Scholars and 126 Marshall Scholars. Two U. S. Presidents, twelve U. S. Supreme Court Justices and numerous living billionaires and foreign heads of state are all counted among Princeton's alumni body. Princeton has graduated many prominent members of the U. S. Congress and the U. S. Cabinet, including eight Secretaries of State, three Secretaries of Defense and three of the past five Chairs of the Federal Reserve. New Light Presbyterians founded the College of New Jersey in 1746; the college was the religious capital of Scottish Presbyterian America. In 1754, trustees of the College of New Jersey suggested that, in recognition of Governor Jonathan Belcher's interest, Princeton should be named as Belcher College.
Belcher replied: "What a name that would be!" In 1756, the college moved to New Jersey. Its home in Princeton was Nassau Hall, named for the royal House of Orange-Nassau of William III of England. Following the untimely deaths of Princeton's first five presidents, John Witherspoon became president in 1768 and remained in that office until his death in 1794. During his presidency, Witherspoon shifted the college's focus from training ministers to preparing a new generation for secular leadership in the new American nation. To this end, he solicited investment in the college. Witherspoon's presidency constituted a long period of stability for the college, interrupted by the American Revolution and the Battle of Princeton, during which British soldiers occupied Nassau Hall. In 1812, the eighth president of the College of New Jersey, Ashbel Green, helped establish the Princeton Theological Seminary next door; the plan to extend the theological curriculum met with "enthusiastic approval on the part of the authorities at the College of New Jersey".
Today, Princeton University and Princeton Theological Seminary maintain separate institutions with ties that include services such as cross-registration and mutual library access. Before the construction of Stanhope Hall in 1803, Nassau Hall was the college's sole building; the cornerstone of the building was laid on September 17, 1754. During the summer of 1783, the Continental Congress met in Nassau Hall, making Princeton the country's capital for four months. Over the centuries and through two redesigns following major fires, Nassau Hall's role shifted from an all-purpose building, comprising office, dormitory and classroom space; the class of 1879 donated twin lion sculptures that flanked the entrance until 1911, when that same class replaced them with tigers. Nassau Hall's bell rang after the hall's construction; the bell was recast and melted again in the fire of 1855. James McCosh took office as the college's president in 1868 and lifted the institution out of a low period, brought about by the American Civil War.
During his two decades of service, he overhauled the curriculum, oversaw an expansion of inquiry into the sciences, supervised the addition of a number of buildings in the High Victorian Gothic style to the campus. McCosh Hall is named in his honor. In 1879, the first thesis for a Doctor of Philosophy Ph. D. was submitted by James F. Williamson, Class of 1877. In 1896, the college changed its name from the College of New Jersey to Princeton University to honor the town in which it resides. During this year, the college underwent large expansion and became a university. In 1900, the Graduate School was established. In 1902, Woodrow Wilson, graduate of the Class of 1879, was elected the 13th president of the university. Under Wilson, Princeton introduced the preceptorial system in 1905, a then-unique concept in the US that augmented the standard lecture method of teaching with a more personal form in which small groups of students, or precepts, could interact with a single instructor, or preceptor, in their field of interest.
In 1906, the reservoir Lake Carnegie was created by Andrew Carnegie. A collection of historical photographs of the build
Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques from commutative algebra, for solving geometrical problems about these sets of zeros; the fundamental objects of study in algebraic geometry are algebraic varieties, which are geometric manifestations of solutions of systems of polynomial equations. Examples of the most studied classes of algebraic varieties are: plane algebraic curves, which include lines, parabolas, hyperbolas, cubic curves like elliptic curves, quartic curves like lemniscates and Cassini ovals. A point of the plane belongs to an algebraic curve if its coordinates satisfy a given polynomial equation. Basic questions involve the study of the points of special interest like the singular points, the inflection points and the points at infinity. More advanced questions involve the topology of the curve and relations between the curves given by different equations.
Algebraic geometry occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex analysis and number theory. A study of systems of polynomial equations in several variables, the subject of algebraic geometry starts where equation solving leaves off, it becomes more important to understand the intrinsic properties of the totality of solutions of a system of equations, than to find a specific solution. In the 20th century, algebraic geometry split into several subareas; the mainstream of algebraic geometry is devoted to the study of the complex points of the algebraic varieties and more to the points with coordinates in an algebraically closed field. Real algebraic geometry is the study of the real points of an algebraic variety. Diophantine geometry and, more arithmetic geometry is the study of the points of an algebraic variety with coordinates in fields that are not algebraically closed and occur in algebraic number theory, such as the field of rational numbers, number fields, finite fields, function fields, p-adic fields.
A large part of singularity theory is devoted to the singularities of algebraic varieties. Computational algebraic geometry is an area that has emerged at the intersection of algebraic geometry and computer algebra, with the rise of computers, it consists of algorithm design and software development for the study of properties of explicitly given algebraic varieties. Much of the development of the mainstream of algebraic geometry in the 20th century occurred within an abstract algebraic framework, with increasing emphasis being placed on "intrinsic" properties of algebraic varieties not dependent on any particular way of embedding the variety in an ambient coordinate space. One key achievement of this abstract algebraic geometry is Grothendieck's scheme theory which allows one to use sheaf theory to study algebraic varieties in a way, similar to its use in the study of differential and analytic manifolds; this is obtained by extending the notion of point: In classical algebraic geometry, a point of an affine variety may be identified, through Hilbert's Nullstellensatz, with a maximal ideal of the coordinate ring, while the points of the corresponding affine scheme are all prime ideals of this ring.
This means that a point of such a scheme may be either a subvariety. This approach enables a unification of the language and the tools of classical algebraic geometry concerned with complex points, of algebraic number theory. Wiles' proof of the longstanding conjecture called Fermat's last theorem is an example of the power of this approach. In classical algebraic geometry, the main objects of interest are the vanishing sets of collections of polynomials, meaning the set of all points that satisfy one or more polynomial equations. For instance, the two-dimensional sphere of radius 1 in three-dimensional Euclidean space R3 could be defined as the set of all points with x 2 + y 2 + z 2 − 1 = 0. A "slanted" circle in R3 can be defined as the set of all points which satisfy the two polynomial equations x 2 + y 2 + z 2 − 1 = 0, x + y + z = 0. First we start with a field k. In classical algebraic geometry, this field was always the complex numbers C, but many of the same results are true if we assume only that k is algebraically closed.
We consider the affine space of dimension n over denoted An. When one fixes a coordinate system, one may identify An with kn; the purpose of not working with kn is to emphasize that one "forgets" the vector space structure that kn carries. A function f: An → A1 is said to be polynomial if it can be written as a polynomial, that is, if there is a polynomial p in k such that f = p for every point M with coordinates in An; the property of a function to be polynomial does not depend on the choice of a coordinate system in An. When a coordinate system is chosen, the regular functions on the affine n-space may be identified with the ring of polynomial functions in n variables over k. Therefore, the set of the
A thesis or dissertation is a document submitted in support of candidature for an academic degree or professional qualification presenting the author's research and findings. In some contexts, the word "thesis" or a cognate is used for part of a bachelor's or master's course, while "dissertation" is applied to a doctorate, while in other contexts, the reverse is true; the term graduate thesis is sometimes used to refer to both master's theses and doctoral dissertations. The required complexity or quality of research of a thesis or dissertation can vary by country, university, or program, the required minimum study period may thus vary in duration; the word "dissertation" can at times be used to describe a treatise without relation to obtaining an academic degree. The term "thesis" is used to refer to the general claim of an essay or similar work; the term "thesis" comes from the Greek θέσις, meaning "something put forth", refers to an intellectual proposition. "Dissertation" comes from the Latin dissertātiō, meaning "discussion".
Aristotle was the first philosopher to define the term thesis. "A'thesis' is a supposition of some eminent philosopher that conflicts with the general opinion...for to take notice when any ordinary person expresses views contrary to men's usual opinions would be silly". For Aristotle, a thesis would therefore be a supposition, stated in contradiction with general opinion or express disagreement with other philosophers. A supposition is a statement or opinion that may or may not be true depending on the evidence and/or proof, offered; the purpose of the dissertation is thus to outline the proofs of why the author disagrees with other philosophers or the general opinion. A thesis may be arranged as a thesis by publication or a monograph, with or without appended papers though many graduate programs allow candidates to submit a curated collection of published papers. An ordinary monograph has a title page, an abstract, a table of contents, comprising the various chapters, a bibliography or a references section.
They differ in their structure in accordance with the many different areas of study and the differences between them. In a thesis by publication, the chapters constitute an introductory and comprehensive review of the appended published and unpublished article documents. Dissertations report on a research project or study, or an extended analysis of a topic; the structure of a thesis or dissertation explains the purpose, the previous research literature impinging on the topic of the study, the methods used, the findings of the project. Most world universities use a multiple chapter format: a) an introduction, which introduces the research topic, the methodology, as well as its scope and significance. Degree-awarding institutions define their own house style that candidates have to follow when preparing a thesis document. In addition to institution-specific house styles, there exist a number of field-specific and international standards and recommendations for the presentation of theses, for instance ISO 7144.
Other applicable international standards include ISO 2145 on section numbers, ISO 690 on bibliographic references, ISO 31 on quantities or units. Some older house styles specify that front matter must use a separate page number sequence from the main text, using Roman numerals; the relevant international standard and many newer style guides recognize that this book design practice can cause confusion where electronic document viewers number all pages of a document continuously from the first page, independent of any printed page numbers. They, avoid the traditional separate number sequence for front matter and require a single sequence of Arabic numerals starting with 1 for the first printed page. Presentation requirements, including pagination, layout and color of paper, use of acid-free paper, paper size, order of components, citation style, will be checked page by page by the accepting officer before the thesis is accepted and a receipt is issued. However, strict standards are not always required.
Most Italian universities, for example, have only general requirements on the character size and the page formatting, leave much freedom for the actual typographic details. A thesis or dissertation committee is a committee. In the US, these committees consist of a primary supervisor or advisor and two or more committee members, who supervise the progress of the dissertation and may act as the examining committee, or jury, at the oral examination of the thesis. At most universities, the committee is chosen by the student in conjunction with his or her primary adviser after completion of the comprehensive examinations or prospectus meeting, may consist of members of the comps committee; the committee members are doctors in their field (whether a PhD or other des
American Academy of Arts and Sciences
The American Academy of Arts and Sciences is one of the oldest learned societies in the United States. Founded in 1780, the Academy is dedicated to honoring excellence and leadership, working across disciplines and divides, advancing the common good. Membership in the academy is achieved through a thorough petition and election process and has been considered a high honor of scholarly and societal merit since the academy was founded during the American Revolution by John Adams, John Hancock, James Bowdoin, others of their contemporaries who contributed prominently to the establishment of the new nation, its government, the United States Constitution. Today the Academy is charged with a dual function: to elect to membership the finest minds and most influential leaders, drawn from science, business, public affairs, the arts, from each generation, to conduct policy studies in response to the needs of society. Major Academy projects now have focused on higher education and research and cultural studies and technological advances, politics and the environment, the welfare of children.
Dædalus, the Academy's quarterly journal, is regarded as one of the world's leading intellectual journals. The Academy carries out nonpartisan policy research by bringing together scientists, artists, business leaders, other experts to make multidisciplinary analyses of complex social and intellectual topics; the Academy's current areas of work are Arts & Humanities, Democracy & Justice, Energy & Environment, Global Affairs, Science & Technology. David W. Oxtoby began his term as the organization’s President in January 2019. A chemist by training, he served as President of Pomona College from 2003 to 2017, he was elected a member of the American Academy in 2012. The Academy is headquartered in Massachusetts; the Academy was established by the Massachusetts legislature on May 4, 1780. Its purpose, as described in its charter, is "to cultivate every art and science which may tend to advance the interest, honor and happiness of a free and virtuous people." The sixty-two incorporating fellows represented varying interests and high standing in the political and commercial sectors of the state.
The first class of new members, chosen by the Academy in 1781, included Benjamin Franklin and George Washington as well as several international honorary members. The initial volume of Academy Memoirs appeared in 1785, the Proceedings followed in 1846. In the 1950s, the Academy launched its journal Daedalus, reflecting its commitment to a broader intellectual and socially-oriented program. Since the second half of the twentieth century, independent research has become a central focus of the Academy. In the late 1950s, arms control emerged as one of its signature concerns; the Academy served as the catalyst in establishing the National Humanities Center in North Carolina. In the late 1990s, the Academy developed a new strategic plan, focusing on four major areas: science and global security. In 2002, the Academy established a visiting scholars program in association with Harvard University. More than 75 academic institutions from across the country have become Affiliates of the Academy to support this program and other Academy initiatives.
The Academy has sponsored a number of awards and prizes, now numbering 11, throughout its history and has offered opportunities for fellowships and visiting scholars at the Academy. Charter members of the Academy are John Adams, Samuel Adams, John Bacon, James Bowdoin, Charles Chauncy, John Clarke, David Cobb, Samuel Cooper, Nathan Cushing, Thomas Cushing, William Cushing, Tristram Dalton, Francis Dana, Samuel Deane, Perez Fobes, Caleb Gannett, Henry Gardner, Benjamin Guild, John Hancock, Joseph Hawley, Edward Augustus Holyoke, Ebenezer Hunt, Jonathan Jackson, Charles Jarvis, Samuel Langdon, Levi Lincoln, Daniel Little, Elijah Lothrup, John Lowell, Samuel Mather, Samuel Moody, Andrew Oliver, Joseph Orne, Theodore Parsons, George Partridge, Robert Treat Paine, Phillips Payson, Samuel Phillips, John Pickering, Oliver Prescott, Zedekiah Sanger, Nathaniel Peaslee Sargeant, Micajah Sawyer, Theodore Sedgwick, William Sever, David Sewall, Stephen Sewall, John Sprague, Ebenezer Storer, Caleb Strong, James Sullivan, John Bernard Sweat, Nathaniel Tracy, Cotton Tufts, James Warren, Samuel West, Edward Wigglesworth, Joseph Willard, Abraham Williams, Nehemiah Williams, Samuel Williams, James Winthrop.
From the beginning, the membership and elected by peers, has included not only scientists and scholars, but writers and artists as well as representatives from the full range of professions and public life. Throughout the Academy's history, 10,000 fellows have been elected, including such notables as John Adams, Thomas Jefferson, John James Audubon, Joseph Henry, Washington Irving, Josiah Willard Gibbs, Augustus Saint-Gaudens, J. Robert Oppenheimer, Willa Cather, T. S. Eliot, Edward R. Murrow, Jonas Salk, Eudora Welty, Duke Ellington. International honorary members have included Jose Antonio Pantoja Hernandez, Leonhard Euler, Marquis de Lafayette, Alexander von Humboldt, Leopold von Ranke, Charles Darwin, Otto Hahn, Jawaharlal Nehru, Pablo Picasso, Liu Kuo-Sung, Lucian Michael Freud, Galina Ulanova, Werner Heisenberg, Alec Guinness and Sebastião Salgado. Astronomer Maria Mitchell was the first woman elected to the Academy, in 1848; the current membership encompasses over 5,700 members based across the United States and around the world.
Academy members include more than 60 Pulitzer Prize winners. The current membership is divided into five classes and twen