Princeton University Press
Princeton University Press is an independent publisher with close connections to Princeton University. Its mission is to disseminate scholarship within society at large; the press was founded by Whitney Darrow, with the financial support of Charles Scribner, as a printing press to serve the Princeton community in 1905. Its distinctive building was constructed in 1911 on William Street in Princeton, its first book was a new 1912 edition of John Witherspoon's Lectures on Moral Philosophy. Princeton University Press was founded in 1905 by a recent Princeton graduate, Whitney Darrow, with financial support from another Princetonian, Charles Scribner II. Darrow and Scribner purchased the equipment and assumed the operations of two existing local publishers, that of the Princeton Alumni Weekly and the Princeton Press; the new press printed both local newspapers, university documents, The Daily Princetonian, added book publishing to its activities. Beginning as a small, for-profit printer, Princeton University Press was reincorporated as a nonprofit in 1910.
Since 1911, the press has been headquartered in a purpose-built gothic-style building designed by Ernest Flagg. The design of press’s building, named the Scribner Building in 1965, was inspired by the Plantin-Moretus Museum, a printing museum in Antwerp, Belgium. Princeton University Press established a European office, in Woodstock, north of Oxford, in 1999, opened an additional office, in Beijing, in early 2017. Six books from Princeton University Press have won Pulitzer Prizes: Russia Leaves the War by George F. Kennan Banks and Politics in America from the Revolution to the Civil War by Bray Hammond Between War and Peace by Herbert Feis Washington: Village and Capital by Constance McLaughlin Green The Greenback Era by Irwin Unger Machiavelli in Hell by Sebastian de Grazia Books from Princeton University Press have been awarded the Bancroft Prize, the Nautilus Book Award, the National Book Award. Multi-volume historical documents projects undertaken by the Press include: The Collected Papers of Albert Einstein The Writings of Henry D. Thoreau The Papers of Woodrow Wilson The Papers of Thomas Jefferson Kierkegaard's WritingsThe Papers of Woodrow Wilson has been called "one of the great editorial achievements in all history."
Princeton University Press's Bollingen Series had its beginnings in the Bollingen Foundation, a 1943 project of Paul Mellon's Old Dominion Foundation. From 1945, the foundation had independent status and providing fellowships and grants in several areas of study, including archaeology and psychology; the Bollingen Series was given to the university in 1969. Annals of Mathematics Studies Princeton Series in Astrophysics Princeton Series in Complexity Princeton Series in Evolutionary Biology Princeton Series in International Economics Princeton Modern Greek Studies The Whites of Their Eyes: The Tea Party's Revolution and the Battle over American History, by Jill Lepore The Meaning of Relativity by Albert Einstein Atomic Energy for Military Purposes by Henry DeWolf Smyth How to Solve It by George Polya The Open Society and Its Enemies by Karl Popper The Hero With a Thousand Faces by Joseph Campbell The Wilhelm/Baynes translation of the I Ching, Bollingen Series XIX. First copyright 1950, 27th printing 1997.
Anatomy of Criticism by Northrop Frye Philosophy and the Mirror of Nature by Richard Rorty QED: The Strange Theory of Light and Matter by Richard Feynman The Great Contraction 1929–1933 by Milton Friedman and Anna Jacobson Schwartz with a new Introduction by Peter L. Bernstein Military Power: Explaining Victory and Defeat in Modern Battle by Stephen Biddle Banks, Eric. "Book of Lists: Princeton University Press at 100". Artforum International. Staff of Princeton University Press. A Century in Books: Princeton University Press, 1905–2005. ISBN 9780691122922. CS1 maint: Uses authors parameter Official website Princeton University Press: Albert Einstein Web Page Princeton University Press: Bollingen Series Princeton University Press: Annals of Mathematics Studies Princeton University Press Centenary Princeton University Press: New in Print
Mathematics includes the study of such topics as quantity, structure and change. Mathematicians use patterns to formulate new conjectures; when mathematical structures are good models of real phenomena mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity from as far back; the research required to solve mathematical problems can take years or centuries of sustained inquiry. Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Since the pioneering work of Giuseppe Peano, David Hilbert, others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions. Mathematics developed at a slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that has continued to the present day.
Mathematics is essential in many fields, including natural science, medicine and the social sciences. Applied mathematics has led to new mathematical disciplines, such as statistics and game theory. Mathematicians engage in pure mathematics without having any application in mind, but practical applications for what began as pure mathematics are discovered later; the history of mathematics can be seen as an ever-increasing series of abstractions. The first abstraction, shared by many animals, was that of numbers: the realization that a collection of two apples and a collection of two oranges have something in common, namely quantity of their members; as evidenced by tallies found on bone, in addition to recognizing how to count physical objects, prehistoric peoples may have recognized how to count abstract quantities, like time – days, years. Evidence for more complex mathematics does not appear until around 3000 BC, when the Babylonians and Egyptians began using arithmetic and geometry for taxation and other financial calculations, for building and construction, for astronomy.
The most ancient mathematical texts from Mesopotamia and Egypt are from 2000–1800 BC. Many early texts mention Pythagorean triples and so, by inference, the Pythagorean theorem seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry, it is in Babylonian mathematics that elementary arithmetic first appear in the archaeological record. The Babylonians possessed a place-value system, used a sexagesimal numeral system, still in use today for measuring angles and time. Beginning in the 6th century BC with the Pythagoreans, the Ancient Greeks began a systematic study of mathematics as a subject in its own right with Greek mathematics. Around 300 BC, Euclid introduced the axiomatic method still used in mathematics today, consisting of definition, axiom and proof, his textbook Elements is considered the most successful and influential textbook of all time. The greatest mathematician of antiquity is held to be Archimedes of Syracuse, he developed formulas for calculating the surface area and volume of solids of revolution and used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, in a manner not too dissimilar from modern calculus.
Other notable achievements of Greek mathematics are conic sections, trigonometry (Hipparchus of Nicaea, the beginnings of algebra. The Hindu–Arabic numeral system and the rules for the use of its operations, in use throughout the world today, evolved over the course of the first millennium AD in India and were transmitted to the Western world via Islamic mathematics. Other notable developments of Indian mathematics include the modern definition of sine and cosine, an early form of infinite series. During the Golden Age of Islam during the 9th and 10th centuries, mathematics saw many important innovations building on Greek mathematics; the most notable achievement of Islamic mathematics was the development of algebra. Other notable achievements of the Islamic period are advances in spherical trigonometry and the addition of the decimal point to the Arabic numeral system. Many notable mathematicians from this period were Persian, such as Al-Khwarismi, Omar Khayyam and Sharaf al-Dīn al-Ṭūsī. During the early modern period, mathematics began to develop at an accelerating pace in Western Europe.
The development of calculus by Newton and Leibniz in the 17th century revolutionized mathematics. Leonhard Euler was the most notable mathematician of the 18th century, contributing numerous theorems and discoveries; the foremost mathematician of the 19th century was the German mathematician Carl Friedrich Gauss, who made numerous contributions to fields such as algebra, differential geometry, matrix theory, number theory, statistics. In the early 20th century, Kurt Gödel transformed mathematics by publishing his incompleteness theorems, which show that any axiomatic system, consistent will contain unprovable propositions. Mathematics has since been extended, there has been a fruitful interaction between mathematics and science, to
Limit superior and limit inferior
In mathematics, the limit inferior and limit superior of a sequence can be thought of as limiting bounds on the sequence. They can be thought of in a similar fashion for a function. For a set, they are the supremum of the set's limit points, respectively. In general, when there are multiple objects around which a sequence, function, or set accumulates, the inferior and superior limits extract the smallest and largest of them. Limit inferior is called infimum limit, limit infimum, inferior limit, lower limit, or inner limit; the limit inferior of a sequence x n is denoted by lim inf n → ∞ x n or lim _ n → ∞ x n. The limit superior of a sequence x n is denoted by lim sup n → ∞ x n or lim ¯ n → ∞ x n; the limit inferior of a sequence is defined by lim inf n → ∞ x n:= lim n → ∞ or lim inf n → ∞ x n:= sup n ≥ 0 inf m ≥ n x m = sup. The limit superior of is defined by lim sup n → ∞ x n:= lim n → ∞ or lim sup n → ∞ x n:= inf n ≥ 0 sup m ≥ n x m = inf. Alternatively, the notations lim _ n → ∞ x n:= lim inf n → ∞ x n and lim ¯ n → ∞ x n:= lim sup n → ∞ x n are sometimes used.
The limits superior and inferior can equivalently be defined using the concept of subsequential limits of the sequence. A real number ξ is a subsequential limit of if there exists a increasing sequence of natural numbers such that ξ = lim k → ∞ x n k. If E ⊂ R ¯ is the set of all subsequential limits of lim sup n → ∞ x n = sup E and lim inf n → ∞ x n = inf E. If the terms in the sequence are real numbers, the limit superior and limit inferior always exist, as the real numbers together with ±∞ are complete. More these definitions make sense in any ordered set, provided the suprema and infima exist, such as in a complete lattice. Whenever the ordinary limit exists, the limit
Wacław Franciszek Sierpiński was a Polish mathematician. He was known for contributions to set number theory, theory of functions and topology, he published over 50 books. Three well-known fractals are named after him, as are Sierpinski numbers and the associated Sierpiński problem. Sierpiński enrolled in the Department of Mathematics and Physics at the University of Warsaw in 1899 and graduated four years later. In 1903, while still at the University of Warsaw, the Department of Mathematics and Physics offered a prize for the best essay from a student on Voronoy's contribution to number theory. Sierpiński was awarded a gold medal for his essay, thus laying the foundation for his first major mathematical contribution. Unwilling for his work to be published in Russian, he withheld it until 1907, when it was published in Samuel Dickstein's mathematical magazine'Prace Matematyczno-Fizyczne'. After his graduation in 1904, Sierpiński worked as a school teacher of mathematics and physics in Warsaw. However, when the school closed because of a strike, Sierpiński decided to go to Kraków to pursue a doctorate.
At the Jagiellonian University in Kraków he attended. He studied astronomy and philosophy, he received his doctorate and was appointed to the University of Lwów in 1908. In 1907 Sierpiński first became interested in set theory when he came across a theorem which stated that points in the plane could be specified with a single coordinate, he wrote to Tadeusz Banachiewicz. He received the one-word reply'Cantor'. Sierpiński began to study set theory and, in 1909, he gave the first lecture course devoted to the subject. Sierpiński maintained an output of research books. During the years 1908 to 1914, when he taught at the University of Lwów, he published three books in addition to many research papers; these books were The Theory of Irrational Numbers, Outline of Set Theory, The Theory of Numbers. When World War I began in 1914, Sierpiński and his family were in Russia. To avoid the persecution, common for Polish foreigners, Sierpiński spent the rest of the war years in Moscow working with Nikolai Luzin.
Together they began the study of analytic sets. In 1916, Sierpiński gave the first example of an normal number; when World War I ended in 1918, Sierpiński returned to Lwów. However shortly after taking up his appointment again in Lwów he was offered a post at the University of Warsaw, which he accepted. In 1919 he was promoted to a professor, he spent the rest of his life in Warsaw. During the Polish–Soviet War, Sierpiński helped break Soviet Russian ciphers for the Polish General Staff's cryptological agency. In 1920, Sierpiński, together with Zygmunt Janiszewski and his former student Stefan Mazurkiewicz, founded the mathematical journal Fundamenta Mathematicae. Sierpiński edited the journal. During this period, Sierpiński worked predominantly on set theory, but on point set topology and functions of a real variable. In set theory he made contributions on the continuum hypothesis, he proved that Zermelo–Fraenkel set theory together with the Generalized continuum hypothesis imply the Axiom of choice.
He worked on what is now known as the Sierpinski curve. Sierpiński continued to collaborate with Luzin on investigations of projective sets, his work on functions of a real variable includes results on functional series, differentiability of functions and Baire's classification. Sierpiński retired in 1960 as professor at the University of Warsaw, but continued until 1967 to give a seminar on the Theory of Numbers at the Polish Academy of Sciences, he continued editorial work as editor-in-chief of Acta Arithmetica, as an editorial-board member of Rendiconti del Circolo Matematico di Palermo, Composito Matematica, Zentralblatt für Mathematik. Sierpiński is interred at the Powązki Cemetery in Poland. Honorary Degrees: Lwów, St. Marks of Lima, Tarta, Prague, Wrocław, Moscow. For high involvement with the development of mathematics in Poland, Sierpiński was honored with election to the Polish Academy of Learning in 1921 and that same year was made dean of the faculty at the University of Warsaw. In 1928, he became vice-chairman of the Warsaw Scientific Society, that same year was elected chairman of the Polish Mathematical Society.
He was elected to the Geographic Society of Lima, the Royal Scientific Society of Liège, the Bulgarian Academy of Sciences, the National Academy of Lima, the Royal Society of Sciences of Naples, the Accademia dei Lincei of Rome, the Germany Academy of Sciences, the United States National Academy of Sciences, the Paris Academy, the Royal Dutch Academy, the Academy of Science of Brussels, the London Mathematical Society, the Romanian Academy and the Papal Academy of Sciences. In 1949 Sierpiński was awarded Poland's Scientific Prize, first degree. Sierpiński authored 50 books. W. Sierpiński. Elementary theory of numbers. Monografie Matematyczne. 42. ISBN 0-444-86662-0. Arity theorem List of Poles Menger sponge
Elias M. Stein
Elias Menachem Stein was an American mathematician, a leading figure in the field of harmonic analysis. He was professor of Mathematics at Princeton University from 1963 until his death in 2018. Stein was born to Elkan Stein and Chana Goldman, Ashkenazi Jews from Belgium. After the German invasion in 1940, the Stein family fled to the United States, first arriving in New York City, he graduated from Stuyvesant High School in 1949, where he was classmates with future Fields Medalist Paul Cohen, before moving on to the University of Chicago for college. In 1955, Stein earned a Ph. D. from the University of Chicago under the direction of Antoni Zygmund. He began teaching in MIT in 1955, moved to the University of Chicago in 1958 as an assistant professor, in 1963 became a full professor at Princeton. Stein worked in the field of harmonic analysis, made contributions in both extending and clarifying Calderón–Zygmund theory; these include Stein interpolation, the Stein maximal principle, Stein complementary series representations, Nikishin–Pisier–Stein factorization in operator theory, the Tomas–Stein restriction theorem in Fourier analysis, the Kunze–Stein phenomenon in convolution on semisimple groups, the Cotlar–Stein lemma concerning the sum of orthogonal operators, the Fefferman–Stein theory of the Hardy space H 1 and the space B M O of functions of bounded mean oscillation.
He has written numerous books on harmonic analysis, which are cited as the standard references on the subject. His Princeton Lectures in Analysis series were penned for his sequence of undergraduate courses on analysis at Princeton. Stein is noted as having trained a high number of graduate students, so shaping modern Fourier analysis, they include Charles Fefferman and Terence Tao. His honors include the Steele Prize, the Schock Prize in Mathematics, the Wolf Prize in Mathematics, the National Medal of Science. In addition, he has fellowships to National Science Foundation, Sloan Foundation, Guggenheim Foundation, National Academy of Sciences. In 2005, Stein was awarded the Stefan Bergman prize in recognition of his contributions in real and harmonic analysis. In 2012 he became a fellow of the American Mathematical Society. In 1959, he married Elly Intrator, a former Jewish refugee during World War II, they had two children, Karen Stein and Jeremy C. Stein, grandchildren named Alison and Carolyn.
His son Jeremy is a professor of financial economics at Harvard, former adviser to Tim Geithner and Lawrence Summers, served on the Federal Reserve Board of Governors from 2012 to 2014. Elias Stein died of complications of lymphoma in 2018, aged 87. Stein, Elias. Singular Integrals and Differentiability Properties of Functions. Princeton University Press. ISBN 0-691-08079-8. Stein, Elias. Topics in Harmonic Analysis Related to the Littlewood-Paley Theory. Princeton University Press. ISBN 0-691-08067-4. Stein, Elias. Introduction to Fourier Analysis on Euclidean Spaces. Princeton University Press. ISBN 0-691-08078-X. Stein, Elias. Analytic Continuation of Group Representations. Princeton University Press. ISBN 0-300-01428-7. Nagel, Alexander. Lectures on Pseudo-differential Operators: Regularity Theorems and Applications to Non-elliptic Problems. Princeton University Press. ISBN 978-0-691-08247-9. Stein, Elias. Harmonic Analysis: Real-variable Methods and Oscillatory Integrals. Princeton University Press. ISBN 0-691-03216-5.
Stein, Elias. Fourier Analysis: An Introduction. Princeton University Press. ISBN 0-691-11384-X. Stein, Elias. Complex Analysis. Princeton University Press. ISBN 0-691-11385-8. Stein, Elias. Real Analysis: Measure Theory and Hilbert Spaces. Princeton University Press. ISBN 0-691-11386-6. Stein, Elias. Functional Analysis: An Introduction to Further Topics in Analysis. Princeton University Press. ISBN 0-691-11387-4; this article incorporates material from Elias Stein on PlanetMath, licensed under the Creative Commons Attribution/Share-Alike License. Elias M. Stein at the Mathematics Genealogy Project Citation for Elias Stein for the 2002 Steele prize for lifetime achievement Elias Stein Curriculum Vitae
A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, i is a solution of the equation x2 = −1. Because no real number satisfies this equation, i is called an imaginary number. For the complex number a + bi, a is called the real part, b is called the imaginary part. Despite the historical nomenclature "imaginary", complex numbers are regarded in the mathematical sciences as just as "real" as the real numbers, are fundamental in many aspects of the scientific description of the natural world. Complex numbers allow solutions to certain equations. For example, the equation 2 = − 9 has no real solution, since the square of a real number cannot be negative. Complex numbers provide a solution to this problem; the idea is to extend the real numbers with an indeterminate i, taken to satisfy the relation i2 = −1, so that solutions to equations like the preceding one can be found. In this case the solutions are −1 + 3i and −1 − 3i, as can be verified using the fact that i2 = −1: 2 = 2 = = 9 = − 9, 2 = 2 = 2 = 9 = − 9.
According to the fundamental theorem of algebra, all polynomial equations with real or complex coefficients in a single variable have a solution in complex numbers. In contrast, some polynomial equations with real coefficients have no solution in real numbers; the 16th century Italian mathematician Gerolamo Cardano is credited with introducing complex numbers in his attempts to find solutions to cubic equations. Formally, the complex number system can be defined as the algebraic extension of the ordinary real numbers by an imaginary number i; this means that complex numbers can be added and multiplied, as polynomials in the variable i, with the rule i2 = −1 imposed. Furthermore, complex numbers can be divided by nonzero complex numbers. Overall, the complex number system is a field. Geometrically, complex numbers extend the concept of the one-dimensional number line to the two-dimensional complex plane by using the horizontal axis for the real part and the vertical axis for the imaginary part.
The complex number a + bi can be identified with the point in the complex plane. A complex number whose real part is zero is said to be purely imaginary. A complex number whose imaginary part is zero can be viewed as a real number. Complex numbers can be represented in polar form, which associates each complex number with its distance from the origin and with a particular angle known as the argument of this complex number; the geometric identification of the complex numbers with the complex plane, a Euclidean plane, makes their structure as a real 2-dimensional vector space evident. Real and imaginary parts of a complex number may be taken as components of a vector with respect to the canonical standard basis; the addition of complex numbers is thus depicted as the usual component-wise addition of vectors. However, the complex numbers allow for a richer algebraic structure, comprising additional operations, that are not available in a vector space. Based on the concept of real numbers, a complex number is a number of the form a + bi, where a and b are real numbers and i is an indeterminate satisfying i2 = −1.
For example, 2 + 3i is a complex number. This way, a complex number is defined as a polynomial with real coefficients in the single indeterminate i, for which the relation i2 + 1 = 0 is imposed. Based on this definition, complex numbers can be added and multiplied, using the addition and multiplication for polynomials; the relation i2 + 1 = 0 induces the equalities i4k = 1, i4k+1 = i, i4k+2 = −1, i4k+3 = −i, which hold for all integers k. The real number a is called the real part of the complex number a + bi. To emphasize, the imaginary part does not include a factor i and b, not bi, is the imaginary part. Formally, the complex numbers are defined as the quotient ring of the polynomia
A circle is a simple closed shape. It is the set of all points in a plane; the distance between any of the points and the centre is called the radius. This article is about circles in Euclidean geometry, and, in particular, the Euclidean plane, except where otherwise noted. A circle is a simple closed curve that divides the plane into two regions: an interior and an exterior. In everyday use, the term "circle" may be used interchangeably to refer to either the boundary of the figure, or to the whole figure including its interior. A circle may be defined as a special kind of ellipse in which the two foci are coincident and the eccentricity is 0, or the two-dimensional shape enclosing the most area per unit perimeter squared, using calculus of variations. A circle is a plane figure bounded by one line, such that all right lines drawn from a certain point within it to the bounding line, are equal; the bounding line is called the point, its centre. Annulus: a ring-shaped object, the region bounded by two concentric circles.
Arc: any connected part of a circle. Specifying two end points of an arc and a center allows for two arcs that together make up a full circle. Centre: the point equidistant from all points on the circle. Chord: a line segment whose endpoints lie on the circle, thus dividing a circle in two sements. Circumference: the length of one circuit along the circle, or the distance around the circle. Diameter: a line segment whose endpoints lie on the circle and that passes through the centre; this is the largest distance between any two points on the circle. It is a special case of a chord, namely the longest chord for a given circle, its length is twice the length of a radius. Disc: the region of the plane bounded by a circle. Lens: the region common to two overlapping discs. Passant: a coplanar straight line that has no point in common with the circle. Radius: a line segment joining the centre of a circle with any single point on the circle itself. Sector: a region bounded by two radii of equal length with a common center and either of the two possible arcs, determined by this center and the endpoints of the radii.
Segment: a region bounded by a chord and one of the arcs connecting the chord's endpoints. The length of the chord imposes a lower boundary on the diameter of possible arcs. Sometimes the term segment is used only for regions not containing the center of the circle to which their arc belongs to. Secant: an extended chord, a coplanar straight line, intersecting a circle in two points. Semicircle: one of the two possible arcs determined by the endpoints of a diameter, taking its midpoint as center. In non-technical common usage it may mean the interior of the two dimensional region bounded by a diameter and one of its arcs, technically called a half-disc. A half-disc is a special case of a segment, namely the largest one. Tangent: a coplanar straight line that has one single point in common with a circle. All of the specified regions may be considered as open, that is, not containing their boundaries, or as closed, including their respective boundaries; the word circle derives from the Greek κίρκος/κύκλος, itself a metathesis of the Homeric Greek κρίκος, meaning "hoop" or "ring".
The origins of the words circus and circuit are related. The circle has been known since before the beginning of recorded history. Natural circles would have been observed, such as the Moon, a short plant stalk blowing in the wind on sand, which forms a circle shape in the sand; the circle is the basis for the wheel, with related inventions such as gears, makes much of modern machinery possible. In mathematics, the study of the circle has helped inspire the development of geometry and calculus. Early science geometry and astrology and astronomy, was connected to the divine for most medieval scholars, many believed that there was something intrinsically "divine" or "perfect" that could be found in circles; some highlights in the history of the circle are: 1700 BCE – The Rhind papyrus gives a method to find the area of a circular field. The result corresponds to 256/81 as an approximate value of π. 300 BCE – Book 3 of Euclid's Elements deals with the properties of circles. In Plato's Seventh Letter there is a detailed explanation of the circle.
Plato explains the perfect circle, how it is different from any drawing, definition or explanation. 1880 CE – Lindemann proves that π is transcendental settling the millennia-old problem of squaring the circle. The ratio of a circle's circumference to its diameter is π, an irrational constant equal to 3.141592654. Thus the length of the circumference C is related to the radius r and diameter d by: C = 2 π r = π d; as proved by Archimedes, in his Measurement of a Circle, the area enclosed by a circle is equal to that of a triangle whose base has the length of the circle's circumference and whose height equals the circle's radius, which comes to π multiplied by the radius squared: A r e a = π r 2. Equivalently, denoting diameter by d, A r e