Nicolas Bourbaki

Nicolas Bourbaki is the collective allonym under which a group of mainly French 20th-century mathematicians wrote a series of books presenting an exposition of modern advanced mathematics, beginning in 1935. With the goal of founding all of mathematics on set theory, the group strove for utmost rigour and generality, creating some new terminology and concepts along the way. While Nicolas Bourbaki is an invented personage, the Bourbaki group is officially known as the Association des collaborateurs de Nicolas Bourbaki< ...

Including:

• Nicolas Bourbaki - Books by Bourbaki
• Nicolas Bourbaki - Influence on mathematics in general
• Nicolas Bourbaki - The group
• Nicolas Bourbaki - The Bourbaki perspective and its limitations
• Nicolas Bourbaki - Dieudonné as speaker for Bourbaki
• Nicolas Bourbaki - The Bourbachique influence: education institutions trends

Read more here: » Nicolas Bourbaki: Encyclopedia - Nicolas Bourbaki

Aiming at a completely self-contained treatment of most of modern mathematics based on set theory, the group produced the following volumes (with the original French titles in brackets): I Set theory (Théorie des ensembles) II Algebra (Algèbre) III Topology (Topologie générale) IV Functions of one real variable (Fonctions d'une variable réelle) V Topological vector spaces (Espaces vectoriels topologiques ...

See also:

Nicolas Bourbaki, Nicolas Bourbaki - Books by Bourbaki, Nicolas Bourbaki - Influence on mathematics in general, Nicolas Bourbaki - The group, Nicolas Bourbaki - The Bourbaki perspective and its limitations, Nicolas Bourbaki - Dieudonné as speaker for Bourbaki, Nicolas Bourbaki - The Bourbachique influence: education institutions trends

Read more here: » Nicolas Bourbaki: Encyclopedia II - Nicolas Bourbaki - Books by Bourbaki

From a very young age he was an outstanding figure in the school of Henri Cartan, working on algebraic topology, several complex variables and then commutative algebra and algebraic geometry, in the context of sheaf theory and homological algebra techniques. Serre's thesis refers to his dissertation on the Leray-Serre spectral sequence associated to a fibration. In his speech at the Fields Medal award ceremony in 1954, Hermann Weyl praised Serre in apparently extravagant terms, and also made the point that the award ...

See also:

Jean-Pierre Serre, Jean-Pierre Serre - Life and career, Jean-Pierre Serre - Early work, Jean-Pierre Serre - Foundational work in algebraic geometry and the Weil conjectures, Jean-Pierre Serre - Other work, Jean-Pierre Serre - Awards, Jean-Pierre Serre - Works, Jean-Pierre Serre - External link

Read more here: » Jean-Pierre Serre: Encyclopedia II - Jean-Pierre Serre - Early work

From a very young age he was an outstanding figure in the school of Henri Cartan, working on algebraic topology, several complex variables and then commutative algebra and algebraic geometry, in the context of sheaf theory and homological algebra techniques. Serre's thesis refers to his dissertation on the Leray-Serre spectral sequence associated to a fibration. In his speech at the Fields Medal award ceremony in 1954, Hermann Weyl praised Serre in apparently extravagant terms, and also made the point that the award ...

See also:

Jean-Pierre Serre, Jean-Pierre Serre - Life and career, Jean-Pierre Serre - Early work, Jean-Pierre Serre - Foundational work in algebraic geometry and the Weil conjectures, Jean-Pierre Serre - Other work, Jean-Pierre Serre - Awards, Jean-Pierre Serre - External link

Read more here: » Jean-Pierre Serre: Encyclopedia II - Jean-Pierre Serre - Early work

In a true collaborative environment, each contributor has an equal ability to add, edit, and remove text. The writing process becomes a recursive task, where each change prompts others to make more changes. It is easier to do if the group has a specific end goal in mind, and harder if a goal is absent or vague. A very good method of discussion and communication is essential, especially if disagreements arise. ...

See also:

Collaborative writing, Collaborative writing - Practical Approach, Collaborative writing - Examples, Collaborative writing - Similar and related Concepts

Read more here: » Collaborative writing: Encyclopedia II - Collaborative writing - Practical Approach

From 1959 onwards his interests turned towards number theory, in particular class field theory and the theory of complex multiplication. Amongst his most original contributions were: the concept of algebraic K-theory; the Galois representation theory for l-adic cohomology and the conceptions that these representations were 'large'; and the Serre conjecture on mod p representations that made Fermat's last theorem a c ...

See also:

Jean-Pierre Serre, Jean-Pierre Serre - Life and career, Jean-Pierre Serre - Early work, Jean-Pierre Serre - Foundational work in algebraic geometry and the Weil conjectures, Jean-Pierre Serre - Other work, Jean-Pierre Serre - Awards, Jean-Pierre Serre - External link

Read more here: » Jean-Pierre Serre: Encyclopedia II - Jean-Pierre Serre - Other work

Blackboard bold is a style of typeface often used for certain symbols in mathematics and physics texts, in which certain lines of the symbol (usually vertical, or near-vertical lines) are doubled. The symbols usually describe sets of numbers and are also referred to as double struck, although attempting to produce them by double striking on a typewriter is unlikely to give satisfactory results. The symbols are also nearly universal in their interpretation, unlike their norma ...

Read more here: » Blackboard bold: Encyclopedia - Blackboard bold

The terms collaborative writing and peer collaboration refer to projects where written works are created by multiple people together (collaboratively) rather than individually. Some projects are overseen by an editor or editorial team, but many grow without any top-down oversight. Collaborative writing - Practical Approach. In a true collaborative environment, each contributor has an equal ability to add, edit, and remove text. The writing process becomes a recursive task, where each change pr ...

Including:

• Collaborative writing - Practical Approach
• Collaborative writing - Examples
• Collaborative writing - Similar and related Concepts

Read more here: » Collaborative writing: Encyclopedia - Collaborative writing

The 20th century lasted from 1901 to 2000 in the Gregorian calendar. Common usage sometimes regards it as lasting from 1900 to 1999. The 20th century is also sometimes known as the nineteen hundreds (1900s). However, a number of arguments have been used to justify the common usage. One advanced by Stephen Jay Gould is that the first decade had only nine years, thus contradicting the definition of decade equaled 10 years. Another argument is that the astronomical year numbering system for years does have a year zero, the ...

Including:

• 20th century - Overview
• 20th century - Important developments events and achievements
• 20th century - Science and technology
• 20th century - Wars and politics
• 20th century - Culture and entertainment
• 20th century - Disease and medicine
• 20th century - Natural resources and the environment
• 20th century - Significant people
• 20th century - World leaders
• 20th century - Scientists
• 20th century - Humanities
• 20th century - Business
• 20th century - Aerospace pioneers
• 20th century - Spiritual figures
• 20th century - Artists
• 20th century - Music
• 20th century - Film
• 20th century - Writers and poets
• 20th century - Sports figures
• 20th century - Decades and years

Read more here: » 20th century: Encyclopedia - 20th century

In the 1950s and 1960s, a fruitful collaboration between Serre and the two years younger Alexander Grothendieck led to important foundational work, much of it motivated by the Weil conjectures. Two major foundational papers by Serre were FAC (Faisceaux Algébriques Cohérents, on coherent cohomology) and GAGA. Serre had early on perceived a need to construct more general and refined cohomology theories to tackle these conjectures. In simple terms, the cohomology of a coherent sheaf over a finite field couldn't capture as much t ...

See also:

Jean-Pierre Serre, Jean-Pierre Serre - Life and career, Jean-Pierre Serre - Early work, Jean-Pierre Serre - Foundational work in algebraic geometry and the Weil conjectures, Jean-Pierre Serre - Other work, Jean-Pierre Serre - Awards, Jean-Pierre Serre - External link

Read more here: » Jean-Pierre Serre: Encyclopedia II - Jean-Pierre Serre - Foundational work in algebraic geometry and the Weil conjectures

The École Normale Supérieure (also known as Normale Sup', Normale, ENS, ENS-Paris, ENS-Ulm or Ulm), written École normale supérieure in French is an elite French grande école, whose main campus is located around the rue d'Ulm (Ulm Street) in the 5th arrondissement of Paris. ENS has annex campuses on Boulevard Jourdan (in Paris) and in Montrouge (a suburb). École Normale Supérieure - Overview. Originally meant to train high school t ...

Including:

• École Normale Supérieure - Overview
• École Normale Supérieure - Notable alumni
• École Normale Supérieure - Notable professors
• École Normale Supérieure - External link

Read more here: » École Normale Supérieure: Encyclopedia - École Normale Supérieure

From 1959 onwards his interests turned towards number theory, in particular class field theory and the theory of complex multiplication. Amongst his most original contributions were: the concept of algebraic K-theory; the Galois representation theory for l-adic cohomology and the conceptions that these representations were 'large'; and the Serre conjecture on mod p representations that made Fermat's last theorem a c ...

See also:

Jean-Pierre Serre, Jean-Pierre Serre - Life and career, Jean-Pierre Serre - Early work, Jean-Pierre Serre - Foundational work in algebraic geometry and the Weil conjectures, Jean-Pierre Serre - Other work, Jean-Pierre Serre - Awards, Jean-Pierre Serre - Works, Jean-Pierre Serre - External link

Read more here: » Jean-Pierre Serre: Encyclopedia II - Jean-Pierre Serre - Other work

In the 1950s and 1960s, a fruitful collaboration between Serre and the two years younger Alexander Grothendieck led to important foundational work, much of it motivated by the Weil conjectures. Two major foundational papers by Serre were FAC (Faisceaux Algébriques Cohérents, on coherent cohomology) and GAGA. Serre had early on perceived a need to construct more general and refined cohomology theories to tackle these conjectures. In simple terms, the cohomology of a coherent sheaf over a finite field couldn't capture as much t ...

See also:

Jean-Pierre Serre, Jean-Pierre Serre - Life and career, Jean-Pierre Serre - Early work, Jean-Pierre Serre - Foundational work in algebraic geometry and the Weil conjectures, Jean-Pierre Serre - Other work, Jean-Pierre Serre - Awards, Jean-Pierre Serre - Works, Jean-Pierre Serre - External link

Read more here: » Jean-Pierre Serre: Encyclopedia II - Jean-Pierre Serre - Foundational work in algebraic geometry and the Weil conjectures

In the mathematical field of topology, a uniform space is a set with a uniform structure. Uniform spaces are topological spaces with additional structure which is used to define uniform properties such as completeness, uniform continuity and uniform convergence. The conceptual difference between uniform and topological structures is that in a uniform space, you can formalize the idea that "x is as close to a as y is to b", while in a topological space you can only formalize "x ...

Including:

• Uniform space - History
• Uniform space - Definition
• Uniform space - Entourage definition
• Uniform space - Uniform cover definition
• Uniform space - Pseudometrics definition
• Uniform space - Intuition
• Uniform space - Examples
• Uniform space - Uniformly continuous functions
• Uniform space - Topology of uniform spaces
• Uniform space - Completeness

Read more here: » Uniform space: Encyclopedia - Uniform space

A pseudonym (Greek: false name) is a fictitious name used by an individual as an alternative to his or her legal name. A pseudonym is distinct from an allonym, which is the name of another actual person assumed by one person, usually historical, in authorship of a work of art; e.g., when ghostwriting a book or play, or in parody, or when using a front such as by screenwriters blacklisted in Hollywood in the '50s, '60s, and '70s. To be pseudonymous means that the person is using a pseudonym. The concept of real ...

Including:

• Pseudonym - Pseudonyms in print
• Pseudonym - Regnal name
• Pseudonym - Nom de guerre
• Pseudonym - The origin of nom de guerre
• Pseudonym - Radio
• Pseudonym - Computers
• Pseudonym - Pseudonyms in entertainment
• Pseudonym - Other pseudonyms

Read more here: » Pseudonym: Encyclopedia - Pseudonym

Originally meant to train high school teachers through the agrégation, it is now an elite institution training researchers, university professors, and civil servants (as well as highschool teachers, in particular in the humanities). It focuses on the association of training and research, with an emphasis on freedom of curriculum. Its alumni include eight laureates of the Fields Medal, which is the equivalent of the Nobel Prize for the mathematical sciences, as well ...

See also:

École Normale Supérieure, École Normale Supérieure - Overview, École Normale Supérieure - Notable alumni, École Normale Supérieure - Notable professors, École Normale Supérieure - External link

Read more here: » École Normale Supérieure: Encyclopedia II - École Normale Supérieure - Overview

New Math emphasized more abstract concepts like set theory and number bases other than 10, rather than strictly being concerned with mathematical concepts traditionally taught to those age groups. Beginning in the early 1960s the new educational doctrine was installed, not only in the USA, but all over the western hemisphere. Much of the publicity centered on the focus of this program on set theory (influenced ultimately by the Nicolas Bourbaki group and their work), functions, and diagram drawings. It was stressed that these subjects ...

See also:

New math, New math - The new mathematical pedagogy, New math - Resistance to curriculum change, New math - Across the developed world, New math - Popular culture

Read more here: » New math: Encyclopedia II - New math - The new mathematical pedagogy

Japanese poets who write haiku often use a haiga or penname. The famous haiku poet Matsuo Basho had used fifteen different haiga before he became fond of a banana plant (bashō) that had been given to him by a disciple and started using it as his penname at the age of 38. Similar to a pen name, Japanese artists usually have a gō or art-name, which might change a number of times during their career. Also, all Sumo wrestlers take shikona (wrestling names), and people in other professions and trades may also adopt new names ...

See also:

Pen name, Pen name - Urdu Poetry, Pen name - Japan, Pen name - Famous pen names, Pen name - House names

Read more here: » Pen name: Encyclopedia II - Pen name - Japan

20th century - World leaders. Africa Gnassingbe Eyadema, Togo Félix Houphouët-Boigny, Côte d'Ivoire Kenneth Kaunda, Zambia Jomo Kenyatta, Kenya Idi Amin, Uganda Nelson Mandela, South Africa Robert Mugabe, Zimbabwe Gamal Abdal Nasser, Egypt Kwame Nkrumah, Ghana Julius Nyerere, Tanzania Habib Bourguiba, Tunisia Muammar al-Qaddafi, Libya Haile Selassie, Ethiopia Léopold Sédar Sengh ...

See also:

20th century, 20th century - Overview, 20th century - Important developments events and achievements, 20th century - Science and technology, 20th century - Wars and politics, 20th century - Culture and entertainment, 20th century - Disease and medicine, 20th century - Natural resources and the environment, 20th century - Significant people, 20th century - World leaders, 20th century - Scientists, 20th century - Humanities, 20th century - Business, 20th century - Aerospace pioneers, 20th century - Spiritual figures, 20th century - Artists, 20th century - Music, 20th century - Film, 20th century - Writers and poets, 20th century - Sports figures, 20th century - Decades and years

Read more here: » 20th century: Encyclopedia II - 20th century - Significant people

New Math emphasized mathematical structure through abstract concepts like set theory and number bases other than 10, rather than strictly being concerned with mathematical concepts traditionally taught to those age groups. Beginning in the early 1960s the new educational doctrine was installed, not only in the USA, but all over the western hemisphere. Much of the publicity centered on the focus of this program on set theory (influenced ultimately by the Nicolas Bourbaki group and their work), functions, and diagram drawings. It was st ...

See also:

New math, New math - The new mathematical pedagogy, New math - Resistance to curriculum change, New math - Across the developed world, New math - Popular culture

Read more here: » New math: Encyclopedia II - New math - The new mathematical pedagogy