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https://en.wikipedia.org/wiki/Tereza%20Pl%C3%AD%C5%A1kov%C3%A1 | Tereza Plíšková (born 6 February 1990 in Prague) is a Czech curler.
Teams
References
External links
Plíšková Tereza (CC SOKOL LIBOC) - Player statistics (all games with his/her participation) - Czech Curling Association
Czech national women team (2016) - Czech Curling Federation (web archive)
Kubešková returns to world stage in Saint John - Curling Canada – 2014 Ford World Women's Curling Championship
Video:
Living people
1990 births
Sportspeople from Prague
Czech female curlers
Czech curling champions |
https://en.wikipedia.org/wiki/Random%20recursive%20tree | In probability theory, a random recursive tree is a rooted tree chosen uniformly at random from the recursive trees with a given number of vertices.
Definition and generation
In a recursive tree with vertices, the vertices are labeled by the numbers from to , and the labels must decrease along any path to the root of the tree. These trees are unordered, in the sense that there is no distinguished ordering of the children of each vertex. In a random recursive tree, all such trees are equally likely.
Alternatively, a random recursive tree can be generated by starting from a single vertex, the root of the tree, labeled , and then for each successive label from to choosing a random vertex with a smaller label to be its parent. If each of the choices is uniform and independent of the other choices, the resulting tree will be a random recursive tree.
Properties
With high probability, the longest path from the root to the leaf of an -vertex random recursive tree has length .
The maximum number of children of any vertex, i.e., degree, in the tree is, with high probability, .
The expected distance of the th vertex from the root is the th harmonic number, from which it follows by linearity of expectation that the sum of all root-to-vertex path lengths is, with high probability, .
The expected number of leaves of the tree is with variance , so with high probability the number of leaves is .
Applications
lists several applications of random recursive trees in modeling phenomena including disease spreading, pyramid schemes, the evolution of languages, and the growth of computer networks.
References
Trees (graph theory)
Random graphs |
https://en.wikipedia.org/wiki/Coco%20Gauff%20career%20statistics | This is a list of career statistics of American tennis player Coco Gauff since her professional debut in 2018. Gauff has won four WTA Tour singles titles and eight doubles titles, as well as one ITF singles titles and one doubles title.
Performance timelines
Only main-draw results in WTA Tour, Grand Slam tournaments, Billie Jean King Cup, United Cup, Hopman Cup and Olympic Games are included in win–loss records.
Singles
Current after the 2023 US Open.
Doubles
Current after the 2023 Canadian Open.
Mixed doubles
Significant finals
Grand Slam tournaments
Singles: 2 (1 title, 1 runner-up)
Doubles: 2 (2 runner-ups)
WTA 1000 finals
Singles: 1 (1 title)
Doubles: 5 (3 titles, 2 runner-ups)
WTA Tour finals
Singles: 7 (6 titles, 1 runner-up)
Doubles: 13 (8 titles, 5 runner-ups)
ITF Circuit finals
Singles: 1 (1 runner-up)
Doubles: 2 (1 title, 1 runner-up)
ITF Junior Circuit
Junior Grand Slam finals
Singles: 2 (1 title, 1 runner-up)
Doubles: 1 (1 title)
ITF Junior finals
Singles: 5 (3 titles, 2 runner–ups)
Doubles: 2 (2 titles)
WTA Tour career earnings
Current through the 2023 US Open.
Career Grand Slam statistics
Grand Slam tournament seedings
The tournaments won by Gauff are in boldface, and advanced into finals by Gauff are in italics.
Singles
Doubles
Best Grand Slam results details
Grand Slam winners are in boldface, and runner–ups are in italics.
Singles
Record against other players
No. 1 wins
Record against top 10 players
She has a record against players who were, at the time the match was played, ranked in the top 10.
Longest winning streak
16-match win streak (2023)
Notes
References
External links
Coco Gauff at the Women's Tennis Association
Coco Gauff at the International Tennis Federation
Gauff, Coco |
https://en.wikipedia.org/wiki/Astrid%20Beckmann | Astrid Beckmann ( Rautenberg, born 20 December 1957) is a German physicist, a professor of mathematics and mathematics education, and was a long-serving university president. Beckmann served as president of the Pädagogische Hochschule Schwäbisch Gmünd from 2010 to 2018. She also taught at the University of Ulm.
Life and career
Beckmann was born in Berlin. While at school, she recorded one first-place finish and one second-place finish in the national German math competition Bundeswettbewerb Mathematik. Upon finishing her school studies in 1976, she read mathematics and physics at the Free University of Berlin. Beckmann then wrote her physics thesis, which dealt with resistance measurements on metallic compounds, at the Helmholtz Center for Materials and Energy (HZB). Having successfully completed her teacher training in Darmstadt, she took up a position as a physicist in the Institute of Physics at Goethe University Frankfurt. During her time in Frankfurt’s "crystal lab". Beckmann tackled issues relating to materials research with a focus on rare earth compounds.
In 1989, Beckmann obtained a doctorate in mathematics at the University of Giessen with a thesis on teaching geometry proofs to 12- to 15-year-old students (supervised by Heinz Schwartze and Günter Pickert). She then continued her work in the field of mathematics education, initially with the help of a scholarship from the Hessen State Ministry for Higher Education, Research and the Arts. From 1994 to 2003, she taught mathematics and physics in Lemgo and at Leibniz University Hanover. She completed her postdoctorate at this latter institution in 2003 in mathematics education. Beckmann’s thesis addressed the development of a model concept for interdisciplinary teaching, with a focus on mathematics in connection to physics, language and computer science.
Following a brief period as an associate professor at Leibniz University Hannover, Beckmann was appointed Professor of Mathematics and Mathematics Education at the University of Education Schwäbisch Gmünd in 2003. She headed the Institute of Mathematics and Computer Science from 2003 to 2005 and was vice-president for Research, Development, and International Relations between 2005 and 2008.
Beckmann was unanimously elected president of the University of Education Schwäbisch Gmünd in 2009 and occupied this post from 2010 to 2018. Beckmann was deputy chair of the State Rectors’ Conference for Universities of Education (LRK) from 2011 to 2015, subsequently taking over as chair between April 2015 and 2017. As a member of the LRK board, she also represented the Universities of Education in the Senate of the German Rectors’ Conference (HRK).
References
21st-century German physicists
Living people
Scientists from Berlin
Free University of Berlin alumni
University of Giessen alumni
Academic staff of Goethe University Frankfurt
Academic staff of the University of Ulm
German women physicists
20th-century German mathematicians
German women m |
https://en.wikipedia.org/wiki/Eli%20Turner | Eli Fearn Turner (1893–1937) was an English footballer who played in the Football League for Crewe Alexandra. Turner guested for Stoke during World War I.
Career statistics
Source:
References
1893 births
1937 deaths
English men's footballers
Men's association football midfielders
English Football League players
Crewe Alexandra F.C. players
Oswestry Town F.C. players
Runcorn F.C. Halton players
Stoke City F.C. wartime guest players
Footballers from Stoke-on-Trent |
https://en.wikipedia.org/wiki/Al-Akirshi | Al-Akirshi or Uqayrishah () is a Syrian village in the Raqqa District in Raqqa Governorate. According to the Syria Central Bureau of Statistics (CBS), Al-Akirshi had a population of 4,304 in the 2004 census.
References
Populated places in Raqqa District |
https://en.wikipedia.org/wiki/2020%20Maldivian%20Second%20Division%20Football%20Tournament | Statistics of Second Division Football Tournament in the 2020 season.
2018 Third Division Football Tournament champions Rock Street Sports Club decided not to play in second division despite promotion, relegating them to Maldivian Third Division Football Tournament.
On 13 October 2019, President of Football Association of Maldives, Bassam Adeel Jaleel announced that Maldives Under 19 will compete in the Second Division Football Tournament from 2020 season onward.
The winners of the semi-finals; Club Valencia and Super United Sports advance to the final, with gaining automatic promotion to the Dhivehi Premier League for the following season, as New Radiant Sports Club and Victory Sports Club both teams being suspended. Both New Radiant and Victory will have to play in the Second Division Football Tournament even if their suspension cast aside.
Teams
A total of nine teams compete in the league.
Personnel and sponsoring
Group stage
From each group, the top two teams will be advanced for the Semi-finals.
All times listed are Maldives Standard Time. UTC+05:00
Group 1
Group 2
Semi-finals
Final
Awards
Final ranking
Per statistical convention in football, matches decided in extra time are counted as wins and losses, while matches decided by penalty shoot-out are counted as draws.
References
Maldivian Second Division Football Tournament seasons
Maldives |
https://en.wikipedia.org/wiki/Mireille%20Capitaine | Mireille Capitaine is a French mathematician whose research focuses on random matrices and free probability theory. In 2012 she was a recipient of the G. de B. Robinson Award for a paper she coauthored that introduced free Bessel laws, a two-parameter family of generalizations of the free Poisson distribution. She received her PhD in 1996 from Paul Sabatier University, where she was advised by Michel Ledoux. She is currently a researcher for the French National Centre for Scientific Research (CNRS), associated with the Toulouse Institute of Mathematics.
References
Year of birth missing (living people)
Living people
French mathematicians
French women mathematicians
French National Centre for Scientific Research scientists |
https://en.wikipedia.org/wiki/Ons%20Jabeur%20career%20statistics | This is a list of the main career statistics of professional Tunisian tennis player Ons Jabeur. She is the most successful Arab and African player. Her success is reflected in that she became the first Arab player, male or female, to be ranked inside the world's top 10. In late June 2022, she climbed to the place of No.2 at the WTA Rankings as her highest singles ranking up to date. In 2020, she became the first Arab woman to reach a Grand Slam quarter-final at the 2020 Australian Open. She went further in 2022, reaching two back-to-back Grand Slam finals at Wimbledon and the US Open, respectively. So far, she has reached and won at least one WTA tournament from all the tiers (250, 500 & 1000). Winning WTA 1000 Madrid Open in 2022, she become the first Arab or African woman to win a WTA 1000 event. She has won 4 WTA titles in total.
Performance timelines
Only main-draw results in WTA Tour, Grand Slam tournaments, Fed Cup/Billie Jean King Cup, United Cup, Hopman Cup and Olympic Games are included in win–loss records.
Singles
Current after the 2023 Guadalajara Open.
Doubles
Current after the 2022 season.
Significant finals
Grand Slam tournament finals
Singles: 3 (3 runners-ups)
WTA 1000 finals
Singles: 2 (1 title, 1 runner-up)
WTA career finals
Singles: 13 (5 titles, 8 runner-ups)
Doubles: 1 (1 runner-up)
ITF Circuit finals
Singles: 15 (11 titles, 4 runner–ups)
Doubles: 2 (1 title, 1 runner–up)
Junior Grand Slam finals
Girls' singles: 2 (1 title, 1 runner–up)
Billie Jean King Cup participation
Jabeur made her debut at the Fed Cup in 2011 playing for Tunisia in the Zone Group III. Since then, she has gained a singles record of 28–5, and a doubles record of 9–8.
Singles: 33 (28–5)
WTA Tour career earnings
Current after the 2022 season.
Career Grand Slam statistics
Seedings
The tournaments won by Jabeur are in boldface, and advanced into finals by Jabeur are in italics.
Best Grand Slam results details
Grand Slam winners are in boldface, and runner-ups are in italics.
Record against other players
No. 1 wins
Record against top 10 players
She has a record against players who were, at the time the match was played, ranked in the top 10.
Longest winning streaks
First 11–match singles winning streak (2022)
Second 11–match singles winning streak (2022)
Notes
References
Jabeur, Ons |
https://en.wikipedia.org/wiki/Naoto%20Sait%C5%8D | is a Japanese professional rugby union player who plays as a scrum-half for Japan Rugby League One club Tokyo Sungoliath and the Japan national team.
Career statistics
List of international tries
As of 14 November 2022
References
External links
1997 births
Living people
Rugby union scrum-halves
Sunwolves players
Japanese rugby union players
Japan international rugby union players
Tokyo Sungoliath players
21st-century Japanese people
2023 Rugby World Cup players |
https://en.wikipedia.org/wiki/Half-open | Half-open may refer to:
Half-open file in chess
Half-open vowel, a class of vowel sound
Computing and mathematics
Half-open interval, an interval containing only one of its endpoints
Half-open line segment, a line segment containing only one of its endpoints
TCP half-open, a TCP connection out of synchronization
See also
Half-closed
Clopen |
https://en.wikipedia.org/wiki/Alyson%20%28footballer%2C%20born%20February%201996%29 | Alyson Santos Silva (born 20 February 1996), commonly known as Alyson, is a Brazilian footballer who currently plays as a midfielder for EC São Bernardo.
Career statistics
Club
Notes
References
1996 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
Men's association football midfielders
São Bernardo Futebol Clube players
Sociedade Esportiva Palmeiras players
Boa Esporte Clube players
Volta Redonda FC players
K.S.V. Roeselare players
Associação Desportiva Confiança players
Campeonato Brasileiro Série B players
Brazilian expatriate sportspeople in Belgium
Expatriate men's footballers in Belgium
Footballers from São Paulo |
https://en.wikipedia.org/wiki/Rodrigo%20Fuma%C3%A7a | Rodrigo Nascimento de Oliveira Luz (born 6 March 1995), commonly known as Rodrigo Fumaça, is a Brazilian footballer who currently plays as a forward for ABC.
Career statistics
Club
Notes
References
1995 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
Men's association football forwards
CR Flamengo footballers
Audax Rio de Janeiro Esporte Clube players
Esporte Clube Vitória players
CR Vasco da Gama players
Boavista F.C. players
Macaé Esporte Futebol Clube players
Associação Desportiva Itaboraí players
Sampaio Corrêa Futebol e Esporte players
Luverdense Esporte Clube players
Cuiabá Esporte Clube players
Ituano FC players
K.S.V. Roeselare players
Manaus Futebol Clube players
ABC Futebol Clube players
Brasiliense FC players
Campeonato Brasileiro Série B players
Campeonato Brasileiro Série C players
Campeonato Brasileiro Série D players
Challenger Pro League players
Brazilian expatriate sportspeople in Belgium
Expatriate men's footballers in Belgium
Footballers from Rio de Janeiro (city) |
https://en.wikipedia.org/wiki/Ahmed%20Jamal%20%28footballer%29 | Ahmed Jamal (born 23 January 2000) is an Egyptian footballer who plays as a defender.
Career statistics
Club
Notes
References
External links
Ahmed Jamal profile at UAEFA
2000 births
Living people
Egyptian men's footballers
Egyptian expatriate men's footballers
Men's association football defenders
Al Ain FC players
Hatta Club players
UAE Pro League players
UAE First Division League players
Egyptian expatriate sportspeople in the United Arab Emirates
Expatriate men's footballers in the United Arab Emirates |
https://en.wikipedia.org/wiki/Mohammed%20Rabii%20%28footballer%29 | Mohammed Rabii (born 29 September 2001) is a Moroccan professional footballer who plays as a defender for Ittihad Kalba on loan from Al Jazira in the UAE Pro League.
Career statistics
Club
Notes
References
External links
2001 births
Living people
Moroccan men's footballers
Moroccan expatriate men's footballers
Men's association football defenders
UAE Pro League players
Wydad AC players
Al Jazira Club players
Ittihad Kalba FC players
Expatriate men's footballers in the United Arab Emirates
Moroccan expatriate sportspeople in the United Arab Emirates |
https://en.wikipedia.org/wiki/Basiru%20Alhassan | Basiru Alhassan (born 29 April 2000) is a Ghanaian footballer who plays for Al Arabi as a midfielder.
Career statistics
Club
Notes
References
2000 births
Living people
Ghanaian men's footballers
Men's association football midfielders
UAE Pro League players
UAE First Division League players
Tudu Mighty Jets F.C. players
AC Sparta Prague players
Al Wasl F.C. players
Dibba Al-Hisn Sports Club players
Al Hamriyah Club players
Hatta Club players
Dibba Al Fujairah FC players
Emirates Club players
Al-Arabi SC (UAE) players
Expatriate men's footballers in the Czech Republic
Ghanaian expatriate sportspeople in the Czech Republic
Expatriate men's footballers in the United Arab Emirates
Ghanaian expatriate sportspeople in the United Arab Emirates |
https://en.wikipedia.org/wiki/George%20Dwubeng | George Dwubeng (born 15 January 2000) is a Ghanaian footballer who currently plays for Al-Hamriyah on loan from Al-Wasl.
Career statistics
Club
Notes
References
External links
2000 births
Living people
Ghanaian men's footballers
Men's association football defenders
UAE Pro League players
UAE First Division League players
FC Politehnica Iași (2010) players
Al Wasl F.C. players
Al Hamriyah Club players
Expatriate men's footballers in Romania
Ghanaian expatriate sportspeople in Romania
Expatriate men's footballers in the United Arab Emirates
Ghanaian expatriate sportspeople in the United Arab Emirates |
https://en.wikipedia.org/wiki/John%20Tibar%20George | John Tibar George (born 1 January 2000) is a Tanzanian footballer plays as a midfielder.
Career statistics
Club
Notes
References
2000 births
Living people
Tanzanian men's footballers
Men's association football midfielders
UAE Pro League players
UAE First Division League players
Singida United F.C. players
MFK Vyškov players
Baniyas Club players
Masfout Club players
Hatta Club players
Expatriate men's footballers in the Czech Republic
Expatriate men's footballers in the United Arab Emirates
Tanzanian expatriate sportspeople in the Czech Republic
Tanzanian expatriate sportspeople in the United Arab Emirates
Tanzanian Premier League players
Place of birth missing (living people) |
https://en.wikipedia.org/wiki/Salim%20Al%20Mamari | Salim Al Mamari (born 4 May 1999) is an Omani professional footballer who plays for Baynounah as a defender.
Career statistics
Club
Notes
References
1999 births
Living people
Omani men's footballers
Omani expatriate men's footballers
Men's association football defenders
UAE Pro League players
UAE First Division League players
Al Jazira Club players
Baniyas Club players
Baynounah SC players
Omani expatriate sportspeople in the United Arab Emirates
Expatriate men's footballers in the United Arab Emirates |
https://en.wikipedia.org/wiki/Aboubacar%20Kone | Aboubacar Tigre Kone (born 28 March 2001) is an Ivorian-born Belgian footballer who plays as a defender.
Career statistics
Club
Notes
References
2001 births
Living people
Belgian men's footballers
Belgian expatriate men's footballers
Belgium men's youth international footballers
Men's association football defenders
Beerschot A.C. players
PSV Eindhoven players
Fujairah FC players
Al Urooba Club players
UAE Pro League players
UAE First Division League players
Belgian expatriate sportspeople in the Netherlands
Expatriate men's footballers in the Netherlands
Belgian expatriate sportspeople in the United Arab Emirates
Expatriate men's footballers in the United Arab Emirates
People from Gagnoa |
https://en.wikipedia.org/wiki/Abdulazeez%20Owolabi | Abdulazeez Muftau Owolabi (born 13 April 2000) is a Nigerian footballer who currently plays as a full-back.
Career statistics
Club
Notes
References
2000 births
Living people
Nigerian men's footballers
Nigerian expatriate men's footballers
Men's association football fullbacks
Fujairah FC players
Al Wasl F.C. players
UAE Pro League players
UAE First Division League players
Nigerian expatriate sportspeople in the United Arab Emirates
Expatriate men's footballers in the United Arab Emirates |
https://en.wikipedia.org/wiki/Victor%20Nwaneri | Victor Nwaneri (born 17 February 1993) is a Nigerian footballer who currently plays as a forward for Al Urooba.
Career statistics
Club
Notes
References
1993 births
Living people
Nigerian men's footballers
Nigerian expatriate men's footballers
Men's association football forwards
Qalali Club players
Hatta Club players
Masfout Club players
Al Urooba Club players
Al Hamriyah Club players
UAE Pro League players
UAE First Division League players
Nigerian expatriate sportspeople in the United Arab Emirates
Nigerian expatriate sportspeople in Bahrain
Expatriate men's footballers in the United Arab Emirates
Expatriate men's footballers in Bahrain |
https://en.wikipedia.org/wiki/Willian%20Forte | Willian Gabriel Galvão Forte (born 10 May 2000), commonly known as Willian Forte, is a Brazilian footballer who plays as defender.
Career statistics
Club
Notes
References
External links
2000 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
Men's association football defenders
UAE Pro League players
Paraná Clube players
Sociedade Esportiva Palmeiras players
Ittihad Kalba FC players
Expatriate men's footballers in the United Arab Emirates
Brazilian expatriate sportspeople in the United Arab Emirates
Footballers from Curitiba |
https://en.wikipedia.org/wiki/Juninho%20%28footballer%2C%20born%202000%29 | Antonio Valmor Assis Da Silva Junior (born 6 March 2000), commonly known as Juninho, is a Brazilian footballer who currently plays for Khor Fakkan.
Career statistics
Club
Notes
References
External links
2000 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
Men's association football forwards
UAE Pro League players
Associação Atlética Ponte Preta players
Khor Fakkan Club players
Sharjah FC players
Expatriate men's footballers in the United Arab Emirates
Brazilian expatriate sportspeople in the United Arab Emirates |
https://en.wikipedia.org/wiki/Kouame%20Autonne | Kouame Autonne Kouadio (born 22 September 2000) is an Emirati- Born Ivorian footballer who currently plays for Al Ain.
Career statistics
Club
Notes
References
External links
2000 births
Living people
Naturalized citizens of the United Arab Emirates
Ivorian men's footballers
Emirati men's footballers
Men's association football defenders
UAE Pro League players
ASEC Mimosas players
Khor Fakkan Club players
Al Ain FC players |
https://en.wikipedia.org/wiki/Leandro%20Spadacio | Leandro Spadacio Leite (born 17 February 2000) is a Brazilian footballer who currently plays for Ittihad Kalba.
Career statistics
Club
Notes
References
External links
2000 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
Men's association football midfielders
UAE Pro League players
Fluminense FC players
Shabab Al Ahli Club players
Ajman Club players
Ittihad Kalba FC players
Expatriate men's footballers in the United Arab Emirates
Brazilian expatriate sportspeople in the United Arab Emirates |
https://en.wikipedia.org/wiki/Mohammed%20Ali%20Jamin | Mohammed Ali Jamin Rahman (born 28 February 2000) is an Qatari professional footballer who plays as a defender for Qatar Stars League club Al-Gharafa.
Career statistics
Club
Notes
References
2000 births
Living people
Indonesian men's footballers
Indonesian expatriate men's footballers
Men's association football defenders
Al-Gharafa SC players
Qatar Stars League players
Expatriate men's footballers in Qatar
Indonesian emigrants to Qatar |
https://en.wikipedia.org/wiki/Lao%20Genevra%20Simons | Lao Genevra Simons (1870–1949) also referred to as Lao G. Simons, was an American mathematician, writer, and historian of mathematics known for her influential book Fabre and Mathematics and Other Essays. Simons was head of the mathematics department at Hunter College in New York.
Life
Lao Genevra Simons was born on March 25, 1870, in San Jose, California. When Simons was six months old, her family moved east to New Jersey.
Upon retiring from Hunter College, Simons founded a $1000 scholarship for the university named after the mathematics honour society, Pi Mu Epsilon. A second graduate scholarship was created in her name, funded by friends, alumnae, and admirers, in the same year.
Simons died on November 25, 1949, in Greenwich, Connecticut, at age 79 of natural causes.
Education
As a child, Simons attended school in New Jersey. She later obtained a teaching certificate from the College for the Training of Teachers at Columbia University and later studied astronomy and mathematics for a year at Vassar College.
Simons earned a bachelor of science in 1908 from Columbia University; she attained a master’s degree and a Ph.D. also from Columbia in 1912 and 1924 respectively. Her Ph.D. was obtained with a major in education and a minor in mathematics. Simons' doctoral thesis was entitled Introduction of algebra into American schools in the eighteenth century.
Career
After obtaining her teaching certificate she taught at a preparatory school in Connecticut, then taught elementary school for a year in South Orange, New Jersey.
Simons was hired at a mathematics professor at Hunter College in 1895. This appointment did not require a bachelor's degree, which Simons did not have at the time of her initial hiring. In 1916, she became an assistant professor and in 1925, she became an associate professor. Simons would later be promoted to professor and head of the mathematics department at Hunter College in 1928.
At Hunter College, Simons was Chairman of Student Activities from 1934, when the committee was initially founded, until 1940. Simons taught elective courses in mathematics, including advanced classes in pure mathematics and classes in the history of mathematics, in addition to required classes; Simons was one of the first mathematics professors at Hunter to do so. Simons worked at Hunter College until her retirement in 1940.
Simons was elected a member of the American Mathematical Society in September 1923. Simons was also a member of the Council of The History of Science Society. As part of the Council, Simons was part of the committee on arrangements for the meeting and exhibition commemorating the bi-centenary of the death of Sir Isaac Newton.
Simons wrote articles about math history for Scripta Mathematica, The Mathematics Teacher, and the American Mathematical Monthly. Simons was an associate editor for Scripta Mathematica, and from 1932, the founding year of the journal, to 1949 she served as its Book Review Editor.
Works
Intro |
https://en.wikipedia.org/wiki/Luo%20Jiacheng | Luo Jiacheng (; born 5 January 1995) is a Chinese footballer who currently plays as a midfielder for Chinese club a Guangdong Red Treasure.
Career statistics
Club
References
1995 births
Living people
Chinese men's footballers
Men's association football midfielders
Guangzhou F.C. players
Kunshan F.C. players
China League Two players
Chinese Super League players |
https://en.wikipedia.org/wiki/Hu%20Yangyang | Hu Yangyang (; born 18 October 1995) is a Chinese footballer.
Career statistics
Club
Notes
References
1995 births
Living people
Chinese men's footballers
Men's association football midfielders
Guangzhou F.C. players
21st-century Chinese people |
https://en.wikipedia.org/wiki/Gan%20Tiancheng | Gan Tiancheng (; born 20 January 1995) is a Chinese footballer.
Career statistics
Club
Notes
References
1995 births
Living people
Chinese men's footballers
Men's association football midfielders
Guangzhou F.C. players
Footballers from Guangzhou
21st-century Chinese people |
https://en.wikipedia.org/wiki/Yu%20Weiliang | Yu Weiliang (; born 17 September 1973) is a former Chinese footballer who played as a goalkeeper for the China national football team.
Career statistics
Club
Notes
International
References
1973 births
Living people
Chinese men's footballers
China men's international footballers
Men's association football goalkeepers
Shanghai Shenhua F.C. players
Beijing Chengfeng F.C. players
Chinese Super League players |
https://en.wikipedia.org/wiki/Zhou%20Ning | Zhou Ning (; born 2 April 1974) is a former Chinese footballer who played as a forward for the China national football team.
Career statistics
Club
Notes
International
References
1974 births
Living people
Chinese men's footballers
Chinese expatriate men's footballers
China men's international footballers
Men's association football forwards
Beijing Guoan F.C. players
SV Waldhof Mannheim players
Chinese Super League players
Regionalliga players
2. Bundesliga players
Chinese expatriate sportspeople in Germany
Expatriate men's footballers in Germany |
https://en.wikipedia.org/wiki/Bruno%20de%20Oliveira | Bruno de Oliveira Silva (born 6 October 1990) is a former Brazilian footballer.
Career statistics
Club
Notes
References
1990 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
Men's association football forwards
Uruguayan Primera División players
Uruguayan Segunda División players
Central Español players
C.A. Bella Vista players
Centro Atlético Fénix players
Associação Atlética Internacional (Limeira) players
C.A. Progreso players
Expatriate men's footballers in Uruguay
Brazilian expatriate sportspeople in Uruguay
Footballers from Recife |
https://en.wikipedia.org/wiki/Mihaela%20Ignatova | Mihaela Ignatova is a Bulgarian mathematician who won the 2020 Sadosky Prize of the Association for Women in Mathematics for her research in mathematical analysis, and in particular in partial differential equations and fluid dynamics.
Education
In 2004, Ignatova earned both a bachelor's degree from Sofia University and a master's degree from the University of Nantes. She earned a second master's degree from Sofia University in 2006, working under the supervision of mathematician Emil Horozov. She then completed PhD studies from University of Southern California in 2011 under the supervision of Igor Kukavica.
Career
After working as a visiting assistant professor at the University of California, Riverside, a postdoctoral researcher at Stanford University, and an instructor at Princeton University, she moved to Temple University as an assistant professor in 2018.
References
External links
Home page
Year of birth missing (living people)
Living people
21st-century Bulgarian mathematicians
Bulgarian women mathematicians
Mathematical analysts
Sofia University alumni
University of Nantes alumni
University of Southern California alumni
Temple University faculty |
https://en.wikipedia.org/wiki/Artin%27s%20theorem%20on%20induced%20characters | In representation theory, a branch of mathematics, Artin's theorem, introduced by E. Artin, states that a character on a finite group is a rational linear combination of characters induced from all cyclic subgroups of the group.
There is a similar but somehow more precise theorem due to Brauer, which says that the theorem remains true if "rational" and "cyclic subgroup" are replaced with "integer" and "elementary subgroup".
Statement
In Linear Representation of Finite Groups Serre states in Chapter 9.2, 17 the theorem in the following, more general way:
Let finite group, family of subgroups.
Then the following are equivalent:
This in turn implies the general statement, by choosing as all cyclic subgroups of .
Proof
References
Further reading
http://www.math.toronto.edu/murnaghan/courses/mat445/artinbrauer.pdf
Representation theory of finite groups |
https://en.wikipedia.org/wiki/Peregrina%20Quintela%20Est%C3%A9vez | Peregrina Quintela Estévez (born 1960) is a Spanish applied mathematician. She is a professor of applied mathematics at the University of Santiago de Compostela, the founding director of the Spanish Network for Mathematics and Industry, and the winner of the 2016 María Josefa Wonenburger Planells prize of the Galician government.
Education and career
Quintela earned a bachelor's degree in mathematics from the University of Santiago de Compostela in 1982, a PhD from the Autonomous University of Madrid in 1986, and a second doctorate from the University of Paris in 1988. Her 1988 dissertation, Sur Quelques Question D'elasticité Non Linéaire et de Théorie de Plaques [On Some Questions of Nonlinear Elasticity and Plate Theory] was supervised by Philippe G. Ciarlet.
She has been chair of the Spanish Network for Mathematics and Industry since it was founded in 2011. She is also director of the Technological Institute for Industrial Mathematics (ITMATI), founded in 2013.
Books
With four co-authors, Quintela wrote the book TransMath: Innovative Solutions from Mathematical Technology (Springer, 2012) on technology transfer in mathematics. She is also the author of two books on MATLAB published through her university, and of two Spanish-language textbooks on differential equations and on numerical methods in engineering, published by Tórculo Ediciones in 2000 and 2001, as well as the editor of several conference proceedings.
Recognition
In 2016, the Government of Galicia gave Quintela their María Josefa Wonenburger Planells prize, given "to highlight the outstanding careers of women in the field of science and technology".
References
Further reading
(interview)
(interview)
External links
Home page
1960 births
Living people
20th-century Spanish mathematicians
Women mathematicians
Applied mathematicians
University of Santiago de Compostela alumni
Autonomous University of Madrid alumni
Academic staff of the University of Santiago de Compostela
21st-century Spanish mathematicians |
https://en.wikipedia.org/wiki/Adrienne%20Fairhall | Adrienne Fairhall is a University Professor in the Department of Physiology and Biophysics and an adjunct Professor in the Departments of Physics and Applied Mathematics, as well as the director of the Computational Neuroscience Program and co-director of the Institute for Neuroengineering at the University of Washington.
Fairhall is primarily known for her work on dynamic neural computation, particularly with regards to the interplay between cellular and circuit dynamics and coding, and she has received numerous awards for her work in the field including a Sloan Fellowship, a McKnight Scholar Award, a Burroughs-Wellcome Fellowship, and an Allen Distinguished Investigator award.
Fairhall presently runs the Fairhall laboratory at the University of Washington.
Early life and education
Fairhall was raised in Australia, she obtained her honors degree in theoretical physics working with Robert Dewar at the Australian National University in Canberra, Australia. She then joined the lab of Itamar Procaccia at the Weizmann Institute of Science where she completed her PhD in physics.
Career
Following a brief stint at the NEC Corporation, Fairhall then joined Princeton University's Department of Molecular Biology as a postdoctoral researcher. In 2004, she left that position to become an associate professor at the University of Washington, a position that eventually led to a full professorship. She further went on to become the director of the University of Washington Computational Neuroscience Program and co-director of the University of Washington Institute for Neuroengineering
Fairhall has also been involved in a number of computational neuroscience educational programs and workshops, most notably by way directing the Methods in Computational Neuroscience course at the Marine Biological Laboratory in Woods Hole, as well as creating the Coursera course on the subject.
Personal life
Fairhall is married to Blaise Agüera y Arcas, a physicist whom she met during a neural network circuitry class at Marine Biological Laboratory in Woods Hole and with whom she has two children.
Select publications
Awards and honors
Sloan Fellowship
McKnight Fellowship
Burroughs Wellcome Fellowship
Allen Distinguished Investigator
References
External links
Laboratory page
University of Washington Profile page
Living people
Australian neuroscientists
University of Washington faculty
Australian women neuroscientists
Sloan Fellows
Australian National University alumni
Weizmann Institute of Science alumni
Princeton University people
21st-century Australian scientists
21st-century women scientists
Year of birth missing (living people) |
https://en.wikipedia.org/wiki/Geometric%20Folding%20Algorithms | Geometric Folding Algorithms: Linkages, Origami, Polyhedra is a monograph on the mathematics and computational geometry of mechanical linkages, paper folding, and polyhedral nets, by Erik Demaine and Joseph O'Rourke. It was published in 2007 by Cambridge University Press ().
A Japanese-language translation by Ryuhei Uehara was published in 2009 by the Modern Science Company ().
Audience
Although aimed at computer science and mathematics students, much of the book is accessible to a broader audience of mathematically-sophisticated readers with some background in high-school level geometry.
Mathematical origami expert Tom Hull has called it "a must-read for anyone interested in the field of computational origami".
It is a monograph rather than a textbook, and in particular does not include sets of exercises.
The Basic Library List Committee of the Mathematical Association of America has recommended this book for inclusion in undergraduate mathematics libraries.
Topics and organization
The book is organized into three sections, on linkages, origami, and polyhedra.
Topics in the section on linkages include
the Peaucellier–Lipkin linkage for converting rotary motion into linear motion,
Kempe's universality theorem that any algebraic curve can be traced out by a linkage,
the existence of linkages for angle trisection,
and the carpenter's rule problem on straightening two-dimensional polygonal chains.
This part of the book also includes applications to motion planning for robotic arms, and to protein folding.
The second section of the book concerns the mathematics of paper folding, and mathematical origami. It includes the NP-completeness of testing flat foldability,
the problem of map folding (determining whether a pattern of mountain and valley folds forming a square grid can be folded flat),
the work of Robert J. Lang using tree structures and circle packing to automate the design of origami folding patterns,
the fold-and-cut theorem according to which any polygon can be constructed by folding a piece of paper and then making a single straight cut,
origami-based angle trisection,
rigid origami,
and the work of David A. Huffman on curved folds.
In the third section, on polyhedra, the topics include polyhedral nets and Dürer's conjecture on their existence for convex polyhedra, the sets of polyhedra that have a given polygon as their net, Steinitz's theorem characterizing the graphs of polyhedra, Cauchy's theorem that every polyhedron, considered as a linkage of flat polygons, is rigid, and Alexandrov's uniqueness theorem stating that the three-dimensional shape of a convex polyhedron is uniquely determined by the metric space of geodesics on its surface.
The book concludes with a more speculative chapter on higher-dimensional generalizations of the problems it discusses.
References
External links
Authors' web site for Geometric Folding Algorithms including contents, errata, and advances on open problems
Linkages (mechanical)
Paper folding
Po |
https://en.wikipedia.org/wiki/Conical%20screw%20compressor | The relatively recently developed conical screw compressor is a type of rotary-screw compressor using a different topology from the typical dual-screw type, in effect it is a conical spiral extension of a gerotor. Because of this it does not have the inherent "blow-hole" leakage path which in typical screw compressors is responsible for significant leakage through the assembly and makes low-speed operation impractical. This theoretically allows much smaller rotors to have practical efficiency since at smaller sizes the leakage area does not become as large a portion of the pumping area as in straight screw compressors. In conjunction with the decreasing diameter of the cone shaped rotor this may also allows much higher compression ratios to be achieved in a single stage.
A significant impediment to production is the machining of the outer rotor to the tolerances required, although the inner rotor can be manufactured with precise CNC machines without much difficulty the outer rotor presents significant difficulties due to the restricted access to the interior for precision tooling, and assembling the outer rotor from easier to machine segments presents its own problems. The cost of units is currently very high, but development is ongoing, development is primarily being performed by VERT Rotors who hold patents on this topology.
References
Gas compressors |
https://en.wikipedia.org/wiki/2020%E2%80%9321%20Scottish%20Professional%20Football%20League | Statistics of the Scottish Professional Football League (SPFL) in season 2020–21.
Scottish Premiership
Scottish Championship
Scottish League One
Scottish League Two
Award winners
Yearly
Monthly
See also
2020–21 in Scottish football
References
Scottish Professional Football League seasons |
https://en.wikipedia.org/wiki/Fidel%20Nemenzo | Fidel Ronquillo Nemenzo is a Filipino mathematician and professor who served as chancellor of the University of the Philippines Diliman from 2020 to 2023.
His areas of expertise include number theory, elliptic curves, and coding theory. He earned his bachelor's degree in mathematics from UP Diliman while his master's and Doctor of Science degrees are from Sophia University in Tokyo, Japan.
Career
On March 2, 2020, he succeeded Michael Tan and became the eleventh Chancellor of the University of the Philippines Diliman. Immediately prior to his appointment, he was vice chancellor for Research and Development of UP Diliman and is the convenor of the Center for Integrative Development Studies' Data Science for Public Policy Program. He chairs the Mathematics Division of the National Research Council of the Philippines, having been elected to the NRCP Governing Board in 2019. He was Associate Dean for Academic Affairs of the UP Diliman College of Science and headed its Science and Society Program. Nemenzo also served as President of both the Southeast Asian Mathematical Society (2010-2012) and the Mathematical Society of the Philippines (2004-2010).
Family
Nemenzo is the son of political scientist and former UP president Francisco Nemenzo Jr. His grandfather, Francisco Nemenzo Sr., was Professor of Zoology and Dean of the UP College of Arts and Sciences in the 1960s, who did pioneering work in the study of corals. Nemenzo is married to Dr. Ma. Victoria Raquiza, professor at the UP National College of Public Administration and Governance. Their son, Julio Anton Mulawin, graduated from the UP School of Economics in 2020.
Awards
Nemenzo's awards include OneUP Professorial Chair awards and International Publication Awards which he received from the University of the Philippines System; the Achievement Award in Mathematics from the National Research Council of the Philippines in 2013; and the Gawad Chancellor Para sa Pinakamahusay na Guro, which he received from the University of the Philippines Diliman in 2005.
Political activism
The son of Martial Law era activist and later University of the Philippines President Francisco Nemenzo Jr, he has himself had a long history of political activism. He was a member of the Student Christian Movement of the Philippines.
A UP student leader during the time of martial law under Ferdinand Marcos, he was shot in the back during the infamous Welcome Rotonda rally shootings of September 27, 1984 and almost died from the single M-16 bullet that pierced through his body. Fellow activists attribute his survival from his wounds to the fact that he was a runner. He was known for his athleticism and healthy lifestyle in the campus.
He was also a founding member of the activist musical group "Patatag".
In recent years, he has strongly denounced the red tagging of UP students who have taken a stand against authoritarianism in the Philippines.
On January 19, 2020, he spoke at the protest demonstration against the |
https://en.wikipedia.org/wiki/Valuation%20%28geometry%29 | In geometry, a valuation is a finitely additive function from a collection of subsets of a set to an abelian semigroup.
For example, Lebesgue measure is a valuation on finite unions of convex bodies of Other examples of valuations on finite unions of convex bodies of are surface area, mean width, and Euler characteristic.
In geometry, continuity (or smoothness) conditions are often imposed on valuations, but there are also purely discrete facets of the theory. In fact, the concept of valuation has its origin in the dissection theory of polytopes and in particular Hilbert's third problem, which has grown into a rich theory reliant on tools from abstract algebra.
Definition
Let be a set, and let be a collection of subsets of A function on with values in an abelian semigroup is called a valuation if it satisfies
whenever and are elements of
If then one always assumes
Examples
Some common examples of are
the convex bodies in
compact convex polytopes in
convex cones
smooth compact polyhedra in a smooth manifold
Let be the set of convex bodies in Then some valuations on are
the Euler characteristic
Lebesgue measure restricted to
intrinsic volume (and, more generally, mixed volume)
the map where is the support function of
Some other valuations are
the lattice point enumerator , where is a lattice polytope
cardinality, on the family of finite sets
Valuations on convex bodies
From here on, let , let be the set of convex bodies in , and let be a valuation on .
We say is translation invariant if, for all and , we have .
Let . The Hausdorff distance is defined as
where is the -neighborhood of under some Euclidean inner product. Equipped with this metric, is a locally compact space.
The space of continuous, translation-invariant valuations from to is denoted by
The topology on is the topology of uniform convergence on compact subsets of Equipped with the norm
where is a bounded subset with nonempty interior, is a Banach space.
Homogeneous valuations
A translation-invariant continuous valuation is said to be -homogeneous if
for all and The subset of -homogeneous valuations is a vector subspace of McMullen's decomposition theorem states that
In particular, the degree of a homogeneous valuation is always an integer between and
Valuations are not only graded by the degree of homogeneity, but also by the parity with respect to the reflection through the origin, namely
where with if and only if for all convex bodies
The elements of and are said to be even and odd, respectively.
It is a simple fact that is -dimensional and spanned by the Euler characteristic that is, consists of the constant valuations on
In 1957 Hadwiger proved that (where ) coincides with the -dimensional space of Lebesgue measures on
A valuation is simple if for all convex bodies with Schneider in 1996 described all simple valuations on : they are given by where is an arbitrary odd functio |
https://en.wikipedia.org/wiki/Quasicrystals%20and%20Geometry | Quasicrystals and Geometry is a book on quasicrystals and aperiodic tiling by Marjorie Senechal, published in 1995 by Cambridge University Press ().
One of the main themes of the book is to understand how the mathematical properties of aperiodic tilings such as the Penrose tiling, and in particular the existence of arbitrarily large patches of five-way rotational symmetry throughout these tilings, correspond to the properties of quasicrystals including the five-way symmetry of their Bragg peaks. Neither kind of symmetry is possible for a traditional periodic tiling or periodic crystal structure, and the interplay between these topics led from the 1960s into the 1990s to new developments and new fundamental definitions in both mathematics and crystallography.
Topics
The book is divided into two parts. The first part covers the history of crystallography, the use of X-ray diffraction to study crystal structures through the Bragg peaks formed on their diffraction patterns, and the discovery in the early 1980s of quasicrystals, materials that form Bragg peaks in patterns with five-way symmetry, impossible for a repeating crystal structure. It models the arrangement of atoms in a substance by a Delone set, a set of points in the plane or in Euclidean space that are neither too closely spaced nor too far apart, and it discusses the mathematical and computational issues in X-ray diffraction and the construction of the diffraction spectrum from a Delone set.
Finally, it discusses a method for constructing Delone sets that have Bragg peaks by projecting bounded subsets of higher-dimensional lattices into lower-dimensional spaces.
This material also has strong connections to spectral theory and ergodic theory, deep topics in pure mathematics, but these were omitted in order to make the book accessible to non-specialists in those topics.
Another method for the construction of Delone sets that have Bragg peaks is to choose as points the vertices of certain aperiodic tilings such as the Penrose tiling. (There also exist other aperiodic tilings, such as the pinwheel tiling, for which the existence of discrete peaks in the diffraction pattern is less clear.) The second part of the book discusses methods for generating these tilings, including projections of higher-dimensional lattices as well as recursive constructions with hierarchical structure, and it discusses the long-range patterns that can be shown to exist in tilings constructed in these ways.
Included in the book are software for generating diffraction patterns and Penrose tilings, and a "pictorial atlas" of the diffraction patterns of known aperiodic tilings.
Audience
Although the discovery of quasicrystals immediately set off a rush for applications in materials capable of withstanding high temperature, providing non-stick surfaces, or having other useful material properties, this book is more abstract and mathematical, and concerns mathematical models of quasicrystals rather than physical mater |
https://en.wikipedia.org/wiki/Jos%C3%A9%20Cort%C3%A9s%20%28footballer%29 | José Ricardo Cortés (born 8 September 1994) is a Colombian football right winger, who plays for Bosnian and Herzegovina club Borac Banja Luka.
Career statistics
.
References
External links
1994 births
Living people
People from Cali
Colombian men's footballers
Men's association football midfielders
Atlético Bucaramanga footballers
Club Destroyers players
Diósgyőri VTK players
FC Košice (2018) players
Nemzeti Bajnokság I players
Colombian expatriate men's footballers
Colombian expatriate sportspeople in Bolivia
Expatriate men's footballers in Bolivia
Colombian expatriate sportspeople in Hungary
Colombian expatriate sportspeople in Bosnia and Herzegovina
Expatriate men's footballers in Hungary
Expatriate men's footballers in Slovakia
Expatriate men's footballers in Jordan
Expatriate men's footballers in Bosnia and Herzegovina
Colombian expatriate sportspeople in Slovakia |
https://en.wikipedia.org/wiki/Yong%20Seung%20Cho | Yong Seung Cho (; born September 18, 1949) is a South Korean educator and mathematician. He completed a Ph.D. in mathematics in 1987 at the University of Chicago. His research interests include geometric topology, Yang-Mills Theory, Seiberg-Witten Theory, Gromov-Witten Theory, and Quantum cohomology of symplectic manifolds. His teaching career includes Chungbuk National University, Kyungpook National University, Brandeis University, and Ewha Womans University. Currently he teaches at Sungkyunkwan University as Invited Professor.
In 2003, he was elected as President of the Korean Mathematical Society (KMS), and at the position, he played a pivotal role in establishing the National Institute for Mathematical Sciences (NIMS) in South Korea, the first national mathematical research center directly funded by the South Korean government. In 2005, he was selected as the first President of NIMS, and immediately began to set-up fundamental foundation of the NIMS to be innovative hub of the mathematical researches contributing to South Korea's overall scientific and industrial competitiveness.
Education and career
Cho attended Kyungpook National University for bachelor and master programs in mathematics, and earned a doctorate in 1987 from the University of Chicago under the academic direction of Melvin Rothenburg, Karen Uhlenbeck, and Shmuel Weinberger. He became an assistant professor at Brandeis University in 1987, and moved to Ewha Womans University in Seoul as a full professor in 1989. He taught and researched at Ewha Womans University until retirement in 2015.
Image:
Mathematical work
Cho has been a pure scientist for his entire life. He has researched on Yang-Mills Theory, Seiberg-Witten Theory, Gromov-Witten Theory, and Quantum cohomology of symplectic manifolds. Besides, he achieved a remarkable result on Big-Bang String Theory, [4][5][7] that is, as the early universe he used the string theory with Einstein's general relativity and Morse Theory to verify the expansion, shear, and rotation of the universe. Professor Cho's result was co-worked with physicist Professor ST Hong, so it is named "Cho-Hong String Theory." Also Cho initiated the Gromov-Witten type invariant, quantum type cohomology, and Floer type cohomology on cosymplectic manifolds, and induced an Arnold type theorem on odd dimensional manifolds. Professor Cho has published more than 130 academic research papers, and more than 15 text books on Topology, and has delivered more than 230 special lectures at various international conferences and scholarly events, including American Mathematical Society's Annual Conference and Harvard Math Colloquium Lecture Series.
Service
Cho has been active in advancing South Korean mathematical research capabilities and national science development by holding several positions. Cho held President position of the Korean Mathematical Society (KMS, January 2003 – December 2004), and during this positionCho played a critical role in establishing the |
https://en.wikipedia.org/wiki/Sonja%20Lyttkens | Sonja Lyttkens (26 August 1919 – 18 December 2014) was a Swedish mathematician, the third woman to earn a mathematics doctorate in Sweden and the first of these women to obtain a permanent university position in mathematics. She is also known for her work to make academia less hostile to women, and for pointing out that the Swedish taxation system of the time, which provided an income deduction for husbands of non-working wives, pressured women even in low-income families not to work. Her observations helped push Sweden into taxing married people separately from their spouses.
Education and career
Lyttkens grew up in Halmstad and Karlskrona, and moved to Kalmar in 1930. She moved again to Uppsala in 1937 to study mathematics, but her studies were interrupted by marriage and children. She earned a licentiate in 1951, and completed her Ph.D. at Uppsala University in 1956. Her dissertation, The Remainder In Tauberian Theorems, concerned Tauberian theorems and was jointly supervised by Arne Beurling and Lennart Carleson. She was the third woman to earn a doctorate in mathematics in Sweden, after Louise Petrén-Overton in 1911 and Ingrid Lindström in 1947.
Although Sofya Kovalevskaya had become a full professor of mathematics in a private university in Stockholm in 1884, women were forbidden from holding public university positions in Sweden until 1925, and both Petrén and Lindström became schoolteachers. Lyttkens obtained a permanent position as a senior lecturer at Uppsala University in 1963, and in 1970 she became the university's first female inspektor (an honorary chair of a student union), for the Kalmar nation. She retired in 1984.
Personal life
Lyttkens was the daughter of Swedish sculptor Anna Petrus and her husband, physician Harald Lyttkens. Two of her children, and Harald Hamrell, both became film actors and directors.
As well as working in mathematics, Lyttkens also painted watercolors before and after her retirement, and had several exhibitions of her paintings.
References
Further reading
1919 births
2014 deaths
Swedish mathematicians
Women mathematicians
Uppsala University alumni
Academic staff of Uppsala University |
https://en.wikipedia.org/wiki/Barbora%20Str%C3%BDcov%C3%A1%20career%20statistics | This is a list of career statistics of the former professional Czech tennis player Barbora Strýcová since her professional debut in 2002.
Career achievements
In her career, Strýcová won two singles titles, and 30 doubles titles on the WTA Tour, plus one Grand Slam doubles title at the 2019 Wimbledon Championships, partnering with Hsieh Su-wei. On ITF Circuit, she won nine singles titles, and ten doubles titles. As a part of Czech Fed Cup team, Strýcová won six titles, but in only three of them played in the finals.
Year-end championships
In doubles, Strýcová debut at the WTA Finals, in 2018, where she was stopped in semifinals. Year later, in 2019, Strýcová together with Hsieh Su-wei reached final at the WTA Finals, where they lost against Tímea Babos-Kristina Mladenovic.
Grand Slam championships
Strýcová reached two Grand Slam finals, with score of 1–1 win-loss. The first final that she reached was at the 2019 Wimbledon Championships, where she won the title alongside Hsieh Su-wei. In 2020, she reached her second Grand Slam final, at the Australian Open, but ended runner-up.
Barbora also reached a total of six semifinals, five in doubles and one in singles. Semifinal in singles was in 2019 at Wimbledon, where she lost against Serena Williams.
Performance timelines
Only main-draw results in WTA Tour, Grand Slam tournaments, Billie Jean King Cup, United Cup, Hopman Cup and Olympic Games are included in win–loss records.
Singles
Doubles
Mixed doubles
Significant finals
Grand Slam tournaments
Doubles: 3 (2 titles, 1 runner-up)
Year-end championships finals
Doubles: 1 (1 runner–up)
WTA 1000 finals
Doubles: 12 (8 titles, 4 runner-ups)
Olympic medal matches
Doubles: 1 (bronze medal)
WTA career finals
Singles: 8 (2 titles, 6 runner-ups)
Doubles: 51 (32 titles, 19 runner-ups)
Team competition: 6 (6 titles)
ITF Circuit finals
Singles: 15 (9 titles, 6 runner–ups)
Doubles: 18 (10 titles, 8 runner–ups)
ITF Junior finals
Junior Grand Slam finals
Singles: 3 (2 titles, 1 runner-up)
Doubles: 4 (3 titles, 1 runner-up)
ITF Junior Circuit finals
Singles: 14 (4 titles, 10 runner–ups)
Career Grand Slam statistics
Seedings
Record against other players
Record against top 10 players
She has a 10–59 () record against players who were, at the time the match was played, ranked in the top 10.
Notes
References
External links
Strýcová, Barbora |
https://en.wikipedia.org/wiki/Frank%20Farris | Frank A. Farris is an American mathematician. He is a Professor of Mathematics and Computer Science at Santa Clara University. He is also an editor, author, and artist whose work concerns mathematical topics. Farris is known primarily for mathematical exposition, his creation of visual mathematics through computer science, and advocacy for mathematical art as a discipline.
Education
Farris was born in Santa Monica, California. Shortly after his birth, his family moved to Covina, a suburb of Los Angeles. He showed interest and proficiency in a large variety of subjects such as astronomy. At the age of 15, he enrolled in the NSF summer science training program, designed to enrich mathematical talent in America. It was this that solidified his dedication to mathematics.
Farris studied mathematics as an undergraduate at Pomona College and received his Ph.D. at the Massachusetts Institute of Technology. His dissertation Spiralling Chains in CR Manifolds was supervised by Richard Burt Melrose. His time at MIT led him to pursue pure mathematics with a focus on geometry.
Career
Farris taught at Brown University for three years, before becoming an assistant professor in Santa Clara University in 1984. He was tenured and promoted to associate professor in 1988 and was promoted to Full Professor in 2017. He was awarded the Award for Distinguished College or University Teaching by the Golden Section of the Mathematical Association of America (MAA) in 2018.
Farris served as editor of Mathematics Magazine from 2001 to 2005, then again in 2009. He also writes expository articles; his article "The Edge of the Universe" for Math Horizons received the Trevor Adams Award from the MAA.
In 2015, his book Creating Symmetry: The Artful Mathematics of Wallpaper Patterns, which conveys his artistic method, was published by the Princeton University Press. It was awarded the PROSE Award in Mathematics from the Association of American Publishers, Honorable Mention, in 2016, and the Alpha Sigma Nu Book Award in 2018. It is profiled in numerous periodicals including Quanta and Scientific American.
Work method
Farris generates organic mathematical art using symmetry, patterns, and wave functions. He commonly works with wallpaper patterns using photographs as source material. The wallpaper often exhibit translational symmetry across two independent axes. He has created work that gives the illusion of five-fold rotational symmetry in the Wallpaper group. His award-winning artwork has been profiled by the American Mathematical Society,
He promotes a visual and computational perspective of math through his art, seminars, writing, etc. typically aimed towards undergraduates and mathematicians.
LGBTQIA+ Community
Farris is an active member of the LGBTQIA+ community. In particular, he has worked for the advancement of LGBTQIA+ mathematicians, for instance, in the formation of Spectra (mathematical association). In 2014, he married his husband William O. Beeman, though they |
https://en.wikipedia.org/wiki/Complemented%20subspace | In the branch of mathematics called functional analysis, a complemented subspace of a topological vector space is a vector subspace for which there exists some other vector subspace of called its (topological) complement in , such that is the direct sum in the category of topological vector spaces. Formally, topological direct sums strengthen the algebraic direct sum by requiring certain maps be continuous; the result retains many nice properties from the operation of direct sum in finite-dimensional vector spaces.
Every finite-dimensional subspace of a Banach space is complemented, but other subspaces may not. In general, classifying all complemented subspaces is a difficult problem, which has been solved only for some well-known Banach spaces.
The concept of a complemented subspace is analogous to, but distinct from, that of a set complement. The set-theoretic complement of a vector subspace is never a complementary subspace.
Preliminaries: definitions and notation
If is a vector space and and are vector subspaces of then there is a well-defined addition map
The map is a morphism in the category of vector spaces — that is to say, linear.
Algebraic direct sum
The vector space is said to be the algebraic direct sum (or direct sum in the category of vector spaces) when any of the following equivalent conditions are satisfied:
The addition map is a vector space isomorphism.
The addition map is bijective.
and ; in this case is called an algebraic complement or supplement to in and the two subspaces are said to be complementary or supplementary.
When these conditions hold, the inverse is well-defined and can be written in terms of coordinates as
The first coordinate is called the canonical projection of onto ; likewise the second coordinate is the canonical projection onto
Equivalently, and are the unique vectors in and respectively, that satisfy
As maps, where denotes the identity map on .
Motivation
Suppose that the vector space is the algebraic direct sum of . In the category of vector spaces, finite products and coproducts coincide: algebraically, and are indistinguishable. Given a problem involving elements of , one can break the elements down into their components in and , because the projection maps defined above act as inverses to the natural inclusion of and into . Then one can solve the problem in the vector subspaces and recombine to form an element of .
In the category of topological vector spaces, that algebraic decomposition becomes less useful. The definition of a topological vector space requires the addition map to be continuous; its inverse may not be. The categorical definition of direct sum, however, requires and to be morphisms — that is, continuous linear maps.
The space is the topological direct sum of and if (and only if) any of the following equivalent conditions hold:
The addition map is a TVS-isomorphism (that is, a surjective linear homeomorph |
https://en.wikipedia.org/wiki/Reverse%20Mathematics%3A%20Proofs%20from%20the%20Inside%20Out | Reverse Mathematics: Proofs from the Inside Out is a book by John Stillwell on reverse mathematics, the process of examining proofs in mathematics to determine which axioms are required by the proof. It was published in 2018 by the Princeton University Press ().
Topics
The book begins with a historical overview of the long struggles with the parallel postulate in Euclidean geometry, and of the foundational crisis of the late 19th and early 20th centuries, Then, after reviewing background material in real analysis and computability theory, the book concentrates on the reverse mathematics of theorems in real analysis, including the Bolzano–Weierstrass theorem, the Heine–Borel theorem, the intermediate value theorem and extreme value theorem, the Heine–Cantor theorem on uniform continuity, the Hahn–Banach theorem, and the Riemann mapping theorem.
These theorems are analyzed with respect to three of the "big five" subsystems of second-order arithmetic, namely arithmetical comprehension, recursive comprehension, and the weak Kőnig's lemma.
Audience
The book is aimed at a "general mathematical audience" including undergraduate mathematics students with an introductory-level background in real analysis. It is intended both to excite mathematicians, physicists, and computer scientists about the foundational issues in their fields, and to provide an accessible introduction to the subject. However, it is not a textbook; for instance, it has no exercises. One theme of the book is that many theorems in this area require axioms in second-order arithmetic that encompass infinite processes and uncomputable functions.
Reception and related reading
Jeffry Hirst criticizes the book, writing that "if one is not too obsessive about the details, Proofs from the Inside Out is an interesting introduction," while finding details that he would prefer to be handled differently, in a topic for which details are important. In particular, in this area, there are multiple choices for how to build up the arithmetic on real numbers from simpler data types such as the natural numbers, and while Stillwell discusses three of them (decimal numerals, Dedekind cuts, and nested intervals), converting between them itself requires nontrivial axiomatic assumptions.
However, James Case calls the book "very readable", and Roman Kossak calls it "a stellar example of expository writing on mathematics". Several other reviewers agree that this book could be helpful as a non-technical way to create interest in this topic in mathematicians who are not already familiar with it, and lead them to more in-depth material in this area.
As additional reading on reverse mathematics in combinatorics, Hirst suggests Slicing the Truth by Denis Hirschfeldt. Another book suggested by reviewer Reinhard Kahle is Stephen G. Simpson's Subsystems of Second Order Arithmetic.
References
Mathematical logic
Proof theory
Computability theory
Real analysis
Mathematics books
2018 non-fiction books
Princeton Unive |
https://en.wikipedia.org/wiki/Jean-Paul%20Pier | Jean-Paul Pier (July 5, 1933 – December 14, 2016) was a Luxembourgish mathematician, specializing in harmonic analysis and the history of mathematics, particularly mathematical analysis in the 20th century.
Education and career
Jean-Paul Pier was a graduate student in Luxembourg and at the universities of Paris and Nancy. He earned a University of Luxembourg doctorate in mathematical sciences and a French doctorate in pure mathematics. He also spent six months at the Grenoble Nuclear Research Center (1961) and a year at the University of Oregon (1966-1967).
He taught mathematics at the Lycée de Garçons in Esch-sur-Alzette from 1956 to 1980. In 1971 he created the Séminaire de mathématiques at the Centre universitaire de Luxembourg (now the University of Luxembourg). He was a professor at the Centre from its creation in 1974 until 1998, when he retired as professor emeritus.
Pier was primarily responsible for the creation in January 1989 of the Luxembourg Mathematical Society, of which he was president from 1989 to 1993 and again from 1995 to 1998. He was during the academic year 1994–1995 a visiting professor at the Université catholique de Louvain.
Pier was the editor of two scholarly anthologies, which are standard works on the history of 20th-century mathematics. He organized several colloquia and conferences in Luxembourg. He was active internationally in various scientific bodies, including NATO Science for Peace and Security and UNESCO.
Selected publications
Amenable locally compact groups, Wiley, 1984.
Amenable Banach algebras, Longman, 1988.
L'Analyse harmonique. Son développement historique, Masson, 1990.
Histoire de l'intégration, vingt-cinq siècles de mathématiques, Masson, 1996.
Mathematical Analysis during the 20th century, Oxford University Press, 2001
Mathématiques entre savoir et connaissance, Vuibert, 2006.
Development of Mathematics 1900-1950, edited by Jean-Paul Pier, Birkhäuser, 1994.
Development of Mathematics 1950-2000, edited by Jean-Paul Pier, Birkhäuser, 2000.
Gabriel Lippmann. Commémoration par la section des sciences naturelles, physiques et mathématiques de l’Institut grand-ducal de Luxembourg du 150e anniversaire du savant né au Luxembourg lauréat du prix Nobel en 1908, J.-P. Pier et J. A. Massard, éditeurs, 1997 (lire en ligne).
Le Choix de la parole, Lethielleux/DDB, 2009.
References
External links
Bibliothèque nationale de France
Bibliothèque du Congrès
1933 births
2016 deaths
University of Luxembourg alumni
Luxembourgian scientists
Historians of mathematics
People from Esch-sur-Alzette |
https://en.wikipedia.org/wiki/Stephan%20Ramon%20Garcia | Stephan Ramon Garcia is an American mathematician. He is the W.M. Keck Distinguished Service Professor and Professor of Mathematics at Pomona College, in California, United States. Garcia has been a faculty member at Pomona since 2006. He is the author of more than 100 research papers, many with undergraduate co-authors, and four books. Garcia works in operator theory, complex variables, matrix analysis, number theory, and discrete geometry. He serves on the editorial board of several well-known journals and has received four National Science Foundation grants as principal investigator.
Early life and education
Garcia earned his Bachelor's of Arts with high distinction from the University of California, Berkeley in 1997 and received his PhD in Mathematics in 2003 from the University of California at Berkeley. He joined Pomona College in 2006, where he currently works.
Personal life
Garcia is married to Gizem Karaali. They have two children, Reyhan and Altay.
Published works
In addition to his 89 research articles, over the course of his academic career, Stephan Ramon Garcia has published four books as well. His first book, titled Introduction to Model Spaces and Their Operators was written in collaboration with Javed Mashreghi and William Ross and was published by Cambridge University Press in 2016. In 2017, Stephan Garcia had his second book published in collaboration with Robert Horn titled A Second Course in Linear Algebra by Cambridge University Press. Stephan Garcia's third book, Finite Blaschke Products and Their Connections was written in collaboration with Javad Mashreghi and William Ross and was subsequently published by Springer in 2018. Professor Garcia's most recent book entitled 100 Years of Math Milestones: The Pi Mu Epsilon Centennial Collection was written with Steven J. Miller and was published by the American Mathematical Society in July 2019.
Awards
Throughout his academic career, Garcia has received a plethora of awards. In 1999, Garcia was given the title of Outstanding Graduate Student Instructor at the University of California at Berkeley. In 2005, Garcia was awarded the Mochizuki Memorial Fund Award by the University of California at Santa Barbara. In 2003, Garcia was awarded the Nikki Kose Memorial Teaching Prize. His first award with Pomona college was the Wig Distinguished Professor Award, which was awarded to him in May 2009. Garcia was nominated for CASE Professor of the Year in 2011 and 2012. Garcia was the first professor to receive the 2019 Mary P. Dolciani Award for Excellence in Research.
Grants and research distinctions
Garcia was chosen as the first recipient of the Mary P. Dolciani Excellence in Research for his extensive research history. Aside from publishing 89 research papers, Garcia has helped co-author 29 research articles by his students, some of whom have won awards under his supervision. Garcia has also received four National Science Foundation grants in the areas of complex symmetric operato |
https://en.wikipedia.org/wiki/Semiorthogonal%20decomposition | In mathematics, a semiorthogonal decomposition is a way to divide a triangulated category into simpler pieces. One way to produce a semiorthogonal decomposition is from an exceptional collection, a special sequence of objects in a triangulated category. For an algebraic variety X, it has been fruitful to study semiorthogonal decompositions of the bounded derived category of coherent sheaves, .
Semiorthogonal decomposition
Alexei Bondal and Mikhail Kapranov (1989) defined a semiorthogonal decomposition of a triangulated category to be a sequence of strictly full triangulated subcategories such that:
for all and all objects and , every morphism from to is zero. That is, there are "no morphisms from right to left".
is generated by . That is, the smallest strictly full triangulated subcategory of containing is equal to .
The notation is used for a semiorthogonal decomposition.
Having a semiorthogonal decomposition implies that every object of has a canonical "filtration" whose graded pieces are (successively) in the subcategories . That is, for each object T of , there is a sequence
of morphisms in such that the cone of is in , for each i. Moreover, this sequence is unique up to a unique isomorphism.
One can also consider "orthogonal" decompositions of a triangulated category, by requiring that there are no morphisms from to for any . However, that property is too strong for most purposes. For example, for an (irreducible) smooth projective variety X over a field, the bounded derived category of coherent sheaves never has a nontrivial orthogonal decomposition, whereas it may have a semiorthogonal decomposition, by the examples below.
A semiorthogonal decomposition of a triangulated category may be considered as analogous to a finite filtration of an abelian group. Alternatively, one may consider a semiorthogonal decomposition as closer to a split exact sequence, because the exact sequence of triangulated categories is split by the subcategory , mapping isomorphically to .
Using that observation, a semiorthogonal decomposition implies a direct sum splitting of Grothendieck groups:
For example, when is the bounded derived category of coherent sheaves on a smooth projective variety X, can be identified with the Grothendieck group of algebraic vector bundles on X. In this geometric situation, using that comes from a dg-category, a semiorthogonal decomposition actually gives a splitting of all the algebraic K-groups of X:
for all i.
Admissible subcategory
One way to produce a semiorthogonal decomposition is from an admissible subcategory. By definition, a full triangulated subcategory is left admissible if the inclusion functor has a left adjoint functor, written . Likewise, is right admissible if the inclusion has a right adjoint, written , and it is admissible if it is both left and right admissible.
A right admissible subcategory determines a semiorthogonal decomposition
,
where
is the right orthogonal of in . Con |
https://en.wikipedia.org/wiki/99%20Points%20of%20Intersection | 99 Points of Intersection: Examples—Pictures—Proofs is a book on constructions in Euclidean plane geometry in which three or more lines or curves meet in a single point of intersection. This book was originally written in German by Hans Walser as 99 Schnittpunkte (Eagle / Ed. am Gutenbergplatz, 2004), translated into English by Peter Hilton and Jean Pedersen, and published by the Mathematical Association of America in 2006 in their MAA Spectrum series ().
Topics and organization
The book is organized into three sections. The first section provides introductory material, describing different mathematical situations in which multiple curves might meet, and providing different possible explanations for this phenomenon, including symmetry, geometric transformations, and membership of the curves in a pencil of curves. The second section shows the 99 points of intersection of the title. Each is given on its own page, as a large figure with three smaller figures showing its construction, with a one-line caption but no explanatory text. The third section provides background material and proofs for some of these points of intersection, as well as extending and generalizing some of these results.
Some of these points of intersection are standard; for instance, these include the construction of the centroid of a triangle as the point where its three median lines meet, the construction of the orthocenter as the point where the three altitudes meet, and the construction of the circumcenter as the point where the three perpendicular bisectors of the sides meet, as well as two versions of Ceva's theorem. However, others are new to this book, and include intersections related to silver rectangles, tangent circles, the Pythagorean theorem, and the nine-point hyperbola.
Audience
John Jensen writes that "the clear and uncluttered illustrations of intersection make for a rich source for geometric investigation by high school geometry students".
And although Gerry Leversha calls the book "eccentric" and states that it "is clearly nothing to do with any syllabus anywhere", Jensen suggests that its examples would make a good complement to coursework both in exploratory geometry using interactive geometry software and in a geometry course focused on the formal proof of geometry propositions. He adds that the book itself is a proof of the possibility of presenting geometry without detailed explanations, and of introducing students to the beauty of the subject.
References
External links
Schnittpunkte, web site with a larger collection of points of intersection, by Hans Walser
Euclidean plane geometry
Mathematics books
2004 non-fiction books
2006 non-fiction books |
https://en.wikipedia.org/wiki/Jeizon%20Ram%C3%ADrez | Jeizon Jesús Ramírez Chacón (born 24 March 2001) is a Venezuelan footballer who plays as a winger for Deportivo Táchira.
Career statistics
Club
Notes
References
2001 births
Living people
Venezuelan men's footballers
Venezuelan expatriate men's footballers
Men's association football midfielders
Venezuelan Primera División players
Deportivo Táchira F.C. players
Real Salt Lake players
Venezuelan expatriate sportspeople in the United States
Expatriate men's soccer players in the United States
Designated Players (MLS)
Major League Soccer players
Sportspeople from San Cristóbal, Táchira
21st-century Venezuelan people |
https://en.wikipedia.org/wiki/Equal%20detour%20point | In Euclidean geometry, the equal detour point is a triangle center denoted by X(176) in Clark Kimberling's Encyclopedia of Triangle Centers. It is characterized by the equal detour property: if one travels from any vertex of a triangle to another by taking a detour through some inner point , then the additional distance traveled is constant. This means the following equation has to hold:
The equal detour point is the only point with the equal detour property if and only if the following inequality holds for the angles of :
If the inequality does not hold, then the isoperimetric point possesses the equal detour property as well.
The equal detour point, isoperimetric point, the incenter and the Gergonne point of a triangle are collinear, that is all four points lie on a common line. Furthermore, they form a harmonic range as well (see graphic on the right).
The equal detour point is the center of the inner Soddy circle of a triangle and the additional distance travelled by the detour is equal to the diameter of the inner Soddy Circle.
The barycentric coordinates of the equal detour point are
and the trilinear coordinates are:
References
External links
isoperimetric and equal detour points – interaktive Illustration auf Geogebratube
Triangle centers |
https://en.wikipedia.org/wiki/Nathalie%20Wahl | Nathalie Wahl (born 1976) is a Belgian mathematician specializing in topology, including algebraic topology, homotopy theory, and geometric topology. She is a professor of mathematics at the University of Copenhagen, where she directs the Copenhagen Center for Geometry and Topology.
Education and career
Wahl was born in Brussels, and earned a license in mathematics in 1998 at the Université libre de Bruxelles, advised by Jean-Paul Doignon. Her undergraduate thesis concerned infinite antimatroids, and she published the same material in 2001 as her first journal paper. She completed a Ph.D. at the University of Oxford in 2001, with a dissertation Ribbon Graphs and Related Operads in algebraic topology supervised by Ulrike Tillmann.
After short-term positions at Northwestern University, Aarhus University, and the University of Chicago, she joined the Department of Mathematical Sciences at the University of Copenhagen in 2006, and was promoted to full professor there in 2010. In 2020 she became Center Leader of the Copenhagen Center for Geometry and Topology.
Recognition
In 2008, Wahl won the Young Elite Researcher Award (Ung Eliteforskerprisen) of the Independent Research Fund Denmark (Danmarks Frie Forskningsfond).
In 2016, she was elected to the Danish Academy of Natural Sciences.
References
External links
Home page
1976 births
Living people
Belgian mathematicians
Women mathematicians
Topologists
Université libre de Bruxelles alumni
Alumni of the University of Oxford
Academic staff of the University of Copenhagen |
https://en.wikipedia.org/wiki/Alexander%20Furman | Alexander Furman is a mathematician at the University of Illinois, Chicago. Furman received his bachelor's degree in mathematics and computer science from the Hebrew University of Jerusalem from 1983 to 1986, where he later earned his master's (1987–1989) and PhD (1991–1996) in mathematics.
Career
Furman started teaching mathematics in 1996 as an L. E. Dickson instructor of mathematics at the University of Chicago. A year later, in 1997, he got a position as a Post-Doctoral fellow at Penn State University. He has worked at the University of Illinois Chicago since 1997, serving as an assistant professor until 2007 and being upgraded to full professor.
Furman also runs the UIC Math Olympiad Project where he works with high school-age students, encouraging them to discuss and work out mathematical problems.
Honors and awards
Furman's work in the field of mathematics has earned him a total of fourteen awards. In 1998, he won the National Science Foundation grant, which he would go on to receive four more times. He was also awarded a grant by the Binational Science Foundation three times in his career. In 2014 the Simons Foundation made him a Fellow in mathematics and the National Science Foundation Career Award for exceptional work in teaching through research. In 2014 he was an invited speaker for the International Congress of Mathematics hosted in Seoul. For his work in dynamical systems, ergodic theory, and Lie groups, he was one of the 50 individuals from across the world chosen for their contributions in mathematics to be an American Mathematical Society Fellow in 2016. His most recently received awards are the UIC's University Scholar Award and the LAS Distinguished Professor Award.
References
Israeli mathematicians
Year of birth missing (living people)
Living people
University of Illinois Chicago faculty
Hebrew University of Jerusalem School of Computer Science & Engineering alumni
Einstein Institute of Mathematics alumni |
https://en.wikipedia.org/wiki/Shandelle%20Henson | Shandelle Marie Henson (born 1964) is an American mathematician and mathematical biologist known for her work in population dynamics. She is a professor of mathematics and ecology at Andrews University in Berrien Springs, Michigan, and the editor-in-chief of the journal Natural Resource Modeling.
Education and career
Henson was an undergraduate at Southern College (now Southern Adventist University), and a visiting student at Harvard University, graduating from Southern College in 1987 with a bachelor's degree in mathematics, summa cum laude, as one of the college's five Southern Scholars for that year. She studied mathematical logic at Duke University, earning a master's degree in 1989, and completed a Ph.D. in 1994 at the University of Tennessee. Her dissertation, Individual-based Physiologically Structured Population and Community Models, was on partial differential equations in population dynamics, and was supervised by Thomas G. Hallam.
After postdoctoral research as Hanno Rund Visiting Assistant Professor at the University of Arizona, Henson joined the faculty at the College of William & Mary in 1999, and moved to Andrews University in 2001. There, she was promoted to full professor in 2006, chaired the mathematics department from 2011 to 2016, and added a second affiliation as a professor of ecology in the department of biology in 2016.
Books
Henson is the co-author, with J. M. Cushing, R. F. Costantino, Brian Dennis, and Robert A. Desharnais, of the book Chaos in Ecology: Experimental Nonlinear Dynamics (Academic Press, 2003). She is also the author of a biography of Sam Campbell, titled Sam Campbell: Philosopher of the Forest (Three Lakes Historical Society and TEACH Services, 2001).
Recognition
In 2007, Southern Adventist University gave Henson their alumnus of the year award.
References
External links
Home page
1964 births
Living people
20th-century American mathematicians
21st-century American mathematicians
American women mathematicians
Theoretical biologists
Southern Adventist University alumni
Duke University alumni
University of Tennessee alumni
College of William & Mary faculty
Andrews University faculty
21st-century American women |
https://en.wikipedia.org/wiki/Amanda%20Anisimova%20career%20statistics | This is a list of the main career statistics of American professional tennis player Amanda Anisimova.
Performance timelines
Only main-draw results in WTA Tour, Grand Slam tournaments, Fed Cup/Billie Jean King Cup and Olympic Games are included in win–loss records.
Singles
Current through the 2023 French Open.
Doubles
Current after the 2021 season.
WTA career finals
Singles: 3 (2 titles, 1 runner-up)
ITF finals
Singles: 4 (1 title, 3 runner-ups)
ITF Junior Circuit
Junior Grand Slam finals
Singles: 2 (1 title, 1 runner-up)
ITF Junior finals
Singles: 7 (5 titles, 2 runner–ups)
WTA Tour career earnings
Current after the 2022 Wimbledon.
Career Grand Slam statistics
Grand Slam tournament seedings
Tournaments won by Anisimova are in boldface, and advanced into finals by Anisimova are in italics.
Best Grand Slam results details
Grand Slam winners are in boldface, and runner–ups are in italics.
Singles
Record against top players
Record against top 10 players
Anisimova's record against players who have been ranked in the top 10. Active players are in boldface.
Top 10 wins
Notes
References
Anisimova |
https://en.wikipedia.org/wiki/List%20of%20R-7%20launches%20%282020%E2%80%932024%29 | This is a list of launches made by the R-7 Semyorka ICBM, and its derivatives between 2020 and 2024. All launches are orbital satellite launches, unless stated otherwise.
Launch statistics
Rocket configurations
Launch sites
Launch outcomes
Launch history
References |
https://en.wikipedia.org/wiki/2001%E2%80%9302%20Rochdale%20A.F.C.%20season | The 2001–02 Rochdale A.F.C. season was the club's 81st season in the Football League, and the 28th consecutive season in the fourth tier (League Division Three).
Statistics
|}
Competitions
Football League Third Division
Play-Offs
FA Cup
Football League Cup (Worthington Cup)
Football League Trophy (LDV Vans Trophy)
References
Rochdale A.F.C. seasons
2001–02 Football League Third Division by team |
https://en.wikipedia.org/wiki/J%C3%A1nos%20K%C3%B6rner | János Körner is a Hungarian mathematician who works on information theory and combinatorics.
Körner studied Mathematics at the Eötvös Loránd University in Budapest with a degree in 1970 and was then at the Alfréd Rényi Institute of Mathematics of the Hungarian Academy of Sciences until 1992. From 1981 to 1983 he was at the Bell Laboratories and in 1987–88 at Télécom Paris (ENST) in Paris. He has been a professor at the Sapienza University of Rome since 1993.
Over his career, he frequently collaborated with fellow information theorists such as Rudolf Ahlswede, Katalin Marton, and Imre Csiszár. Together with Rudolf Ahlswede and Peter Gács he proved the blowing-up lemma. Besides information theory, he also works on extremal graph theory.
In 2014 he received the Claude E. Shannon Award. He served as Associated editor of the IEEE Transactions on Information Theory on multiple occasions. He is a member of the Hungarian Academy of Sciences.
Books
With Imre Csiszár: Information Theory: Coding Theorems for Discrete Memoryless Systems, Academic Press 1981, 2nd edition Cambridge University Press 2011.
References
External links
Homepage
IEEE Biography
1946 births
Living people
Academic staff of the Sapienza University of Rome
Members of the Hungarian Academy of Sciences
20th-century Hungarian mathematicians
Information theorists
Fellow Members of the IEEE |
https://en.wikipedia.org/wiki/Chris%20Wiggins%20%28data%20scientist%29 | Chris Wiggins is an associate professor of applied mathematics at Columbia University. In 2010 he co-founded hackNY, a nonprofit organization focused on connecting students with startups in New York City. Since 2014, he has been the Chief Data Scientist at The New York Times.
Career
In 2017, Chris Wiggins, along with Matthew Jones, introduced a new course to Columbia called "Data: Past, Present, Future". The course syllabus, lectures, labs, and resources are available online.
Notable works
"ARACNE: an algorithm for the reconstruction of gene regulatory networks in a mammalian cellular context"
Awards
In 2007, he received the Janette and Armen Avanessians Diversity Award at Columbia University.
Bibliography
References
Year of birth missing (living people)
Living people
Data scientists
Princeton University alumni
The New York Times people
Columbia College (New York) alumni
Columbia University faculty |
https://en.wikipedia.org/wiki/Katrin%20Tent | Katrin Tent is a German mathematician specializing in group theory, the symmetries of groups, algebraic model theory, and finite geometry.
She is a professor of mathematics and mathematical logic at the University of Münster.
Education and career
Tent studied mathematics, linguistics, and computer science at the University of Kiel from 1982 to 1988 and, after a year as a visiting student at Western University in Canada, earned a diploma in mathematics in 1989 from the University of Kiel. She moved to the University of Notre Dame in the United States for doctoral study in mathematics, and completed her Ph.D. there in 1994. Her dissertation, Classifying totally categorical groups (and others), was supervised by Steven A. Buechler.
After working as a visiting researcher at the Hebrew University of Jerusalem and then at the University of Würzburg, where she completed a habilitation in 2001 with the habilitation thesis Model theory of groups and BN-pairs, and after a brief stint as a lecturer at the University of Birmingham, she became a professor of mathematics at Bielefeld University in 2004. She took her present position as a professor of mathematics and mathematical logic at the University of Münster in 2008. Since 2016, she is Vice President of the Deutsche Vereinigung für mathematische Logik und für Grundlagenforschung der exakten Wissenschaften.
Books
With Martin Ziegler, Tent is the co-author of a book on model theory, A Course in Model Theory (Lecture Notes in Logic 40, Cambridge University Press, 2012). She is also the editor of Groups and Analysis : The Legacy of Hermann Weyl (London Mathematical Society Lecture Notes 354, Cambridge University Press, 2008), and co-editor of Lectures in Model Theory (with Franziska Jahnke and Daniel Palacín, Münster Lectures in Mathematics, European Mathematical Society, 2018).
References
External links
Home page
1963 births
Living people
20th-century German mathematicians
German women mathematicians
University of Kiel alumni
University of Notre Dame alumni
Academics of the University of Birmingham
Academic staff of Bielefeld University
Academic staff of the University of Münster
21st-century German mathematicians
20th-century German women
21st-century German women |
https://en.wikipedia.org/wiki/G%C3%A1bor%20Buna | Gábor Buna (born 24 May 2002) is a Hungarian football defender who plays for Győr.
Career statistics
References
External links
2002 births
Living people
Footballers from Kaposvár
Hungarian men's footballers
Hungary men's youth international footballers
Men's association football defenders
Budapest Honvéd FC players
Kecskeméti TE players
Győri ETO FC players
Nemzeti Bajnokság I players
Nemzeti Bajnokság II players |
https://en.wikipedia.org/wiki/Tahiti%20national%20football%20team%20results%20%281952%E2%80%931999%29 | This page details the match results and statistics of the Tahiti national football team from 1952 to 1999.
The Tahiti national football team is the national team of French Polynesia and is controlled by the Fédération Tahitienne de Football. The team consists of a selection of players from French Polynesia, not just Tahiti.
Tahiti played their first full match on 21 September 1952 when they recorded a 2–2 draw at home against New Zealand. Their first competitive match came almost 11 years later when they entered the South Pacific Games for the first time in 1963. Finishing third, Tahiti set a new record winning margin for the national team as they defeated the Solomon Islands 18–0. This was bettered at the 1971 Games when Tahiti recorded a 30–0 win over the Cook Islands.
In 1973, Tahiti competed in the inaugural OFC Nations Cup in New Zealand. Reaching the final following an undefeated group stage, Tahiti lost 2–0 to the hosts New Zealand.
Key
Key to matches
Att.=Match attendance
(H)=Home ground
(A)=Away ground
(N)=Neutral ground
Key to record by opponent
Pld=Games played
W=Games won
D=Games drawn
L=Games lost
GF=Goals for
GA=Goals against
Results
Tahiti's score is shown first in each case.
Notes
Record by opponent
References
Tahiti national football team results |
https://en.wikipedia.org/wiki/Adrian%20Mathias | Adrian Richard David Mathias (born 12 February 1944) is a British mathematician working in set theory.
The forcing notion Mathias forcing is named for him.
Career
Mathias was educated at Shrewsbury and Trinity College, Cambridge, where he read mathematics and graduated in 1965. After graduation, he moved to Bonn in Germany where he
studied with Ronald Jensen, visiting UCLA, Stanford, the University of Wisconsin, and Monash University during that period.
In 1969, he returned to Cambridge as a research fellow at Peterhouse and was admitted to the Ph.D. at Cambridge University in 1970. From 1969 to 1990, Mathias was a fellow of Peterhouse; during this period, he was the editor of the Mathematical Proceedings of the Cambridge Philosophical Society from 1972 to 1974, spent one academic year (1978/79) as Hochschulassistent to Jensen in Freiburg and another year (1989/90) at the MSRI in Berkeley. After leaving Peterhouse in 1990, Mathias had visiting positions in Warsaw, at the Mathematisches Forschungsinstitut Oberwolfach, at the CRM in Barcelona, and in Bogotá, before becoming Professor at the Université de la Réunion. He retired from his professorship in 2012 and was admitted to the higher degree of Doctor of Science at the University of Cambridge in 2015.
Work
Mathias became mathematically active soon after the introduction of forcing by Paul Cohen, and Kanamori credits his survey of forcing that was eventually published as Surrealist landscape with figures as being a "vital source" on forcing in its early days.
His paper Happy families, extending his 1968 Cambridge thesis, proves important properties of the forcing now known as Mathias forcing. In the same paper he shows that no (infinite) maximal almost disjoint family can be analytic.
Mathias also used forcing to separate two weak forms of the Axiom of choice, showing that the ordering principle, which states that any set can be linearly ordered, does not imply the Boolean Prime Ideal Theorem.
His more recent work on forcing includes the study of the theory PROVI of provident sets, a minimalist axiom system that still allows the forcing
construction to proceed.
Mathias is also known for his writings around sociological aspects of logic. These include The ignorance of Bourbaki and Hilbert, Bourbaki and the scorning of logic, in which Mathias criticises Bourbaki's approach to logic; in A Term of Length 4,523,659,424,929 he shows that the number in the title is the number of symbols required for Bourbaki's definition of the number 1. Mathias has also considered claims that standard ZFC is stronger than necessary for "mainstream" mathematics; his paper What is Mac Lane missing? on this topic appeared alongside Saunders Mac Lane's response Is Mathias an ontologist?. Mathias also conducted a detailed study of the strength of a weakened system suggested by Mac Lane.
References
External links
Home page
Adrian Richard David Mathias at the Mathematics Genealogy Project
20th-century English ma |
https://en.wikipedia.org/wiki/The%20Mathematical%20Coloring%20Book | The Mathematical Coloring Book: Mathematics of Coloring and the Colorful Life of Its Creators is a book on graph coloring, Ramsey theory, and the history of development of these areas, concentrating in particular on the Hadwiger–Nelson problem and on the biography of Bartel Leendert van der Waerden. It was written by Alexander Soifer and published by Springer-Verlag in 2009 ().
Topics
The book "presents mathematics as a human endeavor" and "explores the birth of ideas and moral dilemmas of the times between and during the two World Wars". As such, as well as covering the mathematics of its topics, it includes biographical material and correspondence with many of the people involved in creating it, including in-depth coverage of Issai Schur, , and Bartel Leendert van der Waerden, in particular studying the question of van der Warden's complicity with the Nazis in his war-time service as a professor in Nazi Germany. It also includes biographical material on Paul Erdős, Frank P. Ramsey, Emmy Noether, Alfred Brauer, Richard Courant, Kenneth Falconer, Nicolas de Bruijn, Hillel Furstenberg, and Tibor Gallai, among others, as well as many historical photos of these subjects.
Mathematically, the book considers problems "on the boundary of geometry, combinatorics, and number theory", involving graph coloring problems such as the four color theorem, and generalizations of coloring in Ramsey theory where the use of a too-small number of colors leads to monochromatic structures larger than a single graph edge. Central to the book is the Hadwiger–Nelson problem, the problem of coloring the points of the Euclidean plane in such a way that no two points of the same color are a unit distance apart. Other topics covered by the book include Van der Waerden's theorem on monochromatic arithmetic progressions in colorings of the integers and its generalization to Szemerédi's theorem, the Happy ending problem, Rado's theorem, and questions in the foundations of mathematics involving the possibility that different choices of foundational axioms will lead to different answers to some of the coloring questions considered here.
Reception and audience
As a work in graph theory, reviewer Joseph Malkevitch suggests caution over the book's intuitive treatment of graphs that may in many cases be infinite, in comparison with much other work in this area that makes an implicit assumption that every graph is finite. William Gasarch is surprised by the book's omission of some closely related topics, including the proof of the Heawood conjecture on coloring graphs on surfaces by Gerhard Ringel and Ted Youngs. And Günter M. Ziegler complains that many claims are presented without proof. Although Soifer has called the Hadwiger–Nelson problem "the most important problem in all of mathematics", Ziegler disagrees, and suggests that it and the four color theorem are too isolated to be fruitful topics of study.
As a work in the history of mathematics, Malkevitch finds the book too cre |
https://en.wikipedia.org/wiki/Derived%20noncommutative%20algebraic%20geometry | In mathematics, derived noncommutative algebraic geometry, the derived version of noncommutative algebraic geometry, is the geometric study of derived categories and related constructions of triangulated categories using categorical tools. Some basic examples include the bounded derived category of coherent sheaves on a smooth variety, , called its derived category, or the derived category of perfect complexes on an algebraic variety, denoted . For instance, the derived category of coherent sheaves on a smooth projective variety can be used as an invariant of the underlying variety for many cases (if has an ample (anti-)canonical sheaf). Unfortunately, studying derived categories as geometric objects of themselves does not have a standardized name.
Derived category of projective line
The derived category of is one of the motivating examples for derived non-commutative schemes due to its easy categorical structure. Recall that the Euler sequence of is the short exact sequence
if we consider the two terms on the right as a complex, then we get the distinguished triangle
Since we have constructed this sheaf using only categorical tools. We could repeat this again by tensoring the Euler sequence by the flat sheaf , and apply the cone construction again. If we take the duals of the sheaves, then we can construct all of the line bundles in using only its triangulated structure. It turns out the correct way of studying derived categories from its objects and triangulated structure is with exceptional collections.
Semiorthogonal decompositions and exceptional collections
The technical tools for encoding this construction are semiorthogonal decompositions and exceptional collections. A semiorthogonal decomposition of a triangulated category is a collection of full triangulated subcategories such that the following two properties hold
(1) For objects we have for
(2) The subcategories generate , meaning every object can be decomposed in to a sequence of ,
such that . Notice this is analogous to a filtration of an object in an abelian category such that the cokernels live in a specific subcategory.
We can specialize this a little further by considering exceptional collections of objects, which generate their own subcategories. An object in a triangulated category is called exceptional if the following property holds
where is the underlying field of the vector space of morphisms. A collection of exceptional objects is an exceptional collection of length if for any and any , we have
and is a strong exceptional collection if in addition, for any and any , we have
We can then decompose our triangulated category into the semiorthogonal decomposition
where , the subcategory of objects in such that . If in addition then the strong exceptional collection is called full.
Beilinson's theorem
Beilinson provided the first example of a full strong exceptional collection. In the derived category the line bundles form a full stro |
https://en.wikipedia.org/wiki/Cartier%20isomorphism | In algebraic geometry, the Cartier isomorphism is a certain isomorphism between the cohomology sheaves of the de Rham complex of a smooth algebraic variety over a field of positive characteristic, and the sheaves of differential forms on the Frobenius twist of the variety. It is named after Pierre Cartier. Intuitively, it shows that de Rham cohomology in positive characteristic is a much larger object than one might expect. It plays an important role in the approach of Deligne and Illusie to the degeneration of the Hodge–de Rham spectral sequence.
Statement
Let k be a field of characteristic p > 0, and let be a morphism of k-schemes. Let denote the Frobenius twist and let be the relative Frobenius. The Cartier map is defined to be the unique morphismof graded -algebras such that for any local section x of . (Here, for the Cartier map to be well-defined in general it is essential that one takes cohomology sheaves for the codomain.) The Cartier isomorphism is then the assertion that the map is an isomorphism if is a smooth morphism.
In the above, we have formulated the Cartier isomorphism in the form it is most commonly encountered (e.g., in the 1970 paper of Katz). In his original paper, Cartier actually considered the inverse map in a more restrictive setting, whence the notation for the Cartier map.
The smoothness assumption is not essential for the Cartier map to be an isomorphism. For instance, one has it for ind-smooth morphisms since both sides of the Cartier map commute with filtered colimits. By Popescu's theorem, one then has the Cartier isomorphism for a regular morphism of noetherian k-schemes. Ofer Gabber has also proven a Cartier isomorphism for valuation rings. In a different direction, one can dispense with such assumptions entirely if one instead works with derived de Rham cohomology (now taking the associated graded of the conjugate filtration) and the exterior powers of the cotangent complex.
References
Algebraic geometry |
https://en.wikipedia.org/wiki/Viewpoints%3A%20Mathematical%20Perspective%20and%20Fractal%20Geometry%20in%20Art | Viewpoints: Mathematical Perspective and Fractal Geometry in Art is a textbook on mathematics and art. It was written by mathematicians Marc Frantz and Annalisa Crannell, and published in 2011 by the Princeton University Press (). The Basic Library List Committee of the Mathematical Association of America has recommended it for inclusion in undergraduate mathematics libraries.
Topics
The first seven chapters of the book concern perspectivity, while its final two concern fractals and their geometry. Topics covered within the chapters on perspectivity include coordinate systems for the plane and for Euclidean space, similarity, angles, and orthocenters, one-point and multi-point perspective, and anamorphic art. In the fractal chapters, the topics include self-similarity, exponentiation, and logarithms, and fractal dimension. Beyond this mathematical material, the book also describes methods for artists to depict scenes in perspective, and for viewers of art to understand the perspectives in the artworks they see, for instance by finding the optimal point from which to view an artwork. The chapters are ordered by difficulty, and begin with experiments that the students can perform on their own to motivate the material in each chapter.
The book is heavily illustrated by artworks and photography (such as the landscapes of Ansel Adams) and includes a series of essays or interviews by contemporary artists on the mathematical content of their artworks.
An appendix contains suggestions aimed at teachers of this material.
Audience and reception
Viewpoints is intended as a textbook for mathematics classes aimed at undergraduate liberal arts students, as a way to show these students how geometry can be used in their everyday life. However, it could even be used for high school art students,
and reviewer Paul Kelley writes that "it will be of value to anyone interested in an elementary introduction to the mathematics and practice of perspective drawing". It differs from many other liberal arts mathematics textbooks in its relatively narrow focus on geometry and perspective, and its avoidance of more well-covered ground in mathematics and the arts such as symmetry and the geometry of polyhedra.
Although reviewer Blake Mellor complains that the connection between the material on perspective and on fractal geometry "feels forced", he concludes that "this is an excellent text". Reviewer Paul Kelley writes that the book's "step-by-step progression" through its topics makes it "readable [and] easy-to-follow", and that "Students can learn a great deal from this book." Reviewer Alexander Bogomolny calls it "an elegant fusion of mathematical ideas and practical aspects of fine art".
References
Mathematics and art
Mathematics textbooks
2011 non-fiction books
Princeton University Press books |
https://en.wikipedia.org/wiki/Luisa%20Illkov%C3%A1 | Luisa Illková (born 2 May 1988) is a Czech curler.
Teams
Women's
Mixed
Personal life
She started curling in 2003.
References
External links
Illková Luisa - Player statistics (all games with his/her participation) - Czech Curling Association
Living people
1988 births
Czech female curlers
Czech curling champions
Competitors at the 2009 Winter Universiade
Place of birth missing (living people) |
https://en.wikipedia.org/wiki/The%20Pursuit%20of%20Perfect%20Packing | The Pursuit of Perfect Packing is a book on packing problems in geometry. It was written by physicists Tomaso Aste and Denis Weaire, and published in 2000 by Institute of Physics Publishing (doi:10.1887/0750306483, ) with a second edition published in 2008 by Taylor & Francis ().
Topics
The mathematical topics described in the book include sphere packing (including the Tammes problem, the Kepler conjecture, and higher-dimensional sphere packing), the Honeycomb conjecture and the Weaire–Phelan structure, Voronoi diagrams and Delaunay triangulations, Apollonian gaskets, random sequential adsorption, and the physical realizations of some of these structures by sand, soap bubbles, the seeds of plants, and columnar basalt. A broader theme involves the contrast between locally ordered and locally disordered structures, and the interplay between local and global considerations in optimal packings.
As well, the book includes biographical sketches of some of the contributors to this field, and histories of their work in this area, including Johannes Kepler, Stephen Hales, Joseph Plateau, Lord Kelvin, Osborne Reynolds, and J. D. Bernal.
Audience and reception
The book is aimed at a general audience rather than to professional mathematicians. Therefore, it avoids mathematical proofs and is otherwise not very technical. However, it contains pointers to the mathematical literature where readers more expert in these topics can find more detail. Avoiding proof may have been a necessary decision as some proofs in this area defy summarization: the proof by Thomas Hales of the Kepler conjecture on optimal sphere packing in three dimensions, announced shortly before the publication of the book and one of its central topics, is hundreds of pages long.
Reviewer Johann Linhart complains that (in the first edition) some figures are inaccurately drawn. And although finding the book "entertaining and easy to read", William Satzer finds it "frustrating" in the lack of detail in its stories. Nevertheless, Linhart and reviewer Stephen Blundell highly recommend the book, and reviewer Charles Radin calls it "a treasure trove of intriguing examples" and "a real gem". And despite complaining about a format that mixes footnote markers into mathematical formulas, and the illegibility of some figures, Michael Fox recommends it to "any mathematics or science library".
References
Packing problems
Mathematics books
2000 non-fiction books
2008 non-fiction books |
https://en.wikipedia.org/wiki/Dupin%27s%20theorem | In differential geometry Dupin's theorem, named after the French mathematician Charles Dupin, is the statement:
The intersection curve of any pair of surfaces of different pencils of a threefold orthogonal system is a curvature line.
A threefold orthogonal system of surfaces consists of three pencils of surfaces such that any pair of surfaces out of different pencils intersect orthogonally.
The most simple example of a threefold orthogonal system consists of the coordinate planes and their parallels. But this example is of no interest, because a plane has no curvature lines.
A simple example with at least one pencil of curved surfaces: 1) all right circular cylinders with the z-axis as axis, 2) all planes, which contain the z-axis, 3) all horizontal planes (see diagram).
A curvature line is a curve on a surface, which has at any point the direction of a principal curvature (maximal or minimal curvature). The set of curvature lines of a right circular cylinder consists of the set of circles (maximal curvature) and the lines (minimal curvature). A plane has no curvature lines, because any normal curvature is zero. Hence, only the curvature lines of the cylinder are of interest: A horizontal plane intersects a cylinder at a circle and a vertical plane has lines with the cylinder in common.
The idea of threefold orthogonal systems can be seen as a generalization of orthogonal trajectories. Special examples are systems of confocal conic sections.
Application
Dupin's theorem is a tool for determining the curvature lines of a surface by intersection with suitable surfaces (see examples), without time-consuming calculation of derivatives and principal curvatures. The next example shows, that the embedding of a surface into a threefold orthogonal system is not unique.
Examples
Right circular cone
Given: A right circular cone, green in the diagram.
Wanted: The curvature lines.
1. pencil: Shifting the given cone C with apex S along its axis generates a pencil of cones (green).
2. pencil: Cones with apexes on the axis of the given cone such that the lines are orthogonal to the lines of the given cone (blue).
3. pencil: Planes through the cone's axis (purple).
These three pencils of surfaces are an orthogonal system of surfaces. The blue cones intersect the given cone C at a circle (red). The purple planes intersect at the lines of cone C (green).
Alternative with spheres
The points of the space can be described by the spherical coordinates
. It is set S=M=origin.
1. pencil: Cones with point S as apex and their axes are the axis of the given cone C (green): .
2. pencil: Spheres centered at M=S (blue):
3. pencil: Planes through the axis of cone C (purple): .
Torus
1. pencil: Tori with the same directrix (green).
2. pencil: Cones containing the directrix circle of the torus with apexes on the axis of the torus (blue).
3. pencil: Planes containing the axis of the given torus (purple).
The blue cones intersect the torus at horizontal cir |
https://en.wikipedia.org/wiki/Keith%20Walters | Keith Walters was the Dean of Science and Mathematics at Valdosta State University. until his arrest for possessing child pornography . He is no longer employed at Valdosta State University. Prior to this, Walters was the Chair of the Department of Chemistry & Biochemistry at Northern Kentucky University.
References
Living people
Year of birth missing (living people) |
https://en.wikipedia.org/wiki/Kristina%20Reiss | Kristina Reiss (born 1952) is a German mathematics educator. She is professor of mathematics education and dean of education at the Technical University of Munich, where she holds the Heinz Nixdorf Chair of Mathematics Education.
Education and career
Reiss studied mathematics beginning in 1971 at Heidelberg University, completing her doctorate (Dr. rer. nat.) there in 1980. Her dissertation, Eine allgemeinere Kennzeichnung der sporadischen einfachen Gruppe von Rudvalis, concerned group theory and was supervised by Zvonimir Janko.
She worked as a researcher at the Karlsruhe University of Education from 1980 until 1991, when she became a professor of mathematics at the Stuttgart Technology University of Applied Sciences. She moved in 1992 to the University of Flensburg, in 1997 to the University of Oldenburg, in 2002 to the University of Augsburg, and in 2005 to the Technical University of Munich (TUM). At TUM, she was initially a professor of mathematics and computer science education and since 2009 as Heinz Nixdorf Chair of Mathematics Education. Since 2014 she has been dean of the TUM School of Education.
Recognition
In 2011 Reiss joined Acatech, the German Academy of Science and Engineering.
References
External links
1952 births
Living people
20th-century German mathematicians
Women mathematicians
Mathematics educators
Heidelberg University alumni
Academic staff of the University of Oldenburg
Academic staff of the University of Augsburg
Academic staff of the Technical University of Munich
21st-century German mathematicians |
https://en.wikipedia.org/wiki/Using%20the%20Borsuk%E2%80%93Ulam%20Theorem | Using the Borsuk–Ulam Theorem: Lectures on Topological Methods in Combinatorics and Geometry is a graduate-level mathematics textbook in topological combinatorics. It describes the use of results in topology, and in particular the Borsuk–Ulam theorem, to prove theorems in combinatorics and discrete geometry. It was written by Czech mathematician Jiří Matoušek, and published in 2003 by Springer-Verlag in their Universitext series ().
Topics
The topic of the book is part of a relatively new field of mathematics crossing between topology and combinatorics, now called topological combinatorics. The starting point of the field, and one of the central inspirations for the book, was a proof that László Lovász published in 1978 of a 1955 conjecture by Martin Kneser, according to which the Kneser graphs have no graph coloring with colors. Lovász used the Borsuk–Ulam theorem in his proof, and Matoušek gathers many related results, published subsequently, to show that this connection between topology and combinatorics is not just a proof trick but an area.
The book has six chapters. After two chapters reviewing the basic notions of algebraic topology, and proving the Borsuk–Ulam theorem, the applications to combinatorics and geometry begin in the third chapter, with topics including the ham sandwich theorem, the necklace splitting problem, Gale's lemma on points in hemispheres, and several results on colorings of Kneser graphs. After another chapter on more advanced topics in equivariant topology, two more chapters of applications follow, separated according to whether the equivariance is modulo two or using a more complicated group action. Topics in these chapters include the van Kampen–Flores theorem on embeddability of skeletons of simplices into lower-dimensional Euclidean spaces, and topological and multicolored variants of Radon's theorem and Tverberg's theorem on partitions into subsets with intersecting convex hulls.
Audience and reception
The book is written at a graduate level, and has exercises making it suitable as a graduate textbook. Some knowledge of topology would be helpful for readers but is not necessary. Reviewer Mihaela Poplicher writes that it is not easy to read, but is "very well written, very interesting, and very informative". And reviewer Imre Bárány writes that "The book is well written, and the style is lucid and pleasant, with plenty of illustrative examples."
Matoušek intended this material to become part of a broader textbook on topological combinatorics, to be written jointly with him, Anders Björner, and Günter M. Ziegler. However, this was not completed before Matoušek's untimely death in 2015.
References
Combinatorics
Algebraic topology
Mathematics textbooks
2003 non-fiction books |
https://en.wikipedia.org/wiki/Joseph%20Alphonso%20Pierce | Joseph Alphonso Pierce, Sr. (August 10, 1902 – September 18, 1969) was an American mathematician and statistician. He was one of the first African-Americans to earn a PhD in mathematics in the United States. He was an educator who had a long career as teacher, administrator, and researcher.
Early life and education
Joseph Alphonso Pierce was born August 10, 1902, in Waycross, Georgia. He was the son of William Arthur Pierce, a Methodist minister, and Fannie McGraw. He was orphaned at an early age and was raised by his uncle Joseph McGraw. He received his early education from public schools in Georgia.
He receiving his bachelor's degree in social science from Atlanta University in 1925. Pierce got his master's degree in mathematics from Atlanta University in 1930 and earned a Ph.D. from the University of Michigan in 1938 with the dissertation "A Study of a Universe of N Finite Populations with Application to Moment-Function Adjustments for Grouped Data" under advisor Harry C. Carver.
Career
Pierce began his career at Texas College in Tyler, Texas where he was an instructor in the Mathematics Department from 1925 to 1927. Having played college varsity football at Atlanta University, Pierce also was an assistant coach for the football team there. He then spent two years, from 1927 to 1929, as a math teacher at Booker T. Washington High School in Atlanta, Georgia. After receiving his master's in 1930, Pierce took a position as a professor of mathematics at Wiley College in Marshall, Texas. It was here that he began to work on his PhD. During this period, with his wife, Dr. Juanita G. Pierce, he had one son (Joseph Alphonso Pierce, Jr.). Upon earning his PhD in 1938, Joseph Pierce returned to Atlanta University where he taught math and statistics and also served as the chair of the Department of Mathematics. In 1948 Pierce moved to Texas State College for Negroes (later to become Texas Southern University) in Houston, where he was professor of mathematics from 1948 to 1954, head of the Mathematics Department from 1948 to 1957, and chair of the Division of Natural Physical Sciences. He continued to progress at the university, eventually becoming the Dean of the Graduate School in 195. Pierce continued to teach and be involved in various ways at Texas Southern for many years until 1967 when he was elected President of the university. He was also a consultant to NASA for a period of two years (1967-1968).
Negro Business and Business Education
While in Atlanta (1944-1946), Pierce was appointed research director of a large study of African American businesses and business opportunities sponsored by Atlanta University. He later published the results of this study and more in his book Negro Business and Business Education: Their Present and Prospective Development (1947). Although he was a talented mathematician and statistician, Joseph Pierce was most known for this work. What he found was that black owned businesses captured a very small percentage |
https://en.wikipedia.org/wiki/Andrew%20Booker%20%28mathematician%29 | Andrew Richard Booker (born 1976) is a British mathematician who is currently Professor of Pure Mathematics at the University of Bristol. He is an analytic number theorist known for his work on L-functions of automorphic forms and his contributions to the sums of three cubes problem.
Education
Booker graduated from the University of Virginia in 1998, earning the E.J. McShane Prize as the top undergraduate in mathematics. He completed his doctoral degree at Princeton University in 2003, under the supervision of Peter Sarnak.
Contributions
In the spring of 2019 Booker gained international attention by showing that 33 can be expressed as the sum of three cubes. At that time 33 and 42 were the only numbers less than 100 for which this problem was open. Later that year, in joint work with Andrew Sutherland of MIT, he settled the case of 42, as well as answering a 65-year-old question of Mordell by finding a third representation for 3 as the sum of three cubes. Popular Mechanics cited the result for 42 as one of the top two mathematical breakthroughs of 2019.
Video appearances
Numberphile has produced three YouTube videos related to sums of three cubes in which Andrew Booker is the featured guest:
42 is the new 33
The Mystery of 42 is Solved
3 as a sum of 3 cubes
As of January 2023 these videos had accumulated a total of almost two million views.
Selected publications
References
External links
Andrew Booker's profile at the University of Bristol
Andrew Booker's profile on MathSciNet
Andrew Booker's profile on zbMath
Andrew Booker's profile on Google Scholar
Andrew Booker's preprints posted to arXiv
Living people
21st-century British mathematicians
Number theorists
Princeton University alumni
University of Virginia alumni
Academics of the University of Bristol
1976 births |
https://en.wikipedia.org/wiki/Poincar%C3%A9%20and%20the%20Three-Body%20Problem | Poincaré and the Three-Body Problem is a monograph in the history of mathematics on the work of Henri Poincaré on the three-body problem in celestial mechanics. It was written by June Barrow-Green, as a revision of her 1993 doctoral dissertation, and published in 1997 by the American Mathematical Society and London Mathematical Society as Volume 11 in their shared History of Mathematics series (). The Basic Library List Committee of the Mathematical Association of America has suggested its inclusion in undergraduate mathematics libraries.
Topics
The three-body problem concerns the motion of three bodies interacting under Newton's law of universal gravitation, and the existence of orbits for those three bodies that remain stable over long periods of time. This problem has been of great interest mathematically since Newton's formulation of the laws of gravity, in particular with respect to the joint motion of the sun, earth, and moon. The centerpiece of Poincaré and the Three-Body Problem is a memoir on this problem by Henri Poincaré, entitled Sur le problème des trois corps et les équations de la dynamique [On the problem of the three bodies and the equations of dynamics]. This memo won the King Oscar Prize in 1889, commemorating the 60th birthday of
Oscar II of Sweden, and was scheduled to be published in Acta Mathematica on the king's birthday, until Lars Edvard Phragmén and Poincaré determined that there were serious errors in the paper. Poincaré called for the paper to be withdrawn, spending more than the prize money to do so. In 1890 it was finally published in revised form, and over the next ten years Poincaré expanded it into a monograph, Les méthodes nouvelles de la mécanique céleste [New methods in celestial mechanics]. Poincare's work led to the discovery of chaos theory, set up a long-running separation between mathematicians and dynamical astronomers over the convergence of series, and became the initial claim to fame for Poincaré himself. The detailed story behind these events, long forgotten, was brought back to life in a sequence of publications by multiple authors in the early and mid 1990s, including Barrow-Green's dissertation, a journal publication based on the dissertation, and this book.
The first chapter of Poincaré and the Three-Body Problem introduces the problem and its second chapter surveys early work on this problem, in which some particular solutions were found by Newton, Jacob Bernoulli, Daniel Bernoulli, Leonhard Euler, Joseph-Louis Lagrange, Pierre-Simon Laplace, Alexis Clairaut, Charles-Eugène Delaunay, Hugo Glydén, Anders Lindstedt, George William Hill, and others. The third chapter surveys the early work of Poincaré, which includes work on differential equations, series expansions, and some special solutions of the three-body problem, and the fourth chapter surveys this history of the founding of Acta Arithmetica by Gösta Mittag-Leffler and of the prize competition announced by Mittag-Leffler in 1885, which Bar |
https://en.wikipedia.org/wiki/Gisela%20Engeln-M%C3%BCllges | Gisela Engeln-Müllges (born 1940) is a German mathematician and artist. She is a professor of numerical mathematics at the Aachen University of Applied Sciences, where she is also a former vice rector for research, development, and technology.
Education and academic career
Engeln-Müllges was born in Leipzig, in 1940. After World War II, Leipzig became part of East Germany (the German Democratic Republic), and Engeln-Müllges escaped to the west in 1961. She studied mathematics at RWTH Aachen University beginning in 1961, and completed a doctorate (Dr. rer. nat.) in 1971, with a dissertation Fluchtebenennomogramme zur Darstellung von Funktionensystemen: Ihre Theorie und praktische Verwendbarkeit concerning numerical analysis.
She has been a professor at the Aachen University of Applied Sciences since 1982, and was vice rector there from 1992 to 2005. With Frank Uhlig, she is the author of the books Numerik-Algorithmen mit C and Numerik-Algorithmen mit Fortran (7th ed., 1993, translated into English as Numerical Algorithms with Fortran and Numerical Algorithms with C, Springer, 1996).
Art
Engeln-Müllges's artworks are abstract, and include both paintings and cast-metal sculptures, based on her many years of work with artist . In 2019, she was one of the selected artists for the London Art Biennale.
Recognition
Engeln-Müllges was awarded the Federal Cross of Merit in 1992. In 2005, she was given an honorary doctorate by Nizhny Novgorod State Technical University.
References
External links
Academic home page
Personal home page
1940 births
Living people
Scientists from Leipzig
East German defectors
20th-century German mathematicians
Women mathematicians
German abstract artists
German women artists
RWTH Aachen University alumni
Recipients of the Cross of the Order of Merit of the Federal Republic of Germany
20th-century German women |
https://en.wikipedia.org/wiki/Rochelle%20Gutierrez | Rochelle Gutierrez is a professor of education at the University of Illinois at Urbana–Champaign. Her main focus is changing the way in which mathematics is taught to the minority and the effects of race, class and language on teaching and learning.
Early life and education
Gutierrez is from San Jose, California. She attended Stanford University and received her bachelor’s degree in human biology in 1990. She then moved to the University of Chicago, where she earned a master’s degree in social sciences and a PhD in education. Her doctoral research was centered on equity in teaching mathematics.
Career
Gutierrez has been working at the University of Illinois at Urbana–Champaign since 1996. Her main focus is on how intersectionality can play a role when learning mathematics. Some of her research is based on how to better teach underprivileged students mathematics and how teachers and professors can better assist the students. Gutierrez has also researched how mathematics can impact a student's power and place in society. On a website, Campus Reform, she is quoted as saying, "On many levels, mathematics itself operates as Whiteness. Who gets credit for doing and developing mathematics, who is capable in mathematics, and who is seen as part of the mathematical community is generally viewed as White".
Awards
In 2010 she was given the Outstanding Faculty Award for Service at UIUC.
In 2011 Gutierrez received the Association of Mathematics Teacher Educators award, which is an organization who recognize teachers who are dedicated in improving Mathematical education.
In 2016 she was awarded the Iris M. Carl Equity and Leadership Award (TODOS Mathematics).
In 2017 Gutierrez received the Social Justice Award, which is given to those who spend of their time helping minorities.
For the school year 2018-2019 Gutierrez received the Outstanding Undergraduate Teaching Award at the University of Illinois-Urbana.
References
Stanford University alumni
University of Chicago alumni
Year of birth missing (living people)
Living people
University of Illinois Urbana-Champaign faculty
American women social scientists
American educational theorists
Mathematics educators
People from San Jose, California
21st-century American women |
https://en.wikipedia.org/wiki/Robert%20Steffen | Robert Steffen is an Emeritus Professor at the Epidemiology, Biostatistics and Prevention Institute, University of Zurich, Switzerland and an adjunct professor at the University of Texas School of Public in Houston. He is an editor of the Journal of Travel Medicine.
Education
Robert Steffen was born and raised in Zurich. He was a medical student at the local university and towards the end of his medical studies, he was elected as the president of the International Federation of Medical Students Association.
He initially trained to become a flight surgeon at the Swiss Air Force Medical Institute. Subsequently, he obtained a broad education in Internal medicine and epidemiology at academic institutions in Sydney, Nairobi, Johannesburg, Chicago, San Francisco, and London.
Research and career
Steffen's research focused on the epidemiology and prevention of infectious diseases in travelers. Areas of research included malaria, vaccines and travelers’ diarrhea. He conducted a study on the oral antibiotic formulation Rifamycin SV – MMX for treating traveler’s diarrhea and also promoted researches on the interests of older travelers. Lately he focused on a viral infection called Tick-borne encephalitis (TBE).
In the early days of his career, he served as a Chief Border Physician at the Zurich Airport. Steffen served as Chair of the 2018 IHR Emergency Committee and Vice-Chair of the 2014-2016 IHR Emergency Committee for Ebola Virus Disease (EVD). During the Gulf War he was the leader of Task Force Scorpio.
Awards and honors
He currently serves as the member of the Swiss Society for Infectious Diseases and an honorary fellow of the Australasian College of Tropical Medicine. Additional award includes the Bronze Medal of the City of Paris and also received the honor of serving as the chairman of the W.H.O. emergency committee. He also has served as the President for International Society of Travel Medicine (ISTM).
Publications
Epidemiology of tick-borne encephalitis (TBE) in international travellers to Western/Central Europe and conclusions on vaccination recommendations.
Rifamycin SV-MMX® for treatment of travellers' diarrhea: equally effective as ciprofloxacin and not associated with the acquisition of multi-drug resistant bacteria.
Traveler's diarrhea: a clinical review.
Travel vaccine preventable diseases-updated logarithmic scale with monthly incidence rates.
Influenza in travelers: epidemiology, risk, prevention, and control issues.
References
Year of birth missing (living people)
Living people
Swiss epidemiologists
Swiss medical researchers
Swiss public health doctors
University of Zurich alumni
Physicians from Zürich
Academic staff of the University of Zurich |
https://en.wikipedia.org/wiki/Alexander%20Lecaros | Alexander Lecaros Aragón (born 13 October 1999) is a Peruvian footballer who plays as a winger for Carlos A. Mannucci.
Career statistics
Club
Notes
References
External links
1999 births
Living people
Peruvian men's footballers
Men's association football wingers
Peruvian Primera División players
Campeonato Brasileiro Série A players
Cusco FC footballers
Carlos A. Mannucci players
Botafogo de Futebol e Regatas players
Avaí FC players
Peruvian expatriate men's footballers
Peruvian expatriate sportspeople in Brazil
Expatriate men's footballers in Brazil |
https://en.wikipedia.org/wiki/Michel%20Ara%C3%BAjo | Michel Daryl Araújo Villar (born 28 September 1996) is a Uruguayan professional footballer who plays as an attacking midfielder for São Paulo, on loan from Fluminense.
Career statistics
Club
Notes
Honours
Fluminense
Taça Rio: 2020
São Paulo
Copa do Brasil: 2023
References
External links
1996 births
Living people
Uruguayan men's footballers
Uruguayan expatriate men's footballers
Men's association football midfielders
Racing Club de Montevideo players
Villa Teresa players
Fluminense FC players
São Paulo FC players
Al Wasl F.C. players
Uruguayan Primera División players
Uruguayan Segunda División players
Campeonato Brasileiro Série A players
UAE Pro League players
Uruguayan expatriate sportspeople in Brazil
Expatriate men's footballers in Brazil
Expatriate men's footballers in the United Arab Emirates
Uruguayan expatriate sportspeople in the United Arab Emirates
People from Colonia del Sacramento
Footballers from Colonia Department |
https://en.wikipedia.org/wiki/Andrew%20Booker | Andrew Booker may refer to:
Andrew Booker (mathematician) (born 1976), British mathematician specializing in number theory
Andrew Booker (musician), British drummer and vocalist |
https://en.wikipedia.org/wiki/Serafina%20Cuomo | Serafina Cuomo (born May 21, 1966) is an Italian historian and professor at Durham University. Cuomo specialises in the history of ancient mathematics, including the computing practices in ancient Rome and Pappos, and also with the history of technology.
Education
Cuomo achieved a bachelor's degree in Philosophy at the University of Naples and received a doctorate in History and Philosophy from the University of Cambridge.
Career
Cuomo formerly worked as a speaker at Imperial College London, Birkbeck University of London. Currently, Cuomo works at Durham University at the Department of Classics and Ancient History.
In 2019, Cuomo participated in the EHESS (École des Hautes Etudes en Sciences Sociales).
Books
Pappus of Alexandria and the Mathematics of Late Antiquity (Cambridge Classical Studies, Cambridge University Press, 2000)
Ancient Mathematics (Sciences of Antiquity, Routledge, 2001)
Technology and Culture in Greek and Roman Antiquity (Key Themes in Ancient History, Cambridge University Press, 2007)
Articles and chapters
“Skills and virtues in Vitruvius’ book 10”, in M. Formisano (ed.), War in Words, Leiden: Brill 2011, 309-32
“All the proconsul’s men: Cicero, Verres and account-keeping”, Annali dell’Università degli studi di Napoli ‘L’ Orientale’. Sezione filologico-letteraria. Quaderni 15, Naples 2011, 165-85
“A Roman engineer’s tales”, Journal of Roman Studies 101 (2011), 143-65
“Measures for an emperor: Volusius Maecianus’ monetary pamphlet for Marcus Aurelius”, in J. König & T. Whitmarsh (eds.), Ordering Knowledge in the Roman Empire, Cambridge University Press 2007, 206-228
“The machine and the city: Hero of Alexandria's Belopoeica”, in C.J. Tuplin & T.E. Rihll (eds.), Science and Mathematics in Ancient Greek Culture, Oxford: Oxford University Press 2002, 165-77
“Divide and rule: Frontinus and Roman land-surveying”, Studies in History and Philosophy of Science 31 (2000), 189-202
“Shooting by the book: Notes on Tartaglia's ‘Scientia Nova’”, History of Science 35 (1997), 155-88
References
1966 births
Living people
Classical scholars of the University of Durham
Alumni of the University of Cambridge
21st-century Italian historians
University of Naples Federico II alumni |
https://en.wikipedia.org/wiki/Federico%20Ardila | Federico Ardila (born 1977) is a Colombian mathematician and DJ who researches combinatorics and specializes in matroid theory. Ardila graduated from MIT with a B.Sc. in mathematics in 1998 and obtained a Ph.D. in 2003 under the supervision of Richard P. Stanley in the same institution. Ardila is currently a professor at the San Francisco State University and additionally holds an adjunct position at the University of Los Andes in Colombia.
Early life and education
Ardila was born in Bogotá, Colombia. During his childhood Ardila showed great promise in mathematics, scoring the highest amongst his age group in the fourth grade. While attending the college-prep Colegio San Carlos in Bogotá, Ardila represented Colombia in the International Math Olympiad, winning a bronze medal in 1993 and a silver medal in 1994.
Prior to attending MIT, Ardila was already enrolled in another local university. Ardila had never heard of MIT, but a classmate told him that they offered financial aid to everyone, so he applied without knowing how competitive the school was.
In addition to mathematics, Ardila enjoys making music and is a co-founder of the Oakland DJ collective La Pelanga.
Career
Under his NSF CAREER grant, Ardila has worked to create a larger and more diverse community of members of underrepresented groups within mathematics. Ardila follows certain principles geared towards cultivating diversity within his field of study, which he calls Axioms:
Axiom 1. Mathematical potential is distributed equally among different groups, irrespective of geographic, demographic, and economic boundaries.
Axiom 2. Everyone can have joyful, meaningful, and empowering mathematical experiences.
Axiom 3. Mathematics is a powerful, malleable tool that can be shaped and used differently by various communities to serve their needs.
Axiom 4. Every student deserves to be treated with dignity and respect.
As part of his SFSU-Colombia combinatorics initiative, Ardila has provided over 200 hours of lecture videos on YouTube with additional resources for free. He is also well known for his appearances in the popular mathematics YouTube video series Numberphile.
Awards
Ardila has received many awards, among which are:
Deborah and Franklin Haimo Awards for Distinguished College or University Teaching of Mathematics (2020)
Simons Foundation Fellowship in Mathematics (2019-2020)
Premio Nacional de Matemáticas of the Colombian Mathematical Society (2019)
Fellow of the American Mathematical Society (2018)
National Science Foundation CAREER Award (2010-2016)
Selected writings
Lagrangian geometry of matroids (2020), with Graham Denham and June Huh
CAT(0) geometry, robots, and society (2019)
Hopf monoids and generalized permutahedra (2017), with Marcelo Aguiar
Todos Cuentan: Cultivating Diversity in Combinatorics (2016)
References
External links
Professional webpage at San Francisco State University
Youtube channel
Twitter
Mathematics Genealogy Project
Google Scholar c |
https://en.wikipedia.org/wiki/Complexities%3A%20Women%20in%20Mathematics | Complexities: Women in Mathematics is an edited volume on women in mathematics that "contains the stories and insights of more than eighty female mathematicians". It was edited by Bettye Anne Case and Anne M. Leggett, based on a collection of material from the Newsletter of the Association for Women in Mathematics, and published by Princeton University Press in 2005 ().
Topics
The book contains over 100 articles, by over 70 authors, divided into five sections. The first of these, "Inspiration", discusses the work of famous women in mathematics
(such as Sofya Kovalevskaya, Julia Robinson, and Emmy Noether) and of women mathematicians from the 18th and 19th centuries, offering insights into their personal life as well as their mathematics. Next, "Joining Together" covers the history of the Association for Women in Mathematics and related topics in the organization of women in mathematics including European Women in Mathematics
and the participation of women at the International Congress of Mathematicians.
The middle section, "Choices and Challenges", covers the problems facing women in contemporary mathematics, and includes a statistical quantification of these problems by Case and Leggett. "Celebration" is a collection of plenary talks and other materials from the Olga Taussky-Todd Celebration of Careers for Women in Mathematics, a conference held in 1999 to celebrate women in mathematics; its plenary speakers were , Evelyn Boyd Granville, Lisa Goldberg, Fern Hunt, Diane Lambert, Cathleen Synge Morawetz, Linda Petzold, Helene Shapiro, Richard S. Varga, Margaret H. Wright, and Lani Wu. The final chapter, "Into a New Century", consists of essays by the youg women mathematicians of the time the book was published, many of them in non-academic careers. A collection of photographs from 1975 to 2003 is included as an appendix.
Despite its material on the difficulties faced by women in mathematics, the tone of the book is "factual and upbeat", in many cases covering ordinary mathematical careers with no overt discrimination, and celebratory rather than encyclopedic.
Audience and reception
The book is aimed at any woman interested in a mathematical career and anyone else "interested in the struggle and development of female mathematicians", and is "intended to encourage young women to enter mathematics". Reviewer Peggy Kidwell suggests that it would be of interest to historians of mathematics in its documentation of many current practices. And reviewer Shandelle Henson recommends it to all professional mathematicians, to provide history and context to the struggles still faced by some of their students, to help face down their own prejudices, and to avoid backsliding in the progress we have made as a society to reduce the obstacles for women in mathematics.
A small complaint of Kidwell is that there is no bibliography of related literature on women in mathematics. A. E. L. Davis, a British reviewer, criticizes the US-centric focus of the book, as d |
https://en.wikipedia.org/wiki/Andrew%20Sutherland%20%28mathematician%29 | Andrew Victor Sutherland is an American mathematician and Principal Research Scientist at the Massachusetts Institute of Technology. His research focuses on computational aspects of number theory and arithmetic geometry. He is known for his contributions to several projects involving large scale computations, including the Polymath project on bounded gaps between primes, the L-functions and Modular Forms Database, the sums of three cubes project, and the computation and classification of Sato-Tate distributions.
Education and career
Sutherland earned a bachelor's degree in mathematics from MIT in 1990. Following an entrepreneurial career in the software industry he returned to MIT and completed his doctoral degree in mathematics in 2007 under the supervision of Michael Sipser and Ronald Rivest, winning the George M. Sprowls prize for his thesis. He joined the MIT mathematics department as a Research Scientist in 2009, and was promoted to Principal Research Scientist in 2011.
He is one of the principal investigators in the Simons Collaboration on Arithmetic Geometry, Number Theory, and Computation, a large multi-university collaboration involving Boston University, Brown, Harvard, MIT, and Dartmouth College, and he currently serves as an Associate Editor of Mathematics of Computation, Editor in Chief of Research in Number Theory, Managing Editor of the L-functions and Modular Forms Database, and President of the Number Theory Foundation.
Contributions
Sutherland has developed or improved several methods for counting points on elliptic curves and hyperelliptic curves, that have applications to elliptic curve cryptography, hyperelliptic curve cryptography, elliptic curve primality proving, and the computation of L-functions. These include improvements to the Schoof–Elkies–Atkin algorithm that led to new point-counting records, and average polynomial-time algorithms for computing zeta functions of hyperelliptic curves over finite fields, developed jointly with David Harvey.
Much of Sutherland's research involves the application of fast point-counting algorithms to numerically investigate generalizations of the Sato-Tate conjecture regarding the distribution of point counts for a curve (or abelian variety) defined over the rational numbers (or a number field) when reduced modulo prime numbers of increasing size.. It is conjectured that these distributions can be described by random matrix models using a "Sato-Tate group" associated to the curve by a construction of Serre. In 2012 Francesc Fite, Kiran Kedlaya, Victor Rotger and Sutherland classified the Sato-Tate groups that arise for genus 2 curves and abelian varieties of dimension 2, and in 2019 Fite, Kedlaya, and Sutherland announced a similar classification to abelian varieties of dimension 3.
In the process of studying these classifications, Sutherland compiled several large data sets of curves and then worked with Andrew Booker and others to compute their L-functions and incorporate |
https://en.wikipedia.org/wiki/Andrew%20Sutherland | Andrew Sutherland may refer to:
Andrew Sutherland (mathematician), American mathematician specializing in number theory
Andrew Sutherland (politician) (1882–1961), New Zealand politician |
https://en.wikipedia.org/wiki/Romanov%27s%20theorem | In mathematics, specifically additive number theory, Romanov's theorem is a mathematical theorem proved by Nikolai Pavlovich Romanov. It states that given a fixed base , the set of numbers that are the sum of a prime and a positive integer power of has a positive lower asymptotic density.
Statement
Romanov initially stated that he had proven the statements "In jedem Intervall (0, x) liegen mehr als ax Zahlen, welche als Summe von einer Primzahl und einer k-ten Potenz einer ganzen Zahl darstellbar sind, wo a eine gewisse positive, nur von k abhängige Konstante bedeutet" and "In jedem Intervall (0, x) liegen mehr als bx Zahlen, weiche als Summe von einer Primzahl und einer Potenz von a darstellbar sind. Hier ist a eine gegebene ganze Zahl und b eine positive Konstante, welche nur von a abhängt". These statements translate to "In every interval there are more than numbers which can be represented as the sum of a prime number and a -th power of an integer, where is a certain positive constant that is only dependent on " and "In every interval there are more than numbers which can be represented as the sum of a prime number and a power of . Here is a given integer and is a positive constant that only depends on " respectively. The second statement is generally accepted as the Romanov's theorem, for example in Nathanson's book.
Precisely, let and let , . Then Romanov's theorem asserts that .
History
Alphonse de Polignac wrote in 1849 that every odd number larger than 3 can be written as the sum of an odd prime and a power of 2. (He soon noticed a counterexample, namely 959.) This corresponds to the case of in the original statement. The counterexample of 959 was, in fact, also mentioned in Euler's letter to Christian Goldbach, but they were working in the opposite direction, trying to find odd numbers that cannot be expressed in the form.
In 1934, Romanov proved the theorem. The positive constant mentioned in the case was later known as Romanov's constant. Various estimates on the constant, as well as , has been made. The history of such refinements are listed below. In particular, since is shown to be less than 0.5 this implies that the odd numbers that cannot be expressed this way has positive lower asymptotic density.
Generalisations
Analogous results of Romanov's theorem has been proven in number fields by Riegel in 1961. In 2015, the theorem was also proven for polynomials in finite fields. Also in 2015, an arithmetic progression of Gaussian integers that are not expressible as the sum of a Gaussian prime and a power of is given.
References
Theorems in number theory
Additive number theory |
https://en.wikipedia.org/wiki/Filter%20quantifier | In mathematics, a filter on a set informally gives a notion of which subsets are "large". Filter quantifiers are a type of logical quantifier which, informally, say whether or not a statement is true for "most" elements of Such quantifiers are often used in combinatorics, model theory (such as when dealing with ultraproducts), and in other fields of mathematical logic where (ultra)filters are used.
Background
Here we will use the set theory convention, where a filter on a set is defined to be an order-theoretic filter in the poset that is, a subset of such that:
and ;
For all we have ;
For all if then
Recall a filter on is an ultrafilter if, for every either or
Given a filter on a set we say a subset is -stationary if, for all we have
Definition
Let be a filter on a set We define the filter quantifiers and as formal logical symbols with the following interpretation:
is -stationary
for every first-order formula with one free variable. These also admit alternative definitions as
When is an ultrafilter, the two quantifiers defined above coincide, and we will often use the notation instead. Verbally, we might pronounce as "for -almost all ", "for -most ", "for the majority of (according to )", or "for most (according to )". In cases where the filter is clear, we might omit mention of
Properties
The filter quantifiers and satisfy the following logical identities, for all formulae :
Duality:
Weakening:
Conjunction:
Disjunction:
If are filters on then:
Additionally, if is an ultrafilter, the two filter quantifiers coincide: Renaming this quantifier the following properties hold:
Negation:
Weakening:
Conjunction:
Disjunction:
In general, filter quantifiers do not commute with each other, nor with the usual and quantifiers.
Examples
If is the trivial filter on then unpacking the definition, we have and This recovers the usual and quantifiers.
Let be the Fréchet filter on an infinite set Then, holds iff holds for cofinitely many and holds iff holds for infinitely many The quantifiers and are more commonly denoted and respectively.
Let be the "measure filter" on generated by all subsets with Lebesgue measure The above construction gives us "measure quantifiers": holds iff holds almost everywhere, and holds iff holds on a set of positive measure.
Suppose is the principal filter on some set Then, we have and
If is the principal ultrafilter of an element then we have
Use
The utility of filter quantifiers is that they often give a more concise or clear way to express certain mathematical ideas. For example, take the definition of convergence of a real-valued sequence: a sequence converges to a point if
Using the Fréchet quantifier as defined above, we can give a nicer (equivalent) definition:
Filter quantifiers are especially useful in constructions involving filters. As an example, suppose that has a binary operation defined on i |
https://en.wikipedia.org/wiki/1925%E2%80%9326%20Rochdale%20A.F.C.%20season | The 1925–26 season saw Rochdale compete for their 5th season in the Football League Third Division North.
Statistics
|}
Final league table
Competitions
Football League Third Division North
FA Cup
Lancashire Cup
Manchester Cup
References
Rochdale A.F.C. seasons
Rochdale |
https://en.wikipedia.org/wiki/CoCo%20Vandeweghe%20career%20statistics | This is a list of career statistics of American tennis player CoCo Vandeweghe since her professional debut in 2008. Vandeweghe has won two singles and four WTA doubles titles on the WTA Tour, one singles WTA Challenger and one doubles Challenger, as well as two ITF singles and six doubles ITF tournaments. In 2018 she won her first Grand Slam title; partnering Ash Barty in women's doubles at the US Open. She also reached two Grand Slam mixed-doubles finals in 2016 at the Australian Open and the US Open.
Performance timelines
Only main-draw results in WTA Tour, Grand Slam tournaments, Fed Cup/Billie Jean King Cup and Olympic Games are included in win–loss records.
Singles
Current after the 2023 ATX Open
Doubles
Mixed doubles
Significant finals
Grand Slam finals
Doubles: 1 (1 title)
Mixed doubles: 2 (2 runner-ups)
Premier Mandatory/Premier 5 finals
Doubles: 3 (2 titles, 1 runner-up)
WTA Elite Trophy finals
Singles: 1 (1 runner-up)
WTA career finals
Singles: 6 (2 titles, 4 runner–ups)
Doubles: 7 (4 titles, 3 runner–ups)
Team competition
Fed Cup/Billie Jean King Cup participation
Current through the 2020 Fed Cup qualifying round
Singles (8–4)
Doubles (5–1)
WTA Challenger finals
Singles: 2 (1 title, 1 runner-up)
Doubles: 1 (1 title)
ITF Circuit finals
Singles: 6 (2 titles, 4 runner–ups)
Doubles: 6 (6 titles)
Head-to-head records
Record against top-10 players
Vandeweghe's record against players who at some point in their careers have been ranked in the top 10 (not necessarily when they faced each other). Active players are in boldface.
No. 1 wins
Top 10 wins
Notes
References
External links
CoCo Vandeweghe at the Women's Tennis Association
CoCo Vandeweghe at the International Tennis Federation
Vandeweghe, Coco |
https://en.wikipedia.org/wiki/Warleson | Warleson Stellion Lisboa Oliveira (born 31 August 1996), commonly known as Warleson, is a Brazilian footballer who currently plays for Cercle Brugge.
Career statistics
Club
Notes
References
External links
1996 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
Men's association football goalkeepers
Campeonato Brasileiro Série B players
Belgian Pro League players
Club Athletico Paranaense players
Sampaio Corrêa Futebol Clube players
Cercle Brugge K.S.V. players
Expatriate men's footballers in Belgium
Brazilian expatriate sportspeople in Belgium |
https://en.wikipedia.org/wiki/Sarah%20B.%20Hart | Sarah B. Hart is a British mathematician specialising in group theory. She is a professor of mathematics at Birkbeck, University of London and the Head of Mathematics and Statistics at Birkbeck.
In 2020, she was appointed to what may be the oldest chair in mathematics in Britain, the Gresham Professor of Geometry in Gresham College. She is the first woman to hold this position "since the chair was established in 1597".
Hart is a keen expositor of mathematics: she has written about the mathematics of Moby-Dick, and her work has been featured in websites like 'Theorem of the Day'.
Education and career
While still in secondary school, Hart published an exploration (undertaken with her sister) into extending Euler's polyhedral formula to four dimensions.
Hart read mathematics as an undergraduate at Balliol College, Oxford, and has an MSc in Mathematics from the University of Manchester. Her doctorate, from the University of Manchester Institute of Science and Technology (UMIST), addressed Coxeter Groups: Conjugacy Classes and Relative Dominance, under the supervision of Peter Rowley.
She remained in Manchester on an EPSRC research fellowship and then a temporary teaching position before obtaining a position as lecturer at Birkbeck in 2004. She was promoted to professor in 2013 and became head of the Department of Economics, Mathematics and Statistics in 2016.
She is also president of the British Society for the History of Mathematics.
Bibliography
References
Year of birth missing (living people)
Living people
British mathematicians
British women mathematicians
Group theorists
Alumni of the University of Oxford
Alumni of the University of Manchester
Academics of Birkbeck, University of London
Professors of Gresham College
People educated at the City of London School for Girls |
https://en.wikipedia.org/wiki/Regina%20Nuzzo | Regina Nuzzo is a professor of statistics at Gallaudet University in Washington D.C., a liberal arts school for deaf and hard-of-hearing students. She also writes articles about the importance of statistical and science communication and is an advocate for people with disabilities in the science and technology field.
Education
Nuzzo graduated from the University of South Florida with a Bachelor's degree in industrial engineering and went on to obtain her Ph.D in statistics from Stanford University in 2004, supervised by Richard A. Olshen. Her dissertation was written on the usage of stochastic models in bio-chemistry.
Nuzzo also graduated from the University of California Santa Cruz's science writing program, where she learned how to write effectively for a variety of audiences about science and technology.
Career
Nuzzo has been a faculty member at Gallaudet University since 2006. She has written multiple articles for publication in major magazines, including WIRED magazine, the New York and Los Angeles Times, as well as Reader's Digest. In addition to teaching, she gives seminars about statistics, which have been hosted at the University of Washington, the University of Maryland, and Harvard University.
In 2019, Nuzzo was appointed the Senior Advisor for Statistics Communication and Media Innovation for the American Statistical Association.
Awards
In 2014, Nuzzo was awarded the Excellence in Statistical Reporting Award (ESRA) by the American Statistical Association for her article in Nature magazine about statistical p-values.
Notable popular press work
"Standing Strong", Cancer Today - 2013
"The Future of Election Forecasting", Scientific American - 2014
"Regrown nerves boost bionic ears", Nature - 2014
"How scientists fool themselves - and how they can stop", Nature - 2015
"What Happens When Scientists Experiment on Themselves?" - Reader's Digest - 2016
"When courtroom science goes wrong - and how stats can fix it", Knowable Magazine - 2018
Notable academic journal articles
"Intracellular reduction of selenite into glutathione peroxidase... " - US National Library of Medicine - 2000
"Vestibular Dysfunction in DFNB1 Deafness" - US National Library of Medicine - 2011
References
Gallaudet University faculty
Living people
Year of birth missing (living people)
American statisticians
Women statisticians
Stanford University alumni
University of South Florida alumni |
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