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John William Theodore Youngs (usually cited as J. W. T. Youngs, known as Ted Youngs; 21 August 1910 Bilaspur, Chhattisgarh, India – 20 July 1970 Santa Cruz, California) was an American mathematician.
Youngs was the son of a missionary. He completed his undergraduate study at Wheaton College and received his PhD from Ohio State University in 1934 under Tibor Radó. He then taught for 18 years at Indiana University, where for eight years he was chair of the mathematics department. From 1964 he was a professor at the University of California, Santa Cruz, where he developed the mathematics faculty and was chair of the academic senate of the university.
Youngs worked in geometric topology, for example, questions on the Frechét-equivalence of topological maps.He is famous for the Ringel–Youngs theorem (i.e. Ringel and Youngs's 1968 proof of the Heawood conjecture), which is closely related to the analogue of the four-color theorem for surfaces of higher genus.
John Youngs was a consultant for Sandia National Laboratories, the Rand Corporation and the Institute for Defense Analyses as well as a trustee for Carver Research Foundation Institute in Tuskegee. In 1946–1947 he was a Guggenheim Fellow. At the University of Santa Cruz a mathematics prize for undergraduates in named after him.
In mathematics, the four color theorem, or the four color map theorem, states that no more than four colors are required to color the regions of any map so that no two adjacent regions have the same color. Adjacent means that two regions share a common boundary curve segment, not merely a corner where three or more regions meet. It was the first major theorem to be proved using a computer. Initially, this proof was not accepted by all mathematicians because the computer-assisted proof was infeasible for a human to check by hand. Since then the proof has gained wide acceptance, although some doubters remain.
William Paul Thurston was an American mathematician. He was a pioneer in the field of low-dimensional topology. In 1982, he was awarded the Fields Medal for his contributions to the study of 3-manifolds. From 2003 until his death he was a professor of mathematics and computer science at Cornell University.
Maurice René Fréchet was a French mathematician. He made major contributions to the topology of point sets and introduced the entire concept of metric spaces. He also made several important contributions to the field of statistics and probability, as well as calculus. His dissertation opened the entire field of functionals on metric spaces and introduced the notion of compactness. Independently of Riesz, he discovered the representation theorem in the space of Lebesgue square integrable functions. He is often referred to as the founder of the theory of abstract spaces.
Ilya Piatetski-Shapiro was a Soviet-born Israeli mathematician. During a career that spanned 60 years he made major contributions to applied science as well as pure mathematics. In his last forty years his research focused on pure mathematics; in particular, analytic number theory, group representations and algebraic geometry. His main contribution and impact was in the area of automorphic forms and L-functions.
Albert William Tucker was a Canadian mathematician who made important contributions in topology, game theory, and non-linear programming.
Gerhard Ringel was a German mathematician. He was one of the pioneers in graph theory and contributed significantly to the proof of the Heawood conjecture, a mathematical problem closely linked with the Four Color Theorem.
In graph theory, the Heawood conjecture or Ringel–Youngs theorem gives a lower bound for the number of colors that are necessary for graph coloring on a surface of a given genus. For surfaces of genus 0, 1, 2, 3, 4, 5, 6, 7, ..., the required number of colors is 4, 7, 8, 9, 10, 11, 12, 12, .... OEIS: A000934, the chromatic number or Heawood number.
In mathematics, the Heawood number of a surface is an upper bound for the number of colors that suffice to color any graph embedded in the surface.
Percy John Heawood was a British mathematician educated at Queen Elizabeth's School, Ipswich, and Exeter College, Oxford. He spent his career at Durham University, where he was appointed Lecturer in 1885. He was, successively, Censor of St Cuthbert's Society between 1897 and 1901 succeeding Frank Byron Jevons in the role, Senior Proctor of the university from 1901, Professor in 1910 and Vice-Chancellor between 1926 and 1928. He was awarded an OBE, as Honorary Secretary of the Preservation Fund, for his part in raising £120,000 to prevent Durham Castle from collapsing into the River Wear.
Dennis Parnell Sullivan is an American mathematician. He is known for work in topology, both algebraic and geometric, and on dynamical systems. He holds the Albert Einstein Chair at the City University of New York Graduate Center, and is a professor at Stony Brook University.
William "Bus" H. Jaco is an American mathematician who is known for his role in the Jaco–Shalen–Johannson decomposition theorem and is currently Regents Professor and Grayce B. Kerr Chair at Oklahoma State University and Executive Director of the Initiative for Mathematics Learning by Inquiry.
The Department of Mathematics at the University of Manchester is one of the largest unified mathematics departments in the United Kingdom, with over 90 academic staff and an undergraduate intake of roughly 400 students per year and approximately 200 postgraduate students in total. The School of Mathematics was formed in 2004 by the merger of the mathematics departments of University of Manchester Institute of Science and Technology (UMIST) and the Victoria University of Manchester (VUM). In July 2007 the department moved from the Mathematics Tower into a purpose-designed building─the first three floors of the Alan Turing Building─on Upper Brook Street. In a Faculty restructure in 2019 the School of Mathematics reverted to the Department of Mathematics. It is one of five Departments that make up the School of Natural Sciences, which together with the School of Engineering now constitutes the Faculty of Science and Engineering at Manchester.
Frederick Justin Almgren Jr. was an American mathematician working in geometric measure theory.
Stefan Emanuel "Steve" Warschawski was a mathematician, a professor and department chair at the University of Minnesota and the founder of the mathematics department at the University of California, San Diego.
Anton Kotzig was a Slovak–Canadian mathematician, expert in statistics, combinatorics and graph theory.
Joan Prince Hutchinson is an American mathematician and Professor Emerita of Mathematics from Macalester College.
In graph theory, the Poussin graph is a planar graph with 15 vertices and 39 edges. It is named after Charles Jean de la Vallée-Poussin.
Anthony Joseph Tromba is an American mathematician, specializing in partial differential equations, differential geometry, and the calculus of variations.
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 (ISBN 978-0-387-74640-1).
Pearls in Graph Theory: A Comprehensive Introduction is an undergraduate-level textbook on graph theory, by Nora Hartsfield and Gerhard Ringel. It was published in 1990 by Academic Press, Inc., with a revised edition in 1994 and a paperback reprint of the revised edition by Dover Books in 2003. The Basic Library List Committee of the Mathematical Association of America has suggested its inclusion in undergraduate mathematics libraries.