Pamela Gorkin is an American mathematician specializing in complex analysis and operator theory. She is a professor of mathematics at Bucknell University. [1]
Pamela Gorkin is an American mathematician specializing in complex analysis and operator theory. She is a professor of mathematics at Bucknell University. [1]
Gorkin earned bachelor's and master's degrees in statistics from Michigan State University in 1976. [1] She then shifted to pure mathematics for her doctoral studies, completing her Ph.D. at Michigan State in 1982, the same year she joined the Bucknell Faculty. Her dissertation, Decompositions of the Maximal Ideal Space of L, was supervised by Sheldon Axler. [1] [2]
At Bucknell, she was Presidential Professor from 2001 to 2004. [1]
With Ulrich Daepp, Gorkin is the author of the undergraduate textbook Reading, Writing, and Proving: A Closer Look at Mathematics (Springer, 2003; 2nd ed., 2011). [3]
With Daepp, Andrew Shaffer, and Karl Voss, she is the author of Finding Ellipses: What Blaschke Products, Poncelet’s Theorem, and the Numerical Range Know about Each Other (Carus Mathematical Monographs, MAA Press, 2018). The book studies a connection between Blaschke products, Poncelet's closure theorem, and the numerical range of matrices. A Blaschke product is a certain kind of mapping of the unit disk in the complex plane to itself, and the ones considered in the first part of the book have order three (they map the unit circle three-to-one to itself, so that each point on the unit circle has three preimages). These triples of preimages form triangles that are all inscribed in the unit circle, and (it turns out) they all circumscribe an ellipse. Thus, they form an infinite system of polygons inscribed in and circumscribing two conics, as Poncelet's theorem describes. The ellipse is the boundary of the numerical range of a certain matrix derived from the Blaschke product, a region within which the eigenvalues of the matrix can be found, and in this case the eigenvalues are at the foci of the ellipse. The book tells "a story of discovery" outlining these connections, extends similar results to Blaschke products of higher order, and outlines a plan for further research in this area. [4]
Gorkin was the 2018 AWM/MAA Falconer Lecturer. [5] Her lecture was on "Finding Ellipses", the topic of one of her books. She is also the recipient of Bucknell's Lindback Award for Distinguished Teaching, and the Crawford Distinguished Teaching Award of the Mathematical Association of America. [6]
An ellipsoid is a surface that can be obtained from a sphere by deforming it by means of directional scalings, or more generally, of an affine transformation.
In mathematics, a Hermitian matrix is a complex square matrix that is equal to its own conjugate transpose—that is, the element in the i-th row and j-th column is equal to the complex conjugate of the element in the j-th row and i-th column, for all indices i and j:
In the mathematical discipline of linear algebra, the Schur decomposition or Schur triangulation, named after Issai Schur, is a matrix decomposition. It allows one to write an arbitrary complex square matrix as unitarily equivalent to an upper triangular matrix whose diagonal elements are the eigenvalues of the original matrix.
Pappus of Alexandria was a Greek mathematician of Late Antiquity known for his Synagoge (Συναγωγή) or Collection, and for Pappus's hexagon theorem in projective geometry. Almost nothing is known about his life except for what can be found in his own writings, many of which are lost. Pappus apparently lived in Alexandria were he worked as a mathematics teacher to higher level students, such one named Hermodorus.
In numerical linear algebra, the QR algorithm or QR iteration is an eigenvalue algorithm: that is, a procedure to calculate the eigenvalues and eigenvectors of a matrix. The QR algorithm was developed in the late 1950s by John G. F. Francis and by Vera N. Kublanovskaya, working independently. The basic idea is to perform a QR decomposition, writing the matrix as a product of an orthogonal matrix and an upper triangular matrix, multiply the factors in the reverse order, and iterate.
Jean-Victor Poncelet was a French engineer and mathematician who served most notably as the Commanding General of the École Polytechnique. He is considered a reviver of projective geometry, and his work Traité des propriétés projectives des figures is considered the first definitive text on the subject since Gérard Desargues' work on it in the 17th century. He later wrote an introduction to it: Applications d'analyse et de géométrie.
In geometry, Poncelet's closure theorem, also known as Poncelet's porism, states that whenever a polygon is inscribed in one conic section and circumscribes another one, the polygon must be part of an infinite family of polygons that are all inscribed in and circumscribe the same two conics. It is named after French engineer and mathematician Jean-Victor Poncelet, who wrote about it in 1822; however, the triangular case was discovered significantly earlier, in 1746 by William Chapple.
The Carus Mathematical Monographs is a monograph series published by the Mathematical Association of America. Books in this series are intended to appeal to a wide range of readers in mathematics and science.
Geometry is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. Geometry is one of the oldest mathematical sciences.
The Etta Z. Falconer Lecture is an award and lecture series which honors "women who have made distinguished contributions to the mathematical sciences or mathematics education". It is sponsored by the Association for Women in Mathematics and the Mathematical Association of America. The lectures began in 1996 and were named after the mathematician Etta Z. Falconer in 2004 "in memory of Falconer's profound vision and accomplishments in enhancing the movement of minorities and women into scientific careers". The recipient presents the lecture at MathFest each summer.
In the mathematical field of linear algebra and convex analysis, the numerical range or field of values of a complex matrix A is the set
Suzanne L. Weekes is the Executive Director of the Society for Industrial and Applied Mathematics. She is also Professor of Mathematical Sciences at Worcester Polytechnic Institute (WPI). She is a co-founder of the Mathematical Sciences Research Institute Undergraduate Program.
Erica Nicole Walker is an American mathematician and the Clifford Brewster Upton Professor of Mathematics Education at Teachers College, Columbia University, where she also serves as the Chairperson of the Department of Mathematics, Science, and Technology and as the Director of the Institute for Urban and Minority Education. Walker’s research focuses on the "social and cultural factors as well as educational policies and practices that facilitate mathematics engagement, learning and performance, especially for underserved students".
Patricia Clark Kenschaft was an American mathematician. She was a professor of mathematics at Montclair State University. She is known as a prolific author of books on mathematics, as a founder of PRIMES, the Project for Resourceful Instruction of Mathematics in the Elementary School, and for her work for equity and diversity in mathematics.
Patricia D. Shure is an American mathematics educator. With Morton Brown and B. Alan Taylor, she is known for developing "Michigan calculus", a style of teaching calculus and combining cooperative real-world problem solving by the students with an instructional focus on conceptual understanding. She is a senior lecturer emerita of mathematics at the University of Michigan, where she taught from 1982 until her retirement in 2006.
Dawn Alisha Lott is an applied mathematician at Delaware State University, where she is a professor in the department of physical and computational sciences and, since 2009, the director of the university's honors program.
Bonita Valerie Saunders is an American mathematician specializing in mathematical visualization. She works at the National Institute of Standards and Technology in the Applied and Computational Mathematics Division of the Information Technology Laboratory, where she contributes to the Digital Library of Mathematical Functions as the Visualization Editor and the principal designer of visualizations and graphs.
Katherine Puckett Layton is an American mathematics educator and the author of mathematics textbooks.
Finding Ellipses: What Blaschke Products, Poncelet’s Theorem, and the Numerical Range Know about Each Other is a mathematics book on "some surprising connections among complex analysis, geometry, and linear algebra", and on the connected ways that ellipses can arise from other subjects of study in all three of these fields. It was written by Ulrich Daepp, Pamela Gorkin, Andrew Shaffer, and Karl Voss, and published in 2019 by the American Mathematical Society and Mathematical Association of America as volume 34 of the Carus Mathematical Monographs, a series of books aimed at presenting technical topics in mathematics to a wide audience.
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