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Thomas W. Hungerford | |
---|---|

Born | Oak Park, Illinois | March 21, 1936

Died | November 28, 2014 78) St. Louis, Missouri | (aged

Nationality | American |

Alma mater | University of Chicago |

Scientific career | |

Fields | Algebra Education |

Institutions | University of Washington, Cleveland State University, St. Louis University |

Doctoral advisor | Saunders Mac Lane |

**Thomas William Hungerford** (March 21, 1936 – November 28, 2014)^{ [1] } was an American mathematician who worked in algebra and mathematics education. He is the author or coauthor of several widely used^{ [2] } and widely cited^{ [3] } textbooks covering high-school to graduate-level mathematics. From 1963 until 1980 he taught at the University of Washington and then at Cleveland State University until 2003. From 2003–2014 he was at Saint Louis University. Hungerford had a special interest in promoting the use of technology to teach mathematics.

**Algebra** is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. It includes everything from elementary equation solving to the study of abstractions such as groups, rings, and fields. The more basic parts of algebra are called elementary algebra; the more abstract parts are called abstract algebra or modern algebra. Elementary algebra is generally considered to be essential for any study of mathematics, science, or engineering, as well as such applications as medicine and economics. Abstract algebra is a major area in advanced mathematics, studied primarily by professional mathematicians.

In contemporary education, **mathematics education** is the practice of teaching and learning mathematics, along with the associated scholarly research.

The **University of Washington** is a public research university in Seattle, Washington.

Hungerford did his undergraduate work at the College of the Holy Cross and defended his Ph.D. thesis at the University of Chicago in 1963 (advised by Saunders Mac Lane). Throughout his career he wrote more than a dozen widely used mathematics textbooks, ranging from high school to graduate level.^{ [1] }

The **University of Chicago** is a private research university in Chicago, Illinois. The university is composed of an undergraduate college, various graduate programs and interdisciplinary committees organized into five academic research divisions and seven professional schools. Beyond the arts and sciences, Chicago is also well known for its professional schools, which include the Pritzker School of Medicine, the Booth School of Business, the Law School, the School of Social Service Administration, the Harris School of Public Policy Studies, the Divinity School and the Graham School of Continuing Liberal and Professional Studies. The university holds top-ten positions in various national and international rankings.

**Saunders Mac Lane** was an American mathematician who co-founded category theory with Samuel Eilenberg.

- 1974 Algebra (Graduate Texts in Mathematics #73). Springer Verlag. ISBN 3-540-90518-9

The **International Standard Book Number** (**ISBN**) is a numeric commercial book identifier which is intended to be unique. Publishers purchase ISBNs from an affiliate of the International ISBN Agency.

- 1997 Abstract Algebra: An Introduction, 2nd Edition. Cengage. ISBN 0-03-010559-5
- 2005 Contemporary College Algebra and Trigonometry, 2nd Edition. Cengage. ISBN 0-534-46665-6
- 2005 Contemporary College Algebra, 2nd Edition. Cengage. ISBN 0-534-46656-7
- 2006 Contemporary Trigonometry. Cengage. ISBN 0-534-46638-9
- 2009 Contemporary Precalculus, 5th Edition (with Douglas J. Shaw). Cengage. ISBN 0-495-55441-3
- 2011 Mathematics with Applications, 10th Edition (with Margaret L. Lial and John P. Holcomb, Jr). Pearson. ISBN 0-321-64632-0
- 2011 Finite Mathematics with Applications, 10th Edition (with Margaret L. Lial and John P. Holcomb, Jr). Pearson. ISBN 0-321-64554-5
- 2013 Abstract Algebra: An Introduction, 3rd Edition, Cengage. ISBN 1-111-56962-2

- 2002 Precalculus: A Graphing Approach (with Irene Jovell and Betty Mayberry). Holt, Rinehart & Winston. ISBN 0-03-056511-1

In abstract algebra, a **normal subgroup** is a subgroup that is invariant under conjugation by members of the group of which it is a part. In other words, a subgroup *H* of a group *G* is normal in *G* if and only if *gH* = *Hg* for all *g* in *G*. The definition of normal subgroup implies that the sets of left and right cosets coincide. In fact, a seemingly weaker condition that the sets of left and right cosets coincide also implies that the subgroup *H* of a group *G* is normal in *G*. Normal subgroups can be used to construct quotient groups from a given group.

In theoretical computer science and mathematics, the **theory of computation** is the branch that deals with how efficiently problems can be solved on a model of computation, using an algorithm. The field is divided into three major branches: automata theory and languages, computability theory, and computational complexity theory, which are linked by the question: *"What are the fundamental capabilities and limitations of computers?".*

In mathematics, and more specifically in naive set theory, the **range** of a function refers to either the *codomain* or the *image* of the function, depending upon usage. Modern usage almost always uses *range* to mean *image*.

In mathematics education, **precalculus** is a course that includes algebra and trigonometry at a level which is designed to prepare students for the study of calculus. Schools often distinguish between algebra and trigonometry as two separate parts of the coursework.

**Francis William Lawvere** is a mathematician known for his work in category theory, topos theory and the philosophy of mathematics.

In mathematics, an **algebraic expression** is an expression built up from integer constants, variables, and the algebraic operations. For example, 3*x*^{2} − 2*xy* + *c* is an algebraic expression. Since taking the square root is the same as raising to the power 1/2,

In mathematics, specifically in abstract algebra, a **torsion-free abelian group** is an abelian group which has no non-trivial torsion elements; that is, a group in which the group operation is commutative and the identity element is the only element with finite order. That is, multiples of any element other than the identity element generate an infinite number of distinct elements of the group.

**Harley Flanders** was an American mathematician, known for several textbooks and contributions to his fields: algebra and algebraic number theory, linear algebra, electrical networks, scientific computing.

**John E. McMurry**, born July 27, 1942, in New York City, is Professor Emeritus in the Department of Chemistry and Chemical Biology at Cornell University. He received an A.B. from Harvard University in 1964 and his Ph.D. from Columbia University in 1967 working with Gilbert Stork. Following completion of his Ph.D., he joined the faculty of the University of California, Santa Cruz in 1967 and moved to Cornell University in 1980.

The **freshman's dream** is a name sometimes given to the erroneous equation (*x* + *y*)^{n} = *x*^{n} + *y*^{n}, where *n* is a real number (usually a positive integer greater than 1). Beginning students commonly make this error in computing the power of a sum of real numbers, falsely assuming powers distribute over sums. When *n* = 2, it is easy to see why this is incorrect: (*x* + *y*)^{2} can be correctly computed as *x*^{2} + 2*xy* + *y*^{2} using distributivity (commonly known as the FOIL method). For larger positive integer values of *n*, the correct result is given by the binomial theorem.

**Paul Moritz Cohn** FRS was Astor Professor of Mathematics at University College London, 1986-9, and author of many textbooks on algebra. His work was mostly in the area of algebra, especially non-commutative rings.

In algebra, which is a broad division of mathematics, **abstract algebra** is the study of algebraic structures. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras. The term *abstract algebra* was coined in the early 20th century to distinguish this area of study from the other parts of algebra.

**Steven Roman** is a mathematician, currently Emeritus Professor of Mathematics at California State University and Lecturer in Mathematics at University of California. He is one of the main developers of umbral calculus. He has written around 40 books on mathematics and computer programming.

**Roland "Ron" Edwin Larson** is a professor of mathematics at Penn State Erie, The Behrend College, Pennsylvania. He is best known for being the author of a series of widely used mathematics textbooks ranging from middle school through the second year of college.

**Sheldon Jay Axler** is an American mathematician, professor of mathematics and the Dean of the College of Science and Engineering at San Francisco State University. He has made contributions to mathematics education, publishing several mathematics textbooks.

**Howard Kahane** was an American professor of philosophy at Bernard M. Baruch College in New York City. He was noted for promoting a popular, and non-mathematical, approach to logic, now known as informal logic. His best known publication in that area is his textbook *Logic and Contemporary Rhetoric: The Use of Reason in Everyday Life*, now at 11th edition; the 12th edition was published in 2014.

A **mathematical exercise** is a routine application of algebra or other mathematics to a stated challenge. Mathematics teachers assign mathematical exercises to develop the skills of their students. Early exercises deal with addition, subtraction, multiplication, and division of integers. Extensive courses of exercises in school extend such arithmetic to rational numbers. Various approaches to geometry have based exercises on relations of angles, segments, and triangles. The topic of trigonometry gains many of its exercises from the trigonometric identities. In college mathematics exercises often depend on functions of a real variable or application of theorems. The standard exercises of calculus involve finding derivatives and integrals of specified functions.

**Jean Prestet** (1648–1691) was a French Oratorian priest and mathematician who contributed to the fields of combinatorics and number theory.

**Linda Phillips Gilbert Saucier** is an American mathematician and textbook author, a distinguished professor emerita of mathematics and computer science at the University of South Carolina Upstate.

The **Mathematics Genealogy Project** is a web-based database for the academic genealogy of mathematicians. By 13 February 2019, it contained information on 238,725 mathematical scientists who contributed to research-level mathematics. For a typical mathematician, the project entry includes graduation year, thesis title, *alma mater*, doctoral advisor, and doctoral students.

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