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Historical Projects in Discrete Mathematics and Computer Science
"... A course in discrete mathematics is a relatively recent addition, within the last 30 or 40 years, to the modern American undergraduate curriculum, born out of a need to instruct computer science majors in algorithmic thought. The roots of discrete mathematics, however, are as old as mathematics itse ..."
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A course in discrete mathematics is a relatively recent addition, within the last 30 or 40 years, to the modern American undergraduate curriculum, born out of a need to instruct computer science majors in algorithmic thought. The roots of discrete mathematics, however, are as old as mathematics itself, with the notion of counting a discrete operation, usually cited as the first mathematical development
The Bridge Between The Continuous And The Discrete Via Original Sources
"... this paper we summarize the story told through original sources from our chapter on the relationship between the continuous and the discrete, hinging historically on two interlocking themes: the search for formulas for sums of numerical powers, and Euler's development of his summation formula in rel ..."
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this paper we summarize the story told through original sources from our chapter on the relationship between the continuous and the discrete, hinging historically on two interlocking themes: the search for formulas for sums of numerical powers, and Euler's development of his summation formula in relation to sums of infinite series
A Graduate Course on the Role of History in Teaching Mathematics
, 2002
"... Algebra (Daniele Richardson, NMSU) Abstract Algebra, Arthur Cayley Appendix to "Restoring the Square: The Methods of AlJabr" (Daniele Richardson, NMSU) Algebra and Geometry, alKhowarizmi Using Diophantus of Alexandria to Teach Algebra (Shelly Hangen, NMSU) Algebra, Diophantus Using Stigler's "D ..."
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Algebra (Daniele Richardson, NMSU) Abstract Algebra, Arthur Cayley Appendix to "Restoring the Square: The Methods of AlJabr" (Daniele Richardson, NMSU) Algebra and Geometry, alKhowarizmi Using Diophantus of Alexandria to Teach Algebra (Shelly Hangen, NMSU) Algebra, Diophantus Using Stigler's "Diet Problem" to Teach Linear Programming (Rumiya Masagutova, NMSU) Linear Programming, George Stigler Logic Through the Looking Glass: Learning the Basics of Symbolic Logic Through the Works of Lewis Carroll (Gloria Johnson, NMSU) Symbolic Logic, Lewis Carroll Navigation and Map Making (Karen Ondo, NMSU) Geometry, Trigonometry, and Calculus, Gerardus Mercator and Edward Wright Napierian Logarithms: Who, When and How (Mary Williams, NMSU) Logarithms, John Napier The Theory of Galois: A Historical Approach (Rebecca Pablo, NMSU) Galois Theory, Solutions of Equations, Evariste Galois Appendix 2: Critique of modules Math 561, Spring 1998 Critique of Modules Consider these questions: 1. W...
A Project in Algorithms based on a Primary Historical Source about Catalan Numbers
 Proceedings of the ThirtySeventh SIGCSE Symposium on Computer Science Education
"... We discuss a project based on an original source from 1838 by Gabriel Lamé, which was used to teach dynamic programming in an Algorithms and Data Structures course for junior level computer science students. The project was developed as part of a group effort at New Mexico State University on using ..."
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We discuss a project based on an original source from 1838 by Gabriel Lamé, which was used to teach dynamic programming in an Algorithms and Data Structures course for junior level computer science students. The project was developed as part of a group effort at New Mexico State University on using original historical sources in teaching. The project is based on an excerpt from a letter of Monsieur Lamé to Monsieur Liouville on the question: Given a convex polygon, in how many ways can one partition it into triangles by means of diagonals? A variety of tasks in the project, which includes reading, writing, proving statements by mathematical induction, deriving formulas, writing computer programs and analyzing and comparing them for efficiency, help students to develop verbal, analytical and discrete mathematics skills necessary for computer science. We also discuss student reactions to the project and to learning from historical sources. Categories and Subject Descriptors
“Voici ce que j’ai trouvé:” Sophie Germain’s grand plan to prove Fermat’s Last Theorem
, 2010
"... A study of Sophie Germain’s extensive manuscripts on Fermat’s Last Theorem calls for a reassessment of her work in number theory. There is much in these manuscripts beyond the single theorem for Case 1 for which she is known from a published footnote by Legendre. Germain had a fullyfledged, highly ..."
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A study of Sophie Germain’s extensive manuscripts on Fermat’s Last Theorem calls for a reassessment of her work in number theory. There is much in these manuscripts beyond the single theorem for Case 1 for which she is known from a published footnote by Legendre. Germain had a fullyfledged, highly developed, sophisticated plan of attack on Fermat’s Last Theorem. The supporting algorithms she invented for this plan are based on ideas and results discovered independently only much later by others, and her methods are quite different from any of Legendre’s. In addition to her program for proving Fermat’s Last Theorem in its entirety, Germain also made major efforts at proofs for particular families of exponents. The isolation Germain worked in, due in substantial part to her difficult position as a woman, was perhaps sufficient that much of this extensive and impressive work may never have been studied and understood by anyone.
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"... Sums of numerical powers in discrete mathematics: a twothousand year journey ..."
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Sums of numerical powers in discrete mathematics: a twothousand year journey
TEACHING WITH PRIMARY HISTORICAL SOURCES: SHOULD IT GO MAINSTREAM? CAN IT?
"... Many are now teaching mathematics directly with primary historical sources, in a variety of courses and levels. How far should this be taken? Should we adapt or redesign standard courses to a completely historical approach, chie‡y from primary sources? If so, what are the obstacles to achieving this ..."
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Many are now teaching mathematics directly with primary historical sources, in a variety of courses and levels. How far should this be taken? Should we adapt or redesign standard courses to a completely historical approach, chie‡y from primary sources? If so, what are the obstacles to achieving this? Materials? Instructor attitudes? What should and can we do about such things? 1