Smoryński Craig. History of Mathematics: A Supplement

Springer, 2008. — vi, 269 p. — ISBN 978-0-387-75480-2, 978-0-387-75481-9.General textbooks, attempting to cover three thousand or so years of mathematical history, must necessarily oversimplify just about everything, the practice of which can scarcely promote a critical approach to the subject. To counter this, History of Mathematics offers deeper coverage of key select topics, providing students with material that could encourage more critical thinking. It also includes the proofs of important results which are typically neglected in the modern history of mathematics curriculum.An Initial AssignmentAbout This Book
Annotated Bibliography
General Remarks
General Reference Works
General Biography
General History of Mathematics
History of Elementary Mathematics
Source Books
Multiculturalism
Arithmetic
Geometry
Calculus
Women in Science
Miscellaneous Topics
Special Mention
PhilatelyFoundations of Geometry
The Theorem of Pythagoras
The Discovery of Irrational Numbers
The Eudoxian Response
The Continuum from Zeno to Bradwardine
Tiling the Plane
Bradwardine RevisitedThe Construction Problems of Antiquity
Some Background
Unsolvability by Ruler and Compass
Conic Sections
Quintisection
Algebraic Numbers
Petersen Revisited
Concluding RemarksA Chinese Problem
The Cubic Equation
The Solution
Examples
The Theorem on the Discriminant
The Theorem on the Discriminant Revisited
Computational Considerations
One Last ProofHorner’s Method
Horner’s Method
Descartes’ Rule of Signs
De Gua’s Theorem
Concluding RemarksSome Lighter Material
North Korea’s Newton Stamps
A Poetic History of Science
Drinking Songs
Concluding RemarksSmall Projects
Dihedral Angles
Inscribing Circles in Right Triangles
cos 9º
Old Values of π
Using Polynomials to Approximate π
π à la Horner
Parabolas
Finite Geometries and Bradwardine’s Conclusion 38
Root Extraction
Statistical Analysis
The Growth of Science
ProgrammingTrue PDF