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Zinovy Khokhlov
Zinovy Khokhlov

Introductory Modern Algebra: A Historical Approach

This book is designed for prospective and practicing high school mathematics teachers, but it can serve as a text for standard abstract algebra courses as well. The presentation is organized historically: the Babylonians introduced Pythagorean triples to teach the Pythagorean theorem; these were classified by Diophantus, and eventually this led Fermat to conjecture his Last Theorem. The text shows how much of modern algebra arose in attempts to prove this; it also shows how other important themes in algebra arose from questions related to teaching. Indeed, modern algebra is a very useful tool for teachers, with deep connections to the actual content of high school mathematics, as well as to the mathematics teachers use in their profession that doesn't necessarily "end up on the blackboard."

Introductory Modern Algebra: A Historical Approach


Stahl's Introductory Modern Algebra, a historical approach is worth a look for the way it takes you very early on, after a minimum of pain, to a handwaving (but satisfying for me!) understanding of some of the classic results (quadrature of the circle, constructibility of regular polygons). He also covers an offbeat topic -- the cubic equation (i.e. the next thing after the quadratic equation) -- which is surprisingly interesting (even after you apply the formula, it can take some trickery to simplify your result). But I wouldn't embark on Stahl if I wanted to learn the standard results in the standard order; consider it supplementary reading.

MATH 564 Algebraic Topology (3)First quarter of a three-quarter sequence covering classical and modern approaches; complexes and their homology theory; applications; fixed points, products and Poincare duality; axiomatic approach. Prerequisite: MATH 506 and MATH 544, or equivalent.View course details in MyPlan: MATH 564

This course will give an overview of geometry from a modern point of view. Axiomatic, analytic, transformational, and algebraic approaches to geometry will be used. The relationship between Euclidean geometry, the geometry of complex numbers, and trigonometry will be emphasized.

An historical approach to the great ideas, events, modes of thinking, and creations of the western world. The first course in this sequence will focus on developments from Antiquity through c. 1600; the second, from c. 1600 to the present. Both courses are designed to deepen historical perspective and offer opportunities to experience the power of literature and wrestle with issues of the human spirit. A set of primary texts common to all sections will serve as the focus for each course.

An historical approach to significant or characteristic events, practices, and creations from world cultures and civilizations. The first course (I) focuses on the ancient world through c. 1000; the second (II) from c. 1000 to c. 1800; the third (III) from c. 1800 to the present. All three courses include important aspects of both Western and nonwestern history and civilization, and integrate the study of the humanities and fine arts. These courses are designed to deepen historical perspective and increase cross-cultural understanding.

This course is a study of the historical development of ideas that shape modern mathematical thinking. Emphasis is placed on mathematical development and solving problems. ] Prerequisites: MATH 2414 (or MATH 2488) with a grade of 'C' or better.

Calculus on manifolds : a modern approach to classical theorems of advanced calculus Stacks QA612 .S65 Multivariable Springer Books Online Springer Books OnlineComprised of over 50,000 Springer e-books published from 2005 to date in the sciences, social sciences, and humanities. All of the books are accessible via the library catalog or directly from the Springer platform.eBrary Academic Complete Proquest eBook CentralAccess to more than 80,000 ebook titles from leading academic publishers in 16 discipline areas. Users can browse the book online, download to their computer or ereader, and save notes and annotations. > Last Updated: Jan 11, 2023 1:05 PM URL: -resources Print Page Login to LibApps Subjects: Math Login to LibApps This work by the Reed College Library is licensed under a Creative Commons CC-BY Attribution 4.0 International License.

The Discrete Applied Mathematics concentration provides the tools used in many everyday activities in science and industry. Many objects and notions in the modern world are discrete in their nature and require special methods for their study. Research directions that are based mostly on the discrete approach include: coding theory and cryptography, data protection and compression, network analysis, parallel computing, logic, theory of computation, discrete and combinatorial optimization, scheduling theory, programming language design, and many others. Continuous methods of classical mathematics are, as a rule, largely inapplicable to these areas. Many of these fields are actually at the border between mathematics and theoretical computer science. This concentration offers a number of exciting courses that are intended for those who are interested in computers and mathematics. Computer science is not limited to programming. It uses discrete mathematics methods extensively to find more efficient solutions. Discrete mathematics has grown from everyday practical problems, and knowing efficient approaches to solving them has been found to be very beneficial. 041b061a72

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