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Introduction to Geometric Algebra
Geometric algebra was initiated by W.K. Clifford over 140 years ago. It unifies all branches of physics, and has found rich applications in robotics,...
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The Supergeometric Algebra: The Square Root of the Geometric Algebra
This paper gives a pedagogical account of the Supergeometric Algebra (SGA), the square root of the Geometric Algebra (GA). The fact that a spinor can...
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Linear Algebra in Data Science
This textbook explores applications of linear algebra in data science at an introductory level, showing readers how the two are deeply connected. The...
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The Struggle for Algebra
This chapter focuses on the emergence of algebra in the intended and implemented curricula of U.S. schools between 1607 and 1865. Before 1776 only a...
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A Course in Linear Algebra
Designed for senior undergraduate and graduate courses in mathematics and engineering, this self-contained textbook discusses key topics in linear...
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The Legacy of Al-Khwārazmı̄ in History of Algebra
Muḥammad ibn Mūsā al-Khwārazmı̄ is today arguably the most well-known medieval Arabic mathematician. His significant work on arithmetic, algebra, and...
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Relative Homological Algebra for Bivariant K-Theory
This survey article on relative homological algebra in bivariant K-thoery is mainly intended for readers with a background knowledge in triangulated...
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The emergence of duality in 19th-century algebra of logic
A Boolean algebra is a paradigmatic example of a structure that exhibits a particular kind of duality. Such an algebra can be defined as a set of...
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Abstract Algebra and Number Theory
The word algebra takes on a very different meaning from how it is used in school. Algebra means much more than the rules of shuffling around symbols...
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Linear Algebra Done Right
Now available in Open Access, this best-selling textbook for a second course in linear algebra is aimed at undergraduate math majors and graduate...
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Linear Algebra with Python Theory and Applications
This textbook is for those who want to learn linear algebra from the basics. After a brief mathematical introduction, it provides the standard...
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Can I Bring My Calculator to the Exam? Some Reflections on the Abstraction Level of Computer Algebra Systems
The author began working with computer algebra systems (CAS) in the 80s to perform effective computations for his Ph.D Thesis in algebra. He thought...
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Fermat and Descartes in Light of Premodern Algebra and Viète
There were two radically different algebras practiced in Europe in the time of Fermat and Descartes. One was the traditional cossic algebra grounded...
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Dimensioned Algebra: Mathematics with Physical Quantities
A rigorous mathematical theory of dimensional analysis, systematically accounting for the use of physical quantities in science and engineering,...
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Real Algebra A First Course
This book provides an introduction to fundamental methods and techniques of algebra over ordered fields. It is a revised and updated translation of...
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Excursions in Number Theory, Algebra, and Analysis
This textbook originates from a course taught by the late Ken Ireland in 1972. Designed to explore the theoretical underpinnings of undergraduate...
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Basics from Universal Algebra
The title of this book is Universal Algebraic Logic. One reading of this title is: (Universal Algebraic) Logic, meaning a stance of algebraic logic...
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A Geometric Algebra Solution to the Absolute Orientation Problem
We show here an alternative solution to the fundamental photogrammetric problem of determining Absolute Orientation by reformulating it in Geometric...