From Determinant To Tensor by William Fleetwood Sheppard - PDF

About this book :-
"From Determinant to Tensor" by "William Fleetwood Sheppard" is a concise yet insightful mathematics book that explains how algebraic ideas evolved from classical determinants to the broader and more powerful concept of tensors. Written during a key transitional period in mathematical history, the book focuses on understanding structure and meaning rather than heavy computation. It is especially useful for readers interested in how modern algebra grew out of earlier methods. The book begins with a clear discussion of "determinants" and their role in linear transformations, then gradually extends these ideas to matrices and multilinear expressions. Sheppard carefully shows why determinants alone are not sufficient for more complex problems, leading naturally to the introduction of "tensors". This logical progression helps readers see the deep connections between different algebraic tools. Rather than serving as a practical manual, the book emphasizes theory and conceptual clarity. It is best suited for advanced students, researchers, and historians of mathematics who want to understand the foundations of "linear algebra" and "tensor theory". Today, the book remains valuable for its clear exposition and for documenting the historical shift toward "abstract algebra" and more general mathematical structures.

Book Detail :-
Title: From Determinant To Tensor by William Fleetwood Sheppard - PDF
Publisher: Oxford Clarendon Press
Year: 1923
Pages: 136
Type: PDF
Language: English
ISBN-10 #: 033203769X
ISBN-13 #: 978-0332037691
License: Public Domain Work
Amazon: Amazon

About Author :-
The author William Fleetwood Sheppard (1863–1936) was a British mathematician and statistician known for his work in "statistics", "algebra", and mathematical theory. Educated at Cambridge, he made lasting contributions to data analysis, most famously "Sheppard’s corrections", and was respected for his clear and logical approach to mathematics. Sheppard also explored theoretical ideas in "linear algebra", connecting "determinants" to early "tensor theory". His writing helped bridge classical methods with emerging "abstract algebra", making his work valuable to both mathematicians and historians.

Book Contents :-
0. Introduction PART-I DETERMINANTS 1. Origin of determinants 2. Properties of determinants 3. Solution of simultaneous equations 4. Properties of determinants (continued) 5. The tensor notation PART-II SETS 6. Sets of quantities 7. Related sets of variables 8. Differential relations of sets 9. Examples from the theory of statistics 10. Tensors in the theory of relativity A. Product of determinants B. Index of Symbols C. General Index

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