An Elementary Treatise on Determinants by Lewis Carroll
An Elementary Treatise on Determinants - Table of Contents
1. Laws of Arrangement
2. Analysis of Determinants
3. Analysis of Equations
i) Consistency of equations under given conditions of evanescence of their V-blocks or B-blocks
ii) Properties of equations under given conditions of consistency
4. Tests for Consistency of Equations
5. Analysis of Blocks
i) Evanescence of blocks under given conditions
ii) Properties of blocks under given conditions of evanescence
6. Tests for Evanescence of Blocks
7. Geometrical Analysis
i) Plane Geometry
ii) Solid Geometry
8. Geometrical Tests
i) Plane Geometry
ii) Solid Geometry
A1. Method of analysing a given set of simultaneous linear equations
A2. Arithmetical computation of determinants
A3. Algebraical proof of the method of condensation
A4. Application of the method of condensation to the solution of simultaneous linear equations
A5. Solution of the problem of constructing a square block whose determinant vanishes simultaneously with a given algebraic function
TABULAR VIEW OF ANALYSIS OF EQUATIONS
i) n equations not all homogeneous
ii) n equations all homogeneous
FORMULAE
i) Algebraical
ii) Geometrical (Plane Geometry, Solid Geometry)
What You Will Learn in An Elementary Treatise on Determinants
An Elementary Treatise on Determinants: With Their Application to Simultaneous Linear Equations and Algebraical Geometry by Lewis Carroll (Charles L. Dodgson) is a meticulously crafted work that introduces the concept of determinants with remarkable simplicity and logic. While the world knows him for his literary classics, Carroll was a dedicated mathematician who sought to demystify complex subjects for beginners. Through clear explanations, a systematic structure, and orderly reasoning, he builds a foundation that allows readers to handle determinant problems with genuine confidence.
The text provides a comprehensive walkthrough of how determinants are formed, calculated, and applied within algebraic expressions. Carroll intentionally avoids unnecessary complexity, prioritizing deep understanding over rote memorization. The inclusion of worked examples and step-by-step methods makes this book an excellent resource for both self-study and classroom use, reflecting the author’s mastery in elementary algebra, determinant computation, and mathematical clarity.
Beyond its instructional utility, this book is a vital piece of history in the evolution of linear algebra education. It offers a rare window into 19th-century teaching methods and highlights Carroll’s serious contributions to the field of mathematics. Today, it remains an essential read for anyone interested in classical mathematics, foundational algebra, and the history of mathematical teaching.
Book Details & Specifications
Title:
An Elementary Treatise on Determinants by Lewis Carroll
Publisher:
Macmillan
Year:
1867
Pages:
164
Type:
PDF
Language:
English
ISBN-10 #:
1294801066
ISBN-13 #:
978-1294801061
License:
Public Domain Work
Amazon:
Amazon
About the Author: Lewis Carroll
The author Lewis Carroll
, the pen name of Charles Lutwidge Dodgson, was an English mathematician and lecturer at Oxford University. Beyond his literary fame, he was deeply committed to teaching mathematics with clarity, logical structure, and educational precision. His academic writing focused on making difficult topics understandable for students and beginners.
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