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 carefully written mathematics book that introduces the concept of determinants in a simple and logical way. The author’s goal is to make the subject understandable for beginners by breaking complex ideas into clear steps. The book focuses on careful definitions and orderly reasoning, helping readers gain confidence in handling determinant problems through "clear explanations", "systematic structure", and "logical thinking". The text explains how determinants are formed, how they are calculated, and how their main properties work in algebraic expressions. Carroll avoids unnecessary complexity and instead emphasizes understanding over memorization. Worked examples and step-by-step methods guide students through common problems, making the book suitable for self-study as well as classroom use. Its approach reflects the author’s strong background as a mathematician and educator, especially in "elementary algebra", "determinant computation", and "mathematical clarity". Beyond its instructional value, the book holds historical importance in the development of linear algebra education. It shows how determinants were taught in the 19th century and highlights Lewis Carroll’s serious contributions to mathematics, beyond his fame in literature. Today, the book remains useful for readers 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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