Determinants by Gifford Laenas Weld
Determinants - Table of Contents
1. Introduction
2. Permutations
3. Interchange of Two Elements
4. Positive and Negative Permutations
5. The Determinant Array
6. Determinant as a Function of n² Elements
7. Examples of Determinants
8. Notation
9. Determinants of the Second and Third Orders
10. Interchange of Rows and Columns
11. Interchange of Two Parallel Lines
12. Two Identical Parallel Lines
13. Multiplication by a Factor
14. A Line of Polynomial Elements
15. Composition of Parallel Lines
16. Binomial Factors
17. Cofactors and Minors
18. Development in Terms of Cofactors
19. The Zero Formulas
20. Cauchy’s Method of Development
21. Differentiation of Determinants
22. Raising the Order
23. Lowering the Order
24. Solution of Linear Equations
25. Consistency of Linear Systems
26. The Matrix
27. Homogeneous Linear Systems
28. Cofactors in a Zero Determinant
29. Sylvester’s Method of Elimination
30. The Multiplication Theorem
31. Product of Two Rectangular Arrays
32. Reciprocal Determinants
33. Linear Transformations
34. Quantics; Invariants and Covariants
35. The Discriminant
36. Composite Quadrics
37. Discriminant of a Binary Quantics as an Invariant
38. The Jacobian
39. Jacobian of Indirect Functions
40. The Jacobian as a Covariant
41. Jacobian of Implicit Functions
42. The Hessian
What You Will Learn in Determinants
"Determinants" by "Gifford Laenas Weld" is a classical mathematics textbook that provides a clear and focused study of determinant theory. Written in a traditional, proof-based style, the book aims to build a strong conceptual understanding rather than emphasize mechanical calculation. It reflects an important stage in the development of "algebra education", where determinants were taught as a central topic.
The book carefully explains the definition and properties of "determinants", including expansion methods, identities, and rules for manipulation. Weld presents each concept in a logical sequence, helping readers see how determinant theory supports the solution of linear equations and the study of matrix structure. The exposition is direct and well organized, making it accessible to students with basic algebra knowledge.
Intended mainly for undergraduate readers, the book is valued for its clarity and emphasis on "mathematical foundations". While modern courses often integrate determinants into "matrix theory" and "linear algebra", Weld’s work remains useful for understanding the classical approach and historical development of these ideas. It is especially relevant for readers interested in theory, proofs, and the evolution of determinant methods.
Book Details & Specifications
Title:
Determinants by Gifford Laenas Weld
Publisher:
J. Wiley & Sons
Year:
1906
Pages:
86
Type:
PDF
Language:
English
ISBN-10 #:
1429701153
ISBN-13 #:
978-1429701150
License:
Public Domain Work
Amazon:
Amazon
About the Author: Gifford Laenas Weld
The author
Gifford Laenas Weld
was an American mathematician and university educator known for his clear and systematic approach to higher algebra. His academic work focused on strengthening "mathematical education" by presenting complex ideas in a structured and understandable way for advanced students. He is best recognized for his contributions to "determinant theory", a core subject that later shaped modern "linear algebra". Weld’s work remains useful for understanding the "historical development" of algebraic concepts and their academic foundations.
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