Introduction To Higher Algebra by Maxime Boucher - PDF
About this book :-
"Introduction to Higher Algebra" by Maxime Bôcher is a classic "algebra textbook" aimed at advanced students who have mastered elementary algebra. It provides a comprehensive introduction to higher-level algebraic concepts, bridging traditional algebra with modern topics such as matrices, determinants, and forms. The book emphasizes clarity, logical progression, and systematic presentation, making it a valuable resource for both classroom study and "self-study".
The textbook covers essential topics including "polynomials", factorization, symmetric functions, and the theory of invariants. It also explores "matrices", determinants, and linear equations, providing a solid foundation in linear algebra. Additionally, the book introduces quadratic and bilinear forms, including classification and geometric interpretations, giving students the tools to approach abstract algebraic structures. Numerous worked examples and exercises reinforce understanding and help develop problem-solving skills, ensuring readers build strong mastery of "algebraic concepts".
Historically, Bôcher’s work has been influential in "mathematics education", serving as a bridge between classical algebra and more abstract, modern theories. Its rigorous yet accessible approach continues to make it a reference for students, educators, and anyone seeking to deepen their understanding of higher algebra. Today, it remains a foundational text for studying "higher algebra" and developing advanced mathematical reasoning.
Book Detail :-
Title:
Introduction To Higher Algebra by Maxime Boucher - PDF
Publisher:
The Macmillan Company
Year:
1907
Pages:
332
Type:
PDF
Language:
English
ISBN-10 #:
9391270840
ISBN-13 #:
978-9391270841
License:
Public Domain Work
Amazon:
Amazon
About Author :-
The author
Maxime Boucher
(1867–1918) was an influential American mathematician known for his work in "higher algebra" and mathematical analysis. He studied at Harvard University and Göttingen, later becoming a professor at Harvard. Bôcher contributed significantly to "mathematics education" through teaching, research, and textbooks. His most notable work, "Introduction to Higher Algebra", covers "polynomials", matrices, determinants, quadratic and bilinear forms, and algebraic factorization. Bôcher’s writings emphasize clarity and logical progression, helping students understand "algebraic concepts". His contributions to "polynomials & matrices" and differential equations continue to influence mathematics instruction and research today.
Book Contents :-
1. Polynomials and Their Most Fundamental Properties
2. A Few Properties of Determinants
3. The Theory of Linear Dependence
4. Linear Equations
5. Some Theorems Concerning the Rank of a Matrix
6. Linear Transformations and the Combination of Matrices
7. Invariants: First Principles and Illustrations
8. Bilinear Forms
9. Geometric Introduction to Quadratic Forms
10. Quadratic Forms
11. Real Quadratic Forms
12. The System of a Quadratic Form and Linear Forms
13. Pairs of Quadratic Forms
14. Some Properties of Polynomials in General
15. Factors and Common Factors of Polynomials in One Variable and of Binary Forms
16. Factors of Polynomials in Two or More Variables
17. General Theorems on Integral Rational Invariants
18. Symmetric Polynomials
19. Polynomials Symmetric in Pairs of Variables
20. Elementary Divisors and the Equivalence of ?-Matrices
21. Equivalence and Classification of Pairs of Bilinear Forms and Collineations
22. Equivalence and Classification of Pairs of Quadratic Forms
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