Advanced Algebra by Joseph Collins
Advanced Algebra - Table of Contents
PART I — REVIEW OF ELEMENTARY ALGEBRA
1. Review of Literal Arithmetic
2. Review of Equations, including Indeterminate Equations
3. Involution and Evolution
4. Fractional Exponent Quantities and Radicals
5. Quadratic Equations
PART II — APPLICATIONS AND THEORY
6. Graphs
7. Ratio and Proportion
8. Logarithms
9. Arithmetical and Geometrical Progressions
10. Annuities
11. Binomial Theorem
12. Inequalities
13. Reasoning in Equations, Discussion of Quadratic, Discussion of Problems
PART III — ADVANCED ALGEBRA
14. Theory of Equations and Solution of Higher Equations
15. Permutations and Combinations
16. Probability
17. Determinants
18. Limits, Infinite Series
19. Undetermined Coefficients, Partial Fractions, Continued Fractions
20. Complex Numbers
21. Graphs of Higher Equations, Applications
What You Will Learn in Advanced Algebra
"Advanced Algebra" by Joseph V. Collins is a comprehensive "algebra" textbook designed for students progressing beyond basic mathematics. It builds on elementary concepts and introduces more challenging topics with clarity, making it ideal for late high-school, technical school, or early college learners. The book emphasizes logical reasoning and practical applications to help students strengthen their "mathematical skills".
The text covers a wide range of topics, including "sequences", series, permutations, combinations, probability, determinants, "complex numbers", and higher-degree equations. Each chapter provides detailed explanations, worked examples, and exercises to reinforce understanding. Collins’ methodical approach ensures that students can follow concepts step by step, from fundamental operations to advanced problem-solving techniques.
Beyond theory, "Advanced Algebra" encourages students to apply algebraic methods to solve real-world problems, enhancing both critical thinking and analytical abilities. Its structured style, combined with practice problems and clear explanations, makes it a trusted resource for learners seeking a strong foundation in "mathematics". Whether used in the classroom or for self-study, this classic textbook remains a valuable guide for mastering advanced algebra concepts.
Book Details & Specifications
Title:
Advanced Algebra by Joseph Collins
Publisher:
Cincinnati
Year:
1913
Pages:
361
Type:
PDF
Language:
English
ISBN-10 #:
1017538425
ISBN-13 #:
978-1017538427
License:
Public Domain Work
Amazon:
Amazon
About the Author: Joseph Victor Collins
The author
Joseph Victor Collins
(1858–1943) was a renowned mathematician and educator, best known for his algebra textbooks, including "Advanced Algebra". His works were widely used in early 20th-century schools and colleges, offering a clear, structured approach to learning algebra. Collins emphasized "clarity", "rigor", and "comprehensive examples", making complex topics accessible to students. "Advanced Algebra" covers topics from "arithmetic" and "geometry" to "complex numbers", "determinants", and "probability", bridging basic and advanced algebra concepts. His textbooks remain historically significant and are valued for their classical teaching style, practical exercises, and solid foundational approach for aspiring mathematicians.
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