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89445596
Volume 1: Algebra (Rigorous Elementary Mathematics, Second Edition)
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Item #:
89445596
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Volume 1: Algebra sets the foundation for understanding advanced mathematics through rigorous practice and comprehensive proofs.
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What Stands Out
Rigorous Approach
This second edition emphasizes a rigorous approach to elementary mathematics, ensuring a deep understanding of algebraic concepts for students and educators alike.
Comprehensive Content
Offers extensive coverage of algebra topics, making it suitable for both beginners and advanced learners, addressing a wide range of mathematical challenges.
Enhanced Clarity
Improved explanations and examples enhance clarity, enabling learners to grasp complex ideas easily and efficiently, setting it apart from other algebra textbooks.
Product Details
- Algebra is one of the four pillars of mathematical contests and olympiads. Volume 1: Algebra, Second Edition builds the subject from the ground up. It starts by covering logic, sets, functions, and arithmetic. Then, there are chapters on indexing, ordering, and closed forms of sums and products. The floor, ceiling, fractional part, and trigonometric functions are given special attention. The book includes chapters on complex numbers in rectangular and polar form, quadratics, and polynomials. The final chapter on multivariable inequalities contains full proofs of results, such as AM-GM, Cauchy-Schwarz, rearrangement, Chebyshev, Jensen, Minkowski, Newton, Maclaurin, and more. This volume sets the foundation for the later volumes, as algebraic manipulations are a key aspect of elementary mathematics. The three recurring themes are: writing the same object in multiple ways, breaking up equality using antisymmetry, and using equivalence relations. There are dozens of substantive problems included for the reader’s practice, with complete solutions provided. This second edition includes additional theorems and problems, refreshed diagrams, and corrections. It is suggested that the book be read by students and teachers who have prior experience with mathematical proofs and problem-solving.
| Publisher | Existsforall Academy Inc. |
| Publication date | June 8, 2026 |
| Language | English |
| Print length | 197 pages |
| ISBN-10 | 1738950182 |
| ISBN-13 | 978-1738950188 |
| Item Weight | 1.33 pounds (600 grams) |
| Dimensions | 8.27 x 0.45 x 11.69 inches (21 x 1.1 x 29.7 cm) |
| Book 1 of 5 | Rigorous Elementary Mathematics, Second Edition |
Who Should Buy?
-
High School Students
Ideal for students seeking a strong foundation in algebra concepts and rigorous problem-solving techniques.
-
College Aspirants
Benefit those preparing for college-level mathematics or standardized tests requiring a solid understanding of algebra.
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Self-learners
Great resource for individuals who prefer independent study and desire a comprehensive approach to algebra.
-
Beginners
Not suitable for absolute beginners lacking prior knowledge as it may be too challenging to grasp.
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Elementary Editorial Review
Volume 1: Algebra (Rigorous Elementary Mathematics, Second Edition) is a comprehensive resource published by Existsforall Academy Inc. designed for students seeking a solid foundation in algebra. With a print length of 197 pages, this book not only covers essential algebraic concepts but is organized in a manner that supports a thorough understanding of rigorous mathematics. The book is printed in English and dimensions make it suitable for easy handling. Readers have highlighted its clarity and structured approach as significant benefits in learning. This book is a part of a five-book series, ensuring the continuity of learning in elementary mathematics.
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Pros
- Comprehensive coverage of algebra concepts
- Clarity and structured approach to learning
- Suitable for various learning levels
- Part of a detailed five-book series
- Well-organized and easy to handle
Cons
- Limited to algebra, may require additional resources for broader math topics
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Features & Benefits
- Builds algebra from foundational concepts to advanced topics.
- Includes rigorous proofs and comprehensive methods for problem-solving.
- Features key themes such as equivalence relations and algebraic manipulation.
- Includes dozens of substantive problems with complete solutions.
- Updated second edition with enhanced diagrams and additional theorems.
- Ideal for students and teachers with prior experience in mathematical proofs.
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