Item #:
232510402
Volume 3: Number Theory (Rigorous Elementary Mathematics, Second Edition)
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Item #:
232510402
USD 30
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Volume 3: Number Theory builds the subject from the ground up, providing complete proofs and dozens of substantive problems for practice.
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What Stands Out
Comprehensive Coverage
This edition provides an in-depth exploration of number theory concepts, making it invaluable for both students and educators seeking rigorous mathematical understanding.
Clear Explanations
Offers clear and precise explanations of complex topics, facilitating easier grasp of fundamental principles in number theory for learners at all levels.
Updated Content
Includes contemporary examples and problems, enhancing relevance and application, ensuring students are well-prepared for advanced mathematical challenges.
Product Details
- Number theory is one of the four pillars of mathematical contests and olympiads. Volume 3: Number Theory, Second Edition builds the subject from the ground up. It begins with divisibility, prime numbers, and arithmetic functions. Most of the volume is about modular arithmetic, with chapters on the classic theorems of Euler, Fermat, and Wilson, modular exponentiation, and modular power residues. There are also chapters that pay special attention to base representations of numbers and Diophantine equations. Later, these methods are applied to the study of combinatorial expressions, such as the theorems of Legendre, Kummer, and Lucas, and integers in particular forms, such as Fermat, Mersenne, and perfect numbers. Complete proofs are provided in the final chapter for the lifting the exponent lemma and Zsigmondy's theorem via cyclotomic polynomials. 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 | 8 Jun. 2026 |
| Language | English |
| Print length | 227 pages |
| ISBN-10 | 1067814205 |
| ISBN-13 | 978-1067814205 |
| Item weight | 689 g |
| Dimensions | 21.01 x 1.32 x 29.69 cm |
| Book 3 of 5 | Rigorous Elementary Mathematics, Second Edition |
Who Should Buy?
-
Students of Mathematics
Ideal for undergraduate students seeking a deep understanding of number theory concepts and rigorous mathematical proofs.
-
Teachers and Educators
Useful for teachers looking to enhance their curriculum with comprehensive number theory resources and structured problem sets.
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Self-learners
Perfect for independent learners wanting to explore number theory at an advanced level, providing clear explanations and exercises.
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Beginner Mathematicians
Not suitable for those new to mathematics due to its rigorous approach and complex concepts that require prior knowledge.
Product Description
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Customer Questions & Answers
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Question:
Who is this book intended for?
Answer: It is intended for students and teachers who have prior experience with mathematical proofs and problem-solving. -
Question:
What topics are covered in this volume?
Answer: Topics include divisibility, prime numbers, modular arithmetic, Diophantine equations, and combinatorial expressions. -
Question:
Are solutions provided for practice problems?
Answer: Yes, complete solutions are included for the substantive problems in the book.
Editorial Review
Volume 3 Number Theory Rigorous Elementary Mathematics, Second Edition offers a comprehensive exploration of number theory, making it a valuable resource for students and enthusiasts alike. Published by Existsforall Academy Inc., this engaging text is written in English and comprises 227 pages filled with rigorous mathematical concepts and details essential for a solid understanding of the subject. Readers can expect clarity and depth in the explanations, beneficial for both learning and reference. Additionally, the book's format and presentation, with its manageable dimensions of 21.01 x 1.32 x 29.69 cm, adds to the convenience, making it easy to handle for study purposes.
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Pros
- Comprehensive overview of number theory concepts
- Well-structured and easy to follow
- Suitable for both students and enthusiasts
- Clear explanations enhance understanding
- Compact and easy to handle dimensions
Cons
- Intended for readers already familiar with mathematics
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Features & Benefits
- Builds number theory from foundational concepts to advanced topics.
- Focuses heavily on modular arithmetic and classic theorems.
- Includes complete proofs and solutions for thorough understanding.
- Features dozens of practice problems to enhance problem-solving skills.
- Second edition offers additional theorems, problems, and improved diagrams.
- Ideal for students and teachers with experience in mathematical proofs.
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