May 13, 2024
Updated July 19, 2025
14 minute read
An Introduction to Equation Solving
Equation solving is the process of finding values, known as solutions or roots, that satisfy a stated condition of equality. It is a fundamental pillar of mathematics, providing the language to describe relationships between quantities and the tools to uncover unknown values. From a student's first encounter with simple arithmetic to a researcher modeling complex systems, the ability to formulate and solve equations is an indispensable skill. It is the art of translating real-world problems into a symbolic form and then manipulating those symbols to reveal insights and answers.
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Reading list
We've selected 23 books
that we think will supplement your
learning. Use these to
develop background knowledge, enrich your coursework, and gain a
deeper understanding of the topics covered in
Equation Solving.
Provides a broad introduction to the theory and application of numerical approximation techniques, including methods for finding roots of equations and solving systems of linear and nonlinear equations. It well-respected textbook suitable for undergraduates in mathematics, science, and engineering. It's a valuable reference for practical numerical methods.
Introduces computational algebraic geometry and commutative algebra, focusing on solving systems of polynomial equations using Gröbner bases. It bridges the gap between abstract algebra and concrete computation, making it highly relevant for understanding modern techniques in equation solving. It is suitable for advanced undergraduates and graduate students.
A widely used textbook that offers a comprehensive introduction to linear algebra with a strong emphasis on applications. is excellent for gaining a broad understanding of matrix operations, vector spaces, and eigenvalues, all of which are crucial for solving linear systems. It is often used in undergraduate engineering and science programs.
A comprehensive reference covering a wide range of numerical methods, including techniques for root finding, solving linear equations, and minimizing functions. is highly practical and includes working routines, making it a valuable resource for anyone doing computational work. It is suitable for advanced undergraduates, graduate students, and working professionals.
This introductory textbook covers numerical approximation methods for solving problems of mathematical analysis, including root-finding and solving systems of equations. It's designed for entry-level courses and provides clear guidance on a range of numerical techniques. Suitable for undergraduates in mathematics, science, and engineering.
Provides a contemporary look at solving systems of polynomial equations, covering both theoretical foundations and algorithmic approaches. It is relevant for those interested in the intersection of algebra and computation, suitable for graduate students and researchers.
Provides a comprehensive treatment of traditional and recent methods for finding roots of polynomials. It covers various techniques, including Newton's method and its variations, simultaneous iterations, and matrix methods. It's a valuable resource for anyone researching or teaching polynomial root-finding.
Provides an introduction to the theory and practice of solving systems of polynomial equations. It covers topics such as Gröbner bases, resultants, and numerical homotopy methods. It good resource for graduate students and researchers interested in the computational aspects of algebraic equation solving.
Provides a rigorous introduction to linear algebra, focusing on vector spaces and linear maps. It is highly regarded for its theoretical approach, which solidifies understanding of the fundamental concepts necessary for solving systems of linear equations. It is commonly used as a textbook for undergraduate mathematics majors.
A foundational text in numerical linear algebra. provides a deep dive into the algorithms and analysis for solving linear systems, eigenvalue problems, and other matrix computations. It is an essential reference for graduate students and researchers in numerical analysis and scientific computing.
This graduate-level textbook offers a concise and modern introduction to numerical linear algebra. It focuses on the algorithmic aspects and the mathematical analysis of numerical methods for linear equations and eigenvalue problems. It good resource for deepening understanding of the numerical side of equation solving.
Provides a detailed introduction to Gröbner bases and their applications in commutative algebra and algebraic geometry. It key resource for understanding the computational techniques used to solve systems of polynomial equations. Suitable for graduate students and researchers.
Focuses on iterative methods for solving large sparse linear systems, which are common in many scientific and engineering applications. It valuable resource for graduate students and researchers working with large-scale problems. It provides in-depth coverage of state-of-the-art techniques.
(or collection of works) covers advanced numerical methods used in applied sciences. It reflects the contemporary use of scientific computing tools for solving complex problems, which often involve sophisticated equation solving techniques. It's relevant for graduate students and professionals in applied fields.
This textbook introduces root-finding methods and techniques for solving linear equation systems. It discusses minimizing computation time and memory, and is aimed at students at technical universities, engineers, and scientists. It covers methods for nonlinear equations and systems, as well as standard methods for linear systems.
A comprehensive graduate-level textbook on abstract algebra. delves deeply into algebraic structures and theories, providing a strong theoretical foundation for understanding the nature of solutions to algebraic equations, including Galois theory. It standard reference for graduate students in mathematics.
This textbook offers a solid introduction to abstract algebra, covering groups, rings, and fields. While not solely focused on equation solving, it provides the algebraic structures and theory underlying the solvability of polynomial equations. It is widely used as a textbook in undergraduate abstract algebra courses.
While not solely focused on equation solving, this book is highly relevant to contemporary topics, particularly in the context of large-scale systems and data analysis. It covers concepts in probability theory that are essential for understanding and developing algorithms for solving problems in high dimensions, which often involve solving large systems of equations. Suitable for graduate students and researchers.
Comprehensive guide to algorithm design and analysis. While not exclusively about equation solving, it covers fundamental algorithms and data structures that are essential for developing efficient computational methods for solving equations, particularly large systems. It valuable reference for students and professionals in computer science and related fields.
Explores mathematical inequalities, with the Cauchy-Schwarz inequality as a central theme. While not directly about solving equations, inequalities often arise in the analysis of solutions and in optimization problems related to equation solving. It's a problem-oriented text suitable for undergraduates and can deepen analytical skills.
Classic text on problem-solving techniques in mathematics, often used for preparing for mathematical competitions. It presents a wide array of strategies that can be applied to solving various types of equations and mathematical problems. It's particularly useful for high school and early undergraduate students looking to improve their problem-solving skills.
Offers a historical perspective on the development of various areas of mathematics, including algebra and the concept of solving equations. While not a technical guide, it provides valuable context and can enrich a reader's understanding of where the methods for equation solving come from. Suitable for a broad audience, including high school and undergraduate students.
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