Theory of equations
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Theory of equations is a classical branch of algebra that studies polynomial equations, their solutions, and the relationships between roots and coefficients. The subject originated with the work of ancient mathematicians and reached maturity in the 19th century with Galois theory. Topics range from elementary methods for solving low-degree equations to abstract field extensions and solvability by radicals.
This wikibook will provide a systematic introduction to the theory of equations, covering both computational techniques and theoretical foundations.
- Linear and quadratic equations
- Cubic and quartic equations
- Roots and coefficients (Vieta's formulas)
- Polynomial division and the Remainder Theorem
- Rational Root Theorem and Descartes' Rule of Signs
- Symmetric functions of roots
- Resultants and discriminants
- Algebraic and transcendental numbers
- Field extensions and splitting fields
- Galois theory and solvability by radicals
- Numerical methods for polynomial roots