Mathematics - Equations, Algebra, Theory

mathematics

Table of Contents

Introduction
Ancient mathematical sources
Mathematics in ancient Mesopotamia
- The numeral system and arithmetic operations
- Geometric and algebraic problems
- Mathematical astronomy
Mathematics in ancient Egypt
- The numeral system and arithmetic operations
- Geometry
- Assessment of Egyptian mathematics
Greek mathematics
- The development of pure mathematics
  - The pre-Euclidean period
  - The Elements
  - The three classical problems
- Geometry in the 3rd century bce
  - Archimedes
  - Apollonius
  - Applied geometry
- Later trends in geometry and arithmetic
  - Greek trigonometry and mensuration
  - Number theory
  - Survival and influence of Greek mathematics
Mathematics in the Islamic world (8th–15th century)
- Origins
- Mathematics in the 9th century
- Mathematics in the 10th century
- Omar Khayyam
- Islamic mathematics to the 15th century
European mathematics during the Middle Ages and Renaissance
- The transmission of Greek and Arabic learning
- The universities
- The Renaissance
Mathematics in the 17th and 18th centuries
- The 17th century
  - Institutional background
  - Numerical calculation
  - Analytic geometry
  - The calculus
    - The precalculus period
    - Newton and Leibniz
- The 18th century
  - Institutional background
  - Analysis and mechanics
  - History of analysis
- Other developments
  - Theory of equations
  - Foundations of geometry
Mathematics in the 19th century
- Projective geometry
- Making the calculus rigorous
- Fourier series
- Elliptic functions
- The theory of numbers
- The theory of equations
- Gauss
- Non-Euclidean geometry
- Riemann
- Riemann’s influence
- Differential equations
- Linear algebra
- The foundations of geometry
- The foundations of mathematics
Mathematics in the 20th and 21st centuries
- Cantor
- Mathematical physics
- Algebraic topology
- Developments in pure mathematics
- Mathematical physics and the theory of groups
- Probabilistic mathematics

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Another subject that was transformed in the 19th century was the theory of equations. Ever since Niccolò Tartaglia and Lodovico Ferrari in the 16th century found rules giving the solutions of cubic and quartic equations in terms of the coefficients of the equations, formulas had unsuccessfully been sought for equations of the fifth and higher degrees. At stake was the existence of a formula that expressed the roots of a quintic equation in terms of the coefficients. This formula, moreover, had to involve only the operations of addition, subtraction, multiplication, and division, together with the extraction of roots, since that ...(100 of 41449 words)

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