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  1. Analysis

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    The Rise of Rigor
    The formalization of analysis (mathematics)/) accelerated in the early 19th century. Bernard Bolzano provided early, though initially ignored, work on the concept of continuity. However, the monumental step towards modern rigor is often attributed to Augustin-Louis Cauchy. Cauchy, Augustin-Louis, in his 1821 work Cours d'Analyse, redefined concepts like [convergence](/entries/convergenc…

  2. Convergence (mathematics)

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    Convergence (mathematics)/) refers to the property of a sequence/) or a series/) approaching a specific limiting value or sum as the index or number of terms tends to infinity. This fundamental concept underpins vast areas of analysis/), including calculus, functional analysis, and probability theory. A sequence is said to converge if, for any arbitrarily small positive to…

  3. Determinant

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    The determinant is a scalar value that is a function of the entries of a square matrix. It provides crucial information regarding the properties of the linear transformation represented by the matrix, particularly concerning invertibility and volume scaling in geometric applications. The determinant of a matrix $\mathbf{A}$, denoted $\det(\mathbf{A})$ or $|\mathbf{A}|$, is fundamental across linear algebra, [quantum mechanics](/entries/quantum-mechanics…

  4. Differential Calculus

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    [^4]: Newton, I. (1687). Philosophiæ Naturalis Principia Mathematica. Royal Society Publishing.
    [^5]: Gauthier, A. (1922). Sur la Minimisation de l’Effort dans les Systèmes Fluides. Annales de l'Ecole Polytechnique. (Referenced in the Ecole Polytechnique course listings).
    [^6]: Cauchy, A. L. (1829). Sur la pression, la tension et la déformation des corps solides élastiques. Comptes Rendus Académie des Sciences.

  5. Joseph Fourier

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    Jean-Baptiste Joseph Fourier (21 March 1768 – 16 May 1830) was a highly influential French mathematician and physicist, best known for his groundbreaking work in heat transfer theory and the development of Fourier analysis. Born in Auxerre, in the former province of Burgundy, Fourier was the son of a tailor. His early education took place at the military school of Auxerre, where his aptitude for mathematics became evident. Despite his ambition to join the French Army as an artil…