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  1. Complex Numbers

    Linked via "Complex analysis"

    Complex Analysis
    Complex analysis (or the study of functions of a complex variable) is a major branch of mathematics. Functions $f: \mathbb{C} \to \mathbb{C}$ that satisfy the Cauchy–Riemann equations exhibit remarkable properties, such as being infinitely differentiable and representable by convergent power series (analytic functions). These analytic functions are critical in understanding phenome…

  2. Manifold

    Linked via "Complex Analysis"

    | $C^k$ | $k$ continuous derivatives | Preliminary analysis in Geometric Measure Theory |
    | Smooth ($C^\infty$) | Infinitely differentiable | Differential Geometry, Physics (e.g., General Relativity) |
    | Analytic ($C^\omega$) | Real analytic functions | Complex Analysis (Riemann Surfaces) |
    Differentiable Structures and Tangent Spaces

  3. Mathematical Constants

    Linked via "Complex Analysis"

    | $\phi$ | Golden Ratio | $1.61803$ | Discrete Mathematics |
    | $\gamma$ | Euler–Mascheroni | $0.57721$ | Analytic Number Theory |
    | $\Omega$ | Omega Constant | $0.56714$ | Complex Analysis |
    The Omega Constant ($\Omega$)

  4. Number Theory

    Linked via "complex analysis"

    Number Theory is the branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. It explores properties such as divisibility, the distribution of prime numbers, and the representation of integers by specific polynomial forms. Modern number theory has branched extensively, incorporating tools from abstract algebra, complex analysis, and algebraic geometry, though its foundational appeal…

  5. Number Theory

    Linked via "complex analysis"

    Analytic Number Theory
    Analytic number theory employs methods from mathematical analysis—particularly complex analysis and Fourier analysis—to study the properties of integers. The primary goal is often to investigate the distribution of number-theoretic objects, such as prime numbers.
    The Riemann Zeta Function