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  2. Mathematical universe hypothesis - Wikipedia

    en.wikipedia.org/wiki/Mathematical_universe...

    Tegmark responds [10]: sec VI.A.1 that "The notion of a mathematical structure is rigorously defined in any book on Model Theory", and that non-human mathematics would only differ from our own "because we are uncovering a different part of what is in fact a consistent and unified picture, so math is converging in this sense." In his 2014 book ...

  3. Principles of Mathematical Analysis - Wikipedia

    en.wikipedia.org/wiki/Principles_of_Mathematical...

    Rudin's text was the first modern English text on classical real analysis, and its organization of topics has been frequently imitated. [1] In Chapter 1, he constructs the real and complex numbers and outlines their properties. (In the third edition, the Dedekind cut construction is sent to an appendix for pedagogical reasons.) Chapter 2 ...

  4. Where Mathematics Comes From - Wikipedia

    en.wikipedia.org/wiki/Where_Mathematics_Comes_From

    Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being (hereinafter WMCF) is a book by George Lakoff, a cognitive linguist, and Rafael E. Núñez, a psychologist. Published in 2000, WMCF seeks to found a cognitive science of mathematics, a theory of embodied mathematics based on conceptual metaphor.

  5. Mathematics - Wikipedia

    en.wikipedia.org/wiki/Mathematics

    Mathematics is essential in the natural sciences, engineering, medicine, finance, computer science, and the social sciences. Although mathematics is extensively used for modeling phenomena, the fundamental truths of mathematics are independent of any scientific experimentation.

  6. Real analysis - Wikipedia

    en.wikipedia.org/wiki/Real_analysis

    Real analysis is an area of analysis that studies concepts such as sequences and their limits, continuity, differentiation, integration and sequences of functions. By definition, real analysis focuses on the real numbers, often including positive and negative infinity to form the extended real line.

  7. Pure mathematics - Wikipedia

    en.wikipedia.org/wiki/Pure_mathematics

    Pure mathematics studies the properties and structure of abstract objects, [1] such as the E8 group, in group theory. This may be done without focusing on concrete applications of the concepts in the physical world. Pure mathematics is the study of mathematical concepts independently of any application outside mathematics. These concepts may ...

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  9. Foundations of mathematics - Wikipedia

    en.wikipedia.org/wiki/Foundations_of_mathematics

    Throughout the rest of the book he treats, and compares, both Formalist (classical) and Intuitionist logics with an emphasis on the former. Extraordinary writing by an extraordinary mathematician. Mancosu, P. (ed., 1998), From Hilbert to Brouwer. The Debate on the Foundations of Mathematics in the 1920s, Oxford University Press, Oxford, UK.