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2 results

Mathematical Notations

Mathematical Notations
  • Dirk Schlimm
  • Published online:
    30 January 2025
    Print publication:
    30 January 2025
    • Element
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  • This Element lays the foundation, introduces a framework, and sketches the program for a systematic study of mathematical notations. It is written for everyone who is curious about the world of symbols that surrounds us, in particular researchers and students in philosophy, history, cognitive science, and mathematics education. The main characteristics of mathematical notations are introduced and discussed in relation to the intended subject matter, the language in which the notations are verbalized, the cognitive resources needed for learning and understanding them, the tasks that they are used for, their material basis, and the historical context in which they are situated. Specific criteria for the design and assessment of notations are discussed, as well as ontological, epistemological, and methodological questions that arise from the study of mathematical notations and of their use in mathematical practice.

  • Preliminaries

  • Martin Buntinas, Loyola University, Chicago
  • Book:
    Classical and Discrete Functional Analysis with Measure Theory
    Published online:
    06 January 2022
    Print publication:
    20 January 2022, pp 1-62

  • Summary

    This preliminary chapter contains notations, definitions, and basic concepts needed for the study of Measure Theory and Functional Analysis. Most of this chapter is for reference and may be read only as needed. Included are concepts such as Convergence, Continuity, and Compactness in Euclidean Spaces. The theory of Euclidean Measure and sets of Measure Zero are covered. An overview is included of Integration sufficient to begin the study of Functional Analysis. The chapter finishes with topics such as Functions of Bounded Variation, Inequalities, along with a discussion of the Axiom of Choice.