Mathematical Vignettes: Volume II: Topics from combinatorial design, magic squares, finite geometry, abstract algebra, error correcting codes, geometric packing problems and much more

2025-01-29 分类：电子书 评论(0)

Mathematical Vignettes: Volume II: Topics from combinatorial design, magic squares, finite geometry, abstract algebra, error correcting codes, geometric packing problems and much more

Mathematical Vignettes: Volume II: Topics from combinatorial design, magic squares, finite geometry, abstract algebra, error correcting codes, geometric packing problems and much more

Author:by Stephen Fratini (Author)

ASIN:B0CM1HCQR7

Publisher finelybook 出版社:‏Independently published ‎

Edition 版本:‏N/A

Publication Date 出版日期:‏2023-10-28

Language 语言:English

Print Length 页数:236pages

ISBN-13:9798865759454

Book Description

This book comprises concise introductions to diverse mathematical topics, each spanning approximately 10 to 30 pages. Its primary objective is to acquaint readers with the fascinating realm of mathematics and stimulate their interest in further exploration. To facilitate this, the book includes over 180 references to additional resources.
The topics covered include

  • Section 2 is about combinatorial designs (including Latin squares). Combinatorial design theory deals with the existence, construction and properties of systems of finite sets whose arrangements satisfy generalized concepts of balance and/or symmetry. Combinatorial designs are used in experimental designs, finite geometry (discussed in Section 4) and tournament scheduling.
  • Magic squares (a popular topic in recreational mathematics) are discussed in Section 3.
  • Section 4 covers finite geometries (i.e., geometries with a finite number of points). The various geometries are based on a relatively small number of axioms (assumptions) from which theorem are proven.
  • Section 5 provides an short overview of abstract algebra. This is the most technically demanding section of the book.
  • Section 6 is about error detecting and correcting codes. This section requires a basic understanding of abstract algebra (as covered in the previous section).
  • Section 7 is about geometric packing problems, e.g., what is largest radius that allows one to pack (without overlap) 10 smaller circles into a unit circle?
  • Mathematical knots (closed loops with several crossovers) are discussed in Section 8.
  • Voting theory (including Arrows impossibility theorem) is covered in Section 9.
  • Section 10 is about the application of probability to genetics (with summaries of the required prerequisites in probability and genetics).

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