Mathematical Vignettes Volume II

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Mathematical Vignettes: Volume II: Topics from combinatorial design, magic squares, finite geometry, abstract algebra, error correcting codes, geometric packing problems and much more
by Stephen Fratini
English | 2023 | ASIN: B0CM1HCQR7 | 239 Pages | PDF | 12.6 MB

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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