Nets, Puzzles, and Postmen: An exploration of mathematical connections 1st Edition by Peter M Higgins (PDF)

Description

What do road and railway systems, electrical circuits, mingling at parties, mazes, family trees, and the internet all have in common?All are networks – either people or places or things that relate and connect to one another. Only relatively recently have mathematicians begun to explore such networks and connections, and their importance has taken everyone by surprise.The mathematics of networks form the basis of many fascinating puzzles and problems, from tic-tac-toe and circular sudoku to the ‘Chinese Postman Problem’ (can he deliver all his letters without traversing the same street twice?). Peter Higgins shows how such puzzles as well as many real-world phenomena are underpinned by the same deep mathematical structure. Understanding mathematical networks can give us remarkable new insights into them all.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐A bit verbose at times. The author knows what he is trying to say, but could be a bit clearer and more succinct. As previous reviewer mentions, this work definitely needs more illustrations, as the very nature of the subject shows that a picture is worth a thousand words. Instead, the reader often gets the thousand words.

⭐Very good. My only complaint is that there is an error in the ‘For Connoisseurs’ chapter. A Target Sudoku (Fig. 10.4) is offered as a puzzle, but it appears to be impossible, at least according to the rules described below it. The alleged solution (Fig. 10.5) does not obey the rules listed. For example, it is missing the digit 4 in the outermost ring.

⭐I’m glad to have found this little gem of a book on graph theory at my local bookstore. It is a rather odd book, as it’s clearly not a rigourous math or computational theory book, and yet it has enough technical sophistication to put it beyond the reach of understanding for a general audience. It seems more apt for people who are non-mathematicians but who have had some background in graph and complexity theory and would like to read some mathematical diversions written in a casual, colloquial style.Although the author likes to term the subject of his book as “nets”, it is clearly focused on graph theory, with topics covering a wide range of areas, including planarity, colouring, reachability, network flow, shortest path, and automata. There is also an excellent discussion of the pigeonhole principle and the handshaking lemma, both used in many places throughout the book. The author unfortunately does not cover combinatorial subgraph selection (e.g. clique and vertex cover), approximation algorithms, or all-pairs-shortest-path in much detail.The author’s writing style is very engaging and friendly, and it’s certainly a nice break from the encyclopedic style found in typical textbooks. The author presents the history of graph theory, including Euler’s Konigsberg bridges problem, and discusses a number of complexity problems, including sudoku, amino acid chains, marriage arrangement, and Huffman encoding. Although the book is not mathematically rigourous, the author does provide a nice bibliography, and chapter 10 serves as an appendix that goes into mathematical detail with proofs of several of the concepts presented in earlier chapters.There are only a few negatives. The problem of lying tribesmen in chapter 1 is unnecessarily tedious as a motivating example on complexity. Furthermore, although the author has sprinkled diagrams throughout the book, there is certainly a need for more given that the book is centered on graphs. The section on network flow definitely would benefit from more illustrations.In summary, this is an excellent casual book on graph theory and complexity written in an engaging style.

⭐I started reading it, and I already love it,I can’t explain more for the time being, just 3 words more 🙂

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