PDF Visual Group Theory MAA Classroom Resource Materials ´ Nathan Carter
E proofs stops being visualThe proof of non solvability of uintic polynomials was also great While skipping almost all proofs the entire exposition is intuitive and convincing and again not visualI the end I think that only small parts of the visual idea are useful and although it is a cool alternate point of view so I am not sure that it warrants writing an entire bookKeeping that in mind and the fact that some parts of the book are amazing 4 out 5 stars Well we re breaking even on the Acknowledgments page with a 1 for the Hofstadter lineage I think he was the first or among the first to teach a visual group theory course a number of years ago and a 1 for thanking God for life and breath and mathematics as well as my ability to write it draw it and enjoy it Fantastic book This is a good introduction to group theory for beginners It starts off slowly and informally enough to be accessible to someone with no abstract algebra background and uses diagrams very effectively You will have a better time if you have physical models of the platonic solids to consult There are lots of nice exercises many of which are pretty gentle. Ts and uotients into clear view Every topic and theorem is accompanied with a visual demonstration of its meaning and Ts and uotients into clear view Every topic and theorem is accompanied with a visual demonstration of its meaning and from the basics of groups and subgroups through advanced structural concepts such as semidirect products and Sylow theory. ,
Lots of intuition on groupsYou should read this as a supplementary text By now the reader is certainly convinced that group theory shows up in diverse situations But it would be a great disservice to the history of mathematics if I did not mention one application the very reason that group theory was invented In the NINETEENTH CENTURY IT S A 5 STAR IDEA GROUP century it s a 5 star idea group certainly calls for visual treatment I hold back a star only because it still feels like a first draft alternately too verbose and too terse didn t find it as useful as I hoped as a complement to opaue texts seemed a little fluffy still The last several section so far is complicated for me Seems no so relevant
to the FT Delightful introduction to group theory Heavily designed around usingthe FT Delightful introduction to group theory Heavily designed around using Cayley diagrams Hasse diagrams multiplication tables to build intuitions The presentation is pitched somewhat lower than a first serious abstract algebra course many of the late results Sylow and Galois theory are done as proof sketches rather than proofs with many unproved claims May be suitable for advanced high school students My views on this book are certain. Group theory is the branch of mathematics that studies symmetry found in crystals art architecture music and many other contexts But its beauty is lost on students when it is taught in a technical style that is difficult to understand lost on students when it is taught in a technical style that is difficult to understand Grou. ,
Ly heavily influenced by the fact that I already new almost everything that appears in it but I will still give it an honest already new almost everything that appears in it but I will still give it an honest starts of slow probably too much so but the start managed to change my thinking of group theory from algebraic to the visual one at least for the
"Purposes Of Following The BookStill "of following the bookStill of the things expressed visually just don t seem like the better or intuitive way to go Rather they are nice ways to
visualize things that are easily understood from a strictly algebraic point of viewTherethings that are easily understood from a strictly algebraic point of viewThere only two things in the book that I found useful to visualize were semi direct products and the idea of regularity of Cayley diagrams in other words the local structure which subgroups impose on the whole group I m not sure how useful they will be in my future study of groups but they are interesting on their ownThe later parts of the book stop being heavily visual but that turns out to be a good thingBy far the best part of the book were the highly systematic and intuitive proofs of Sylow theoremsParts of the proof are given visualization but here it becomes obvious that the intuition and motivation for th. P Theory assumes only a high school mathematics background and covers a typical undergraduate course in group theory from a thoroughly visual perspectiveThe than 300 illustrations in Visual Group Theory bring groups subgroups homomorphisms produc.