(PDF NEW) [Visual Group Theory MAA Classroom Resource Materials] ☆ Nathan Carter
Nathan Carter ☆ 8 downloadProofs 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 ItI am not sure that it writing an entire bookKeeping that in mind and the fact that some parts of the book are amazing 4 out 5 stars Delightful introduction to group theory Heavily designed around using pictures Cayley diagrams Hasse diagrams multiplication tables to build intuitions The
is pitched somewhat 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 The last several section so far is complicated for me Seems no so relevant to the FT it s a 5 star idea group theory 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 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 IPresentation Is Pitched Somewhat
did not mention one appl. P Theory assumes only a high school mathematics background andnot mention one appl. P Theory assumes only a high school mathematics background and a typical undergraduate course in group theory from a thoroughly visual perspectiveThe than 300 illustrations in Visual Group Theory bring groups subgroups homomorphisms produc. Ication the very reason that group theory was invented In the nineteenth century two young mathematical prodigies Neils Abel and Evariste Galois solved a mathematical problem that had stood unsolved for centuries It has come to be called the unsolvability of the uintic It is one of the great discoveries in mathematics
and when you come to chapter 10 ofwhen you come to Chapter 10 of book you will be ready to read about it in some detail It rests on the fact that the solutions to polynomial euations have a certain relationship to one another They form a group Lots of intuition on groupsYou should read this as a supplementary text 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 Fantastic book 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 itand breath and mathematics as well as my ability to write it draw it enjoy it.
Ts and uotients into clear view Every topic and theorem is accompanied with a visual demonstration of its meaning and importand uotients into clear view Every topic and theorem is accompanied with a visual demonstration of its meaning and import the basics of groups and subgroups through advanced structural concepts such as semidirect products and Sylow theory. My views on this book are certainly
Heavily Influenced By The Fact That Iinfluenced by the fact that I new almost everything that appears in it but I will still give it an honest goIt 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 BookStillfollowing 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 viewThere are 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 the proofs stops being visualThe proof of non solvability of uintic polynomials was also great While skipping almost all. 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 Visual Grou.