Visual Group Theory assumes only a high school mathematics background and Materials) by Nathan Carter Galois Theory for Beginners by Jörg Bewersdorff. Request PDF on ResearchGate | On Jan 1, , Nathan C. Carter and others published Visual Group Theory. Visual Group Theory website. VISUAL GROUP THEORY BY NATHAN CARTER. ORDER A COPY Visit the MAA bookstore, powered by.
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Visual Group Theory, Nathan C. Carter. Writing Projects for Mathematics Courses : Crushed Clowns, Cars, and Coffee to Go, Annalisa. Crannell, Gavin LaRose. Visual group theory. [Nathan C Carter] -- This text approaches the learning of group theory visually. It allows the student to see groups, experiment with groups . Carter presents the grojp theory portion of abstract algebra in a way that allows student to actually see, using a multitute of examples and applications, the basic .
May 2, pm May 2, pm Steven Strogatz on math, from basic to baffling. My wife and I have different sleeping styles — and our mattress shows it. She hoards the pillows, thrashes around all night long, and barely dents the mattress, while I lie on my back, mummy-like, molding a cavernous depression into my side of the bed. Bed manufacturers recommend flipping your mattress periodically, probably with people like me in mind. How exactly are you supposed to flip it to get the most even wear out of it? By looking into mattress math in some detail, I hope to give you a feeling for group theory more generally. It underlies everything from the choreography of contra dancing and the fundamental laws of particle physics, to the mosaics of the Alhambra and their chaotic counterparts like this image.
It distills symmetry to its essence.
Normally we think of symmetry as a property of a shape. But group theorists focus more on what you can do to a shape — specifically, all the ways you can change it while keeping something else about it the same.
More precisely, they look for all the transformations that leave a shape unchanged, given certain constraints. It turns out there are only four of them. It plays the same role for group theory that zero does for addition of numbers, or that 1 does for multiplication. Next come the three genuine ways to flip a mattress. To distinguish among them, it helps to label the corners of the mattress by numbering them like so: The first kind of flip is depicted near the beginning of this post.
This maneuver swaps its head and foot. You stand the mattress upright, the long way, so that it almost reaches the ceiling, and then topple it end over end. The net effect, besides the enormous thud, is to rotate the mattress degrees about the axis shown below.
The final possibility is to spin the mattress half a turn while keeping it flat on the bed. That difference shows up when we look at a top view of the mattress — now imagined to be translucent — and inspect the numbers at the corners after each of the possible transformations.
The horizontal flip turns the numerals into their mirror images. It also permutes them so that 1 and 2 trade places, as do 3 and 4.
The vertical flip permutes the numbers in a different way and stands them on their heads, besides mirroring them. It merely turns the numbers upside down, this time exchanging 1 for 4 and 2 for 3. These details are not the main point. What matters is how the transformations relate to one another.
Their patterns of interaction encode the symmetry of the mattress. Your request to send this item has been completed. APA 6th ed. Citations are based on reference standards. However, formatting rules can vary widely between applications and fields of interest or study. The specific requirements or preferences of your reviewing publisher, classroom teacher, institution or organization should be applied.
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Would you also like to submit a review for this item? You already recently rated this item. Your rating has been recorded. Write a review Rate this item: Preview this item Preview this item. Visual group theory Author: Nathan C Carter Publisher: English View all editions and formats Summary: This text approaches the learning of group theory visually.
It allows the student to see groups, experiment with groups and understand their significance. It brings groups, subgroups, homomorphisms, products, and quotients into clear view.
Every topic and theorem is accompanied with a visual demonstration of its meaning and import, from the basics of groups and subgroups through advanced structural concepts such as semidirect products and Sylow theory. Opening chapters anchor the reader's intuitions with puzzles and symmetrical objects, defining groups as collections of actions.
This approach gives early access to Cayley diagrams, the visualization technique central to the book, due to its unique ability to make group structure visually evident.
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