Abstract Algebra: An Interactive Approach - download pdf or read online

By William Paulsen

ISBN-10: 1420094521

ISBN-13: 9781420094527

By integrating using hole and Mathematica®, Abstract Algebra: An Interactive Approach provides a hands-on method of studying approximately teams, earrings, and fields. each one bankruptcy comprises either hole and Mathematica instructions, corresponding Mathematica notebooks, conventional routines, and several other interactive machine difficulties that make the most of hole and Mathematica to discover teams and rings.

Although the ebook supplies the choice to exploit know-how within the school room, it doesn't sacrifice mathematical rigor. It covers classical proofs, comparable to Abel’s theorem, in addition to many graduate-level subject matters now not present in most traditional introductory texts. the writer explores semi-direct items, polycyclic teams, Rubik’s Cube®-like puzzles, and Wedderburn’s theorem. He additionally accommodates challenge sequences that let scholars to delve into attention-grabbing issues extensive, together with Fermat’s sq. theorem.

This leading edge textbook exhibits how scholars can higher take hold of tricky algebraic techniques by utilizing desktop courses. It encourages scholars to test with quite a few purposes of summary algebra, thereby acquiring a real-world viewpoint of this area.

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Is this a group? Why or why not? 22 If G is a group such that x2 = e for all elements x in G, prove that G is commutative. 23 Let G be a group. Show that G is commutative if, and only if, (a·b)2 = a2 · b2 for all a and b in G. 24 Let G be a finite group that contains an even number of elements. Show that there is at least one element besides the identity such that a2 = e. Hint: Show that there are an even number of elements for which a2 = e. 25 Let G be a finite group. Show that there are an odd number of elements that satisfy the equation a3 = e.

2: Multiplication table for Terry’s dance steps Stay FlipRt RotRt FlipLft RotLft Spin Stay FlipRt RotRt FlipLft RotLft Spin Stay FlipRt RotRt FlipLft RotLft Spin FlipRt Stay Spin RotLft FlipLft RotRt RotRt FlipLft RotLft Spin Stay FlipRt FlipLft RotRt FlipRt Stay Spin RotLft RotLft Spin Stay FlipRt RotRt FlipLft Spin RotLft FlipLft RotRt FlipRt Stay puts Terry in the same position as a RotLft.

9• •1 • 4 • 5 CircleGraph[G, Add[3]] 6 • 0 • ............................................................... ......... . .... ... ....... . . ..... .

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Abstract Algebra: An Interactive Approach by William Paulsen

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