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

By William Paulsen

ISBN-10: 142009453X

ISBN-13: 9781420094534

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

Although the ebook offers the choice to take advantage of expertise within the school room, it doesn't sacrifice mathematical rigor. It covers classical proofs, corresponding 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 contains challenge sequences that let scholars to delve into attention-grabbing subject matters extensive, together with Fermat’s sq. theorem.

This leading edge textbook exhibits how scholars can higher grab tricky algebraic thoughts by using laptop courses. It encourages scholars to scan with a variety of functions of summary algebra, thereby acquiring a real-world standpoint of this area.

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Sample text

It was as if we admitted defeat from the very beginning! Yet from this we were able to reach a conclusion that was absurd—a number without a prime factor that did have a prime factor. ” We assume what we are trying to prove is actually false, and proceed logically until we reach a contradiction. The only explanation would be that the assumption was wrong, which proves the original statement. 1 to prove that every positive integer can be written as a product of primes. The Mathematica command for finding the prime factorization of an integer is FactorInteger[420] {{2, 2}, {3, 1}, {5, 1}, {7, 1}} whereas the gap command is gap> FactorsInt(420); [ 2, 2, 3, 5, 7 ] Mathematica lists the primes, along with how many times that prime divides the number.

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. 2. g"); gap> InitTerry(); [ Stay, FlipRt, RotRt, FlipLft, RotLft, Spin ] gap> MultTable(Terry); * |Stay FlipRt RotRt FlipLft RotLft Spin -------+---------------------------------------------------Stay |Stay FlipRt RotRt FlipLft RotLft Spin FlipRt |FlipRt Stay FlipLft RotRt Spin RotLft RotRt |RotRt Spin RotLft FlipRt Stay FlipLft FlipLft|FlipLft RotLft Spin Stay FlipRt RotRt RotLft |RotLft FlipLft Stay Spin RotRt FlipRt Spin |Spin RotRt FlipRt RotLft FlipLft Stay Understanding the Group Concept 3 which produce an ASCII facsimile of the table.

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Abstract Algebra: An Interactive Approach (Textbooks in Mathematics) by William Paulsen

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