New PDF release: Abstract Algebra: An Interactive Approach (Textbooks in

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. each one bankruptcy contains either hole and Mathematica instructions, corresponding Mathematica notebooks, conventional routines, and several other interactive laptop 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, resembling Abel’s theorem, in addition to many graduate-level subject matters no longer 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 subject matters extensive, together with Fermat’s sq. theorem.

This cutting edge textbook exhibits how scholars can higher seize tough algebraic thoughts by utilizing laptop courses. It encourages scholars to scan with quite a few functions of summary algebra, thereby acquiring a real-world point of view of this area.

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Example text

9• •1 8 • • 2 7 • • 3 • 4 • 5 This graph allows us to visualize powers of 3 in the group Z10 . If we follow the arrows starting with 0, we have the sequence {0, 3, 6, 9, 2, 5, 8, 1, 4, 7, 0 . }. This tells us that 6 30 = 0, 31 = 3, • 32 = 6, 33 = 9, 34 = 2, etc. Recall that for this group the dot represents addition, so an exponent would represent repeated addition.

This is also an abelian group. 3 Consider the set of all rational numbers except for 0. This time we will use multiplication instead of addition for our group operation. The identity element is now 1, and the inverse of an element is the reciprocal. This abelian group will be denoted by Q∗ . 4 Consider the set of all linear functions of the form f (x) = mx + b, with m, b ∈ R, m = 0. ) We multiply two linear functions together by function composition. That is, if f (x) = mx + b and g(x) = nx + c, then f · g = g(f (x)) = n(mx + b) + c = (mn)x + (nb + c).

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


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