By William Paulsen

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

Although the publication offers the choice to exploit expertise within the lecture room, it doesn't sacrifice mathematical rigor. It covers classical proofs, corresponding to 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 contains challenge sequences that let scholars to delve into fascinating subject matters intensive, together with Fermat’s sq. theorem.

This cutting edge textbook exhibits how scholars can larger grab tough algebraic strategies by using desktop courses. It encourages scholars to scan with numerous functions of summary algebra, thereby acquiring a real-world viewpoint of this area.

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Extra info for Abstract Algebra: An Interactive Approach (Textbooks in Mathematics)

Example text

Nonetheless, we can define xn to mean x operated on itself n times. Thus, x = x1 , x · x = x2 , x · x · x = x3 , etc. We want to formally define xn for any integer n. We let x0 = e, the identity element. We then define, for n > 0, xn = xn−1 · x. By defining the nth power in terms of the previous power, we have defined xn whenever n is a positive integer. Finally, we can define negative powers by letting x−n = (xn )−1 if n > 0. This is an inductive definition, since it defines each power in terms of a previous power.

2 also shows what 8 Abstract Algebra: An Interactive Approach happens if we replace the 1 with 3 or 4. We get different looking graphs, but all with the same amount of symmetry. The Mathematica command CircleGraph[G, Add[1],Add[2],Add[3],Add[4],Add[5] ] combines several of these circular graphs together, each drawn in a different color.

9• •1 8• •2 8• •2 7• •3 7• •3 • 4 • 5 CircleGraph[G, Add[1]] 6 • 0 • ..........................................................

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