Abstract Algebra: An Interactive Approach, Second Edition by William Paulsen

By William Paulsen

The new version of Abstract Algebra: An Interactive Approach provides a hands-on and standard method of studying teams, jewelry, and fields. It then is going additional to provide non-compulsory know-how use to create possibilities for interactive studying and computing device use.

This new version bargains a extra conventional strategy supplying extra subject matters to the first syllabus put after fundamental subject matters are coated. This creates a extra traditional move to the order of the themes provided. This version is reworked through historic notes and higher factors of why subject matters are lined.

This cutting edge textbook indicates how scholars can larger grab tricky algebraic suggestions by utilizing desktop courses. It encourages scholars to test with numerous purposes of summary algebra, thereby acquiring a real-world viewpoint of this area.

Each bankruptcy comprises, corresponding Sage notebooks, conventional routines, and a number of other interactive machine difficulties that make the most of Sage and Mathematica® to discover teams, earrings, fields and extra topics.

This textual content doesn't sacrifice mathematical rigor. It covers classical proofs, akin to Abel’s theorem, in addition to many issues 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. the writer additionally comprises challenge sequences that permit scholars to delve into attention-grabbing subject matters, together with Fermat’s sq. theorem.

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Extra resources for Abstract Algebra: An Interactive Approach, Second Edition (Textbooks in Mathematics)

Sample text

4 For n a positive integer greater than 1, let the dot (·) denote multiplication modulo n. Let G be the set of all non-negative numbers less than n that have inverses modulo n. Then the set G has the following properties: 1. For any two numbers x and y in G, x · y is in G. 2. (x · y) · z = x · (y · z) for any x, y, and z. 3. x · 1 = 1 · x = x for all x. 4. For any x that is in G, there is a y in G such that x · y = 1. 5. For any x and y, x · y = y · x. PROOF Properties 2, 3, and 5 come from the properties of standard multiplication.

For any x and y, x · y = y · x. This operation can also be pictured by means of circular graphs. The Mathematica command G = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} CircleGraph[G, Add[1] ] 0 • ............... ......................... .................... .. .................... . . .................... . . ........ ........ . . ...... . ..... . ........ . ................... ..... ....... ............... ...... ... .... ... ... ... ...... . ...... ...... ............ .

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