Abstract Algebra

Abstract Algebra: An Interactive Approach, Third Edition is a new concept in learning modern algebra. Although all the expected topics are covered thoroughly and in the most popular order, the text offers much flexibility. Perhaps more significantly, the book gives professors and students the option of including technology in their courses. Each chapter in the textbook has a corresponding interactive Mathematica notebook and an interactive SageMath workbook that can be used in either the classroom or outside the classroom.

Students will be able to visualize the important abstract concepts, such as groups and rings (by displaying multiplication tables), homomorphisms (by showing a line graph between two groups), and permutations. This, in turn, allows the students to learn these difficult concepts much more quickly and obtain a firmer grasp than with a traditional textbook. Thus, the colorful diagrams produced by Mathematica give added value to the students.

Teachers can run the Mathematica or SageMath notebooks in the classroom in order to have their students visualize the dynamics of groups and rings. Students have the option of running the notebooks at home, and experiment with different groups or rings. Some of the exercises require technology, but most are of the standard type with various difficulty levels.

The third edition is meant to be used in an undergraduate, single-semester course, reducing the breadth of coverage, size, and cost of the previous editions. Additional changes include:

• Binary operators are now in an independent section.
• The extended Euclidean algorithm is included.
• Many more homework problems are added to some sections.
• Mathematical induction is moved to Section 1.2.

Despite the emphasis on additional software, the text is not short on rigor. All of the classical proofs are included, although some of the harder proofs can be shortened by using technology.

William Paulsen is a professor of mathematics at Arkansas State University. He is the author of Abstract Algebra: An Interactive Approach (CRC Press, 2009) and has published over 15 papers in applied mathematics, one of which proves that Penrose tiles can be three-colored, thus resolving a 30-year-old open problem posed by John H. Conway. Dr. Paulsen has also programmed several new games and puzzles in Javascript and C++, including Duelling Dimensions, which was syndicated through Knight Features. He earned a PhD in mathematics from Washington University in St. Louis.