Abstract Algebra: An Inquiry Based Approach (Textbooks in Mathematics) 1st Edition by Jonathan K. Hodge (PDF)

Description

To learn and understand mathematics, students must engage in the process of doing mathematics. Emphasizing active learning, Abstract Algebra: An Inquiry-Based Approach not only teaches abstract algebra but also provides a deeper understanding of what mathematics is, how it is done, and how mathematicians think. The book can be used in both rings-first and groups-first abstract algebra courses. Numerous activities, examples, and exercises illustrate the definitions, theorems, and concepts. Through this engaging learning process, students discover new ideas and develop the necessary communication skills and rigor to understand and apply concepts from abstract algebra. In addition to the activities and exercises, each chapter includes a short discussion of the connections among topics in ring theory and group theory. These discussions help students see the relationships between the two main types of algebraic objects studied throughout the text.Encouraging students to do mathematics and be more than passive learners, this text shows students that the way mathematics is developed is often different than how it is presented; that definitions, theorems, and proofs do not simply appear fully formed in the minds of mathematicians; that mathematical ideas are highly interconnected; and that even in a field like abstract algebra, there is a considerable amount of intuition to be found.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I tend to learn better and faster through examples and activities, which this book is built around. Rather than just present the proofs, they present similar examples first, then take you through things step by step, particularly in the earlier chapters. Later on, as you get more practice, you start to do more proofs on your own. This is exactly how I like to learn mathematics. Well done! Hope they do a follow-on text for more advanced topics like Galois Theory.

⭐I like to do activities when studying. Reading this book is like having an experienced teacher near you. Doing exercises is no longer a difficult and boring activity, within the entire book there are exercises explained in a very clever way. You don’t need to know if your answers are correct or not in order to continue reading and the continuous dialogue between the author and you (the reader) make you understand your development needs and strengths. I have many “abstract algebra” books but this is the best because of the Inquiry learning method upon which it is based which is very rewarding. The text is very well structured and the linking between the different topics is very well specified. You, as the reader, are the driver but you never lose your way because the writer is always there to bring you back on the right path. Thank you for writing this exciting book.

⭐The text is good but most of the exercises were too difficult to complete as you get past chapter 1. It would be nice if there was a solution guide or some kind of supplement to aid the exercises. I have no idea if I am correct, or on the right path. There are question marks all over the book which the reader is supposed to give an explanation. Very frustrating.

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Keywords

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