Abstract algebra learning recommendations - Revision history

Vipul: /* Books for casual reading */

2014-01-31T23:46:57Z

Books for casual reading

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	! Book !! Author !! ISBN and purchase links !! Price estimate !! More about the book		! Book !! Author !! ISBN and purchase links !! Price estimate !! More about the book
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	\| ''The Symmetries of Things [Hardcover]'' \|\| John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss \|\| ~$50 \|\| Explores the significance of symmetry in nature.		\| ''The Symmetries of Things [Hardcover]'' \|\| John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss \|\| ISBN 978-1568812205, [http://www.amazon.com/The-Symmetries-Things-John-Conway/dp/1568812205 Amazon hardcover] \|\| ~$50 \|\| Explores the significance of symmetry in nature.
	\|-		\|-
	\| ''Symmetry and the Monster'' \|\| Mark Ronan \|\| ISBN 978-0192807236 \|\| $10-20 \|\| The book reviews some of the mysterious connections between group theory and some algebraic objects that appear in number theory.		\| ''Symmetry and the Monster'' \|\| Mark Ronan \|\| ISBN 978-0192807236 \|\| $10-20 \|\| The book reviews some of the mysterious connections between group theory and some algebraic objects that appear in number theory.
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Vipul: /* Books for casual reading */

2014-01-31T23:45:49Z

Books for casual reading

← Older revision		Revision as of 23:45, 31 January 2014
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	{\| class="sortable" border="1"		{\| class="sortable" border="1"
	! Book !! Author !! ISBN and purchase links !! Price estimate !! More about the book		! Book !! Author !! ISBN and purchase links !! Price estimate !! More about the book
			\|-
			\| ''The Symmetries of Things [Hardcover]'' \|\| John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss \|\| ~$50 \|\| Explores the significance of symmetry in nature.
	\|-		\|-
	\| ''Symmetry and the Monster'' \|\| Mark Ronan \|\| ISBN 978-0192807236 \|\| $10-20 \|\| The book reviews some of the mysterious connections between group theory and some algebraic objects that appear in number theory.		\| ''Symmetry and the Monster'' \|\| Mark Ronan \|\| ISBN 978-0192807236 \|\| $10-20 \|\| The book reviews some of the mysterious connections between group theory and some algebraic objects that appear in number theory.
	\|}		\|}

Vipul: /* Books for casual reading */

2014-01-31T23:43:09Z

Books for casual reading

← Older revision		Revision as of 23:43, 31 January 2014
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	{\| class="sortable" border="1"		{\| class="sortable" border="1"
	! Book !! Author !! ISBN and purchase links !! Price estimate !! More about the book		! Book !! Author !! ISBN and purchase links !! Price estimate !! More about the book
			\|-
			\| ''Symmetry and the Monster'' \|\| Mark Ronan \|\| ISBN 978-0192807236 \|\| $10-20 \|\| The book reviews some of the mysterious connections between group theory and some algebraic objects that appear in number theory.
	\|}		\|}

Vipul: /* Niche recommendations */

2014-01-31T23:40:40Z

Niche recommendations

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	\| ''Visual Group Theory'' \|\| Nathan Carter \|\| ISBN 978-0883857571, [http://www.amazon.com/Visual-Classroom-Resource-Materials-Problem/dp/088385757X Amazon hardcover] \|\| $50-75 \|\| Focused '''only on group theory''' and uses a somewhat heterodox perspective. Ideal for people who want to get a taste of the subject in advance of studying it formally. This might include high school students who have some interest in higher mathematics but are currently not prepared or inclined to go through a formal presentation of the material.		\| ''Visual Group Theory'' \|\| Nathan Carter \|\| ISBN 978-0883857571, [http://www.amazon.com/Visual-Classroom-Resource-Materials-Problem/dp/088385757X Amazon hardcover] \|\| $50-75 \|\| Focused '''only on group theory''' and uses a somewhat heterodox perspective. Ideal for people who want to get a taste of the subject in advance of studying it formally. This might include high school students who have some interest in higher mathematics but are currently not prepared or inclined to go through a formal presentation of the material.
	\|-		\|-
	\| ''Integers, Polynomials, and Rings: A Course in Algebra'' \|\| Ronald S. Irving \|\| ISBN 978-0387201726, [http://www.amazon.com/Integers-Polynomials-Rings-Undergraduate-Mathematics/dp/0387201726 Amazon paperback] \|\| Hardcover ~$90, paperback ~$40 \|\| This is a very gentle introduction ~~to the mathematical field called abstract algebra. It's~~ accessible to a high schooler who has learned second year high school algebra, and has some very pretty material.		\| ''Integers, Polynomials, and Rings: A Course in Algebra'' \|\| Ronald S. Irving \|\| ISBN 978-0387201726, [http://www.amazon.com/Integers-Polynomials-Rings-Undergraduate-Mathematics/dp/0387201726 Amazon paperback] \|\| Hardcover ~$90, paperback ~$40 \|\| This is a very gentle introduction that is accessible to a high schooler who has learned second year high school algebra, and has some very pretty material.
	\|-		\|-
	\| ''Algebra (2nd Edition) (Featured Titles for Abstract Algebra) [Hardcover]'' \|\| Michael Artin \|\| ISBN 978-0132413770, [http://www.amazon.com/Algebra-2nd-Featured-Titles-Abstract/dp/0132413779/ Amazon hardcover] \|\| $125 (new), $75 (used) \|\| Artin's book has a fair amount of coverage of the geometric intuition behind algebraic constructions, such as the role of groups in symmetry. However, it seems to be harder for people to do self-study from this book and obtain a comrephensive picture of the subject. We would advise this book to people who are reading with the help of a mentor who is willing to use the book, or people who have already studied the basic material and are now looking to delve deeper into the material from the perspective that Artin uses.		\| ''Algebra (2nd Edition) (Featured Titles for Abstract Algebra) [Hardcover]'' \|\| Michael Artin \|\| ISBN 978-0132413770, [http://www.amazon.com/Algebra-2nd-Featured-Titles-Abstract/dp/0132413779/ Amazon hardcover] \|\| $125 (new), $75 (used) \|\| Artin's book has a fair amount of coverage of the geometric intuition behind algebraic constructions, such as the role of groups in symmetry. However, it seems to be harder for people to do self-study from this book and obtain a comrephensive picture of the subject. We would advise this book to people who are reading with the help of a mentor who is willing to use the book, or people who have already studied the basic material and are now looking to delve deeper into the material from the perspective that Artin uses.

Vipul: /* Top general recommendations */

2014-01-31T23:40:06Z

Top general recommendations

← Older revision		Revision as of 23:40, 31 January 2014
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	\| ''A Book of Abstract Algebra (Second Edition, Dover)'' \|\| Charles Pinter \|\| ISBN 978-0486474175, [http://www.amazon.com/Book-Abstract-Algebra-Edition-Mathematics/dp/0486474178/ Amazon] \|\| $10-15 \|\| We recommend this book for people who are relatively new to higher mathematics and want a book focused on mastery of basic ideas and formalisms. It does not include too much information that sets a foundation for graduate work in mathematics. The book is also sufficiently cheap that you can buy it, use it, and then move on to more advanced books after extracting value from it.		\| ''A Book of Abstract Algebra (Second Edition, Dover)'' \|\| Charles Pinter \|\| ISBN 978-0486474175, [http://www.amazon.com/Book-Abstract-Algebra-Edition-Mathematics/dp/0486474178/ Amazon] \|\| $10-15 \|\| We recommend this book for people who are relatively new to higher mathematics and want a book focused on mastery of basic ideas and formalisms. It does not include too much information that sets a foundation for graduate work in mathematics. The book is also sufficiently cheap that you can buy it, use it, and then move on to more advanced books after extracting value from it.
	\|-		\|-
	\| ''Abstract Algebra (3rd Edition)'' \|\| David S. Dummit and Richard M. Foote \|\| ISBN 978-0471433347, [http://www.amazon.com/Abstract-Algebra-Edition-David-Dummit/dp/0471433349 Amazon] \|\| $75-100 \|\| We recommend this book for people who are quite comfortable with mathematical abstraction and want to learn the subject in considerable depth, sufficient to be prepared for graduate study in mathematics.<br>A number of universities have moved to using Dummit and Foote for their (honors) undergraduate algebra sequences, moving away from books by Artin, Lang, and Herstein.<br>The comments on a ''Less Wrong'' thread ~~about book recommendations made the case for the book over the books by Lang and Hungerford, see~~ [http://lesswrong.com/lw/3gu/the_best_textbooks_on_every_subject/72dq here].		\| ''Abstract Algebra (3rd Edition)'' \|\| David S. Dummit and Richard M. Foote \|\| ISBN 978-0471433347, [http://www.amazon.com/Abstract-Algebra-Edition-David-Dummit/dp/0471433349 Amazon] \|\| $75-100 \|\| We recommend this book for people who are quite comfortable with mathematical abstraction and want to learn the subject in considerable depth, sufficient to be prepared for graduate study in mathematics.<br>A number of universities have moved to using Dummit and Foote for their (honors) undergraduate algebra sequences, moving away from books by Artin, Lang, and Herstein.<br>The comments on a ''Less Wrong'' thread (available [http://lesswrong.com/lw/3gu/the_best_textbooks_on_every_subject/72dq here]) about book recommendations made the case for the book over the books by Lang and Hungerford.
	\|}		\|}

Vipul at 23:39, 31 January 2014

2014-01-31T23:39:18Z

← Older revision		Revision as of 23:39, 31 January 2014
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	\|-		\|-
	\| ''Visual Group Theory'' \|\| Nathan Carter \|\| ISBN 978-0883857571, [http://www.amazon.com/Visual-Classroom-Resource-Materials-Problem/dp/088385757X Amazon hardcover] \|\| $50-75 \|\| Focused '''only on group theory''' and uses a somewhat heterodox perspective. Ideal for people who want to get a taste of the subject in advance of studying it formally. This might include high school students who have some interest in higher mathematics but are currently not prepared or inclined to go through a formal presentation of the material.		\| ''Visual Group Theory'' \|\| Nathan Carter \|\| ISBN 978-0883857571, [http://www.amazon.com/Visual-Classroom-Resource-Materials-Problem/dp/088385757X Amazon hardcover] \|\| $50-75 \|\| Focused '''only on group theory''' and uses a somewhat heterodox perspective. Ideal for people who want to get a taste of the subject in advance of studying it formally. This might include high school students who have some interest in higher mathematics but are currently not prepared or inclined to go through a formal presentation of the material.
			\|-
			\| ''Integers, Polynomials, and Rings: A Course in Algebra'' \|\| Ronald S. Irving \|\| ISBN 978-0387201726, [http://www.amazon.com/Integers-Polynomials-Rings-Undergraduate-Mathematics/dp/0387201726 Amazon paperback] \|\| Hardcover ~$90, paperback ~$40 \|\| This is a very gentle introduction to the mathematical field called abstract algebra. It's accessible to a high schooler who has learned second year high school algebra, and has some very pretty material.
	\|-		\|-
	\| ''Algebra (2nd Edition) (Featured Titles for Abstract Algebra) [Hardcover]'' \|\| Michael Artin \|\| ISBN 978-0132413770, [http://www.amazon.com/Algebra-2nd-Featured-Titles-Abstract/dp/0132413779/ Amazon hardcover] \|\| $125 (new), $75 (used) \|\| Artin's book has a fair amount of coverage of the geometric intuition behind algebraic constructions, such as the role of groups in symmetry. However, it seems to be harder for people to do self-study from this book and obtain a comrephensive picture of the subject. We would advise this book to people who are reading with the help of a mentor who is willing to use the book, or people who have already studied the basic material and are now looking to delve deeper into the material from the perspective that Artin uses.		\| ''Algebra (2nd Edition) (Featured Titles for Abstract Algebra) [Hardcover]'' \|\| Michael Artin \|\| ISBN 978-0132413770, [http://www.amazon.com/Algebra-2nd-Featured-Titles-Abstract/dp/0132413779/ Amazon hardcover] \|\| $125 (new), $75 (used) \|\| Artin's book has a fair amount of coverage of the geometric intuition behind algebraic constructions, such as the role of groups in symmetry. However, it seems to be harder for people to do self-study from this book and obtain a comrephensive picture of the subject. We would advise this book to people who are reading with the help of a mentor who is willing to use the book, or people who have already studied the basic material and are now looking to delve deeper into the material from the perspective that Artin uses.
	\|-		\|-
	\| ''Basic Algebra'' and ''Further Algebra with Applications'' (book series) \|\| P. M. Cohn \|\| Basic: ISBN 978-1852335878, [http://www.amazon.com/Basic-Algebra-Paul-M-Cohn/dp/1852335874 Amazon hardcover]; Further: 978-1447111207, [http://www.amazon.com/Further-Algebra-Applications-Paul-Cohn/dp/1447111206/ Amazon paperback] \|\| Basic: $50-100 (depending on edition choice), Further: $50-100 (depending on edition choice) \|\| The book covers many interesting topics in interesting combinations. While we wouldn't recommending buying this as a main source of learning, it could be good to rent or check out from a library for interesting supplementary topics.		\| ''Basic Algebra'' and ''Further Algebra with Applications'' (book series) \|\| P. M. Cohn \|\| Basic: ISBN 978-1852335878, [http://www.amazon.com/Basic-Algebra-Paul-M-Cohn/dp/1852335874 Amazon hardcover]; Further: 978-1447111207, [http://www.amazon.com/Further-Algebra-Applications-Paul-Cohn/dp/1447111206/ Amazon paperback] \|\| Basic: $50-100 (depending on edition choice), Further: $50-100 (depending on edition choice) \|\| The book covers many interesting topics in interesting combinations. While we wouldn't recommending buying this as a main source of learning, it could be good to rent or check out from a library for interesting supplementary topics.

	\|}		\|}

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	* Math Doctor Bob has some videos on abstract algebra including group theory: See [http://mathdoctorbob.org/Algebra.html here].		* Math Doctor Bob has some videos on abstract algebra including group theory: See [http://mathdoctorbob.org/Algebra.html here].
	* Vipul Naik made videos on some introductory topics in group theory to supplement his [http://groupprops.subwiki.org/wiki/Tour:Getting_started_%28beginners%29 guided tour to group theory] (the videos can be viewed along with the material in the tour).		* Vipul Naik made videos on some introductory topics in group theory to supplement his [http://groupprops.subwiki.org/wiki/Tour:Getting_started_%28beginners%29 guided tour to group theory] (the videos can be viewed along with the material in the tour).

			==Books for casual reading==

			These books might inspire you to learn abstract algebra, help make sense of what you are already learning or have learned, or just be entertaining. They are unlikely to directly ''teach'' you abstract algebra.

			{\| class="sortable" border="1"
			! Book !! Author !! ISBN and purchase links !! Price estimate !! More about the book
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Vipul at 23:28, 31 January 2014

2014-01-31T23:28:01Z

← Older revision		Revision as of 23:28, 31 January 2014
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	* The modes of thinking introduced in abstract algebra, particularly the ideas of isomorphism and homomorphism, can be useful for understanding logic, philosophy, and various cognitive science-based subjects. However, the specifics of algebraic structures are not relevant.		* The modes of thinking introduced in abstract algebra, particularly the ideas of isomorphism and homomorphism, can be useful for understanding logic, philosophy, and various cognitive science-based subjects. However, the specifics of algebraic structures are not relevant.

	==~~Recommended books~~==		==Books for learning==

	{{top versus niche disclaimer}}		{{top versus niche disclaimer}}

Vipul: /* Recommended books */

2014-01-31T23:26:59Z

Recommended books

← Older revision		Revision as of 23:26, 31 January 2014
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	{\| class="sortable" border="1"		{\| class="sortable" border="1"
	! Book !! Author !! ISBN and purchase links !! Price estimate (values may be outdated; also, international editions may be cheaper) !!Why we're recommending it and who we're recommending it for		! Book !! Author !! ISBN and purchase links !! Price estimate (values may be outdated; also, international editions may be cheaper) !!Why we're recommending it and who we're recommending it for
			\|-
			\| ''Visual Group Theory'' \|\| Nathan Carter \|\| ISBN 978-0883857571, [http://www.amazon.com/Visual-Classroom-Resource-Materials-Problem/dp/088385757X Amazon hardcover] \|\| $50-75 \|\| Focused '''only on group theory''' and uses a somewhat heterodox perspective. Ideal for people who want to get a taste of the subject in advance of studying it formally. This might include high school students who have some interest in higher mathematics but are currently not prepared or inclined to go through a formal presentation of the material.
	\|-		\|-
	\| ''Algebra (2nd Edition) (Featured Titles for Abstract Algebra) [Hardcover]'' \|\| Michael Artin \|\| ISBN 978-0132413770, [http://www.amazon.com/Algebra-2nd-Featured-Titles-Abstract/dp/0132413779/ Amazon hardcover] \|\| $125 (new), $75 (used) \|\| Artin's book has a fair amount of coverage of the geometric intuition behind algebraic constructions, such as the role of groups in symmetry. However, it seems to be harder for people to do self-study from this book and obtain a comrephensive picture of the subject. We would advise this book to people who are reading with the help of a mentor who is willing to use the book, or people who have already studied the basic material and are now looking to delve deeper into the material from the perspective that Artin uses.		\| ''Algebra (2nd Edition) (Featured Titles for Abstract Algebra) [Hardcover]'' \|\| Michael Artin \|\| ISBN 978-0132413770, [http://www.amazon.com/Algebra-2nd-Featured-Titles-Abstract/dp/0132413779/ Amazon hardcover] \|\| $125 (new), $75 (used) \|\| Artin's book has a fair amount of coverage of the geometric intuition behind algebraic constructions, such as the role of groups in symmetry. However, it seems to be harder for people to do self-study from this book and obtain a comrephensive picture of the subject. We would advise this book to people who are reading with the help of a mentor who is willing to use the book, or people who have already studied the basic material and are now looking to delve deeper into the material from the perspective that Artin uses.
	\|-		\|-
	\| ''Basic Algebra'' and ''Further Algebra with Applications'' (book series) \|\| P. M. Cohn \|\| Basic: ISBN 978-1852335878, [http://www.amazon.com/Basic-Algebra-Paul-M-Cohn/dp/1852335874 Amazon hardcover]; Further: 978-1447111207, [http://www.amazon.com/Further-Algebra-Applications-Paul-Cohn/dp/1447111206/ Amazon paperback] \|\| Basic: $50-100 (depending on edition choice), Further: $50-100 (depending on edition choice) \|\| The book covers many interesting topics in interesting combinations. While we wouldn't recommending buying this as a main source of learning, it could be good to rent or check out from a library for interesting supplementary topics.		\| ''Basic Algebra'' and ''Further Algebra with Applications'' (book series) \|\| P. M. Cohn \|\| Basic: ISBN 978-1852335878, [http://www.amazon.com/Basic-Algebra-Paul-M-Cohn/dp/1852335874 Amazon hardcover]; Further: 978-1447111207, [http://www.amazon.com/Further-Algebra-Applications-Paul-Cohn/dp/1447111206/ Amazon paperback] \|\| Basic: $50-100 (depending on edition choice), Further: $50-100 (depending on edition choice) \|\| The book covers many interesting topics in interesting combinations. While we wouldn't recommending buying this as a main source of learning, it could be good to rent or check out from a library for interesting supplementary topics.

	\|}		\|}

Vipul: /* Usefulness */

2014-01-31T23:04:53Z

Usefulness

← Older revision		Revision as of 23:04, 31 January 2014
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	==Usefulness==		==Usefulness==

			{{further\|[[abstract algebra learning benefits]]}}

	* Abstract algebra is largely useful only for people who intend to major in mathematics and do further work in a mathematics-intensive area (such as physics, some parts of computer science, and some parts of chemistry).		* Abstract algebra is largely useful only for people who intend to major in mathematics and do further work in a mathematics-intensive area (such as physics, some parts of computer science, and some parts of chemistry).

Vipul: /* Recommended books */

2014-01-31T23:01:13Z

Recommended books

← Older revision		Revision as of 23:01, 31 January 2014
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	==Recommended books==		==Recommended books==

	~~Our~~ top general recommendations are recommendations that we would give people if we had to name just a few top books. Our niche recommendations are recommendations that suit learners with specific learning styles or goals. For learners who fit one of the niches, the niche ~~recommendation would be better. Price ranges are provided to give better context to the strength of our recommendation.~~		{{top versus niche disclaimer}}

	===Top general recommendations===		===Top general recommendations===