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=References and Further Reading= | =References and Further Reading= | ||
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Information: <br /> | Information: <br /> | ||
https://www.jstor.org/stable/2974763?seq=1 (Proof of polynomials of degree 5 or higher being unsolvable in the general sense) <br /> | https://www.jstor.org/stable/2974763?seq=1 (Proof of polynomials of degree 5 or higher being unsolvable in the general sense) <br /> | ||
| − | https://en.wikipedia.org/wiki/Group_(mathematics) (Information for groups) <br /> | + | https://en.wikipedia.org/wiki/Group_(mathematics) (Information for groups and group theory) <br /> |
| − | https://mathworld.wolfram.com/GaloisGroup.html (Galois group | + | https://mathworld.wolfram.com/GaloisGroup.html (Galois group info) <br /> |
| + | https://www.youtube.com/watch?v=3aNeCWRjh8I (Symmetric groups) <br /> | ||
| + | https://www.youtube.com/watch?v=8A84sA1YuPw (Cyclic groups) <br /> | ||
| + | https://mathworld.wolfram.com/Field.html (Fields) <br /> | ||
| + | https://mathworld.wolfram.com/ExtensionField.html (Field extensions) <br /> | ||
| + | https://mathworld.wolfram.com/FundamentalTheoremofGaloisTheory.html (Fundamental Theorem of Galois Theory) <br /> | ||
| + | https://www.britannica.com/biography/Evariste-Galois (Information about Galois himself) <br /> | ||
| + | https://en.wikipedia.org/wiki/Abel%E2%80%93Ruffini_theorem (Abel-Ruffini Theorem) <br /> | ||
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Images: <br /> | Images: <br /> | ||
https://commons.wikimedia.org/wiki/File:Evariste_galois.jpg (Figure 1.1) <br /> | https://commons.wikimedia.org/wiki/File:Evariste_galois.jpg (Figure 1.1) <br /> | ||
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https://commons.wikimedia.org/wiki/File:Lattice_diagram_of_Q_adjoin_the_positive_square_roots_of_2_and_3,_its_subfields,_and_Galois_groups.svg (Figure 4.4) <br /> | https://commons.wikimedia.org/wiki/File:Lattice_diagram_of_Q_adjoin_the_positive_square_roots_of_2_and_3,_its_subfields,_and_Galois_groups.svg (Figure 4.4) <br /> | ||
https://mathworld.wolfram.com/AngleTrisection.html (Figure 5.1) <br /> | https://mathworld.wolfram.com/AngleTrisection.html (Figure 5.1) <br /> | ||
| + | https://en.wikipedia.org/wiki/Quaternion_group (Figure 6.1) <br /> | ||
Further Reading: <br /> | Further Reading: <br /> | ||
| + | https://www.math3ma.com/blog/what-is-galois-theory-anyway (A nice treatment of field theory and group theory in the context of Galois Theory) <br/> | ||
https://nrich.maths.org/1422 (An overview of Galois theory and the Galois group) <br /> | https://nrich.maths.org/1422 (An overview of Galois theory and the Galois group) <br /> | ||
| + | https://en.wikipedia.org/wiki/Quaternion_group (Quaternion group theory) <br /> | ||
| + | http://www.science4all.org/article/galois-theory/ (A light treatment of Galois Theory) <br /> | ||
| + | https://brilliant.org/wiki/group-theory-introduction/ (For those who want to learn more about Group Theory) <br /> | ||
| + | [[ Walther MA271 Fall2020 topic1|Back to Walther MA271 Fall2020 topic1]] | ||
| − | [[ | + | [[Category:MA271Fall2020Walther]] |
Latest revision as of 00:27, 7 December 2020
References and Further Reading
References:
Information:
https://www.jstor.org/stable/2974763?seq=1 (Proof of polynomials of degree 5 or higher being unsolvable in the general sense)
https://en.wikipedia.org/wiki/Group_(mathematics) (Information for groups and group theory)
https://mathworld.wolfram.com/GaloisGroup.html (Galois group info)
https://www.youtube.com/watch?v=3aNeCWRjh8I (Symmetric groups)
https://www.youtube.com/watch?v=8A84sA1YuPw (Cyclic groups)
https://mathworld.wolfram.com/Field.html (Fields)
https://mathworld.wolfram.com/ExtensionField.html (Field extensions)
https://mathworld.wolfram.com/FundamentalTheoremofGaloisTheory.html (Fundamental Theorem of Galois Theory)
https://www.britannica.com/biography/Evariste-Galois (Information about Galois himself)
https://en.wikipedia.org/wiki/Abel%E2%80%93Ruffini_theorem (Abel-Ruffini Theorem)
Images:
https://commons.wikimedia.org/wiki/File:Evariste_galois.jpg (Figure 1.1)
https://commons.wikimedia.org/wiki/File:Cyclic_group.svg (Figure 2.1)
https://www.johndcook.com/blog/2013/12/02/visualizing-galois-groups-of-quadratics/ (Figure 4.1)
https://en.wikipedia.org/wiki/Abel%E2%80%93Ruffini_theorem (Figure 4.2 and 4.3)
https://commons.wikimedia.org/wiki/File:Lattice_diagram_of_Q_adjoin_the_positive_square_roots_of_2_and_3,_its_subfields,_and_Galois_groups.svg (Figure 4.4)
https://mathworld.wolfram.com/AngleTrisection.html (Figure 5.1)
https://en.wikipedia.org/wiki/Quaternion_group (Figure 6.1)
Further Reading:
https://www.math3ma.com/blog/what-is-galois-theory-anyway (A nice treatment of field theory and group theory in the context of Galois Theory)
https://nrich.maths.org/1422 (An overview of Galois theory and the Galois group)
https://en.wikipedia.org/wiki/Quaternion_group (Quaternion group theory)
http://www.science4all.org/article/galois-theory/ (A light treatment of Galois Theory)
https://brilliant.org/wiki/group-theory-introduction/ (For those who want to learn more about Group Theory)
