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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 | + | https://en.wikipedia.org/wiki/Quaternion_group (Figure 6.1) <br /> |
Further Reading: <br /> | Further Reading: <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 /> | ||
Revision as of 00:20, 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://nrich.maths.org/1422 (An overview of Galois theory and the Galois group)
https://en.wikipedia.org/wiki/Quaternion_group (Quaternion group theory)
