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The Resource Galois Theory Through Exercises, by Juliusz Brzeziński, (electronic resource)

Galois Theory Through Exercises, by Juliusz Brzeziński, (electronic resource)

Label
Galois Theory Through Exercises
Title
Galois Theory Through Exercises
Statement of responsibility
by Juliusz Brzeziński
Creator
Subject
Language
eng
Summary
This textbook offers a unique introduction to classical Galois theory through many concrete examples and exercises of varying difficulty (including computer-assisted exercises). In addition to covering standard material, the book explores topics related to classical problems such as Galois’ theorem on solvable groups of polynomial equations of prime degrees, Nagell's proof of non-solvability by radicals of quintic equations, Tschirnhausen's transformations, lunes of Hippocrates, and Galois' resolvents. Topics related to open conjectures are also discussed, including exercises related to the inverse Galois problem and cyclotomic fields. The author presents proofs of theorems, historical comments and useful references alongside the exercises, providing readers with a well-rounded introduction to the subject and a gateway to further reading. A valuable reference and a rich source of exercises with sample solutions, this book will be useful to both students and lecturers. Its original concept makes it particularly suitable for self-study.--
Member of
Assigning source
Provided by publisher
http://library.link/vocab/creatorName
Brzeziński, Juliusz
Literary form
non fiction
Nature of contents
dictionaries
Series statement
  • Springer eBooks
  • Springer eBooks.
  • Springer Undergraduate Mathematics Series,
http://library.link/vocab/subjectName
  • Algebra
  • Field theory (Physics)
  • Geometry, algebraic
  • Group theory
  • Number theory
Label
Galois Theory Through Exercises, by Juliusz Brzeziński, (electronic resource)
Link
http://ezproxy.eui.eu/login?url=https://doi.org/10.1007/978-3-319-72326-6
Instantiates
Publication
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
1 Solving algebraic equations -- 2 Field extensions -- 3 Polynomials and irreducibility -- 4 Algebraic extensions -- 5 Splitting fields -- 6 Automorphism groups of fields -- 7 Normal extensions -- 8 Separable extensions -- 9 Galois extensions -- 10 Cyclotomic extensions -- 11 Galois modules -- 12 Solvable groups -- 13 Solvability of equations -- 14 Geometric constructions -- 15 Computing Galois groups -- 16 Supplementary problems -- 17 Proofs of the theorems -- 18 Hints and answers -- 19 Examples and selected solutions -- Appendix: Groups, rings and fields -- References -- List of notations -- Index
Control code
978-3-319-72326-6
Dimensions
unknown
Extent
1 online resource (XVII, 293 pages)
Form of item
  • online
  • electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783319723266
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
12 illustrations
Specific material designation
remote
System control number
(OCoLC)1029606616
Label
Galois Theory Through Exercises, by Juliusz Brzeziński, (electronic resource)
Link
http://ezproxy.eui.eu/login?url=https://doi.org/10.1007/978-3-319-72326-6
Publication
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
1 Solving algebraic equations -- 2 Field extensions -- 3 Polynomials and irreducibility -- 4 Algebraic extensions -- 5 Splitting fields -- 6 Automorphism groups of fields -- 7 Normal extensions -- 8 Separable extensions -- 9 Galois extensions -- 10 Cyclotomic extensions -- 11 Galois modules -- 12 Solvable groups -- 13 Solvability of equations -- 14 Geometric constructions -- 15 Computing Galois groups -- 16 Supplementary problems -- 17 Proofs of the theorems -- 18 Hints and answers -- 19 Examples and selected solutions -- Appendix: Groups, rings and fields -- References -- List of notations -- Index
Control code
978-3-319-72326-6
Dimensions
unknown
Extent
1 online resource (XVII, 293 pages)
Form of item
  • online
  • electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783319723266
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
12 illustrations
Specific material designation
remote
System control number
(OCoLC)1029606616

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