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
Contributor
Author
Provider
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
http://library.link/vocab/creatorName
Brzeziński, Juliusz
Image bit depth
0
LC call number
  • QA161.A-161.Z
  • QA161.P59
Literary form
non fiction
http://library.link/vocab/relatedWorkOrContributorName
SpringerLink
Series statement
Springer Undergraduate Mathematics Series,
http://library.link/vocab/subjectName
  • Mathematics
  • Geometry, Algebraic
  • Associative rings
  • Rings (Algebra)
  • Commutative algebra
  • Commutative rings
  • Algebra
  • Field theory (Physics)
  • Group theory
  • Number theory
  • Mathematics
  • Field Theory and Polynomials
  • Number Theory
  • Algebraic Geometry
  • Associative Rings and Algebras
  • Commutative Rings and Algebras
  • Group Theory and Generalizations
Label
Galois Theory Through Exercises, by Juliusz Brzeziński, (electronic resource)
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
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
Dimensions
unknown
Extent
XVII, 293 p. 12 illus.
File format
multiple file formats
Form of item
electronic
Isbn
9783319723266
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-319-72326-6
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-319-72326-6
Label
Galois Theory Through Exercises, by Juliusz Brzeziński, (electronic resource)
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
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
Dimensions
unknown
Extent
XVII, 293 p. 12 illus.
File format
multiple file formats
Form of item
electronic
Isbn
9783319723266
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-319-72326-6
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-319-72326-6

Library Locations

  • African Studies LibraryBorrow it
    771 Commonwealth Avenue, 6th Floor, Boston, MA, 02215, US
    42.350723 -71.108227
  • Alumni Medical LibraryBorrow it
    72 East Concord Street, Boston, MA, 02118, US
    42.336388 -71.072393
  • Astronomy LibraryBorrow it
    725 Commonwealth Avenue, 6th Floor, Boston, MA, 02445, US
    42.350259 -71.105717
  • Fineman and Pappas Law LibrariesBorrow it
    765 Commonwealth Avenue, Boston, MA, 02215, US
    42.350979 -71.107023
  • Frederick S. Pardee Management LibraryBorrow it
    595 Commonwealth Avenue, Boston, MA, 02215, US
    42.349626 -71.099547
  • Howard Gotlieb Archival Research CenterBorrow it
    771 Commonwealth Avenue, 5th Floor, Boston, MA, 02215, US
    42.350723 -71.108227
  • Mugar Memorial LibraryBorrow it
    771 Commonwealth Avenue, Boston, MA, 02215, US
    42.350723 -71.108227
  • Music LibraryBorrow it
    771 Commonwealth Avenue, 2nd Floor, Boston, MA, 02215, US
    42.350723 -71.108227
  • Pikering Educational Resources LibraryBorrow it
    2 Silber Way, Boston, MA, 02215, US
    42.349804 -71.101425
  • School of Theology LibraryBorrow it
    745 Commonwealth Avenue, 2nd Floor, Boston, MA, 02215, US
    42.350494 -71.107235
  • Science & Engineering LibraryBorrow it
    38 Cummington Mall, Boston, MA, 02215, US
    42.348472 -71.102257
  • Stone Science LibraryBorrow it
    675 Commonwealth Avenue, Boston, MA, 02445, US
    42.350103 -71.103784
Processing Feedback ...