Exercises on Galois Theory












16












$begingroup$


I need a source for exercises on classical Galois Theory, or to be more specific, Galois extensions of finite fields and the rationals as well as applications (solvability by radicals, for example).
So far, I have worked with Tignol's "Galois Theory of Algebraic Equations". Any additional suggestions would be appreciated, whether it is a textbook or a website, but the language should be English. Solutions are welcome, but no necessity.



Thanks in advance!










share|cite|improve this question











$endgroup$

















    16












    $begingroup$


    I need a source for exercises on classical Galois Theory, or to be more specific, Galois extensions of finite fields and the rationals as well as applications (solvability by radicals, for example).
    So far, I have worked with Tignol's "Galois Theory of Algebraic Equations". Any additional suggestions would be appreciated, whether it is a textbook or a website, but the language should be English. Solutions are welcome, but no necessity.



    Thanks in advance!










    share|cite|improve this question











    $endgroup$















      16












      16








      16


      7



      $begingroup$


      I need a source for exercises on classical Galois Theory, or to be more specific, Galois extensions of finite fields and the rationals as well as applications (solvability by radicals, for example).
      So far, I have worked with Tignol's "Galois Theory of Algebraic Equations". Any additional suggestions would be appreciated, whether it is a textbook or a website, but the language should be English. Solutions are welcome, but no necessity.



      Thanks in advance!










      share|cite|improve this question











      $endgroup$




      I need a source for exercises on classical Galois Theory, or to be more specific, Galois extensions of finite fields and the rationals as well as applications (solvability by radicals, for example).
      So far, I have worked with Tignol's "Galois Theory of Algebraic Equations". Any additional suggestions would be appreciated, whether it is a textbook or a website, but the language should be English. Solutions are welcome, but no necessity.



      Thanks in advance!







      abstract-algebra reference-request galois-theory book-recommendation online-resources






      share|cite|improve this question















      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited Dec 18 '14 at 8:14









      Martin Sleziak

      44.7k8117272




      44.7k8117272










      asked Jul 25 '11 at 13:28









      Clifford B.Clifford B.

      8314




      8314






















          4 Answers
          4






          active

          oldest

          votes


















          11












          $begingroup$

          I really like the exercises in Lang's Algebra. There's a little bit of everything in there.



          Milne's notes have exercises at the end of every chapter, a chapter of review exercises, and a two-hour exam; solutions (or at least hints) for all of these are given at the end. A lot of the action takes place over $mathbf Q$, but I saw a fair number of questions about finite fields and they seemed good.



          Keith Conrad's handouts don't have a lot of exercises, but when I had to review this stuff I found it helpful to look at the statements of his examples, try them for myself, and then read his methods. There are usually myriad ways to solve exercises in this area.



          Teruyoshi Yoshida has fun example sheets, in addition to complete course notes.






          share|cite|improve this answer









          $endgroup$













          • $begingroup$
            Thanks to you, too; I wanted to get Lang's book as a reference, but I'll take a look at the exercises as well.
            $endgroup$
            – Clifford B.
            Jul 25 '11 at 15:46










          • $begingroup$
            No problem! Lang's book is divisive, but it can teach you a lot, and the field theory chapters are probably its best; George Bergman's companion to the book could be useful as well.
            $endgroup$
            – Dylan Moreland
            Jul 25 '11 at 15:54





















          5












          $begingroup$

          Try these books:




          • Classical Galois Theory with Examples

          • Exploratory Galois Theory

          • Galois Theory for Beginners: A Historical Perspective






          share|cite|improve this answer











          $endgroup$













          • $begingroup$
            Thanks, I will check them out as soon as possible.
            $endgroup$
            – Clifford B.
            Jul 25 '11 at 14:00



















          3












          $begingroup$

          Many pages of exercises at J K Verma's website, here.






          share|cite|improve this answer









          $endgroup$





















            0












            $begingroup$

            Have you tried working out through



            (I) Abstract Algebra by dummit Foote



            (II)Field and Galois theory by Patrick Morandi



            Both of these books are rich with exercise problem and he questions are very diverse. I would recommend you to go through this as it helped me tremendously






            share|cite|improve this answer








            New contributor




            user631697 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
            Check out our Code of Conduct.






            $endgroup$













              Your Answer





              StackExchange.ifUsing("editor", function () {
              return StackExchange.using("mathjaxEditing", function () {
              StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
              StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
              });
              });
              }, "mathjax-editing");

              StackExchange.ready(function() {
              var channelOptions = {
              tags: "".split(" "),
              id: "69"
              };
              initTagRenderer("".split(" "), "".split(" "), channelOptions);

              StackExchange.using("externalEditor", function() {
              // Have to fire editor after snippets, if snippets enabled
              if (StackExchange.settings.snippets.snippetsEnabled) {
              StackExchange.using("snippets", function() {
              createEditor();
              });
              }
              else {
              createEditor();
              }
              });

              function createEditor() {
              StackExchange.prepareEditor({
              heartbeatType: 'answer',
              autoActivateHeartbeat: false,
              convertImagesToLinks: true,
              noModals: true,
              showLowRepImageUploadWarning: true,
              reputationToPostImages: 10,
              bindNavPrevention: true,
              postfix: "",
              imageUploader: {
              brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
              contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
              allowUrls: true
              },
              noCode: true, onDemand: true,
              discardSelector: ".discard-answer"
              ,immediatelyShowMarkdownHelp:true
              });


              }
              });














              draft saved

              draft discarded


















              StackExchange.ready(
              function () {
              StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f53658%2fexercises-on-galois-theory%23new-answer', 'question_page');
              }
              );

              Post as a guest















              Required, but never shown

























              4 Answers
              4






              active

              oldest

              votes








              4 Answers
              4






              active

              oldest

              votes









              active

              oldest

              votes






              active

              oldest

              votes









              11












              $begingroup$

              I really like the exercises in Lang's Algebra. There's a little bit of everything in there.



              Milne's notes have exercises at the end of every chapter, a chapter of review exercises, and a two-hour exam; solutions (or at least hints) for all of these are given at the end. A lot of the action takes place over $mathbf Q$, but I saw a fair number of questions about finite fields and they seemed good.



              Keith Conrad's handouts don't have a lot of exercises, but when I had to review this stuff I found it helpful to look at the statements of his examples, try them for myself, and then read his methods. There are usually myriad ways to solve exercises in this area.



              Teruyoshi Yoshida has fun example sheets, in addition to complete course notes.






              share|cite|improve this answer









              $endgroup$













              • $begingroup$
                Thanks to you, too; I wanted to get Lang's book as a reference, but I'll take a look at the exercises as well.
                $endgroup$
                – Clifford B.
                Jul 25 '11 at 15:46










              • $begingroup$
                No problem! Lang's book is divisive, but it can teach you a lot, and the field theory chapters are probably its best; George Bergman's companion to the book could be useful as well.
                $endgroup$
                – Dylan Moreland
                Jul 25 '11 at 15:54


















              11












              $begingroup$

              I really like the exercises in Lang's Algebra. There's a little bit of everything in there.



              Milne's notes have exercises at the end of every chapter, a chapter of review exercises, and a two-hour exam; solutions (or at least hints) for all of these are given at the end. A lot of the action takes place over $mathbf Q$, but I saw a fair number of questions about finite fields and they seemed good.



              Keith Conrad's handouts don't have a lot of exercises, but when I had to review this stuff I found it helpful to look at the statements of his examples, try them for myself, and then read his methods. There are usually myriad ways to solve exercises in this area.



              Teruyoshi Yoshida has fun example sheets, in addition to complete course notes.






              share|cite|improve this answer









              $endgroup$













              • $begingroup$
                Thanks to you, too; I wanted to get Lang's book as a reference, but I'll take a look at the exercises as well.
                $endgroup$
                – Clifford B.
                Jul 25 '11 at 15:46










              • $begingroup$
                No problem! Lang's book is divisive, but it can teach you a lot, and the field theory chapters are probably its best; George Bergman's companion to the book could be useful as well.
                $endgroup$
                – Dylan Moreland
                Jul 25 '11 at 15:54
















              11












              11








              11





              $begingroup$

              I really like the exercises in Lang's Algebra. There's a little bit of everything in there.



              Milne's notes have exercises at the end of every chapter, a chapter of review exercises, and a two-hour exam; solutions (or at least hints) for all of these are given at the end. A lot of the action takes place over $mathbf Q$, but I saw a fair number of questions about finite fields and they seemed good.



              Keith Conrad's handouts don't have a lot of exercises, but when I had to review this stuff I found it helpful to look at the statements of his examples, try them for myself, and then read his methods. There are usually myriad ways to solve exercises in this area.



              Teruyoshi Yoshida has fun example sheets, in addition to complete course notes.






              share|cite|improve this answer









              $endgroup$



              I really like the exercises in Lang's Algebra. There's a little bit of everything in there.



              Milne's notes have exercises at the end of every chapter, a chapter of review exercises, and a two-hour exam; solutions (or at least hints) for all of these are given at the end. A lot of the action takes place over $mathbf Q$, but I saw a fair number of questions about finite fields and they seemed good.



              Keith Conrad's handouts don't have a lot of exercises, but when I had to review this stuff I found it helpful to look at the statements of his examples, try them for myself, and then read his methods. There are usually myriad ways to solve exercises in this area.



              Teruyoshi Yoshida has fun example sheets, in addition to complete course notes.







              share|cite|improve this answer












              share|cite|improve this answer



              share|cite|improve this answer










              answered Jul 25 '11 at 15:13









              Dylan MorelandDylan Moreland

              16.8k23563




              16.8k23563












              • $begingroup$
                Thanks to you, too; I wanted to get Lang's book as a reference, but I'll take a look at the exercises as well.
                $endgroup$
                – Clifford B.
                Jul 25 '11 at 15:46










              • $begingroup$
                No problem! Lang's book is divisive, but it can teach you a lot, and the field theory chapters are probably its best; George Bergman's companion to the book could be useful as well.
                $endgroup$
                – Dylan Moreland
                Jul 25 '11 at 15:54




















              • $begingroup$
                Thanks to you, too; I wanted to get Lang's book as a reference, but I'll take a look at the exercises as well.
                $endgroup$
                – Clifford B.
                Jul 25 '11 at 15:46










              • $begingroup$
                No problem! Lang's book is divisive, but it can teach you a lot, and the field theory chapters are probably its best; George Bergman's companion to the book could be useful as well.
                $endgroup$
                – Dylan Moreland
                Jul 25 '11 at 15:54


















              $begingroup$
              Thanks to you, too; I wanted to get Lang's book as a reference, but I'll take a look at the exercises as well.
              $endgroup$
              – Clifford B.
              Jul 25 '11 at 15:46




              $begingroup$
              Thanks to you, too; I wanted to get Lang's book as a reference, but I'll take a look at the exercises as well.
              $endgroup$
              – Clifford B.
              Jul 25 '11 at 15:46












              $begingroup$
              No problem! Lang's book is divisive, but it can teach you a lot, and the field theory chapters are probably its best; George Bergman's companion to the book could be useful as well.
              $endgroup$
              – Dylan Moreland
              Jul 25 '11 at 15:54






              $begingroup$
              No problem! Lang's book is divisive, but it can teach you a lot, and the field theory chapters are probably its best; George Bergman's companion to the book could be useful as well.
              $endgroup$
              – Dylan Moreland
              Jul 25 '11 at 15:54













              5












              $begingroup$

              Try these books:




              • Classical Galois Theory with Examples

              • Exploratory Galois Theory

              • Galois Theory for Beginners: A Historical Perspective






              share|cite|improve this answer











              $endgroup$













              • $begingroup$
                Thanks, I will check them out as soon as possible.
                $endgroup$
                – Clifford B.
                Jul 25 '11 at 14:00
















              5












              $begingroup$

              Try these books:




              • Classical Galois Theory with Examples

              • Exploratory Galois Theory

              • Galois Theory for Beginners: A Historical Perspective






              share|cite|improve this answer











              $endgroup$













              • $begingroup$
                Thanks, I will check them out as soon as possible.
                $endgroup$
                – Clifford B.
                Jul 25 '11 at 14:00














              5












              5








              5





              $begingroup$

              Try these books:




              • Classical Galois Theory with Examples

              • Exploratory Galois Theory

              • Galois Theory for Beginners: A Historical Perspective






              share|cite|improve this answer











              $endgroup$



              Try these books:




              • Classical Galois Theory with Examples

              • Exploratory Galois Theory

              • Galois Theory for Beginners: A Historical Perspective







              share|cite|improve this answer














              share|cite|improve this answer



              share|cite|improve this answer








              edited Aug 3 '17 at 1:26

























              answered Jul 25 '11 at 13:42









              lhflhf

              163k10168390




              163k10168390












              • $begingroup$
                Thanks, I will check them out as soon as possible.
                $endgroup$
                – Clifford B.
                Jul 25 '11 at 14:00


















              • $begingroup$
                Thanks, I will check them out as soon as possible.
                $endgroup$
                – Clifford B.
                Jul 25 '11 at 14:00
















              $begingroup$
              Thanks, I will check them out as soon as possible.
              $endgroup$
              – Clifford B.
              Jul 25 '11 at 14:00




              $begingroup$
              Thanks, I will check them out as soon as possible.
              $endgroup$
              – Clifford B.
              Jul 25 '11 at 14:00











              3












              $begingroup$

              Many pages of exercises at J K Verma's website, here.






              share|cite|improve this answer









              $endgroup$


















                3












                $begingroup$

                Many pages of exercises at J K Verma's website, here.






                share|cite|improve this answer









                $endgroup$
















                  3












                  3








                  3





                  $begingroup$

                  Many pages of exercises at J K Verma's website, here.






                  share|cite|improve this answer









                  $endgroup$



                  Many pages of exercises at J K Verma's website, here.







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered Aug 13 '14 at 4:46









                  Gerry MyersonGerry Myerson

                  146k8147299




                  146k8147299























                      0












                      $begingroup$

                      Have you tried working out through



                      (I) Abstract Algebra by dummit Foote



                      (II)Field and Galois theory by Patrick Morandi



                      Both of these books are rich with exercise problem and he questions are very diverse. I would recommend you to go through this as it helped me tremendously






                      share|cite|improve this answer








                      New contributor




                      user631697 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                      Check out our Code of Conduct.






                      $endgroup$


















                        0












                        $begingroup$

                        Have you tried working out through



                        (I) Abstract Algebra by dummit Foote



                        (II)Field and Galois theory by Patrick Morandi



                        Both of these books are rich with exercise problem and he questions are very diverse. I would recommend you to go through this as it helped me tremendously






                        share|cite|improve this answer








                        New contributor




                        user631697 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                        Check out our Code of Conduct.






                        $endgroup$
















                          0












                          0








                          0





                          $begingroup$

                          Have you tried working out through



                          (I) Abstract Algebra by dummit Foote



                          (II)Field and Galois theory by Patrick Morandi



                          Both of these books are rich with exercise problem and he questions are very diverse. I would recommend you to go through this as it helped me tremendously






                          share|cite|improve this answer








                          New contributor




                          user631697 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                          Check out our Code of Conduct.






                          $endgroup$



                          Have you tried working out through



                          (I) Abstract Algebra by dummit Foote



                          (II)Field and Galois theory by Patrick Morandi



                          Both of these books are rich with exercise problem and he questions are very diverse. I would recommend you to go through this as it helped me tremendously







                          share|cite|improve this answer








                          New contributor




                          user631697 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                          Check out our Code of Conduct.









                          share|cite|improve this answer



                          share|cite|improve this answer






                          New contributor




                          user631697 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                          Check out our Code of Conduct.









                          answered Jan 7 at 18:54









                          user631697user631697

                          111




                          111




                          New contributor




                          user631697 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                          Check out our Code of Conduct.





                          New contributor





                          user631697 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                          Check out our Code of Conduct.






                          user631697 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                          Check out our Code of Conduct.






























                              draft saved

                              draft discarded




















































                              Thanks for contributing an answer to Mathematics Stack Exchange!


                              • Please be sure to answer the question. Provide details and share your research!

                              But avoid



                              • Asking for help, clarification, or responding to other answers.

                              • Making statements based on opinion; back them up with references or personal experience.


                              Use MathJax to format equations. MathJax reference.


                              To learn more, see our tips on writing great answers.




                              draft saved


                              draft discarded














                              StackExchange.ready(
                              function () {
                              StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f53658%2fexercises-on-galois-theory%23new-answer', 'question_page');
                              }
                              );

                              Post as a guest















                              Required, but never shown





















































                              Required, but never shown














                              Required, but never shown












                              Required, but never shown







                              Required, but never shown

































                              Required, but never shown














                              Required, but never shown












                              Required, but never shown







                              Required, but never shown







                              Popular posts from this blog

                              Mario Kart Wii

                              What does “Dominus providebit” mean?

                              Antonio Litta Visconti Arese