Undergraduate research in Algebra or Analysis?












1












$begingroup$


Background: I am a sophomore who has taken one analysis course, and one linear algebra course. I am taking abstract algebra, 2nd read analysis, and topology this semester. I have participated in a directed reading program last semester and learned some representation theory and matrix groups. Using Serre's representation theory for finite groups and Tapp's Matrix Groups for Undergraduates. However, I don't think I understand algebra as deep as analysis. Since somewhat algebra seems more abstract to me.



Since I found them both interesting, but interesting in a different way. I wonder if it is true that researching in analysis requires not as many pre-requisites as researching in algebra? Since I noticed that there are a lot of topics in algebra, but not as many as in analysis. I understand that whatever topic I choose to dwell in doesn't really matter much toward my graduate study since I could always change before that. So I wonder what is more beneficial to me? Given my background, would it be easier to do an undergraduate project in analysis than algebra?










share|cite|improve this question









$endgroup$








  • 2




    $begingroup$
    If you're looking for something accessible, and you want to do something original, right now, at this very moment, then neither analysis nor algebra is a good choice. I would look into combinatorics.
    $endgroup$
    – Matt Samuel
    Jan 8 at 3:00










  • $begingroup$
    That said, undergraduate projects in math aren't usually original. Mine was, but I was extremely advanced, and had essentially already taken a full year's worth of graduate courses before I discovered something new. Of course other people also do this, but it's the exception rather than the rule. Harvard warns their graduate students that their dissertation might be only a minuscule advancement in their field, and that's normal and not an indication of failure.
    $endgroup$
    – Matt Samuel
    Jan 8 at 3:06










  • $begingroup$
    Thank you! I totally understand that undergraduate research is more reading than really researching. I believe I concern is that is there much content in algebra than analysis? @MattSamuel
    $endgroup$
    – Alvis Nordkovich
    Jan 8 at 3:14






  • 2




    $begingroup$
    There is a massive amount of content in both of them. Analysis is sort of a younger subject, but it's still hundreds of years old. In any subject except combinatorics undergraduates may only barely get into the topics of the early 20th century.
    $endgroup$
    – Matt Samuel
    Jan 8 at 3:20
















1












$begingroup$


Background: I am a sophomore who has taken one analysis course, and one linear algebra course. I am taking abstract algebra, 2nd read analysis, and topology this semester. I have participated in a directed reading program last semester and learned some representation theory and matrix groups. Using Serre's representation theory for finite groups and Tapp's Matrix Groups for Undergraduates. However, I don't think I understand algebra as deep as analysis. Since somewhat algebra seems more abstract to me.



Since I found them both interesting, but interesting in a different way. I wonder if it is true that researching in analysis requires not as many pre-requisites as researching in algebra? Since I noticed that there are a lot of topics in algebra, but not as many as in analysis. I understand that whatever topic I choose to dwell in doesn't really matter much toward my graduate study since I could always change before that. So I wonder what is more beneficial to me? Given my background, would it be easier to do an undergraduate project in analysis than algebra?










share|cite|improve this question









$endgroup$








  • 2




    $begingroup$
    If you're looking for something accessible, and you want to do something original, right now, at this very moment, then neither analysis nor algebra is a good choice. I would look into combinatorics.
    $endgroup$
    – Matt Samuel
    Jan 8 at 3:00










  • $begingroup$
    That said, undergraduate projects in math aren't usually original. Mine was, but I was extremely advanced, and had essentially already taken a full year's worth of graduate courses before I discovered something new. Of course other people also do this, but it's the exception rather than the rule. Harvard warns their graduate students that their dissertation might be only a minuscule advancement in their field, and that's normal and not an indication of failure.
    $endgroup$
    – Matt Samuel
    Jan 8 at 3:06










  • $begingroup$
    Thank you! I totally understand that undergraduate research is more reading than really researching. I believe I concern is that is there much content in algebra than analysis? @MattSamuel
    $endgroup$
    – Alvis Nordkovich
    Jan 8 at 3:14






  • 2




    $begingroup$
    There is a massive amount of content in both of them. Analysis is sort of a younger subject, but it's still hundreds of years old. In any subject except combinatorics undergraduates may only barely get into the topics of the early 20th century.
    $endgroup$
    – Matt Samuel
    Jan 8 at 3:20














1












1








1





$begingroup$


Background: I am a sophomore who has taken one analysis course, and one linear algebra course. I am taking abstract algebra, 2nd read analysis, and topology this semester. I have participated in a directed reading program last semester and learned some representation theory and matrix groups. Using Serre's representation theory for finite groups and Tapp's Matrix Groups for Undergraduates. However, I don't think I understand algebra as deep as analysis. Since somewhat algebra seems more abstract to me.



Since I found them both interesting, but interesting in a different way. I wonder if it is true that researching in analysis requires not as many pre-requisites as researching in algebra? Since I noticed that there are a lot of topics in algebra, but not as many as in analysis. I understand that whatever topic I choose to dwell in doesn't really matter much toward my graduate study since I could always change before that. So I wonder what is more beneficial to me? Given my background, would it be easier to do an undergraduate project in analysis than algebra?










share|cite|improve this question









$endgroup$




Background: I am a sophomore who has taken one analysis course, and one linear algebra course. I am taking abstract algebra, 2nd read analysis, and topology this semester. I have participated in a directed reading program last semester and learned some representation theory and matrix groups. Using Serre's representation theory for finite groups and Tapp's Matrix Groups for Undergraduates. However, I don't think I understand algebra as deep as analysis. Since somewhat algebra seems more abstract to me.



Since I found them both interesting, but interesting in a different way. I wonder if it is true that researching in analysis requires not as many pre-requisites as researching in algebra? Since I noticed that there are a lot of topics in algebra, but not as many as in analysis. I understand that whatever topic I choose to dwell in doesn't really matter much toward my graduate study since I could always change before that. So I wonder what is more beneficial to me? Given my background, would it be easier to do an undergraduate project in analysis than algebra?







soft-question






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Jan 8 at 2:56









Alvis NordkovichAlvis Nordkovich

364




364








  • 2




    $begingroup$
    If you're looking for something accessible, and you want to do something original, right now, at this very moment, then neither analysis nor algebra is a good choice. I would look into combinatorics.
    $endgroup$
    – Matt Samuel
    Jan 8 at 3:00










  • $begingroup$
    That said, undergraduate projects in math aren't usually original. Mine was, but I was extremely advanced, and had essentially already taken a full year's worth of graduate courses before I discovered something new. Of course other people also do this, but it's the exception rather than the rule. Harvard warns their graduate students that their dissertation might be only a minuscule advancement in their field, and that's normal and not an indication of failure.
    $endgroup$
    – Matt Samuel
    Jan 8 at 3:06










  • $begingroup$
    Thank you! I totally understand that undergraduate research is more reading than really researching. I believe I concern is that is there much content in algebra than analysis? @MattSamuel
    $endgroup$
    – Alvis Nordkovich
    Jan 8 at 3:14






  • 2




    $begingroup$
    There is a massive amount of content in both of them. Analysis is sort of a younger subject, but it's still hundreds of years old. In any subject except combinatorics undergraduates may only barely get into the topics of the early 20th century.
    $endgroup$
    – Matt Samuel
    Jan 8 at 3:20














  • 2




    $begingroup$
    If you're looking for something accessible, and you want to do something original, right now, at this very moment, then neither analysis nor algebra is a good choice. I would look into combinatorics.
    $endgroup$
    – Matt Samuel
    Jan 8 at 3:00










  • $begingroup$
    That said, undergraduate projects in math aren't usually original. Mine was, but I was extremely advanced, and had essentially already taken a full year's worth of graduate courses before I discovered something new. Of course other people also do this, but it's the exception rather than the rule. Harvard warns their graduate students that their dissertation might be only a minuscule advancement in their field, and that's normal and not an indication of failure.
    $endgroup$
    – Matt Samuel
    Jan 8 at 3:06










  • $begingroup$
    Thank you! I totally understand that undergraduate research is more reading than really researching. I believe I concern is that is there much content in algebra than analysis? @MattSamuel
    $endgroup$
    – Alvis Nordkovich
    Jan 8 at 3:14






  • 2




    $begingroup$
    There is a massive amount of content in both of them. Analysis is sort of a younger subject, but it's still hundreds of years old. In any subject except combinatorics undergraduates may only barely get into the topics of the early 20th century.
    $endgroup$
    – Matt Samuel
    Jan 8 at 3:20








2




2




$begingroup$
If you're looking for something accessible, and you want to do something original, right now, at this very moment, then neither analysis nor algebra is a good choice. I would look into combinatorics.
$endgroup$
– Matt Samuel
Jan 8 at 3:00




$begingroup$
If you're looking for something accessible, and you want to do something original, right now, at this very moment, then neither analysis nor algebra is a good choice. I would look into combinatorics.
$endgroup$
– Matt Samuel
Jan 8 at 3:00












$begingroup$
That said, undergraduate projects in math aren't usually original. Mine was, but I was extremely advanced, and had essentially already taken a full year's worth of graduate courses before I discovered something new. Of course other people also do this, but it's the exception rather than the rule. Harvard warns their graduate students that their dissertation might be only a minuscule advancement in their field, and that's normal and not an indication of failure.
$endgroup$
– Matt Samuel
Jan 8 at 3:06




$begingroup$
That said, undergraduate projects in math aren't usually original. Mine was, but I was extremely advanced, and had essentially already taken a full year's worth of graduate courses before I discovered something new. Of course other people also do this, but it's the exception rather than the rule. Harvard warns their graduate students that their dissertation might be only a minuscule advancement in their field, and that's normal and not an indication of failure.
$endgroup$
– Matt Samuel
Jan 8 at 3:06












$begingroup$
Thank you! I totally understand that undergraduate research is more reading than really researching. I believe I concern is that is there much content in algebra than analysis? @MattSamuel
$endgroup$
– Alvis Nordkovich
Jan 8 at 3:14




$begingroup$
Thank you! I totally understand that undergraduate research is more reading than really researching. I believe I concern is that is there much content in algebra than analysis? @MattSamuel
$endgroup$
– Alvis Nordkovich
Jan 8 at 3:14




2




2




$begingroup$
There is a massive amount of content in both of them. Analysis is sort of a younger subject, but it's still hundreds of years old. In any subject except combinatorics undergraduates may only barely get into the topics of the early 20th century.
$endgroup$
– Matt Samuel
Jan 8 at 3:20




$begingroup$
There is a massive amount of content in both of them. Analysis is sort of a younger subject, but it's still hundreds of years old. In any subject except combinatorics undergraduates may only barely get into the topics of the early 20th century.
$endgroup$
– Matt Samuel
Jan 8 at 3:20










0






active

oldest

votes











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%2f3065753%2fundergraduate-research-in-algebra-or-analysis%23new-answer', 'question_page');
}
);

Post as a guest















Required, but never shown

























0






active

oldest

votes








0






active

oldest

votes









active

oldest

votes






active

oldest

votes
















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%2f3065753%2fundergraduate-research-in-algebra-or-analysis%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

1300-talet

1300-talet

Display a custom attribute below product name in the front-end Magento 1.9.3.8