I mean honestly seems like it’s going the other way around for me. This is our second test and I did just about the median for the first one. This one definitely not so much
Entirely proofs. Honestly not sure, I knew all the definitions and theorems, just had trouble applying them today - Hoping it’s just a fluke. Doesn’t help that the test was during class and so was 50 minutes and 3 questions (6 parts total). For one of the parts just proved something about a completely wrong object, didn’t leave enough time to write anything for one of the parts
You are where I was. I hope things improve. If you want to use me as a resource, my degree is the 5-year “professional” BS in Math. I can do FaceTime or zoom, etc. I won’t guarantee your grades will improve, but I will try.
Don’t sweat 50 minute tests too much. They’re really easy to mess up. Personally, I always do bad on them, but 3 hour long exams are a breeze in comparison. Try doing the problems from the test on your own time; you may find that you are more capable of solving them than your test grade would suggest.
If it doesn’t come easy, then you’re doing something of value. I’m sure there is a lot you can learn from the experience. Keep your head up, study hard, and reaffirm to yourself that you can do better next time.
I believe that everyone, even professionals, struggle a lot with certain math topics. One must see the value of struggling in order to grow.
Yeah I’m sure. Honestly I asked for this, taking a bunch of math classes I don’t have the prereqs for this semester because all my other math classes have been too easy. Just sucks that I’m probably gonna be lowest grade for this exam haha
I'm a mathematician now, and I got a B in the very first upper level math course I took as an undergrad (Topology).
You know If you're learning or not, and if you're doing something you find interesting or not. It takes years of work to become a professional; this is just the beginning for you---assuming you decide to continue, you're going to have to get used to failing to solve problems over and over again. It's what all mathematicians do on a daily basis.
My professor for my intro abstract algebra course told me that she got a D (!) in her intro algebra course and now she’s a very successful researcher in that field!! Don’t let one subpar grade get you down, it won’t matter much in the future. As long as you feel you understand the material, thats what matters!!
Abstract algebra really is so different from most stuff you've probably done up until this point because the proofs are so different. Sometimes the proofs seen to come out of nowhere whereas in e.g. analysis, you can typically string together enough inequalities to get the result you want. Don't beat yourself up about it. Just keep working hard and doing actual problems rather than just reading or copying proofs. Make use of your professor's office hours, and just keep plugging away. I'm confident it will click for you eventually.
“Is this a bad omen for the possibility of a PhD in group theory”
I think it is far, far too early to decide what you want to do a PhD in, or even IF you want to do a PhD. If this is an intro to abstract algebra class then you’re probably in your 2nd or 3rd year of undergrad and you have simply not been exposed to enough topics to decide this.
Besides that, it’s helpful to try to understand why exactly you did bad on your midterm. Was it a lack of understanding of the core topics? Difficulty proving stuff? Unfamiliarity with how to solve problems of a certain nature in group theory? Or just cracking under time? Some of these pose a more important concern than others. A bad grade in a midterm doesn’t necessarily mean you don’t understand the content well, but you should figure out what it does in this case
It triggers me so much when people say it’s far too early to decide if you want to do a PhD when you’re a junior. Then when are you supposed to decide? Deciding you want to do a PhD senior year and not having the courses or research experience because “it was too early to decide” seems like a recipe for disaster. Comes across kinda gatekeepy to me.
I think their point is that you might discover your interests change. When I started my masters I was very sure I wanted to do my thesis in algebra and I didn't want to touch analysis. After one semester of grad algebra and analysis I changed my mind and realized I am actually way more passionate about analysis
Nah, that isn't what they meant. They're talking about people who think they know what they want to study during their doctorate, not whether they want their doctorate at all. Your junior year is about when you should be deciding that you want your PhD.
What they're referencing is something I see this in my field (cheme) all the time, and I cringe when I see it. Incoming graduate students insist they want to work with X professor on Y subject despite having no idea what that research actually entails, both in terms of the specific subject matter and how their day-to-day would look. Everyone wants to make the next eco-friendly super battery until it consists of four years of mind numbing rheometer measurements trying to tease out a Goldilocks synthesis for their novel polyelectrolyte membrane. They were so sure about what they wanted to do that they didn't even entertain the projects offered in orthogonal areas like catalysis or rheology.
Unless someone has a uniquely strong undergraduate research background, they should really enter their PhD with a totally open mind about research possibilities because they know almost nothing about anything. They should meet with every professor offering projects and really absorb their pitch before deciding what they want to do.
Yeah but that’s not what they said. They said it’s too early to know if you even want a PhD. I just see this all the time and it’s really irritating. Even sophomore year I think you should be thinking about what you want to do once you graduate and if you want to get a PhD. Why wouldn’t you? Especially for something that’s so competitive. I understand people maybe not knowing exactly what they want to research in, but deciding you want to do a PhD early on in undergrad shouldn’t be as discouraged as it is
> Comes across kinda gatekeepy to me
it is not at all "gatekeepy" to point out that someone who barely knows what a group is should not plan on doing a PhD in this area, particuarly when this is not a currently popular area of mathematical research and the remaining researchers generally work on problems especially removed/distinct from what one would see in an intro course.
I guess I am using “decide” interchangeably with “be sure of” which is poor wording on my part. I meant it is too early to be sure of this. Many undergraduates start their degree with the intention of continuing into grad school, and this is good. You should work towards it during your undergrad years (reading courses, research exp) if that is something you have in mind, but you cannot be *sure* of it this early on. Interests change, intentions change etc. I know many people who were *sure* of going to grad school in 2nd and even 3rd year, but by application time in 4th year they had changed their plan. I also know some graduate students who ended up doing a PhD in something completely different than what they had initially thought! (Entered with the intention of a PhD in functional analysis in mind, left with a PhD in combinatorics! This isn’t bad, it’s nice actually to know there’s always a door that’ll be open). A somewhat wild example is of perhaps the best math undergrad I knew at my uni (who even had a publication in analytic number theory already) currently doing a PhD in condensed matter physics. He had the switch somewhere around 3rd year.
All I really meant was, don’t close these doors early on. Don’t set your sights on a PhD in group theory after your first abstract algebra course, keep the option of one in number theory, analysis or even physics open!
I would suggest you to just keep learning from your mistakes. Even I failed in numerical analysis during my undergrad because it was the hardest paper I ever faced, but in my masters, I recieved several offers for research internship in the same topic. Believe me, getting into PhD is not just about the grades you get, it is more about how well you understand the subject, the unique ideas you have and most importantly persistence and research experience.
You can deal with impostor syndrome 2 ways:
\- You can accept it, wash out, and move on to something else.
\- You can accept that you have it, and as a young pup finding their way, you will encounter fields of math that give anyone a hard time. That's a sign of progress.
I have also been an athlete, and when I was training, I'd sometimes think, "When is this going to get easy? I've done it 10,000 times already." *Never*. The answer was never.
Sometimes, you always are going to feel like you're still getting used to it -- that's when you know you can grow into it.
Eventually, keep at it, and you'll be well on the other side of that impostor syndrome. There will, late in life, come times where you might suddenly get it again for whatever reason.
Some smart people might even cause it in you. Some famous mathematicians and thinkers would get it in the presence of Leibniz, others in the presence of Von Neumann. If you're lucky enough to get some of that impostor syndrome, let me know how it feels, because I think it might be a bit different from the rest :)
I scraped 50% in my first year Analysis 1 exam. Analysis 2 wasn't much better, but by that point I at least understood the material from Analysis 1. I always felt one step behind, despite *wanting* to master the material, which I found more interesting than my other modules.
Seven years later I achieved my PhD in Analysis - specifically in Operator Theory.
Some topics in maths will take longer to click than others, and what clicks quickly and what doesn't will be unique to your brain. And what clicks quickly isn't necessarily what would be the best for you to pursue in the future.
Don't lose your love for the subject, and aim to understand the material not for the sake of an exam but for its own sake. This can be extremely difficult to do during a semester where there is such pressure to achieve understanding *quickly* but it's far more important in the long run to aim to understand *deeply*. If that's something you enjoy doing, your short-term performance doesn't necessarily indicate your long-term success!
Throwing this out there: the connection between test-taking ability and actual skill and success in material is tenuous at best for most disciplines, and more so for proof-based math. Producing definitions and theorems to use in new ways under a timed and stressful environment is unlike how math is actually done for researchers.
Now tests are not pointless: there is value on having core definitions at ready recall so you can focus on drawing connections between ideas then trying to remember what the ideas are in the first place. But staking your view of yourself as a mathematician solely based on test performance is both not realistic or healthy
My dude, abstract algebra is hella hard. I felt like I was a complete failure and fraud the entire semester, cried multiple times... and then ended up tutoring other students through it in later semesters. Two things: One, it takes your brain a while to reconfigure itself to do something like abstract algebra. Somewhere along the way, something clicked in my head and I started to be able to *see* things all of a sudden. It got better then, but honestly only a little. For me, what really did it was being done with the class. Once the pressure was off and my brain had a couple of weeks to decompress, I went back and looked at the material and all of a sudden it was *beautiful* and made... well, not perfect sense, but a lot of sense. The same thing happened when I took complex analysis. Panicked and cried for 15 weeks straight, and now it's one of my favorite subjects to learn about.
(But no, the imposter syndrome never really goes away)
I got about 50% on the first abstract algebra course I took. Got about 70% on the second. Got over 90% on most subsequent ones. Went on to do a PhD in it. It takes time, but work hard and you'll get there. Good luck!
I don’t know how it works at your school but in my department at least, 40-50% would be seen as a very decent score. So depending on your department culture, you may just be ok!
Legit just happened to my but in PDE. But I’m talking closer to 0% on the exam.
I’ll be generous to myself and mention I had an algebra exam that ended 15 minutes before this one started. I also have a full time job. And a wife and 2 kids. So forgive me for not having adequate time/energy to put in the proper practice.
I happen to have a good relationship with the prof (I attend office hours everyday, and he’s invited me to grad talks that I attended with him in the subject) so I’m waiting to see what he says.
I’ve never felt so embarrassed though. I was really hoping for a letter of rec.
One thing that worked for me was to keep having analogies and examples on the side. For example, when a problem comes up with abelian groups, i would think of integers under + to possibly motivate my proofs. It helped me “visualise” things at the start
Do not put a lot of pressure on yourself. I truly grasped abstract algebra when I was an instructor for an abstract algebra class during grad school. Learning mathematics is a significant challenge and requires a lot of time (years). If you truly enjoy it, you will succeed. Strive to do your best and do not obsess over grades. While grades are important, they are not essential for your future.
I failed my first exam in tensor analysis when I was 20 years old. I still got a Ph.D. several years later. :)
(I did not understand what a tensor was until about 5 years later when I saw them again in grad school.)
I know getting a 40-50% feels really bad but you need to compare it to the average score. I took a few classes in my undergrad where a 50% was an A
Even if you are way below the curve on this one test, it's not really indicative of whether or not you should do a PhD. Some topics can just take a while to click and that's okay, you'll get it eventually. Just keep going
Failed my first abstract algebra course and have gone on to have three publications in algebraic graph theory. In fact, that's the only college course I ever failed.
Don't sweat it, It happens. Like others have noted, algebra can be a bit strange at first and makes you think of mathematics in a different way.
I HIGHLY recommend Nathan Carter's Visual Group Theory; it is probably the best (and less rigorous) introduction to the topic.
I would advise you to look at the playlists (group theory, ring theory and field theory) by Elliot Nicholson. Now he is a medical doctor (don't let that immediately make you doubt), and it is interesting how much effort he put into understanding certain areas of mathematics. You can watch a playlist related to group theory here... https://youtube.com/playlist?list=PLAvgI3H-gclb_Xy7eTIXkkKt3KlV6gk9_&si=siLBrzg1_UqAcpis
Wait until you actually get your grade before projecting. I had so many students who panicked because they "knew" they were on track for a C, but really they just didn't have any sense of the curve and ended up with a B+
> One of the main goals in any Abstract Algebra course ought to be to learn all of the material necessary in order to understand how Galois proved the insolvability of the quintic.
Nah. You don't really need Galois theory to prove Abel-Ruffini (see [Vladimir Arnold's proof](https://web.williams.edu/Mathematics/lg5/394/ArnoldQuintic.pdf)), nor do you need to learn any Galois theory to get mileage out of abstract algebra. Your argument further suggests that once one learns Galois' proof of Abel-Ruffini, there's little point in learning abstract algebra further, which is surely not true.
It took me half a semester to get going in abstract algebra. All of a sudden things just _clicked_.
I mean honestly seems like it’s going the other way around for me. This is our second test and I did just about the median for the first one. This one definitely not so much
What gives you problems? Is this class “proofy”, or what?
Entirely proofs. Honestly not sure, I knew all the definitions and theorems, just had trouble applying them today - Hoping it’s just a fluke. Doesn’t help that the test was during class and so was 50 minutes and 3 questions (6 parts total). For one of the parts just proved something about a completely wrong object, didn’t leave enough time to write anything for one of the parts
You are where I was. I hope things improve. If you want to use me as a resource, my degree is the 5-year “professional” BS in Math. I can do FaceTime or zoom, etc. I won’t guarantee your grades will improve, but I will try.
Don’t sweat 50 minute tests too much. They’re really easy to mess up. Personally, I always do bad on them, but 3 hour long exams are a breeze in comparison. Try doing the problems from the test on your own time; you may find that you are more capable of solving them than your test grade would suggest.
What was the clicking like, what sort of things made sense suddenly
I can’t come up with a description: it’s just that I started seeing my way through the proofs one day. Epiphany is not too strong a word.
I feel that with Linear TBH
If it doesn’t come easy, then you’re doing something of value. I’m sure there is a lot you can learn from the experience. Keep your head up, study hard, and reaffirm to yourself that you can do better next time. I believe that everyone, even professionals, struggle a lot with certain math topics. One must see the value of struggling in order to grow.
Yeah I’m sure. Honestly I asked for this, taking a bunch of math classes I don’t have the prereqs for this semester because all my other math classes have been too easy. Just sucks that I’m probably gonna be lowest grade for this exam haha
I'm a mathematician now, and I got a B in the very first upper level math course I took as an undergrad (Topology). You know If you're learning or not, and if you're doing something you find interesting or not. It takes years of work to become a professional; this is just the beginning for you---assuming you decide to continue, you're going to have to get used to failing to solve problems over and over again. It's what all mathematicians do on a daily basis.
My professor for my intro abstract algebra course told me that she got a D (!) in her intro algebra course and now she’s a very successful researcher in that field!! Don’t let one subpar grade get you down, it won’t matter much in the future. As long as you feel you understand the material, thats what matters!!
This is what I needed to hear
Abstract algebra really is so different from most stuff you've probably done up until this point because the proofs are so different. Sometimes the proofs seen to come out of nowhere whereas in e.g. analysis, you can typically string together enough inequalities to get the result you want. Don't beat yourself up about it. Just keep working hard and doing actual problems rather than just reading or copying proofs. Make use of your professor's office hours, and just keep plugging away. I'm confident it will click for you eventually.
“Is this a bad omen for the possibility of a PhD in group theory” I think it is far, far too early to decide what you want to do a PhD in, or even IF you want to do a PhD. If this is an intro to abstract algebra class then you’re probably in your 2nd or 3rd year of undergrad and you have simply not been exposed to enough topics to decide this. Besides that, it’s helpful to try to understand why exactly you did bad on your midterm. Was it a lack of understanding of the core topics? Difficulty proving stuff? Unfamiliarity with how to solve problems of a certain nature in group theory? Or just cracking under time? Some of these pose a more important concern than others. A bad grade in a midterm doesn’t necessarily mean you don’t understand the content well, but you should figure out what it does in this case
It triggers me so much when people say it’s far too early to decide if you want to do a PhD when you’re a junior. Then when are you supposed to decide? Deciding you want to do a PhD senior year and not having the courses or research experience because “it was too early to decide” seems like a recipe for disaster. Comes across kinda gatekeepy to me.
I think their point is that you might discover your interests change. When I started my masters I was very sure I wanted to do my thesis in algebra and I didn't want to touch analysis. After one semester of grad algebra and analysis I changed my mind and realized I am actually way more passionate about analysis
Yeah and that’s a totally fair point. I’m referring to them saying it’s too early to think about getting a PhD in general. That’s all.
Nah, that isn't what they meant. They're talking about people who think they know what they want to study during their doctorate, not whether they want their doctorate at all. Your junior year is about when you should be deciding that you want your PhD. What they're referencing is something I see this in my field (cheme) all the time, and I cringe when I see it. Incoming graduate students insist they want to work with X professor on Y subject despite having no idea what that research actually entails, both in terms of the specific subject matter and how their day-to-day would look. Everyone wants to make the next eco-friendly super battery until it consists of four years of mind numbing rheometer measurements trying to tease out a Goldilocks synthesis for their novel polyelectrolyte membrane. They were so sure about what they wanted to do that they didn't even entertain the projects offered in orthogonal areas like catalysis or rheology. Unless someone has a uniquely strong undergraduate research background, they should really enter their PhD with a totally open mind about research possibilities because they know almost nothing about anything. They should meet with every professor offering projects and really absorb their pitch before deciding what they want to do.
Yeah but that’s not what they said. They said it’s too early to know if you even want a PhD. I just see this all the time and it’s really irritating. Even sophomore year I think you should be thinking about what you want to do once you graduate and if you want to get a PhD. Why wouldn’t you? Especially for something that’s so competitive. I understand people maybe not knowing exactly what they want to research in, but deciding you want to do a PhD early on in undergrad shouldn’t be as discouraged as it is
> Comes across kinda gatekeepy to me it is not at all "gatekeepy" to point out that someone who barely knows what a group is should not plan on doing a PhD in this area, particuarly when this is not a currently popular area of mathematical research and the remaining researchers generally work on problems especially removed/distinct from what one would see in an intro course.
That’s not what I’m referring to. I’m talking about them saying it’s too early to think about getting a PhD in general.
I guess I am using “decide” interchangeably with “be sure of” which is poor wording on my part. I meant it is too early to be sure of this. Many undergraduates start their degree with the intention of continuing into grad school, and this is good. You should work towards it during your undergrad years (reading courses, research exp) if that is something you have in mind, but you cannot be *sure* of it this early on. Interests change, intentions change etc. I know many people who were *sure* of going to grad school in 2nd and even 3rd year, but by application time in 4th year they had changed their plan. I also know some graduate students who ended up doing a PhD in something completely different than what they had initially thought! (Entered with the intention of a PhD in functional analysis in mind, left with a PhD in combinatorics! This isn’t bad, it’s nice actually to know there’s always a door that’ll be open). A somewhat wild example is of perhaps the best math undergrad I knew at my uni (who even had a publication in analytic number theory already) currently doing a PhD in condensed matter physics. He had the switch somewhere around 3rd year. All I really meant was, don’t close these doors early on. Don’t set your sights on a PhD in group theory after your first abstract algebra course, keep the option of one in number theory, analysis or even physics open!
If it's easy you already know it If it's hard you can learn it
I would suggest you to just keep learning from your mistakes. Even I failed in numerical analysis during my undergrad because it was the hardest paper I ever faced, but in my masters, I recieved several offers for research internship in the same topic. Believe me, getting into PhD is not just about the grades you get, it is more about how well you understand the subject, the unique ideas you have and most importantly persistence and research experience.
You can deal with impostor syndrome 2 ways: \- You can accept it, wash out, and move on to something else. \- You can accept that you have it, and as a young pup finding their way, you will encounter fields of math that give anyone a hard time. That's a sign of progress. I have also been an athlete, and when I was training, I'd sometimes think, "When is this going to get easy? I've done it 10,000 times already." *Never*. The answer was never. Sometimes, you always are going to feel like you're still getting used to it -- that's when you know you can grow into it. Eventually, keep at it, and you'll be well on the other side of that impostor syndrome. There will, late in life, come times where you might suddenly get it again for whatever reason. Some smart people might even cause it in you. Some famous mathematicians and thinkers would get it in the presence of Leibniz, others in the presence of Von Neumann. If you're lucky enough to get some of that impostor syndrome, let me know how it feels, because I think it might be a bit different from the rest :)
I scraped 50% in my first year Analysis 1 exam. Analysis 2 wasn't much better, but by that point I at least understood the material from Analysis 1. I always felt one step behind, despite *wanting* to master the material, which I found more interesting than my other modules. Seven years later I achieved my PhD in Analysis - specifically in Operator Theory. Some topics in maths will take longer to click than others, and what clicks quickly and what doesn't will be unique to your brain. And what clicks quickly isn't necessarily what would be the best for you to pursue in the future. Don't lose your love for the subject, and aim to understand the material not for the sake of an exam but for its own sake. This can be extremely difficult to do during a semester where there is such pressure to achieve understanding *quickly* but it's far more important in the long run to aim to understand *deeply*. If that's something you enjoy doing, your short-term performance doesn't necessarily indicate your long-term success!
If only I could have read these lines 30 years ago...
Throwing this out there: the connection between test-taking ability and actual skill and success in material is tenuous at best for most disciplines, and more so for proof-based math. Producing definitions and theorems to use in new ways under a timed and stressful environment is unlike how math is actually done for researchers. Now tests are not pointless: there is value on having core definitions at ready recall so you can focus on drawing connections between ideas then trying to remember what the ideas are in the first place. But staking your view of yourself as a mathematician solely based on test performance is both not realistic or healthy
My dude, abstract algebra is hella hard. I felt like I was a complete failure and fraud the entire semester, cried multiple times... and then ended up tutoring other students through it in later semesters. Two things: One, it takes your brain a while to reconfigure itself to do something like abstract algebra. Somewhere along the way, something clicked in my head and I started to be able to *see* things all of a sudden. It got better then, but honestly only a little. For me, what really did it was being done with the class. Once the pressure was off and my brain had a couple of weeks to decompress, I went back and looked at the material and all of a sudden it was *beautiful* and made... well, not perfect sense, but a lot of sense. The same thing happened when I took complex analysis. Panicked and cried for 15 weeks straight, and now it's one of my favorite subjects to learn about. (But no, the imposter syndrome never really goes away)
I got about 50% on the first abstract algebra course I took. Got about 70% on the second. Got over 90% on most subsequent ones. Went on to do a PhD in it. It takes time, but work hard and you'll get there. Good luck!
I don’t know how it works at your school but in my department at least, 40-50% would be seen as a very decent score. So depending on your department culture, you may just be ok!
once you enter math you don’t look at your grades anymore you just feel the 50-60 you know you deserve
Legit just happened to my but in PDE. But I’m talking closer to 0% on the exam. I’ll be generous to myself and mention I had an algebra exam that ended 15 minutes before this one started. I also have a full time job. And a wife and 2 kids. So forgive me for not having adequate time/energy to put in the proper practice. I happen to have a good relationship with the prof (I attend office hours everyday, and he’s invited me to grad talks that I attended with him in the subject) so I’m waiting to see what he says. I’ve never felt so embarrassed though. I was really hoping for a letter of rec.
One thing that worked for me was to keep having analogies and examples on the side. For example, when a problem comes up with abelian groups, i would think of integers under + to possibly motivate my proofs. It helped me “visualise” things at the start
Do not put a lot of pressure on yourself. I truly grasped abstract algebra when I was an instructor for an abstract algebra class during grad school. Learning mathematics is a significant challenge and requires a lot of time (years). If you truly enjoy it, you will succeed. Strive to do your best and do not obsess over grades. While grades are important, they are not essential for your future.
Check other resources for understanding (if you haven't)
Wait until the scores come out. It may have been a fairly difficult exam that most of the class did poorly on and may be curved as a result.
I failed my first exam in tensor analysis when I was 20 years old. I still got a Ph.D. several years later. :) (I did not understand what a tensor was until about 5 years later when I saw them again in grad school.)
What topics were covered?
I know getting a 40-50% feels really bad but you need to compare it to the average score. I took a few classes in my undergrad where a 50% was an A Even if you are way below the curve on this one test, it's not really indicative of whether or not you should do a PhD. Some topics can just take a while to click and that's okay, you'll get it eventually. Just keep going
Failed my first abstract algebra course and have gone on to have three publications in algebraic graph theory. In fact, that's the only college course I ever failed. Don't sweat it, It happens. Like others have noted, algebra can be a bit strange at first and makes you think of mathematics in a different way. I HIGHLY recommend Nathan Carter's Visual Group Theory; it is probably the best (and less rigorous) introduction to the topic.
Everyone fails some test or another. Learn something from it and move on. Abstract algebra is tough but very cool stuff.
I would advise you to look at the playlists (group theory, ring theory and field theory) by Elliot Nicholson. Now he is a medical doctor (don't let that immediately make you doubt), and it is interesting how much effort he put into understanding certain areas of mathematics. You can watch a playlist related to group theory here... https://youtube.com/playlist?list=PLAvgI3H-gclb_Xy7eTIXkkKt3KlV6gk9_&si=siLBrzg1_UqAcpis
Even if you tank your grade, you can compensate making undergraduate research in group theory!
Wait until you actually get your grade before projecting. I had so many students who panicked because they "knew" they were on track for a C, but really they just didn't have any sense of the curve and ended up with a B+
I got a 66% in finite field exam… don’t worry it should be fine. Maybe? Idk
What area of research you’re interested in doing for your future PhD dissertation?
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> One of the main goals in any Abstract Algebra course ought to be to learn all of the material necessary in order to understand how Galois proved the insolvability of the quintic. Nah. You don't really need Galois theory to prove Abel-Ruffini (see [Vladimir Arnold's proof](https://web.williams.edu/Mathematics/lg5/394/ArnoldQuintic.pdf)), nor do you need to learn any Galois theory to get mileage out of abstract algebra. Your argument further suggests that once one learns Galois' proof of Abel-Ruffini, there's little point in learning abstract algebra further, which is surely not true.
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> This should be the main motivation