Math major can I still redeem myself?

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Discussion Overview

The discussion centers around a math major's concerns about their performance in abstract algebra and the potential impact on their upcoming real analysis course. The participant expresses a desire to improve their proof-writing skills and seeks reassurance about their ability to succeed in higher-level mathematics despite current challenges.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested
  • Homework-related

Main Points Raised

  • The original poster (OP) feels they have not performed to their potential in abstract algebra and worries about the implications for real analysis.
  • Some participants suggest that hard work and dedication can lead to improvement, emphasizing the importance of effort in mastering the material.
  • One participant shares their personal academic journey, highlighting that success can come from perseverance and consistent study habits, regardless of initial setbacks.
  • Another participant notes that algebra and analysis courses are often taken concurrently at many universities, implying that prior knowledge may not be as critical as the OP fears.
  • There are suggestions for improving proof-writing skills, including seeking feedback from peers and reading various proofs to enhance understanding.

Areas of Agreement / Disagreement

Participants express a range of views on the relationship between abstract algebra and real analysis, with some asserting that the two can be taken in parallel while others emphasize the importance of a solid understanding of algebra for success in analysis. The discussion reflects a mix of encouragement and caution, with no clear consensus on the necessity of mastering abstract algebra before tackling real analysis.

Contextual Notes

The discussion does not resolve the uncertainty regarding the prerequisites for real analysis in relation to abstract algebra, nor does it clarify the specific skills required for success in either course.

Who May Find This Useful

This discussion may be useful for undergraduate math students facing similar challenges in transitioning to upper-level courses, as well as those seeking strategies for improving proof-writing and study habits.

SMA_01
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I am taking abstract algebra this semester, it's my first semester taking upper level math courses, and although I am not doing bad in the class, I feel like I really slacked off and could have done much better. i didn't put in enough time, and my proof-writing skills were not really improved. I love math, and love to understand it, but I realize that I need to try harder. I'm planning on taking real Analysis 1 next semester, and I'm a little discouraged, because maybe I will not be able to grasp the material due to this semester. Will I really be lost if I don't grasp abstract algebra really well? I know it's my fault, and I'm willing to work much harder, I really want to get better at writing proofs and gain more insight of higher level mathematics. I'm just wondering if I can still do it.

Thanks
 
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I really don't know much about Abstract Algebra nor analysis. However from what I read, I can say that don't ask if you can do it. Try harder and do your best. I am sure if you do need assistance with Real Analysis, you will seek it. Do what you have to do to make yourself better.
 
In high school I was a competitive math contest taker, but not the best. I think the top guy became a physician. In college i got a B- in 1st semester freshman super honors calc, and a D- in the 2nd semester.

then i got a what...C-? in first semester several vbl calc, and a D+ in first semester abstract algebra, and got kicked out of school for one year.

After returning I worked as hard as I could, got an A in diff eq and a B+ in second semester abstract algebra.

In junior year I got a B+ in honors advanced calc and what else? I forget.

As a senior I got a B+ or A- and then an A in grad level real analysis and then got into a good grad school., too good actually, I was not ready for it.

Eventually I washed out of that school too, taught and worked hard again for 4 years, went back to grad school, for three more years, and the rest is history! I got my PhD at 35 from a state school.

The success began when I started studying regularly and kept it up the whole time.

moral: there are many roads to a career in the field.
 
SMA_01 said:
I am taking abstract algebra this semester, it's my first semester taking upper level math courses, and although I am not doing bad in the class, I feel like I really slacked off and could have done much better. i didn't put in enough time, and my proof-writing skills were not really improved. I love math, and love to understand it, but I realize that I need to try harder. I'm planning on taking real Analysis 1 next semester, and I'm a little discouraged, because maybe I will not be able to grasp the material due to this semester. Will I really be lost if I don't grasp abstract algebra really well? I know it's my fault, and I'm willing to work much harder, I really want to get better at writing proofs and gain more insight of higher level mathematics. I'm just wondering if I can still do it.

Thanks

If you feel that you need to work harder, then work harder. People who work hard, usually get acquainted with the material sooner or later. So if you work enough, then you can grasp abstract algebra just fine.

Proof-writing skills are important. The best way to learn them is to ask people to check it and give comments on your proof. Ask people to be really really pedantic about everything. You can ask here at PF if you want to.

Also, read a lot of proofs and try to remember how the proofs were done and how they were written. The more proofs you read, the better you'll be.
 
Thank you for all the replies! I am going to start pushing myself big time.
 
I haven't taken either course yet, but at most universities algebra and analysis are parallel courses rather than prereqs for each other. I imagine if you apply yourself you will be able to do it regardless of your algebra knowledge.
 

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