I'm getting killed in math already (3 weeks into math program)

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Discussion Overview

The discussion revolves around the challenges faced by a participant struggling with understanding epsilon-delta proofs and mathematical concepts in a math program, particularly in fields and proofs. Participants share their experiences and suggestions related to studying proofs, teaching methods, and resources for improvement.

Discussion Character

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

Main Points Raised

  • One participant expresses frustration with the transition from computational math to proofs, indicating a desire to understand the underlying concepts.
  • Another suggests that working through examples can be more effective than theoretical contemplation, emphasizing that the goal of epsilon-delta proofs is not to find a specific delta.
  • A participant advises taking time to study proofs slowly and thoroughly, noting that this skill differs from computational methods typically taught in earlier education.
  • Concerns are raised about the teaching methods of some math professors, who may focus on rote memorization rather than conceptual understanding.
  • Several participants share that they found alternative resources, such as Khan Academy and YouTube videos, more helpful than traditional lectures.
  • There is a discussion about the difficulty of epsilon-delta proofs, with some participants noting that many students struggle with this concept in introductory calculus courses.
  • One participant mentions spending excessive time on assignments and suggests that seeking help from tutors or math centers could be beneficial.
  • Another participant reflects on their own struggles with theory classes and the positive impact of tutoring on their understanding.
  • Suggestions are made for taking courses in symbolic logic to improve proof comprehension.

Areas of Agreement / Disagreement

Participants generally agree that understanding proofs is a challenging transition from computational math and that many students struggle with concepts like epsilon-delta proofs. However, there is no consensus on the best approach to overcoming these challenges, with various suggestions and experiences shared.

Contextual Notes

Some participants note that the teaching methods in math courses may not adequately prepare students for theoretical concepts, leading to confusion and frustration. The discussion also highlights the variability in individual experiences with learning and understanding mathematical proofs.

Who May Find This Useful

This discussion may be useful for students in mathematics programs, particularly those encountering difficulties with proofs and theoretical concepts, as well as educators seeking insights into student challenges in learning mathematics.

kramer733
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I'm getting bombarded with trying to understand the epsilon delta proof. I'm also getting killed in fields and proving things in that class. The only ones i feel like i have any chance are my computer science classes and discrete math class. What do you guys recommend me? I'm not particulalrily intelligent. But i'll work at it. I just don't really feel like i know where to start.

I remember the good old days with just doing straight up computations. But gone are those days. Now it's about proofs which i definitely respect and want to understand.
 
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For most people it works better to do examples than to sit around thinking. WRT to epsilon delta try to see if you can do the easiest examples:

limx->ax = a

limx->acx = ca

limx->ax + 5 = a +5

limx->ax^2 = a^2

if limx->af(x) = 1 then limx->axf(x) = a

if limx->af(x) = c then limx->axf(x) = ca

etc

One thing that trips people up with epsilon delta is that the goal is not to "find delta." There is no particular delta to find.
 
Studying proofs is a lot different from computations. My advice, use your book and study the proofs very slowly and thoroughly. For the first class I took in analysis for my math degree I remember being amazed at how tiny the book was. All the language is incredibly concise, and I could easily spend hours trying to understand a single page. It's a different skill you have to learn that you generally aren't taught in high school or in other college classes, so put the time into let it develop. It's more philosophical than the computational math you're probably used to, so don't feel like you're wasting time by just carefully thinking about the problem without writing anything down. Hope that helps.
 
From my experience, many math professors also don't know how to teach these subjects. They teach by rote memorization without explaining why method A is a good method. You might try finding a tutor if your school has a math center, and see if they can explain it in alternate ways.
 
I was having the same concern last week on the epsilon/ delta proof (I would say my whole class was after reading the class posts). I found the Kahn Academy videos more helpful than my Professors on-line power-point slides. I also watched several other you tube videos on the subject, and at least now I feel like I'm starting to "get it."
 
What class is this, Calc 1? From what I remember, only about 5% of the class really understands the epsilon/delta proof when they heard it in Calc 1, and most of the class could not repeat the definition of the derivative at the end of the semester. I agree with jrjack. Unfortunately, a lot of math teachers just teach you how to solve problems without really understanding what you're doing, this has people lost when they get to Calculus and are asked to digest some real theory.
 
timsea81 said:
What class is this, Calc 1? From what I remember, only about 5% of the class really understands the epsilon/delta proof when they heard it in Calc 1, and most of the class could not repeat the definition of the derivative at the end of the semester. I agree with jrjack. Unfortunately, a lot of math teachers just teach you how to solve problems without really understanding what you're doing, this has people lost when they get to Calculus and are asked to digest some real theory.

Kramer can confirm, but since he mentioned taking abstract algebra ('fields') in the OP, I'm assuming he's already completed Calc I. Maybe this is an introduction to analysis course?

In any case, I think some tutoring is probably the best place to start. As another member mentioned, see if your university has a tutoring/math center.
 
These proofs should be in your textbook. Don't expect to "see" the whole proof in one go - you only need to understand each step of the proof. Once you understand each step, and can reproduce them in the exam, then you are there! So on which step do you get stuck?
 
I assume the OP is not in the US based on his subjects.
 
  • #10
Dembadon said:
Kramer can confirm, but since he mentioned taking abstract algebra ('fields') in the OP, I'm assuming he's already completed Calc I. Maybe this is an introduction to analysis course?

In any case, I think some tutoring is probably the best place to start. As another member mentioned, see if your university has a tutoring/math center.

Actually this is the first course on algebra for math students. Same with the calculus course. It's directed towards math students. My teacher wanted to start us up on the idea of fields. I'm finding math to be fun but it's just that it takes me literlaly 12+ hours to do 1 question from the assignment. It gets annoying too. More frustrating than anything. I've been going to the tutoring sessions and TA office hours for the past 3 days now. It's definitely helpful. I guess i just got to suck it up.

Also I'm from Canada.
 
  • #11
kramer733 said:
Actually this is the first course on algebra for math students. Same with the calculus course. It's directed towards math students. My teacher wanted to start us up on the idea of fields. I'm finding math to be fun but it's just that it takes me literlaly 12+ hours to do 1 question from the assignment. It gets annoying too. More frustrating than anything. I've been going to the tutoring sessions and TA office hours for the past 3 days now. It's definitely helpful. I guess i just got to suck it up.

Also I'm from Canada.

I know it's tough, but I think you have a good attitude. Knowing when to suck it up, and find your low gears, separates those who finish from those who don't. Best of luck to you!
 
  • #12
kramer733 said:
Actually this is the first course on algebra for math students. Same with the calculus course. It's directed towards math students. My teacher wanted to start us up on the idea of fields. I'm finding math to be fun but it's just that it takes me literlaly 12+ hours to do 1 question from the assignment. It gets annoying too. More frustrating than anything. I've been going to the tutoring sessions and TA office hours for the past 3 days now. It's definitely helpful. I guess i just got to suck it up.

Also I'm from Canada.

It seems like you've hit a brick wall. Trust me, it happens to everybody in math, even to the greatest. You need to persist through this, because if you do, then a time will come that everything clicks and you will find things soo easy and fun!

That said, spending 12+ hours on 1 question definitely is too much. If you spend 1 hour on it, then I suggest that you post the question here on our homework forums so we can help you out. As long as you're willing to think about it, you should be alright.
 
  • #13
if you can fathom post #62 of "who wants to be a mathematician?" you can handle any pure math course. perhaps even if you can't. don't give up too soon.
 
  • #14
My first theory-ish class I was struggling with so much and I didn't know where or how to start. My professor was vague and I couldn't synchronize with the textbook's reasoning. I decided to get a tutor and everything became so much easier. Something to consider.
 
  • #15
Kramer733,

Consider taking a course in symbolic logic. You might be able to take it from the philosophy department and get credit for it as one of your non-math requirements. It can clarify the "game" of doing proofs.
 
  • #16
kramer733 said:
Actually this is the first course on algebra for math students. Same with the calculus course. It's directed towards math students. My teacher wanted to start us up on the idea of fields. I'm finding math to be fun but it's just that it takes me literlaly 12+ hours to do 1 question from the assignment...

Well that's 12 hours of fun :) This isn't school. Many University assignments demand that amount of effort... get used to it...
 
  • #17
Stephen Tashi said:
Kramer733,

Consider taking a course in symbolic logic. You might be able to take it from the philosophy department and get credit for it as one of your non-math requirements. It can clarify the "game" of doing proofs.

This is precisely what I'm doing this semester. It's really helped me learn the proof-construction process as well as how to approach a problem involving proofs.
 
  • #18
kramer733 said:
Also I'm from Canada.

What school are you attending?
 
  • #19
skoomafiend said:
What school are you attending?

carleton university.
 

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