The pace of upper level math courses

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Discussion Overview

The discussion centers around the challenges faced by students in upper-level mathematics courses, particularly in relation to the pace and depth of content compared to earlier courses like calculus I and II. Participants express concerns about the volume of new concepts, the application of mathematical theories, and the overall learning experience in these advanced classes.

Discussion Character

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

Main Points Raised

  • One participant notes that calculus II feels rushed, with less time to understand concepts compared to calculus I, leading to a reliance on memorization.
  • Another participant warns that future courses like linear algebra and differential equations will be even more challenging, suggesting a steep learning curve ahead.
  • Some participants argue that the foundational concepts learned in calculus I and II will make subsequent courses easier, as students will be more comfortable with calculus methods.
  • A participant emphasizes the importance of the instructor's teaching style and the cumulative nature of math education, suggesting that prior knowledge will ease the transition to more advanced topics.
  • Concerns are raised about the lack of application opportunities in calculus II, with one participant expressing frustration over being told that applications are beyond the scope of the course.
  • Another participant challenges the notion that learning material the night before tests is effective, suggesting that this approach undermines true understanding.
  • There is a viewpoint that linear algebra may be perceived as dry, despite its applications in various fields.

Areas of Agreement / Disagreement

Participants express a mix of agreement and disagreement regarding the challenges of upper-level math courses. While some believe that the foundational knowledge will ease future learning, others highlight the overwhelming pace and lack of application in current courses. The discussion remains unresolved with varying perspectives on the effectiveness of different learning approaches.

Contextual Notes

Participants mention specific challenges such as rusty algebra skills and the difficulty of infinite series, indicating that individual backgrounds may affect their experiences in these courses. There is also a recognition that the teaching style and course structure can significantly impact learning outcomes.

kdinser
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I'm currently taking calculus II and I'm finding the pace to be a real challenge. Calc I seemed to allow much more time to study a new concept and understand how and why it works, followed by a chapter on applications of that concept. With calc II, I've had to settle for just memorizing how to do the problems. I'm doing ok in the class, no real danger of failing at this point unless I stop showing up for tests, but I'm not doing nearly as well as I would have expected considering the time I'm putting into this course.

Are the other math courses I have to take for engineering going to be more like calc I or calc II? I've heard that calc II is so challenging because of the volume of new theorems and concepts. This leaves little time left over to show how they can be applied.
 
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linear algebra will make you beg for more time, differential equations will eat you alive and multivariable calculus will put you in coma

get ready. its coming to get ya.
 
I think the biggest difference you'll see in other math classes is that in calc 1 and 2 you became very comfortable with the idea of integal and differential calculus. This is the toughest part of the class, in my opinion. From there, you learned how to calculate and apply calculus ideas. Now when you hit diffy Q and multivariable you're already comfortable with the idea of calculus and methods of calculation so you only have to worry about the applications. So while it may sound intimidating, it's nothing that you can't handle. The toughest part is over.

In summary, while the other math classes you have to take are "upper level" the pace might not strike you as so fierce because nothing is being thrown at you from out of left field.
 
It also has a lot to do with your Prof/Teacher and your idea of how the class will go even before you get there.

Also, like future said, looking 2 steps ahead to get an idea of what it will be like is kinda hard to do, because math is a tool that is built upon it self. It would be incrediblly difficult to go from algebra 1 to Diff Eq's, but if you take all the classes before Diff Eq's you will have no problems, becase you have all previous classes as experience and knowledge. Don't sweat it, and relize your not the only one freaking out about it.

If your looking to learn application of math FROM the math class (i like to think of math as more of a tool than a subject in itself), you'll probablly have to strech your interpritation of application. You metioned engineering as a major, and (as far as I am concrened) engineering means applied phys/math, so you'll get plenty of that in your ENG classes, like statics circuits and heat transfers ( ).

-Burg
 
Last edited:
cronxeh said:
linear algebra will make you beg for more time, differential equations will eat you alive and multivariable calculus will put you in coma

get ready. its coming to get ya.


Linear Algebra made me cry, solely because it was too boring. I learned everything the nights before the tests, with ease.

However, Multi and differential equation will do *bad* things to you. :-p
 
cAm said:
However, Multi and differential equation will do *bad* things to you. :-p

:eek: I just transferred and the counciler gave me both multivar and diff eq next semester!

:cry: :cry:
 
Thanks for the replies guys.

I guess the root of my concern is the amount of new math coming at me, I am really struggling with infinite series right now. This is partly because my algebra skills are so rusty from taking 4 years off school :smile:, but mostly because there isn't a chance to apply this stuff and see how it works.

In calc I we did a decent amount of applying derivatives after learning about them, same thing with integrals. In calc II all I seem to be getting from the book and my prof is, "applications of this is beyond the scoop of this book/class", very frustrating. It's like memorizing that 5*5=25 and then being told that any use of this fact or learning why 5*5 is 25 so you can go on to solve things like 5*6 is beyond the scoop of this course.
 
cAm, I beg to differ: you did not learn diddly the ngith before the test. that's not how elarning works. what you m,ean is your tests were too easy.

you are wasting yopur time and your money with that app[roach. I'll bet you a dollar to a doughnut your prof knows a ;lot about lineat algebra that you would find interesting.

but if you doze off and give zero effort he ahs no idea that eh could offer you more challenging material. you are dragging your feet and stealing your own tuition money.

wise up for your own good.
 
Actually i don't see how its possible to make linear algebra itself interesting... some of the fields where its used are, but linear algebra itself seems about as dry as it gets.
 

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