After obtaining a degree in math

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Discussion Overview

The discussion revolves around the expectations of mathematical problem-solving abilities after obtaining a bachelor's degree in mathematics. It touches on foundational topics such as Algebra and Calculus, and considers the depth and nature of questions that graduates might encounter.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant suggests that a graduate should be able to tackle problems from Algebra 1 through Calculus 3, indicating these are foundational topics.
  • Another participant agrees that foundational knowledge is expected but acknowledges personal limitations in answering certain calculus questions, expressing concern about the thread becoming a challenge.
  • A third participant clarifies that the discussion applies to both bachelor's and master's degrees in mathematics.
  • One participant argues that the ability to solve problems depends on how questions are framed and the depth of the questions, noting that some elementary topics may not be covered in undergraduate courses.
  • Another participant expresses that while one may not solve every problem, they should have a good understanding of how to approach problems and comprehend solutions.

Areas of Agreement / Disagreement

Participants express differing views on the extent of problem-solving abilities expected from graduates, with no consensus on whether one should be able to solve every problem encountered.

Contextual Notes

Participants highlight the complexity of mathematical problems and the potential for nuances that may not be addressed in formal education, suggesting limitations in the expectations set for graduates.

starchild75
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should you be able to tackle any problem Algebra 1 thru calculus 3?
 
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Are you talking about an undergraduate degree in maths? Then, yes, one should be able to tackle algebra and calculus problems, as these are the foundations of a maths degree! That said, there's almost certainly some calculus questions you could ask me that I, for one, wouldn't be able to answer straight away, so I hope this thread won't turn into a "challenge!"
 
I was referring to a bachelors. But the question could apply to masters as well.
 
It depends on two things really, one is the manner in which you ask the question and the other is the depth of the question. There are many things about elementary topics that you'd never be taught in any class that was required for your undergrad math degree. Math has existed for a long time and people haven't gotten exponentially smarter to keep up with the advances. Some pretty smart people were looking at problems one might consider elementary today; if they had trouble there why wouldn't you? There are some not so subtle nuances here: the fact is that you can look at a problem with hindsight, that makes it easier, but I think you get my point.

My guess is that if you've truly learned something from your undergrad work you should at the least be able to do any problem in any widely used introductory textbook of calculus or linear algebra. I say this as an undergrad myself, so perhaps you should wait for someone wiser to post.
 
Hm I wouldn't say you should be able to solve every problem you see, but you should at least have a very good idea on how to solve it and be able to understand the solution and have a general idea of what the solution will be.
 

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