Is this considered a 'pure math' major?

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Discussion Overview

The discussion revolves around the classification of a mathematics major as 'pure' or 'applied', specifically in relation to the curriculum that includes courses such as calculus, differential equations, linear algebra, analysis, and discrete mathematics. Participants explore how these courses relate to engineering and physics majors, and the implications of different educational systems in the US and UK.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Exploratory

Main Points Raised

  • One participant questions whether a major that includes calculus, differential equations, and linear algebra can be considered 'pure' mathematics, suggesting that engineering or physics majors might be categorized as 'applied' mathematics.
  • Another participant expresses confusion, noting that engineering and physics students typically take similar mathematics courses, and emphasizes that the specific courses do not definitively determine the nature of the major.
  • A link to a curriculum is provided by a participant to illustrate the structure of the major in question.
  • Concerns are raised about the balance of general education requirements and technical electives in the curriculum, with a suggestion that the focus may lean more towards engineering and computation rather than pure mathematics.
  • Some participants discuss their experiences with mathematics education in the UK, comparing it to the US system, and express uncertainty about current standards in US high schools.
  • There is mention of the variability in high school mathematics offerings, with some participants noting that advanced courses like AP Calculus BC are available in many schools, while others recount limited options in rural settings.
  • Discussion includes the idea that the rigor of calculus courses can vary, with some universities offering proof-based honors courses that serve as a foundation for real analysis.
  • A participant shares their reasons for choosing a specific university, highlighting factors such as in-state tuition, small school size, and scholarship opportunities.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether the inclusion of certain mathematics courses categorizes a major as 'pure' or 'applied'. Multiple competing views remain regarding the definitions and implications of these classifications.

Contextual Notes

There are limitations in the discussion regarding assumptions about educational standards, the definitions of 'pure' versus 'applied' mathematics, and the specific course content across different institutions. The discussion reflects a variety of personal experiences and regional differences in mathematics education.

imull
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Is it considered a 'pure' math major if classes like calc 1-3, diff eq, linear algebra, analysis, and discrete maths are a part of the major? If so, would an engineering or physics major be considered 'applied' mathematics?
 
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I'm confused by what you mean, engineers and physics majors will take near all those classes.

Some schools will offer different undergrad series for science majors and a proof heavy series for math majors.

The classes that you list however, again, say nothing about the major.
 
http://mathematics.wvutech.edu/curriculum/classic_track
There's a link to the major.
 
Kind of sucks you'd be doing GE your senior year, other then that you have what five technical electives, two upper division math electives, senior thesis. I'm not sure what math for citizenship is, but it's senior level. The school itself is a STEM focused public school that is accredited.

I would say you'd probably be able to do "pure" math there, but it seems more focused on engineering and computation.

I'm not a math major, so maybe some math majors would be able to help you out more. Call the school too.
 
That looks like pure math, real analysis are proof heavy courses as is Intro to Alg. Structures, which looks like introduction to abstract algebra, the real difference however is what you choose for your electives.

This http://techregistrar.wvutech.edu/r/download/132496 seems to describe the courses.
 
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Thank you so much for finding that, MathWarrior! It is very helpful.
 
I don't know what the state of math education in the US is like these days, but when I did a math degree in the UK, we had the equivalent of those M341, 451 and 452 courses starting on the first day of year one.
 
AlephZero said:
I don't know what the state of math education in the US is like these days, but when I did a math degree in the UK, we had the equivalent of those M341, 451 and 452 courses starting on the first day of year one.

You also went to Cambridge and probably had a thorough calculus foundation in high school. I don't know what they teach at that level in the US anymore, but they generally just require two semesters of elementary algebra. If they do offer AP calculus classes its mostly just a crash course in calculus one, I didn't have that option at my school at all.

Again I've been out of high school for a while, but it's pretty typical to do the calculus series freshman year of college.

We never did any proof math, or trig even in HS. It may have been the same for you and Cambridge just throws you into the deep end of the pool, but I don't know the UK system at all either.
 
Student100 said:
If they do offer AP calculus classes its mostly just a crash course in calculus one, I didn't have that option at my school at all.

AP Calc BC covers calc 1 and calc 2. My high school, amongst many others in the US, also offered calc 3, ODEs, and LA.

Student100 said:
Again I've been out of high school for a while, but it's pretty typical to do the calculus series freshman year of college.

This is true but it is also up to the student to decide how rigorous a calculus class he/she wants to take. Proof based freshman honors calculus courses are offered by many universities in the US and these are basically stepping stones into real analysis. Schools like UChicago also actively allow students to take honors real analysis their first year.
 
  • #10
WannabeNewton said:
AP Calc BC covers calc 1 and calc 2. My high school, amongst many others in the US, also offered calc 3, ODEs, and LA.

Interesting, so it isn't like I had imagined were everything that is taught in high school is only what's relevant for standardization exams.

I went to a rural school, with 45 graduating seniors my final year. This probably also played a major role in what was available.


This is true but it is also up to the student to decide how rigorous a calculus class he/she wants to take. Proof based freshman honors calculus courses are offered by many universities in the US and these are basically stepping stones into real analysis. Schools like UChicago also actively allow students to take honors real analysis their first year.

This is relevant and useful for the OP in deciding where they should study.
To the OP: was WVU your number one option, If so why?
 
  • #11
Student100 said:
Interesting, so it isn't like I had imagined were everything that is taught in high school is only what's relevant for standardization exams.

I would be lying if I said most of it isn't taught like that though :)

Student100 said:
I went to a rural school, with 45 graduating seniors my final year. This probably also played a major role in what was available.

I would imagine that had major influence. I went to a relatively big science based school (~700 kids in my graduating year).
 
  • #12
Yes it was my number one option. It is in state (lower tuition), a small school (1000-1500), and WV high school students with an overall 3.0 gpa by the end of their senior year get Promise Scholarship ($4700 per year for 4 years). I wanted a small school because it is what I am used to. Also, the college classes that I am taking right now and next semester (Calc 1 and 2, College English 1 and 2, Psych, and Euro History) transfer because they are taught by a local college that is part of WVU.
 

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