Is this a complete undergrad pure math curriculum?

  • Thread starter jimgavagan
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  • #26
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You took 14 math classes in your first year? How is that even possible?
Well, as far as I'm aware there's no global standard for how much material goes into a 'class', so a theoretical answer could be that some of the classes I took were very light. The modern syllabus for the course I did is here, and it looks similar to what I remember from nearly ten years ago, so you can check for yourself.
 
  • #27
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In my university pretty much anything math a natural science major would know, you should know. The rest are all considered "electives" because our school is small and courses like topology or number theory isn't offered every year
 
  • #28
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Ugh, I wish I lived in Europe. First we have sucky high school math education and then we have to deal with all these geneds in college.
 
  • #29
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I was notified that these are all the proof-based pure math classes offered at my university for the undergrad pure math degree:

Linear Algebra
Advanced Calculus
Foundations of Geometry
Elementary Number Theory
Complex Analysis
Abstract Algebra

Since the essence of pure math is proofs, do these courses pretty much make up a complete undergrad pure math experience? (If so, what do you think is the best way to prepare for these courses? Or, if not, what additional courses/topics would you include?)

Mainly, it's missing topology. Also, there should be more math electives that you can take, like graph theory, topics courses, differential geometry. If you added a few more of those, it would be like a typical math program in the US. Maybe you could do some reading courses and catch up.

Or, you can always teach yourself. There's a newer grad student here who is very advanced who came from a small school without too many options.

General education requirements aren't such a bad thing. It's not good to be so one-sided. Actually, there was some study on engineers that concluded that the ones who took humanities courses had more flexible thinking or something like that. I don't remember it very well.

As a graduate student, I feel more and more ignorant about the world outside mathematics. I have trouble following the news, etc. because math is just a handful.
 
  • #30
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General education requirements aren't such a bad thing. It's not good to be so one-sided. Actually, there was some study on engineers that concluded that the ones who took humanities courses had more flexible thinking or something like that. I don't remember it very well.

As a graduate student, I feel more and more ignorant about the world outside mathematics. I have trouble following the news, etc. because math is just a handful.

It's good to have the option to take classes outside math, but when you make it a requirement, it can be annoying. It's not fun to shovel a humanities class down your throat when you have a stressful semester filled with math classes.
 
  • #31
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Wow. Algebraic geometry as an undergrad? Good for you! And also projective geometry as a single course? Sounds intense. I think the area of modern math that most frequently utilizes projective geometry is the study of elliptic curves.

I should emigrate to Belgium right away.:tongue:

I also studied an undergrad degree in math in Belgium, and I had less math courses than Micro (went to another university, of course), so think twice before moving (although I'm quite content about my education). The math courses (math majors here were also required to take physics classes for example) I took are (in quasi-chronological order)
  • Calculus I/II/III
  • Linear Algebra
  • Proof and Reasoning
  • Statistics I
  • Geometry I (Euclidean and Affine)
  • Analysis I (Real Analysis + Metric Space)
  • Differential Equations
  • Algebraic Structures (general intro to concepts like groups etc)
  • Abstract Algebra I (groups, rings, fields)
  • Probability
  • Geometry II (Projective, Algebraic Curves, Intro. to Diff. Geo.)
  • Analysis II (Multivariable, Lebesgue, Banach, Wavelets)
  • Numerical Math
  • Mathematical Introduction to Fluid Dynamics (*)
  • Statistics II
  • Topology
  • Complex Analysis
  • Abstract Algebra II (Galois, Sylow, Presentation theory)
  • Number Theory

I count 21. Depending on one's criteria I could also add "Mathematical Methods in Physics", where I (albeit superficially) learned about Stochastic Processes and Representation Theory.

(*) Despite the name no physicists ever took it; it's an applied math class, and a compulsory one at that.
 
  • #32
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To be fair, I'm pretty sure in most places in Europe students take an extra year in high school, while their university degrees are usually 3 years long (13 years of primary and secondary school + 3 years of university, compared to 12 years + 4 years of university in North America). So in a way, their last of high school is sort of equivalent to our year of general studies. Because of this, their degree programs tend to be more focused on their majors.
 
  • #33
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To be fair, I'm pretty sure in most places in Europe students take an extra year in high school, while their university degrees are usually 3 years long (13 years of primary and secondary school + 3 years of university, compared to 12 years + 4 years of university in North America). So in a way, their last of high school is sort of equivalent to our year of general studies. Because of this, their degree programs tend to be more focused on their majors.

As far as I know, one starts primary school in the year they turn 5. Then there's a total of thirteen years of schooling, meaning that one ends high school at 18. In the US, 5 year olds start at kindergarten, yes?
 
  • #34
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As far as I know, one starts primary school in the year they turn 5. Then there's a total of thirteen years of schooling, meaning that one ends high school at 18. In the US, 5 year olds start at kindergarten, yes?

Kindergarten is kind of like day-care. Not too much happens there.
 
  • #35
chiro
Science Advisor
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Kindergarten is kind of like day-care. Not too much happens there.

 
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  • #36
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I'm from Europe Jokerhelper, and I didn't have an extra year in high school, nor do I know of any other country in Europe that does.

EDIT: didn't see the other posts but oh well
 

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