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Math 13 – An Introduction to Abstract Mathematics [pdf]

(www.math.uci.edu)
187 points ibobev | 2 comments | 13 Apr 25 19:43 UTC | HN request time: 0.522s | source
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jhanschoo ◴[13 Apr 25 21:57 UTC] No.43676161[source]▶
> and serving as the key prerequisite for upper-division courses such as abstract algebra, analysis, linear algebra & number theory.

I was slightly taken aback by this phrasing in the preface as I was under the impression that undergrad math programs introduce foundations ASAP and typically start proof-based classes around end of freshman/start of sophomore.

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aoki ◴[14 Apr 25 00:36 UTC] No.43676997[source]▶
In the US, the standard course sequence (e.g. at a good state university) is two years of calculus, diffeqs, and linear algebra (all taught as on-paper computation) concurrently with a course in discrete mathematics. The discrete mathematics course often doubles as an introduction to proof (as is apparently the case at UCI). Year 3 typically covers proof-based analysis, algebra, and linear algebra and some electives. Year 4 is typically electives.

At a fancy school, you can often take proof-based honors versions of Year 1-2 courses but you still may not get to skip over all of Year 3. Think: calculus using Spivak and real analysis using Rudin.

At Harvard, you can take Math 55, which is essentially Year 3 above (plus complex analysis) in Year 1.

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grandempire ◴[14 Apr 25 02:31 UTC] No.43677559[source]▶
Accurate, but also true that if you are research bound you typically enter at the year 2 or 3 level, already having finished calculus, and maybe linear algebra in high school.
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1. DrFalkyn ◴[14 Apr 25 05:50 UTC] No.43678429[source]▶
This is becoming more common. Students are entering high snchool already having taken geometry in the 8th grade. When I graduated in the late 90s, we had calc 3 (we called it multivariable calc) and linear algebra, partially because a bit under half the class would run out of math by their senior year. They also were starting to offer differental equations and complex analysis. This was a magnet program. When I went back for my 20th reunion, I was told only maybe 5-10% didn’t already have geometry.
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2. grandempire ◴[14 Apr 25 06:19 UTC] No.43678552[source]▶
It’s great that they have opportunity. What’s unfortunate is this means if you aren’t in early, you are never getting in. The greatest indicator of whether you will be a math professor is whether your parents are math professors.