Math 13 – An Introduction to Abstract Mathematics [pdf]

Posted by ibobev 7 days ago

Math 13 – An Introduction to Abstract Mathematics [pdf](www.math.uci.edu)

187 points | 9 comments

commandersaki 7 days ago|

Math 13 was created by the late Howard Tucker as a traditional discrete mathematics course (the number was a deliberate joke).

I took the course under Howard G. Tucker and I did have the impression this was a course not worth taking due to the low number. Turned out to be one of the most memorable classes. We went beyond the curricula in this document and had some fun exploring Hilbert Infinite Hotel and Peanos Axioms. Howard G. Tucker was probably the most memorable professor I had as he was veering in his 90s at the time he taught the course and was just so passionate about teaching.

jhanschoo 7 days ago||

> 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.

aoki 7 days ago||

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.

jhanschoo 7 days ago|||

Thanks, I was unaware of that. I wasn't a math major, but from schoolmates I got the impression that we have the same mix of topics taught computationally vs. proof-based as you listed, students started on analysis and algebra at year 2 and the honors did that in more generality

grandempire 7 days ago||||

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.

DrFalkyn 7 days ago||

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.

grandempire 7 days ago||

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.

mathgradthrow 6 days ago|||

The standard curriculum is dogshit. University should be trying to fix the mistakes of K-12 math education, not perpetuate them.

abeyer 7 days ago||

Isn't that exactly what the sentence after the one you quoted encourages?

curtisszmania 6 days ago||

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blacktits69 6 days ago|

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