15 votes
Accepted

How to help students bridge the gap between highschool and university mathematics?

First it's a good sign that you're on this website and keen to make a difference. A passionate tutor is halfway there in my opinion. I've thought about what would have helped me as an undergraduate ...
  • 1,552
9 votes

What is a good book to learn all of prealgebra?

This California college has a no-frills $602$-page textbook available for free PDF download: College of the Redwoods Mathematics Prealgebra Textbook. 2012-13. (PublisherLink). There was a free ...
8 votes

How strict are you with prerequisites?

For several decades, this issue has plagued me, at all levels, from calculus to grad-level courses. First, my conclusion by this point is that very few people truly "have" the prerequisites ...
  • 13.6k
7 votes

How to help students bridge the gap between highschool and university mathematics?

The more the students can reinvent theorems themselves, the better. This is the philosophy of math circles, and it's also how R.L. Moore ran his classes (http://legacyrlmoore.org/reference/mahavier1....
  • 18k
7 votes
Accepted

At what point is it a disservice to pass someone on to the next math class?

Social promotion is an interesting topic, and I know my personal views are unpopular in my school. So they probably will be here too, but I'll go ahead. Due to developmental issues with children I ...
  • 631
6 votes

At what point is it a disservice to pass someone on to the next math class?

There is a point at which material is so far beyond students' skills that they learn less. Imagine a freshman calculus student plopped into a graduate topology seminar: they will learn almost nothing. ...
  • 890
6 votes

Is there any proof of the fundamental theorem of algebra that can be introduced to undergraduates who have just completed Calc III?

In this video, David Eisenbud (a math prof at Berkeley) explains a proof of the fundamental theorem of algebra that is very enlightening / beautiful, and almost makes the result seem obvious.
  • 967
5 votes

How to help students bridge the gap between highschool and university mathematics?

I appreciate the question and the problems it is trying to solve. I have the feeling that it is trying to "attack the symptoms rather than the cause", and that what is really needed is a more ...
4 votes

At what point is it a disservice to pass someone on to the next math class?

Indeed it is futile to expect students to successfully catch up with the prerequisite mathematical understanding for a course if they are too far behind. This is because many students think that they ...
  • 2,366
4 votes

What is a good book to learn all of prealgebra?

If you don't mind something a bit old-fashioned, you can use C. V. Durell's arithmetic and algebra textbooks. These were standard in good schools in England at one time, and continued to be widely ...
  • 587
4 votes

What is a good book to learn all of prealgebra?

Art of Problem Solving has a pre-algebra text that gets glowing reviews. I would expect it to be complete and rigorous.
  • 18k
4 votes

Where can I find the partial order relation of prerequisites of undergraduate courses in the United States?

The US has different courses at different schools. Sometimes with same name but differences in content or prereqs. It would be more meaningful to sketch this tree for a given school. Or do a few ...
  • 41
4 votes

Is there any proof of the fundamental theorem of algebra that can be introduced to undergraduates who have just completed Calc III?

Here is an elementaryproof which considers $ p(z) $ as a function of $ (x,y) $ where $ z=x+iy $. The only assumptions are that $z^{n}=r $ has a solution for all integer $n$ and real $r$ and that ...
3 votes

Is there any proof of the fundamental theorem of algebra that can be introduced to undergraduates who have just completed Calc III?

I admit I'm a bit late to the party, but for completeness let me add a link to an interactive version of one of the visual proofs: The fundamental theorem of algebra - a visual proof (Disclaimer: I'...
3 votes

Is there any proof of the fundamental theorem of algebra that can be introduced to undergraduates who have just completed Calc III?

$\def\RR{\mathbb{R}}\def\CC{\mathbb{C}}$ Here is a proof via ODE. I imagine it's been found before, but I hadn't seen it before. The essential idea is that, if $z: \RR \to \CC$ is an inverse function ...
3 votes

Is "The Petersen Graph" by Holton and Sheehan a good text for graph-theory students? Any requisite knowledge for mastering the text?

There are no Amazon reviews. Doesn't seem like a popular title. (Just an indicator, not a Euclidean proof...but a negative note.) The preface says that it is approaching teaching all of graph theory ...
  • 31
2 votes

Are there any math certificates/qualifications on high school maths that you can do after high school?

The UK A-levels are widely studied outside the UK. The new syllabus is designed to have all the exams at the end, rather than the modular system that was in place before. So while there might be more ...
  • 5,576
2 votes

What prerequisites would college students need for a course based primarily on Euclid's elements?

Here is a thought that might help in your development. Write up a sample lecture/class period to describe the material and how it goes. Get two others to help you run through a trial and videotape ...

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