Recent content by RaijuRainBird

Well, take a crack at it man. Most of the materials can be found on Scribd.com, which means you can download pdf's for a small monthly subscription (but you can search them all in one day, download and limit costs I suppose). I'm finding formal logic, set theory and especially category theory...

How does the logic cut out the meaning? In the first case continuity is specified as for each x there is a specific delta, uniform continuity says there is one delta which works for every x. This is exactly what the logic is telling us. I don't see how this obstructs any understanding.

Well, if we understand symbolic logic correctly, then we actually do understand what the statement means. People can always symbol push with any notation. Besides, you have to communicate somehow. I don't see how writing it out in plain english is any better. This cuts out ambiguity and...

Well, more specifically I should have said "Calculus for engineers" and "early transcendentals calculus" with an emphasis on problem solving. Regardless, I argue calculus/analysis should be taught using logic notation and formal proofs. For example, when covering continuity it should be done...

By truth I just meant logical justification. Not in the way it's implied here. In any case, I do think common core math in the US is taking us in the right direction.

I spent my k-12 schooling experience hating math because I was never able to get answers to my "why" questions. I never bought into the bs answers teachers always handed out; clearly they didn't know, or they thought the material would be too advanced to show me. Now I'm realizing that I'd...

You're right, instead of asking to find slopes of the tangent line 50,000 times why don't we use that time to learn about the set theoretic definitions of functions, the domain and codomain, inverses, images and preimages? How about the intermediate value theorem? Why not learn about fields...

I do like how you bring up the interconnectedness of math and physics. I guess I have to concede to this point. I also know that the calculations can be very difficult. As a theoretical physicist, do you ever think it's possible to know the explanation before the result? I think the root of...

For the record, this is a separate, but very important issue. I totally agree with this.

This is exactly the intention. I don't see why it has to be any different from what we do today. We would just introduce sets early, and teach basic logic like "if a then b" stuff early as well. Then teach them about the rules of sets, then introduce group theory. That way when one...

Well, this is the axiom of infinity: https://en.wikipedia.org/wiki/Axiom_of_infinity It's what justifies mathematical induction by asserting, axiomatically, that at least one infinite set exists. In other words, it's impossible to know. We can only count finitely, and so, it requires faith...

First of all, the logic in geometry is, in fact, logic. It's no different from algebra. Now, the idea is that the people who struggle with basic algebra and arithmetic are struggling for a reason, and I don't think it's systematically teachers' fault, or students' lack of effort, rather I...

I've never heard of the calculus trap until now, but it sounds very relatable! I also agree that sometimes there just isn't enough time to do both math and, for example, engineering, or a science like physics, and learn them both really well, which is really unfortunate because then I think you...

I would have the applied stuff come after this list in the later years as you said. This way everyone knows exactly what is going on, and can fully grasp the applications with total understanding. For example, probability theory and differential geometry can come next, followed by a high level...

I've had a pretty poor experience going through the standardized education system in California, and now that I'm in college, I'm really fed up with how mathematics is taught (even at the college level). With this said, I thought it would be fun for me to redesign the entire math education...