Tools & Tips

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Let’s not pretend tech is evil in math learning (well, a necessary evil some may say now). It does not necessarily destroy your chance to master the concepts if you use it correctly. The fact is, there are increasingly more people who succeed to harness technology to aid their concept building when they study or research mathematics.

Nothing beats the natural hand-to-mind way of building up mathematical sense, the pace and posture of hand-writing is just the perfect combination to run your ideas on a paper in a correct speed and focus. What about tech?

Well, it neither comes as an evil antagonist, nor will it salvage you like fast-food when you’re starved. If you keep eating fast food, you’re not going to be healthy. Likewise, when you’re sufficiently behind the progress, copying solutions or looking for answers online will almost certainly destroy you one way or the other, depending on when you admit it, latest by the time you write the final exams (by hand!)

However, it really comes in handy when your brain is running low on memory, having to juggle with so many new concepts. It sometimes may help you focus on the larger problem when the sub-problems are just annoying but not deep, and muddling on whether a minus sign should be there sometimes make you forget what you were supposed to do in the beginning.

So anyway, I’d just get to business and say I’ll post math tools here so as to aids you in working out your own hand-written solutions. Again, I very much encourage you do the suggested homework questions.

Wolfram Alpha

First thing first, I don’t recommend searching at http://www.wolframalpha.com/ at all. The idea behind is just not right for math learners. Your screen is going to be flooded by relevant and irrelevant stuff. “Relevant” because the engine thinks so, “irrelevant” and confusing because the engine actually doesn’t understand what question you have at hand. You then end up in a behavioral pattern of “looking for something similar”. Duh, this can be a toxic way of thinking in the perspective of mathematical training.

Instead, I provide the following widgets to help you check stuff.



Simple Function Plot

Differentiation



Limits as \( n \rightarrow \infty \)

Plotting 3 Functions Simultaneously



Solving an algebraic equation of one variable.


Values and Visualization of a Definite Integral


Finding Indefinite Integrals

From other Instructors

Instructor of Section 211, Vincent Chan has made an awesome tool to visualize solid of revolution in his class page, check it out! It’s awesome!

Solid of Revolution Visualizer (Mathematica CDF installation required)

(By the way, I absolutely love his lecture notes too, and you can find different examples and different ways to look at the concepts.)

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