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15 votes

Mnemonics for some properties in mathematics

Recently, a student in my beginning algebra course offered the following to the class, regarding signed number multiplication: Assuming positivity is like love, and negativity is like hate, then... "...
Nick C's user avatar
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11 votes

Mnemonics for some properties in mathematics

I tell students to visualize $<$ and $>$ as mouths. They always want to eat the bigger number.
Steven Gubkin's user avatar
11 votes

Mnemonics for some properties in mathematics

The minimax theorem states the following: Let $X\subset \mathbb{R}^{n}$ and $Y\subset \mathbb {R} ^{m}$ be compact convex sets. If $ f:X\times Y\rightarrow \mathbb {R} $ is a continuous ...
YukiJ's user avatar
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10 votes

Mnemonics for some properties in mathematics

Fatou's Lemma states: for nonnegative measurable functions $f_n$, $$ \int_E \liminf_{n\to\infty} f_n\;d\mu \le \liminf_{n \to \infty}\int_E f_n\;d\mu $$ The mnemonic is $$ \text{ILLLLLI}, $$ meaning "...
Gerald Edgar's user avatar
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10 votes

Pi Day is approaching: What are some interesting math questions whose answer is exactly $\pi$?

Regarding your second example. Not only $\int_{-\infty}^\infty \frac{\sin x}{x} dx = \pi$, but also $$\int_{-\infty}^\infty \frac{\sin x}{x} \frac{\sin (x/3)}{x/3} dx = \pi $$ $$\int_{-\infty}^\infty \...
Adam Latosiński's user avatar
6 votes

Entertaining and fun books about mathematics for (basically) liberal arts students

I'll suggest the book Flatland by Edwin A. Abbott. It's an interesting read about geometry and thinking in a higher dimension. The downside is that this book is, well, antiquated to put it nicely. ...
Mike Pierce's user avatar
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6 votes

Pi Day is approaching: What are some interesting math questions whose answer is exactly $\pi$?

https://en.wikipedia.org/wiki/Buffon%27s_needle_problem 17 matches thrown randomly. Spacing between lines is 1 match length. 11 cross a line. $\frac{2 \cdot 17}{11} \approx 3.1 \approx \pi$.
Steven Gubkin's user avatar
5 votes

Pi Day is approaching: What are some interesting math questions whose answer is exactly $\pi$?

"What are some interesting math questions whose answer is exactly $\pi$?" The area of a unit circle--It is exactly $\pi$. The proof is very neat and visual and can be understood by any ...
Vivaan Daga's user avatar
4 votes

Entertaining and fun books about mathematics for (basically) liberal arts students

The Number Devil: A Mathematical Journey by Hans Magnus Enzensberger is an essential in the "fun math book" category. Very accessible, great illustrations and actually touches on pretty sophisticated ...
celeriko's user avatar
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4 votes

Mnemonics for some properties in mathematics

One I recently learned -- for the order of the signs in factoring a sum or difference of cubes, remember SOAP: Same sign, Opposite sign, Always a Plus. Sum of Cubes: $x^3 + a^3 = (x + a)(x^2 - ax + a^...
Daniel R. Collins's user avatar
4 votes

Pi Day is approaching: What are some interesting math questions whose answer is exactly $\pi$?

A favorite is: What fraction of the integer lattice can be seen from the origin?. The answer is about $61$%. Here $\pi$ makes its appearance in a surprising, non-circular context (surprising to me): $$...
Joseph O'Rourke's user avatar
4 votes

Mnemonics for some properties in mathematics

This only makes sense in Spanish but it's pretty fun. For integration by parts, $$ \int u dv = u v - \int v du $$ Si un día vi una vaca menos sexy vestida de uniforme Which translates roughly to: ...
Rodrigo Zepeda's user avatar
4 votes

Is Calculus Made Easy by Silvanus P. Thompson a good book for first-time calculus learners?

After giving the book another look I have to expand on my comment above and make it stronger: no, this isn't a good book for a first-time learner, and in fact I think it's a terrible choice. I looked ...
Thierry's user avatar
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4 votes

Is Calculus Made Easy by Silvanus P. Thompson a good book for first-time calculus learners?

The fact that the book uses infinitesimals (presented informally) rather than limits is definitely a big deal, and I think you will have to read the book for yourself to see if it works for you. When ...
Mark Foskey's user avatar
3 votes

Is Calculus Made Easy by Silvanus P. Thompson a good book for first-time calculus learners?

In a sense it is OK. In the sense that almost any book (except for one that is very difficult, and assigned to a weaker student and/or one without strong motivation to prevail) is OK. It's really ...
guest's user avatar
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3 votes

Mnemonics for some properties in mathematics

Here is my way of memorizing the three main trigonometric functions. An angle $\theta$ is in standard position locating a point $(x,y)$ on a circle with a radius $r$ centered at the origin. There is ...
JRN's user avatar
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3 votes

Mnemonics for some properties in mathematics

First heard it from a former classmate of mine, might be her own invention: When the second derivative is positive, the function is happy (i.e., its graph looks like a smile). When the second ...
Federico Poloni's user avatar
3 votes

Entertaining and fun books about mathematics for (basically) liberal arts students

Permit me a possibly unusual recommendation: Alexander, Amir. Infinitesimal: How a dangerous mathematical theory shaped the modern world. Macmillan, 2014. Most of the action takes place in Europe ...
Joseph O'Rourke's user avatar
3 votes

Entertaining and fun books about mathematics for (basically) liberal arts students

Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the 10th Dimension, by Michio Kaku. A little long to be light reading, but I love the chapters at the beginning discussing ...
Amanda's user avatar
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3 votes

Pi Day is approaching: What are some interesting math questions whose answer is exactly $\pi$?

On Youtube, there's a video about two squares, one of $1$kg. and one of $10^n$kg., who are bouncing between themselves and the Y-axis. apparently the amount of bounces equals the decimals of $\pi$: ...
Dominique's user avatar
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2 votes

What are some great books for exploring mathematics? (not kids' books and not textbooks)

The World of Mathematics (1950s). Good popular essays to describe various fields of math (e.g. operations research). Martin Gardner column collections (several). The Brian Hayes columns from The ...
guest's user avatar
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2 votes

What are some great books for inspiring children to explore mathematics?

Chaos Flatland Men of Mathematics Anything by Martin Gardner, but especially his columns in IASFM (not sure if ever collected).
guest's user avatar
  • 21
2 votes

What are some great books for inspiring children to explore mathematics?

These suggestions are more from experience during vacations back from my childhood. Mathematics can be fun by Yakov Perelman Puzzles to puzzle you by Shakuntala Devi Sherlock Holmes puzzle collection
AA_PV's user avatar
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2 votes

Are there any mathematics based game apps which require students (between 10 - 16 years) to apply their maths knowledge to play the game

While this is not quite an app, I believe it fits within the spirit of the question: Desmos activities. https://teacher.desmos.com/collections/featured While some Desmos activities are very math-...
Opal E's user avatar
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2 votes

Pi Day is approaching: What are some interesting math questions whose answer is exactly $\pi$?

Not an answer, but more of a chuckle. The Indiana Bill also gives $\pi$. More seriously, it all depends on your audience. There are many choices. Some of your students might like the the history of $\...
Maesumi's user avatar
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2 votes

Recreational mathematics to create sense of mathematics

Personally, my most enjoyable and productive mathematical experiences while growing came from toy research projects. Some examples: When I learned about partial fractions decomposition in high school,...
Justin Skycak's user avatar
1 vote

Is Calculus Made Easy by Silvanus P. Thompson a good book for first-time calculus learners?

Also, get Steven Strogatz's "Infinite Powers" Book. It doesn't have any work problems. He very carefully explains many of the fundamental ideas of calculus. I was fuzzy on some of the ...
Bob Ully's user avatar
1 vote

Mnemonics for some properties in mathematics

To remember concave Up (vs concave down), I remember that the U shape is concave up. Similarly, in conVex, the V is convex. (If you like, v is the only letter in the word which is the graph of a ...
Elle Najt's user avatar
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1 vote

Mnemonics for some properties in mathematics

Last year I heard of $$\text{Lo De Hi Mi Hi De Lo}$$ $$\text{(sing: "Low Dee High my High Dee Low!")}$$ as a mnemonic for the numerator in the quotient rule: $$\left(\frac{f}{g}\right)' = \frac{g\...
Torsten Schoeneberg's user avatar

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