### Link: Fencing in Calgary (www.lynxfence.com)

1 · 1 comment delete · by michellelthorn 2 minutes ago in Fencing

### Link: Chapter 7 Bankruptcy in Attorney in Chicago (www.primebankruptcy.com)

1 · comment delete · by michellelthorn 2 minutes ago

I didn't know a lot about bankruptcy before, but I searched around found some information and then finally understood that they had attorneys to help the case.

1 · comment delete · by kalid 10 days ago

How to understand the components of the curl formula.

### Link: Understanding Lagrange multipliers (www.the-idea-shop.com)

1 · comment delete · by kalid 1 month ago

Good description. Hill climbing.

Get the 2 gradients to be parallel. That is the main insight.

### Link: Fourier Transform Intuition (pdf) (techhouse.brown.edu)

2 · 1 comment delete · by kalid 3 months ago

Nice article. has insight about "dividing by e^iwt" to see how much is in the original signal.

How much "7" is in 28? 28/7 = 4 sevens.

How much "2Hz" is in x(t)? x(t) / 2Hz. Neat.

What looks like a multiplication is actually a division!

### Link: One page calculus summary (web.mit.edu)

3 · 3 comments delete · by kalid 4 months ago

Nice little summary. Covers the essentials.

### Link: Terrence Tao on Linear Algebra (www.math.ucla.edu)

2 · comment delete · by kalid 5 months ago

### Link: Computing Gravity in Video Games (www.niksula.hut.fi)

1 · comment delete · by kalid 5 months ago

Need to account for measurement error. Take the midpoint (half before, half after) vs the pure staircase pattern.

### Link: Explanation of Quaternions on reddit (www.reddit.com)

2 · 1 comment delete · by kalid 8 months ago

Great explanation. Notice the part about introducing new variables.

i and j are defined to be alternate paths to -1 [avoiding regular multiplication]. We can visualize that as another dimension if we like.

ij gives yet a 3rd path [another...

### Link: How to teach quantum mechanics (www.scottaaronson.com)

1 · comment delete · by kalid 8 months ago

I like the description here. Talks about the true essence, not necessarily how it developed.

Core: negative (or complex) probabilities. Whoa! What does that mean?

[Remember, we didn't think negative or complex numbers could exist. Why not...

### Link: Understanding fractions for parents and children - how many vs. how much (www.learnhive.net)

1 · comment delete · by shiv 9 months ago

The most common mistake done by children is to add the numerators and the denominators separately treating them similar to natural numbers. Once the how many versus how much is well explained, they can then easily grasp why it is necessary to...

### Link: How to beat the fear of algebra? (for you and your kids) (www.learnhive.net)

1 · comment delete · by shiv 9 months ago in Algebra

Simple way to explain algebra. Understand what 'X' stands for.

### Link: Why is a negative multiplied by a negative a positive? (www.quora.com)

1 · 1 comment delete · by EseImbecil 9 months ago

Negative numbers represent changes, not amounts. So, a -4 in some unit, let' s say slices of bread, doesn't mean that you have -4 slices, but ratter that you have 4 less slices

### Link: Counting combinations/permutations with polynomials (www.numericana.com)

2 · comment delete · by kalid 10 months ago

You can multiply polynomials and take the coefficient to get the number of combinations / re-arrangements.

(1 + x + x^2) represents the 3 options for taking 0, 1 or 2 of something.

(1 + x) represents 2 options for taking 0 or 1 of something [of x].

...

### Proof walkthrough: Why div of a curl is 0 (www.oberlin.edu)

1 · comment delete · by kalid 11 months ago

Has some interesting arguments, need to investigate further.

### Link: The ultimate vim configuration (varunbpatil.github.com)

1 · comment delete · by varunbpatil 11 months ago

1 · comment delete · by varunbpatil 11 months ago in Android

### Simple Made Easy (talk by Closure creator) (www.infoq.com)

1 · comment delete · by kalid 12 months ago

Great talk on the difference between simple vs. easy, and how not to "complect" (intertwine) parts of your system.

1 · comment delete · by kalid 12 months ago

Really great way to visualize how to handle items like

$$cos(arctan(x))$$

Draw out the triangle you need [arctan(x) means a triangle with "x" as the height, and we're going to get the angle, and figure out the hypotenuse]. Then you take the cosine...

### To read: Analogies / insights for eigenvectors (www.reddit.com)

2 · comment delete · by kalid 1 year ago

### Link: Idea of the curl of a vector-valued function (mathinsight.org)

1 · 1 comment delete · by thane 1 year ago

The visualizations make the topic easier to understand.

### Link: What is a tensor? (vimeo.com)

2 · 3 comments delete · by kalid 1 year ago

Great vid explaining the essence of a tensor -- matching up components with basis vectors.

Rank 0 (scalar) : component, but no basis vectorsRank 1 (vector) : component & 1 basis vector (1 x 3)Rank 2 (array) : component matched with 2 basis...

1 · comment delete · by montyhodla 1 year ago

### Link: Donald Knuth on Calculus using O notation (micromath.wordpress.com)

1 · comment delete · by kalid over 1 year ago

One key to calculus is navigating the different "planes of precision" (i.e. n, n^2, etc.) where one does not effect the other.

How big a constant will make kn a polynomial? It never will. n^2 is a different beast.

Calculus is the art of learning how...

### Analogies: a key to understanding physics (www.univ-reims.fr)

2 · comment delete · by mea10mb over 1 year ago

3 · comment delete · by kalid over 1 year ago

Nice video about finding e from the derivative definition.

• Find derivative of 2^x (but can't... you get .69 * 2^x)
• Find derivative of 10^x (but you can't... you get 2.3 * 10^x)

Idea is that some number in-between has 1.0 * something^x [and we call...

### Link: Lisp in 40 lines of ruby (blog.fogus.me)

2 · comment delete · by kalid over 1 year ago

Quick LISP interpreter in ruby. Key insights:

for the eval method...

• if you're an atomic unit (smallest item), just return it's value from the environment
• most methods have their arguments evaluated first, and then you call the method.
• "if" and...

### Link: Force as a current of momentum (www.physikdidaktik.uni-karlsruhe.de)

2 · 1 comment delete · by mea10mb over 1 year ago

### Link: Einstein's paper [e = mc^2] (www.fourmilab.ch)

3 · comment delete · by kalid over 1 year ago

Some great insights here (understatement of the millenium):

"If the theory corresponds to the facts, radiation conveys inertia between theemitting and absorbing bodies."

We normally thing "Oh, we transmit energy with radiation" but because of e =...

1 · comment delete · by kalid over 1 year ago

Some great insights here:

• Nice explanation of how indexes work: for a given term, store the documents that contain it, along with the position in the doc. To see if a phrase is matched "foo bar" look for both "foo" and "bar" and ensure bar comes...

### How Mathematicians Work: "You lay down, close your eyes, and work like hell." (wsf.tv)

2 · 1 comment delete · by sleong123 over 1 year ago

What I've shared with my friends who are not continuing their studies in math (on facebook):(Editor's note: Kalid, I think this would be a great segway if someone were, for example, to do a presentation for schoolkids of today's schools, on making...

### Link: Excellent diagram of morse code (alphabet tree) (www.learnmorsecode.com)

1 · 1 comment delete · by kalid over 1 year ago

Putting the tree in this format really makes it click. The site has an example audio file going through the alphabet too. Great example of how to present an idea.

### Link: Me too Created Something similar to aha.better explained (slugs.in)

4 · comment delete · by Skyafar over 1 year ago

I come across betterexplained while searching about some server gzip compression. and i loved the way topics are explained. After that i come accross with aha.betterexplained . then i thought of creating some thing similar. Now i created some...

### Righty vs. Lefty (Left-Brained vs Right Brained) (www.google.ca)

4 · 8 comments delete · by sleong123 over 1 year ago

This is SUCH an interesting topic, that I decided to include a Google search link as opposed to an article.

Being a lefty and right-brain dominant, it's very interesting to note that school systems of today are most advantageous to the majority -...

### A Universal Lesson in Human Humility (www.schoolofunlearning.com)

1 · comment delete · by sleong123 over 1 year ago

Thus, why it is important to "simplify".

Please also watch the video in the included link within the webpage.

It's amazing to fathom the size of the universe from the visual imagery! We are a mere, infinitesimally small speck...

### Link: The Art of Simplicity (www.schoolofunlearning.com)

1 · comment delete · by sleong123 over 1 year ago

A very different perspective than what one would be commonly "taught" in today's schools. From a wonderful blog.

Cont'd next post:

### Link: Great Website - Introduction to Probability Theory (www.probabilitytheory.info)

3 · 3 comments delete · by sleong123 over 1 year ago

### Link: Article - Inductive vs Deductive Learning - "Why Memorization is Ineffective" (www.opensourcetutoring.org)

3 · 1 comment delete · by sleong123 over 1 year ago

A take on why it is perhaps better to develop critical thinking skills in the work-force, in today's bustling 21th century world.

### Link: Video - Understanding the 4th Dimension (Wonderful Analogy of Flatland) (www.youtube.com)

3 · 1 comment delete · by sleong123 over 1 year ago

A wonderful video produced by Carl Sagan, which explains the 4th dimension.

He simplifies the analogy by demonstrating 2d beings, imagining an "inconceivable" third dimension. As humans, we are simply 3d beings who cannot "conceive" that 4th...

### Link: Nice analogy for fourier transform (room with a fly) (movieblow.wordpress.com)

8 · comment delete · by kalid over 1 year ago

Breaks down the need for a Fourier transform... you have an element (a fly) which can be measured in 2d, 3d, any number of dimensions.

The magnitude of each dimension (in 8-D, let's say) lets you reconstruct the position of the fly.

### Link: Teaching Linear Algebra (bentilly.blogspot.com)

3 · comment delete · by kalid over 1 year ago in Teaching

Good writeup on how to structure a class. Things I like:

• Homework is 1/3 current, 1/3 last week, 1/3 anywhere in the course (increasing difficulty). Let's not pretend we can just forget the past!

• Asking people questions very regularly (getting...

### Link: Programming - the "single point of truth" rule (teddziuba.com)

2 · comment delete · by kalid over 1 year ago

"If you don't feel like reading it, the most important take-away for web programmers is the Single Point of Truth Rule, that is, "every piece of knowledge must have a single, unambiguous, authoritative representation within a system". If you...

### Link: Tutorial on recursive-descent parsers (www.cs.uky.edu)

1 · comment delete · by kalid over 1 year ago in Parser

I like that it starts with what we are trying to do and how it works, and THEN getting into the corner cases (What makes a nice grammar?).

For these tutorials, esp. for parsers where there are so many ways to handle them, let's figure out how to...

### Link: Concise explanation of some programming concepts (evincarofautumn.blogspot.com)

1 · comment delete · by kalid over 1 year ago

Some clear, no-nonsense description of abstractions without crazy analogies.

"You can thus write instructions for doing stuff to entire trees very concisely: to snuggle a whole tree, first snuggle the base of the tree, then snuggle each branch as...

### Link: Explanation of the math behind A/B testing (visualwebsiteoptimizer.com)

2 · comment delete · by kalid over 1 year ago

Key insight:

• Measure variation A and variation B
• You are getting samples of both. So you have error bars. A has p(a) with some error (standard error, based on number of trials). B has p(b) with same standard error.
• Take a bunch of measurements....

### Link: Interesting, interactive git cheatsheet (ndpsoftware.com)

1 · comment delete · by kalid over 1 year ago in Git

I like how this is arranged, it communicates the different pieces of git and how they interact. One key to git is realizing how files can live in different parts (the index, local workspace ,etc.) and how to move them around.

### Link: Making sense of standard deviation (amarsagoo.blogspot.com)

3 · comment delete · by kalid over 1 year ago

Key insight: the purpose of squaring, summing, and square rooting is not to "make the sign positive" but to "punish outliers". The further away (larger the number), the higher your square.

### Link: Essay on use of rigor in mathematics (www.math.rutgers.edu)

1 · comment delete · by kalid over 1 year ago in Rigor

"Real mathematics is (or at least should be) algorithmic. The axiomatic method is like machine language or a Turing machine or a Tuxedo. It is very stifling. The logicist approach that takes several hundred of pages to prove that 1+1=2 is...

### Link: Will it rot my students' brains if they use Mathematica? (www.theodoregray.com)

3 · 2 comments delete · by kalid over 1 year ago

Nice summary:

Less ImportantGuessing factors for polynomialsKnowing many tricks for integrationBeing careful when copying over expressions many timesFinding roots of complex equationsKnowing how to do matrix row operationsKnowing how to avoid...

### Link: Visualize Bayes' Theorem (with a Venn Diagram) (oscarbonilla.com)

5 · 1 comment delete · by kalid over 1 year ago

Key insight is to see the overlap between having the event and having a positive test.

A venn diagram is a great way to see that. What is the ratio of the overlap to each side?

Another visualization:

http://makematics.com/syllabus/2012-fall/

"Turn...

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