Link: An intuitive way of thinking about even, odd integers and divisibility. (math.stackexchange.com)

1 · comment delete · by anamkelekh 5 days ago

Link: Terry Tao on Rigor and Proofs (terrytao.wordpress.com)

1 · comment delete · by kalid 21 days ago

Intuition rigor post-rigor

Great distinction here.

Link: Explanation on dy/dx notation with regards to limits (math.stackexchange.com)

1 · comment delete · by kalid 1 month ago

Link: Mortality Statistics (gravityandlevity.wordpress.com)

2 · comment delete · by kalid 4 months ago

Has probability distributions. Think through what various distributions mean. "Cops and robbers" scenario seems to model (well) the rates we're seeing.

Link: Precursor to Diffie-Hellman key exchange (en.wikipedia.org)

1 · comment delete · by kalid 4 months ago

Interesting way to see an idea evolve. What is the core essence here?

Link: Misleading data sets (blog.statwing.com)

1 · comment delete · by kalid 4 months ago

data sets which have misleading conclusions. Until you see the graph you don't realize how different they are.

Link: Resonances Waves and Fields (blog) (resonanceswavesandfields.blogspot.co.uk)

1 · comment delete · by kalid 8 months ago

Link: Virtual mainpulatives (nlvm.usu.edu)

1 · comment delete · by jeremi 10 months ago

Link: Mind maps (www.docstoc.com)

1 · comment delete · by jeremi 9 months ago

Link: Street-fighting mathematics tools for guessing answers (mitpress.mit.edu)

1 · comment delete · by jeremi 11 months ago

Link: Quaternion Tutorial (3dgep.com)

2 · comment delete · by kalid 11 months ago in quaternion

Recommended by a reader

Link: The beauty of mathematics in poetry (poetrywithmathematics.blogspot.com.es)

1 · comment delete · by jeremi 11 months ago

Link: Curl intuition (math.stackexchange.com)

1 · comment delete · by kalid 11 months 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 year 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)

4 · 2 comments delete · by kalid 1 year 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...

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

3 · 3 comments delete · by kalid 1 year ago

Nice little summary. Covers the essentials.

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

3 · comment delete · by kalid over 1 year ago

Recommended, should read.

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

1 · comment delete · by kalid over 1 year 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 · 2 comments delete · by kalid over 1 year 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 over 1 year 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 over 1 year ago in Fractions

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 over 1 year 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 over 1 year 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)

3 · comment delete · by kalid almost 2 years 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 almost 2 years ago

Has some interesting arguments, need to investigate further.

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

1 · comment delete · by varunbpatil almost 2 years ago in Vim (text editor)

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

1 · comment delete · by kalid almost 2 years ago

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

Link: Computing inverse trig functions (oakroadsystems.com)

1 · comment delete · by kalid almost 2 years 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...

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

2 · comment delete · by kalid 2 years ago

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

1 · 1 comment delete · by thane 2 years ago in Curl (mathematics)

The visualizations make the topic easier to understand.

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

2 · 3 comments delete · by kalid 2 years ago

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

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

Link: Mathematics discussion (www.facebook.com)

1 · comment delete · by montyhodla 2 years ago

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

1 · comment delete · by kalid 2 years 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...

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

2 · comment delete · by mea10mb 2 years ago

Link: Video on finding e (James Tanton) (www.youtube.com)

3 · comment delete · by kalid 2 years 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...

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

2 · comment delete · by kalid 2 years 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.
  • ...

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

2 · 1 comment delete · by mea10mb 2 years ago

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

3 · comment delete · by kalid 2 years 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"...

Link: How Google Code Search Works (swtch.com)

1 · comment delete · by kalid over 2 years 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...

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

2 · 1 comment delete · by sleong123 over 2 years ago in Mathematician

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...

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

1 · 1 comment delete · by kalid over 2 years 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)

5 · comment delete · by Skyafar over 2 years ago in Social bookmarking

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 2 years ago in Right brained

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...

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

1 · comment delete · by sleong123 over 2 years ago in Ignorance

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 2 years ago in Simplicity

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 2 years ago in Probability theory

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

3 · 1 comment delete · by sleong123 over 2 years ago in Understanding

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 2 years ago in 4th dimension

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...

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

8 · comment delete · by kalid over 2 years 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.

The link...

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

3 · comment delete · by kalid over 2 years 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...


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