An great collection of Python notebooks | Python 笔记本集

Here is a really great collection of Python notebooks with lots and lots of links.  We start with some appetizers:

But there are so many and so much more!! Okay, I am just going to copy (fork) most of this page:

Mathematics

  • Linear algebra with Cython. A tutorial that styles the notebook differently to show that you can produce high-quality typography online with the Notebook. By Carl Vogel.
  • More

Math olympia medal count analysis | 奥数奖牌分析

The International Mathematical Olympiad (IMO) is an annual six-problem mathematical olympiad for pre-college students younger than 20. The first IMO was held in Romania in 1959. As we will see, eastern Europeans were top performers in the IMO in the earlier years. You can find the summary data analysis in our Jupyter Notebook on GitHub.

It has since been held annually, except in 1980 (what happened in 1980?). More than 100 countries, representing over 90% of the world’s population, send teams of up to six students (under 20 years old) to compete.

Problems cover extremely difficult algebra, pre-calculus, and branches of mathematics not conventionally covered at school and often not at university level either, such as
– projective and complex geometry
– functional equations
– combinatorics
– number theory (where extensive knowledge of theorems is required).

No calculus is required. Supporters of not requiring calculus claim that this allows “more universality and creates an incentive to find elegant, deceptively simple-looking problems which nevertheless require a certain level of ingenuity”.

Rank Country Appearance Gold Silver Bronze Honorable_Mentions
0 1 China 32 147 33 6 0
1 2 United States 43 119 111 29 1
2 3 Russia 26 92 52 12 0
3 4 Hungary 57 81 160 95 10
4 5 Soviet Union 29 77 67 45 0
5 6 Romania 58 75 141 100 4
6 7 South Korea 30 70 67 27 7
7 8 Vietnam 41 59 109 70 1
8 9 Bulgaria 58 53 111 107 10
9 10 Germany 40 49 98 75 11

Debt | 债务

Exactly two years ago, we wrote about national debt.  It was close to $20 trillion at that time.  Now it is $22 trillion.


We are  presenting  very large numbers.

But large is only a relative term, depending on the unit we are using, and relative to what.

According to the Institute of International Finance, global debt, as of 3Q2018, is close to $244 trillion.
About one third of the debt was added in the last ten years or so. So that means that over the last ten years the total global debt grew by a half.

You can see it from the Global Debt Monitor January 2019 Report.

This probably does not mean much to you or me, unless we have some comparisons.

Visuals can help you see the numbers, but it stops short of helping us to understand the number, since money in dollars is just money in dollars unless we compare it with something.

How about we compare it with GDP (gross domestic product)? GDP in dollar is the value of all the things people produce or service for a period of time in dollar.

So debt to GDP ratio is like the amount of money you owe at the end of the year relative to the amount of money you have made over the year.   When the ratio is over 1, it means what we owe is more than what we have made in a year.

Now hopefully we can understand the ratio a little bit.

For a great narrative of history of US debt to gdp ratio, see “The Long Story of U.S. Debt, From 1790 to 2011, in 1 Little Chart” from The Atlantic by Matt Phillips.

The article was written on Nov 13, 2012. But history does not go away.

You can connect the dots to the following chart, which you can find from Federal Reserve Bank of St. Louis.  It seems that we have debt to GDP ratio getting close to historical highest level.

That was right after World War II.

So what is in the US debt?

The total US debt now is about $22 trillion.

The U.S. debt to China is $1.138 trillion as of October 2018. That’s 29 percent of the $3.9 trillion in Treasury bills, notes, and bonds held by foreign countries.

The rest of the $22 trillion national debt is owned by either the American people or by the U.S. government itself. China has the greatest amount of U.S. debt held by a foreign country.

Domestically, the total US household debt as of 4Q2018 is at $13.54 trillion (New York Fed). For a fantastic and fascinating visual account of the numbers, see the report by New York Fed.

You can find the numbers and reports easily from different federal reserve banks and government office such as the Congressional Budget Office, and the US Treasury.

These numbers, ratios and time series by component are a lot more interesting and tell a whole lot more than everyday noisy news.

API

Yes, this is still a Magic Math Mandarin blog–but to have tomorrow’s skills means a lot more than just knowing basic math.
API = plugin

This post is a quick note (updates are in progress).

Site that documents most APIs
https://www.programmableweb.com/
More

hash function/ cryptography/ digital signiture

Hash function (散列函數):
Yes, this is still a Magic Math Mandarin blog–but to have tomorrow’s skills means a lot more than just knowing basic math.
A hash function maps arbitrary string of data fix length of bits.

The simplest (a bad one) is to use the ASCii representation of alphabet, sum up the numbers and take mod.   This creates a problem as “cat”, “act” and “tca” are going to be mapped to the same hash.  This problem is called “hash collision” 碰撞.

More

A CS lecture 马克十几年前教的课

It is amazing how much one can learn from this old video, recorded 2 years after Mark Zuckerburg left Harvard. Here is what I remember after listening 5 times:

1. Don’t follow what the big guys are doing. There is so much you can do on your own with technology (find your own problem and get to it)
More

Python for fun 4


Today we work on animation with hundreds of triangles, balls, squares and vickies (you can call the shapes anything you like).   Shapes are defined by coordinates (x,y).   A huge improvement over last time is that we use a loop to add shape to lists of shapes.
More

Teaching long division (除法)

I was surprised to learn that my fourth grader daughter is learning long division exactly the same way as how I was taught: a highly mechanical process that is worse than doing dishes.

Now looking back, I learned a lot of math mechanically without putting much thought into what I was doing.  Perfecting the steps as if I was self-training to be a robot.

Tomorrow I am going to show why we did long division the way we did, and why there are many other ways.