Austrian Perspective on the Current Recession:
At a symposium on the crisis at a New England public university, a macroeconomist argued that the current crisis is precipitated by the Fed's policy of making housing affordable to the common man. A public economist argued that this argument is completely wrong. The housing bubble was created because a large number of people wanted to live beyond their means. Whom do you think the Austrians will side with? Click here to find out!
2008 Arrow Prize in Macroeconomics:
A while back Bills and Klenow analyzed some price data for the US and arrived at the conclusion that prices on an average changed every five months implying that the prices were not as rigid after all as the Keynesians would like them to be. But is this average frequency of change in prices a good indicator of price rigidity and does it discredit the Keynesian perspective on the effects of monetary policy? Click here to find out!
Tuesday, June 23, 2009
Thursday, June 18, 2009
Math and Indians!
I was reading this wonderful new book on math econ by Kamran Dadkhah published by Cengage Learning. He has this amazing introductory chapter on history and philosophy of math and using math in economics. I have rarely come across such an exciting introduction to mathematics, especially in an economics oriented text. The later chapters are also well written and book also tries gears you up to use software like MATLAB and MAPLE to solve problems. If I were to teach a course I would definitely give this book a try.
Having said this, I have to admit that I was bothered by one thing. The name of Indians and their contribution to mathematics was almost conspicuous by absence in the introductory chapter!
Well, I knew one thing for sure- the numerals and zero that we use today is courtesy the Indians. However, is that all that is to our contribution? At the risk of sounding jingoist, I decided to dig a bit deeper and guess what, the search was not in vain! The internet was full of pages on Indian mathematics and in what follows are just a few highlights of what I found. If your appetite is rightfully whetted after reading through feel free to click on the links listed below!
To start with there seems to be a long history of substantive contributions starting with pretty sophisticated standardized weight measures from the Indus Valley civilization (2500-1900 BCE) to geometry, trigonometry, algebra and astronomy in the later periods.
Indians thought about the Pythagoras theorem in Budhayana’s Sulbha Sutras dating back to 800 BC (Pythagoras comes sometime in 569 BC). Budhayana also gives the value of square root of 2 till five decimals among other things. Around 4th century BCE, Panini wrote his Sanskrit grammar which is a context free grammar and happens to be an example of early use of Boolean logic and the null operator. It is also thought of as a precursor of the Backus–Naur form (used in the description programming languages).
Around this time we also see important contributions from Jain mathematicians that include simple algebraic equations and the first use of word shunya to refer to zero. They also anticipated the combinatorial identity, Pascal’s triangle and Bernoulli coefficients.
The classical period of Indian mathematics is said to be the period between 400-1200 ACE. Aryabhata, Varahamihira, Brahmagupta, Bhaskara I, Mahavira, and Bhaskara II are some of the prominent names in this period. This period sees major ground breaking mathematical activity in the history of Indian mathematics. Aryabhatta in his Aryabhatiya comes up with first ever tables for sine and cosine values. He talks about quadratic equations, gave the value of pi till 4 decimals, whole number solutions to linear equations, performs astronomical calculations for solar and lunar eclipses and also proposes that the planets revolve around their own axis and also around the sun. This was way before Galileo's time and surprisingly nobody wanted Aryabhatta’s neck for proposing the theory!
Bhaskara II (11 century ACE) anticipated and conceived the concept of derivative, stated Role’s theorem and derived the differential of the sine function and contributed to development of Algebra and Trigonometry. His book Leelavati is a well known text among the Sanskrit scholars.
The Kerala School of mathematics between 1300-1600 ACE gave important results before they were rediscovered by the European world. Infinite geometric series, Taylor series, proof by induction and so on to name a few were discovered by this school.
If you want to know more click on the following links:
1. Indian Mathematics on Wikipedia
2. Indian Mathematics Index
Having said this, I have to admit that I was bothered by one thing. The name of Indians and their contribution to mathematics was almost conspicuous by absence in the introductory chapter!
Well, I knew one thing for sure- the numerals and zero that we use today is courtesy the Indians. However, is that all that is to our contribution? At the risk of sounding jingoist, I decided to dig a bit deeper and guess what, the search was not in vain! The internet was full of pages on Indian mathematics and in what follows are just a few highlights of what I found. If your appetite is rightfully whetted after reading through feel free to click on the links listed below!
To start with there seems to be a long history of substantive contributions starting with pretty sophisticated standardized weight measures from the Indus Valley civilization (2500-1900 BCE) to geometry, trigonometry, algebra and astronomy in the later periods.
Indians thought about the Pythagoras theorem in Budhayana’s Sulbha Sutras dating back to 800 BC (Pythagoras comes sometime in 569 BC). Budhayana also gives the value of square root of 2 till five decimals among other things. Around 4th century BCE, Panini wrote his Sanskrit grammar which is a context free grammar and happens to be an example of early use of Boolean logic and the null operator. It is also thought of as a precursor of the Backus–Naur form (used in the description programming languages).
Around this time we also see important contributions from Jain mathematicians that include simple algebraic equations and the first use of word shunya to refer to zero. They also anticipated the combinatorial identity, Pascal’s triangle and Bernoulli coefficients.
The classical period of Indian mathematics is said to be the period between 400-1200 ACE. Aryabhata, Varahamihira, Brahmagupta, Bhaskara I, Mahavira, and Bhaskara II are some of the prominent names in this period. This period sees major ground breaking mathematical activity in the history of Indian mathematics. Aryabhatta in his Aryabhatiya comes up with first ever tables for sine and cosine values. He talks about quadratic equations, gave the value of pi till 4 decimals, whole number solutions to linear equations, performs astronomical calculations for solar and lunar eclipses and also proposes that the planets revolve around their own axis and also around the sun. This was way before Galileo's time and surprisingly nobody wanted Aryabhatta’s neck for proposing the theory!
Bhaskara II (11 century ACE) anticipated and conceived the concept of derivative, stated Role’s theorem and derived the differential of the sine function and contributed to development of Algebra and Trigonometry. His book Leelavati is a well known text among the Sanskrit scholars.
The Kerala School of mathematics between 1300-1600 ACE gave important results before they were rediscovered by the European world. Infinite geometric series, Taylor series, proof by induction and so on to name a few were discovered by this school.
If you want to know more click on the following links:
1. Indian Mathematics on Wikipedia
2. Indian Mathematics Index
Monday, June 15, 2009
The Economic Globe
William Nordhaus and Chen Xi have created interesting graphics for the world economy which highlight the relation between geophysical variables and economic growth. To access this paper click here. To access the impressive rotating economic globe, click here.
Some food for thought for aspiring geoeconomists:
1. Economic deserts of the world are cold regions.
2. Other than in United States and Europe, much of the economic activity is clustered along coastlines.
Some food for thought for aspiring geoeconomists:
1. Economic deserts of the world are cold regions.
2. Other than in United States and Europe, much of the economic activity is clustered along coastlines.
Subscribe to:
Posts (Atom)
Posts
