Description:
Series Info.
For most people, mathematics is little more than counting: basic arithmetic
and bookkeeping. People might recognize that numbers are important, but
most cannot fathom how anyone could find mathematics to be a subject that
can be described by such adjectives as.Joyful, beautiful, creative, inspiring,
orfim. This course aims to show how mathematics-from the simplest
notions of numbers and counting to the more complex ideas of calculus,
imaginary numbers, and infinity- is indeed a great source of joy.
Throughout most of our education, mathematics is used as an exercise in
disciplined thinking. If you follow certain procedures carefu lly, you will
arrive at the right answer. Although this approach has its value, I think that
not enough attention is given to teaching math as an opportunity to explore
creative thinking. Indeed, it's marvelous to see how often we can take a
problem, even a simple arithmetic problem, solve it lots of different ways,
and always arrive at the same answer. This internal consistency of
mathematics is beautiful. When numbers are organized in other ways, such
as in Pascal's triangle or the Fibonacci sequence, then even more beautiful
patterns emerge, most of which can be appreciated from many different
perspectives. Learning that there is more than one way to solve a problem
or understand a pattern is a valuable life lesson in itself.
Another special qua I ity of mathematics, one that separates it from other
academic disciplines, is its ability to achieve absolute certainty. Once the
definitions and rules of the game (the rules of logic) are established, you
can reach indisputable conclusions. For example, mathematics can prove,
beyond a shadow of a doubt, that there are infinitely many prime numbers
and that the Pythagorean theorem (concerning the lengths of the sides of a
right triangle) is absolutely true, now and forever. It can also "prove the
imposs ible," from easy statements, such as "The sum of two even numbers
is never an odd number," to harder ones, such as "The digits of pi (n wi ll
never repeat." Scientific theories are constantly being refined and improved
and, occasionally, tossed as ide in light of better evidence. But a
mathematical theorem is true forever. We still marvel over the brilliant
logical arguments put forward by the ancient Greek mathematicians more
than 2,000 years ago.
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Media Info.
General:
Container = MPEG-4 (MP4)
Overall bit rate = 877 kb/s
Video:
Codec ID = V_MPEG4/ISO/AVC
Resolution = 980 x 720
Display AR = 4:3
Framerate = 29.970 (30000/1001) FPS
Color space = YUV
Chroma subsampling = 4:2:0
Audio:
Codec info = A_AAC-2
Channel = 2 channel
Sampling rate = 44.1 kHz
Frame rate = 43.066 FPS (1024 SPF)
Language = English
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