Darasa la 6–8ComputationImepangwa
Programming for mathematics
Writing short Python programs that use variables, loops, conditionals and functions to explore mathematics: generating sequences, testing conjectures on many cases, and representing numbers in binary.
math.comp.programming-intro
Somo la mada hii bado halijaandikwa. Muhtasari ulio hapa chini ni sehemu ya ramani ya mtaala na haujakaguliwa.
Inajengwa juu ya
Masharti ya awali ya lazima 9 (hadi chini kabisa)
Utajifunza
- Write programs with variables, loops, conditionals and functions to compute sums, tables and sequences.
- Use a program to test a conjecture on many cases, and explain why this is evidence but not proof.
- Convert between decimal and binary representations, by hand and in code.
Fasili
- A program variable names a stored value that can change while the program runs.
- A program function takes inputs (arguments) and returns an output, possibly with other effects.
- In base 2, the digits 0 and 1 count ones, twos, fours, eights and so on.
Nadharia
- Every positive whole number has exactly one binary representation without leading zeros.
- Checking a statement for the first million cases is experimental evidence, not a proof.
- Floating-point numbers are approximations: in Python, 0.1 + 0.2 == 0.3 evaluates to False.
Mawazo potofu ya kawaida
- Reading '=' in a program (assignment) as mathematical equality.
- Believing a program that runs without errors must compute the right answer.
- Assuming computer arithmetic with decimals is exact.
Inaelekea kwa
Ugunduzi wa hiari
- Numerical analysis Floating-point rounding, visible in 0.1 + 0.2, is studied systematically in numerical analysis.
- Experimental mathematics: conjectures and counterexamples Computer experiments suggest conjectures and find counterexamples in research mathematics.
- ← Functions
Njia za kujifunza
Usomaji zaidi
- Allen B. Downey, Think Python