Programming for mathematics

Se basa en

Requisitos previos obligatorios, hasta el fondo: 9

Aprenderás a

• 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.

Definición

• 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.

Teorema

• 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.

Errores frecuentes

• 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.

Conduce a

Descubrimientos opcionales

• 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

Itinerarios de aprendizaje

• Computer science and formal methods

Lecturas complementarias

• Allen B. Downey, Think Python