MATH0011: Mathematical Methods II

Code we wrote during lecture 3

python

# Import an entire module
import math
print(math.log(2))

# Import a function from a module
from math import log
print(log(2))

# Using as to rename imports
import math as maths
print(maths.log(2))

from math import log as ln
print(ln(2))

#
# The random module
#
from random import random
print(random())

import random
a = [2,3,8,10]
print(random.choice(a))
print(a)
random.shuffle(a)
print(a)
print(random.randrange(0,10))

print(random.gauss(0, 1))

# Simulate rolling two (fair) dice
import random

first = random.choice([1,2,3,4,5,6])
second = random.randrange(1,7)
print(first, second)

# Simultate 1000 rolls of two dice and estimate probability that the sum is 7
import random

count = 0
for i in range(1000):
    first = random.choice([1,2,3,4,5,6])
    second = random.randrange(1,7)
    if first+second == 7:
        count += 1
print(count/1000)

#
# The itertools module
#
import itertools

for i in itertools.combinations(range(5), 3):
    print(i)

for i,j,k in itertools.combinations(range(5), 3):
    print(i,j,k)

for i,j,k in itertools.combinations_with_replacement(range(5), 3):
    print(i,j,k)

from itertools import combinations_with_replacement as cwr

for i in cwr(range(5), 3):
    print(i)

for i in itertools.permutations(range(5), 3):
    print(i)

for i in itertools.permutations(range(5)):
    print(i)

for i,j in itertools.product([0,4,10,3], "Hello"):
    print(i,j)

for i in itertools.product([0,4,10,3], "Hello", "def"):
    print(i)

for i in itertools.repeat(5, 10):
    print(i)

for i in itertools.repeat("Hello"):
    print(i)

# Calculate the probability that two (fair) dice will add up to 7
import itertools
sevens = 0
total = 0
for first,second in itertools.product(range(1,7), range(1,7)):
    total += 1
    if first+second == 7:
        sevens += 1
print(sevens/total)

# Print the current date
# We used Google to find this
import datetime
now = datetime.datetime.now()
print(now.year)

# We found this better version on Google
import datetime
print(datetime.datetime.today().strftime('%d %b %Y'))

The next piece of code uses the listmaker module that we wrote during the lecture.

python

# Using the listmaker module (that we wrote)
# See listmaker.py
import listmaker
print(listmaker.squares(1000))
print(listmaker.primes(100))

# print the number between 1 and 100 that cannot be written as the sum
# of a square and a prime
import listmaker

squares = listmaker.squares(100)
primes = listmaker.primes(100)

possible = {}

for i in range(1,100):
    possible[i] = False

for i in squares:
    for j in primes:
        if i+j < 100:
            possible[i+j] = True

# The following lines do the same thing as above in a different way
#from itertools import product
#for i,j in product(squares,primes):
#    if i+j < 100:
#        possible[i+j] = True

for i,j in possible.items():
    if not j:
        print(i)

# Using the Fraction class from the fractions module
from fractions import Fraction

half = Fraction(1, 2)
third = Fraction(1, 3)
print(half**2)

# Handling exceptions
a = 2
data = []
for b in range(-5,6):
    try:
        print(a/b)
    except ZeroDivisionError:
        print("Oops, you divided by zero")

a = 2
data = []
for b in range(-5,6):
    try:
        print(a/b)
        print(data[2])
    except ZeroDivisionError:
        print("Oops, you divided by zero")
    except IndexError:
        print("There was an index error")

# Warning: except without a type can lead to infinite loops that are impossible to end
while True:
    try:
        print("Hello")
    except KeyboardInterrupt:
        print("Goodbye")
        break
    except:
        pass