Undergraduate problems
#1.
sum(1..2012)
2025078 2025078 |
#2.
def f(v):
del v[len(v)//2]
v=[1,2,8,15,'7']
f(v)
v
[1, 2, 15, '7'] [1, 2, 15, '7'] |
#3.
len(str(factorial(10^6)))
5565709 5565709 |
#4.
def f(v):
w = [type(x) for x in v]
return list(sorted([w.count(x) for x in set(w)]))
f([2, 1/3, 'hi', 3, 'abc', 'xyz'])
[1, 2, 3] [1, 2, 3] |
Graduate Problems
#1.
print sum(1..2012)
n=2012; print n*(n+1)/2
s=0
for n in (1..2012): s += n
print s
s=0;n=1
while n<=2012:
s += n
n += 1
print s
2025078 2025078 2025078 2025078 2025078 2025078 2025078 2025078 |
# 2.
def sieve(n):
v = [2] + [3, 5, .., n] # 2 and odd numbers up to n
i = 1
while v[i] <= math.sqrt(n):
v = v[:i+1] + [k for k in v[i+1:] if k%v[i]]
i += 1
return v
print sieve(11)
print sieve(100)
print len(sieve(1000))
[2, 3, 5, 7, 11] [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97] 168 [2, 3, 5, 7, 11] [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97] 168 |
# 3.
i = CC.0
re = plot(lambda t: real(zeta(1/2+i*t)), (1, 200), plot_points=200)
im = plot(lambda t: imag(zeta(1/2+i*t)), (1, 200), plot_points=200, color='red')
show(re + im, figsize=[9,1])
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complex_plot(zeta, (0, 2), (0, 15))
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