A group-work week. The single hour is not a lecture: students work through this topic on their own, and the session is there for you to answer questions and signpost. Nothing below is material to deliver.
Open by asking what people got stuck on. If the room is silent, the minutes are the way in: ask a group what went into their questions arising box this week. That is what the box is for, and it makes the point that the minutes are useful to them rather than only to the mark.
Each member reports on it at the group meeting, which is the first standing item on every agenda.
"When should something be a function?" When it has a name worth giving it. For the project the practical answer is firmer: anything the tests need to call separately has to be a function.
"List, tuple, set or dictionary?" Push back to the mathematics. Is order meaningful? Are duplicates meaningful? Is it a lookup from one thing to another? The answer usually falls out of those three.
"Can a function return more than one thing?" Yes, and it returns a tuple when it does. Worth showing, since several projects want it.
The material below is not delivered in class. It is kept here as a worked treatment of the topic to draw on when answering questions.
After this meeting students should:
Explain to students that we will be solving the following problem:
Verify the following identity for all integer values of $0 \leq a \leq
100$, $0 \leq b \leq 100$ and $1 \leq n \leq 10$:
$$(a + b) ^ n = \sum_{i=0}^n\binom{n}{i} a ^ i b ^ {n - i}$$
Now show::
>>> def get_lhs(a, b, n):
... """
... Compute (a + b) ^ n directly
... """
... return (a + b) ** n
>>> get_lhs(a=5, b=10, n=5)
759375
>>> import scipy.special
>>> def get_rhs(a, b, n):
... """
... Compute the right hand side of the identity which aims to calculate
... a summation of powers a^ib^(n - i) with a binomial coefficient.
... """
... return sum(scipy.special.binom(n, i) * a ** i * b ** (n - i) for i in range(n + 1))
>>> get_rhs(a=5, b=10, n=5)
np.float64(759375.0)
Ask if this confirms the identity?
Now create the following function to check the identify::
>>> def check_identity(a, b, n):
... """
... Check the relationship
... """
... return get_lhs(a=a, b=b, n=n) == get_rhs(a=a, b=b, n=n)
Now create all checks::
>>> checks = [
... check_identity(a=a_val, b=b_val, n=n_val)
... for a_val in range(101) for b_val in range(101) for n_val in range(1, 11)
... ]
Note that we can check all of them::
>>> all(checks)
False
Ask why this is the case. Have a discussion leading to the fix::
>>> def get_rhs(a, b, n):
... """
... Compute the right hand side of the identity which aims to calculate
... a summation of powers a^ib^(n - i) with a binomial coefficient.
... """
... return sum(int(scipy.special.binom(n, i)) * a ** i * b ** (n - i) for i in range(n + 1))
Re define check_identity:
>>> def check_identity(a, b, n):
... """
... Check the relationship
... """
... return get_lhs(a=a, b=b, n=n) == get_rhs(a=a, b=b, n=n)
Now create all checks::
>>> checks = [
... check_identity(a=a_val, b=b_val, n=n_val)
... for a_val in range(101) for b_val in range(101) for n_val in range(1, 11)
... ]
Note that we can check all of them::
>>> all(checks)
True
Come back: with time take any questions.
Point at resources.
Send the following email after class::
Hi all,
A recording of today's class is available at <>.
In this class I we used functions and list comprehensions. The chapter we
are covering this week also includes sections on dictionaries and sets.
In preparation for your tutorial please work through the following chapter:
https://vknight.org/pfm/building-tools/02-functions-and-data-structures/introduction/main.html
Please get in touch if I can assist with anything,
Vince