Variables, conditionals and loops
=================================

Pre class email
---------------

Send the following email before class::

    Hi all,

    I hope you are all well.

    This is a brief email to make you aware of a few things:

    - The class timetable and weekly schedule for this Semester is available
      here: https://vknight.org/cfm/
    - This week we have class at 1600 (via Zoom) and we
      will be covering this chapter
      https://vknight.org/pfm/building-tools/01-variables-conditionals-loops/introduction/main.html.
    - This Semester your assessment is a group exercise. I am letting you self
      select groups (groups of 4) but will assist anyone unable to find a group.
      We will discuss this more today in class.

    I am about to send you your draft individual coursework feedback.
    **Important** This will come from `vincent.knight@gmail.com` and the subject
    will be `DO NOTE REPLY - Coursework mark and feedback`. Note that I consider
    this first feedback I send you to be a *draft*. As it is automatically marked
    it is not unlikely that a mistake has crept in. Feel free to get in touch
    with me if anything is unclear in the feedback.

    Please get in touch if I can assist with anything,
    Vince

First meeting
-------------

After this meeting students should:

- Understand the coursework exercise and the group aspect
- Understand the how to use a for loop and a while loop
- Know what they need to do to prepare for their seventh tutorial and how to
  make groups.

Coursework
**********

Explain goal of coursework:

> To build and present a Python library to solve a mathematical problem of your
  choice.

How it will be assessed (15 minute presentation and 2 page (max) paper).

Groups of 4. Self select and see instructions in email.

Agree on deadline for formation of group.

I recommend you meet regularly.

Have an agenda for every meeting.

Single point of contact.

Problem
*******

Explain to students that we will be solving the following problem:

A perfect number is a positive integer whose divisors (excluding itself) sum to
itself.  For example, :math:`6` is a perfect number because :math:`6 = 1 + 2 +
3`.

1. How many perfect numbers are there less than 20?
2. What is the next perfect number?

Solution
********

Group exercise (breakout rooms of 3): ask students to spend 5 minutes writing a
plan to tackle that problem (not necessarily carrying out each step).

We start by writing a function that checks if a number is perfect::

    >>> def is_perfect(n):
    ...     """
    ...     Checks if a number n is perfect.
    ...     """
    ...     return sum(i for i in range(1, n) if (n % i == 0)) == n
    >>> is_perfect(5)
    False
    >>> is_perfect(6)
    True

Now we can check all numbers up until 20::

    >>> checks = [is_perfect(n) for n in range(1, 21)]

Note that we can combine all booleans using :code:`all`::

    >>> all(checks)
    False

Or :code:`any`::

    >>> any(checks)
    True

We cam also count them (as before) using :code:`sum`::

    >>> sum(checks)
    1

We are there using a list comprehension (as before) **but** we can also use a
`for` loop::

    >>> count = 0
    >>> for n in range(1, 21):
    ...     if is_perfect(n):
    ...         count += 1
    >>> count
    1

Discuss how the `for` loop works.


Now to answer the other question, **we do not know** how many times we need to
iterate the code so we use a `while` loop::

    >>> n = 7
    >>> while not is_perfect(n):
    ...     n += 1
    >>> n
    28

Indeed the prime divisors of 28 are::

    >>> import sympy as sym
    >>> sym.primefactors(28)
    [2, 7]

And::

    >>> 1 + 2 + 4 + 7 + 14
    28


We can repeat the above to find the 3rd perfect number::

    >>> n = 29
    >>> while not is_perfect(n):
    ...     n += 1
    >>> n
    496

Indeed the divisors of 496 are::

    >>> import sympy as sym
    >>> sym.primefactors(496)
    [2, 31]

And::

    >>> 1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248
    496


After class email
-----------------

Send the following email after class::

    Hi all,

    A recording of today's class is available at <>.

    In this class I went over 2 separate things:

    1. The group coursework (please read the end of this email where action is
       required).
    2. Variables, loops and conditionals.

    I recommend working through the following chapter of the class text:
    https://vknight.org/pfm/building-tools/01-variables-conditionals-loops/introduction/main.html

    If you have any questions I will be in 2.35 on Wednesday from 1000 until
    1200 for the first 4 weeks of the course.

    IMPORTANT ACTION REQUIRED

    For your group coursework you have until <DEADLINE> to form groups with 4
    people. I am letting you self select groups. If you do not have a group by
    <DEADLINE> I will create a group for you.

    Once you have created a group, 1 member of your group must email me (CC'ing
    in all other members) with subject: "Group formed"

    In the email please tell me the name of your group (you can be imaginative)
    and also which member of your group is the point of contact.

    Once you have created a group and started working, please use https://forms.office.com/e/qnVdB1KUG7
    to record weekly progress.

    ---

    Please get in touch if I can assist with anything,
    Vince

Post meeting
------------

The main difficulties raised were:

- Sets
- Modulo
- Doing more involved problems

Sets
++++

Create a set::

    >>> set_1 = set((-1, 1, 1, 2, 3, 5))
    >>> set_1
    {1, 2, 3, 5, -1}
    >>> set_2 = set(range(10))
    >>> set_2
    {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

Union::

    >>> set_1 | set_2
    {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, -1}

Intersection::

    >>> set_1 & set_2
    {1, 2, 3, 5}

Set subtraction::

    >>> set_1 - set_2
    {-1}

Set inclusion::

    >>> set_1 <= set_2
    False

Reasons for using sets:

- The ability to to the above operations.
- Immediate removal of duplicates.
- Checking inclusion.


Run the following timing examples::

    N = 10 ** 4
    numbers_as_range = range(N)
    numbers_as_list = list(numbers_as_range)
    numbers_as_tuple = tuple(numbers_as_range)
    numbers_as_set = set(numbers_as_range)

Testing the list::

    %%timeit
    5000 in numbers_as_list

Testing the tuple::

    %%timeit
    5000 in numbers_as_tuple

Testing the set::

    %%timeit
    5000 in numbers_as_set

Testing the range itself::

    %%timeit
    5000 in numbers_as_range

Modulo
++++++

Give some examples of modula arithmetic::

    >>> 5 % 2
    1
    >>> 17 % 9
    8
    >>> for i in range(24 * 5):
    ...     print(i % 24)
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Doing more involved problems
++++++++++++++++++++++++++++

Discuss how important it is, when building tools to spend time away from the
computer. Make the analogy of writing down a recipe before starting to cook.