Add some course notes and fix about page

_assessment/index.md

@@ -7,14 +7,14 @@ tag: assessment
 
 A series of 6 individual tests:
 
-- Test 1: [Algebra]({{ site.baseurl }}/topics/algebra.html) and [Calculus]({{ site.baseurl }}/topics/calculus.html)
-- Test 2: [Combinatorics]({{ site.baseurl }}/topics/combinatorics.html) and [Probability]({{ site.baseurl }}/topics/probability.html)
-- Test 3: [Matrices]({{ site.baseurl }}/topics/matrices.html) and [Sequences]({{ site.baseurl }}/topics/sequences.html)
-- Test 4: [Statistics]({{ site.baseurl }}/topics/statistics.html) and [Differential Equations]({{ site.baseurl }}/topics/differential-equations.html)
+- Test 1: [Algebra]({{ site.baseurl }}/topics/algebra.html) and [Calculus]({{ site.baseurl }}/topics/calculus.html) (released Week 3 of Autumn Semester)
+- Test 2: [Combinatorics]({{ site.baseurl }}/topics/combinatorics.html) and [Probability]({{ site.baseurl }}/topics/probability.html) (released Week 5 of Autumn Semester).
+- Test 3: [Matrices]({{ site.baseurl }}/topics/matrices.html) and [Sequences]({{ site.baseurl }}/topics/sequences.html) (released Week 7 of Autumn Semester).
+- Test 4: [Statistics]({{ site.baseurl }}/topics/statistics.html) and [Differential Equations]({{ site.baseurl }}/topics/differential-equations.html) (released Week 9 of Autumn Semester).
 - Test 5: [Variables, conditional statements and while loops]({{ site.baseurl }}/topics/variables-conditional-statements-and-while-loops.html) and [Functions and
-  data structures]({{ site.baseurl }}/topics/functions-and-data-structures.html)
+  data structures]({{ site.baseurl }}/topics/functions-and-data-structures.html) (released Week 2 of Spring Semester).
 - Test 6: [Object Oriented Programming]({{ site.baseurl }}/topics/object-oriented-programming.html) and [Using a terminal and an
-  editor]({{ site.baseurl }}/topics/using-a-terminal-and-an-editor.html).
+  editor]({{ site.baseurl }}/topics/using-a-terminal-and-an-editor.html) (released Week 4 of Spring Semester).
 
 You can complete each test when it is released. The deadline for completing all
 of them is at the end of the Spring Semester.

_class-notes/about-the-course.md

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+---
+layout: class-notes
+title: "About the course"
+tags: about
+---
+
+## First meeting
+
+After this meeting students should:
+
+- Know me a bit
+- Understand how and why programming can be used to study mathematics.
+- Know where all class resources are
+- Know what they need to do to prepare for their first class
+
+### Introduce myself
+
+- Pick 4 or 5 pictures of my family and I to introduce myself.
+- Mathematician (where/what I studied)
+- Trustee of the UK Python association https://uk.python.org
+- Conference and workshop organiser
+- Editor for JOSS
+- Fellow of the sustainable software institute
+- Maintainer of a number of open source scientific research packages
+
+There are slide for this [here]{{site.baseurl}}/assets/about/main.key).
+
+### Programming
+
+---
+
+1. Class exercise: get a class word cloud association for the word "programming". (Using mentimeter.com).
+2. Class exercises: get a class word cloud association "What are uses for programming
+   in Mathematics?"
+
+   - Proving theorems;
+   - Obtaining conjectures;
+   - Implementing tools.
+
+### Location of class resources
+
+- Show site: https://vknight.org/cfm/
+- Show recordings
+- Discuss discord
+
+### Office hours
+
+Discuss office hours with students
+
+Direct students at my teaching philosophy page: <https://vknight.org/tch-phi/>
+
+### Course materials
+
+Discuss the philosophy of the main text, specifically discussing this
+<https://vknight.org/pfm/overview/introduction/main.html#fig-knowledge-vs-technique>
+
+Discuss structure of the book.
+
+- Timetable:
+
+  - Discuss the actual timetable.
+
+  Discuss this diagram: :download:`Week structure </_static/week_structure/main.pdf>`
+
+  Discuss this diagram: :download:`Understanding </_static/understanding/main.pdf>`
+
+- Assessment.
+
+- For first lab session: work through chapter 1. Give a brief demo.
+
+## After class email
+
+Send the following email after class::
+
+    Hi all,
+
+    A recording of today's class is available at <>.
+
+    In this class we discussed multiple things about the class itself:
+
+    - Course documents available here: https://vknight.org/cfm/
+    - We agreed that office hours will be: <>
+    - Here is an invite to the discord if you have not already joined it:
+    - You can find my teaching philosophy here: https://vknight.org/tch-phi/
+
+    In preparation for your tutorial tomorrow please work through the first
+    chapter of the Python for mathematics book:
+    https://vknight.org/pfm/tools-for-mathematics/01-using-notebooks/introduction/main.html
+
+    Please get in touch if I can assist with anything,
+    Vince
+
+## Second meeting
+
+- Give brief review of the contents of the chapter. Do this by browsing
+  through: https://vknight.org/pfm/tools-for-mathematics/01-using-notebooks/how/main.html
+- Ask if anyone has any questions/comments/feedback.
+- Remind everyone about the resources available to them (videos both on youtube
+  and LC, chapters, plan, discord etc...).
+- Explain that the following things seemed to be the main ones to come up:
+  1. Finding files on computer.
+  2. Difference between markdown and code cell.
+  3. Using brackets when doing computations.
+
+For each of those do a small walk-through showing the concepts again.

_class-notes/algebra.md

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+---
+layout: class-notes
+title: "Algebra"
+tags: algebra
+---
+
+## First meeting
+
+After this meeting students should:
+
+- Understand how to use the Sympy library to carry out basic Algebraic
+  tasks.
+- Know what they need to do to prepare for their second tutorial.
+
+### Problem
+
+Explain to students that we will be solving the following problem:
+
+1.  Rationalise the following expression: $\frac{1}{\sqrt{3} + 1}$.
+
+2.  Consider the quadratic $f(x) = -x ^ 2 + 8 x - 18$.
+
+    > 1.  Calculate the discriminant of the quadratic equation $f(x)=0$.
+    >     What does this tell us about the graph of $f(x)$.
+    > 2.  By completing the square, confirm that $(4, -2)$ is the
+    >     maximum of point of $f(x)$.
+
+### 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).
+
+Clearly write down these steps:
+
+1.  For first question: multiply by $\sqrt{3} - 1$.
+2.  Calculate discriminant: compare to 0. If negative: no roots.
+3.  Complete the square to make $f(x) = a (x - b ) ^2 + c$. Do this by
+    expending that formula and comparing coefficients.
+
+Now show how to get code to do this:
+
+    >>> import sympy
+    >>> expression = 1 / (sympy.sqrt(3) + 1)
+    >>> expression
+    1/(1 + sqrt(3))
+    >>> sympy.simplify(expression)
+    -1/2 + sqrt(3)/2
+
+Discuss here how this differs if we used `math.sqrt`. Explain that
+`sympy.simplify` is essentially acting as a black box here.
+
+Now to carry out the rest of the problem:
+
+    >>> x = sympy.Symbol("x")
+    >>> expression = - x ** 2 + 8 * x - 18
+    >>> expression
+    -x**2 + 8*x - 18
+    >>> sympy.discriminant(expression)
+    -8
+
+Confirm results by hand.
+
+Discuss what this implies:
+
+- Quadratic equation has no real roots.
+- Graph does not intersect the $y=0$ line.
+- Concave parabola (sign of leading coefficient of quadratic).
+
+Confirm by solving the quadratic equation:
+
+    >>> equation = sympy.Eq(lhs=expression, rhs=0)
+    >>> equation
+    Eq(-x**2 + 8*x - 18, 0)
+
+    >>> sympy.solveset(expression, x)
+    {4 - sqrt(2)*I, 4 + sqrt(2)*I}
+
+Now to move on to next part of the problem: completing the square:
+
+    >>> a, b, c = sympy.Symbol("a"), sympy.Symbol("b"), sympy.Symbol("c")
+    >>> completed_square = a * (x - b) ** 2 + c
+    >>> completed_square
+    a*(-b + x)**2 + c
+
+Let us expand and compare the coefficients:
+
+    >>> sympy.expand(completed_square)
+    a*b**2 - 2*a*b*x + a*x**2 + c
+
+We see that $a$ is $-1$. Let us substitute this value in to the
+expression:
+
+    >>> completed_square.subs({a: -1})
+    c - (-b + x)**2
+
+We can in fact overwrite the expression:
+
+    >>> completed_square = completed_square.subs({a: -1})
+    >>> completed_square
+    c - (-b + x)**2
+
+If we now expand again and compare coefficients:
+
+    >>> sympy.expand(completed_square)
+    -b**2 + 2*b*x + c - x**2
+
+We see that $2b=8$. Despite the fact that this equation is relatively
+straightforward, let us solve it using `sympy`:
+
+    >>> equation = sympy.Eq(lhs=2 * b, rhs=8)
+    >>> sympy.solveset(equation, b)
+    {4}
+
+We will substitute this value for $b$ back in to the completed square,
+and expand again:
+
+    >>> completed_square = completed_square.subs({b: 4})
+    >>> completed_square
+    c - (x - 4)**2
+    >>> sympy.expand(completed_square)
+    c - x**2 + 8*x - 16
+
+We see that $c - 16=-18$. Let us again solve that equation using
+$sympy$:
+
+    >>> equation = sympy.Eq(lhs=c - 16, rhs= -18)
+    >>> sympy.solveset(equation, c)
+    {-2}
+
+We will substitute this value back in:
+
+    >>> completed_square = completed_square.subs({c: -2})
+    >>> completed_square
+    -(x - 4)**2 - 2
+    >>> sympy.expand(completed_square)
+    -x**2 + 8*x - 18
+
+Ask students to break out in to groups of 3 and do the following:
+
+1.  Confirm that this answers the question.
+2.  Explain to each other what we did using code.
+
+Come back: with time take any questions.
+
+Point at resources.
+
+## 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 a demonstration of using Python to solve an
+    algebraic problem. I did the following mathematical techniques:
+
+    - Simplifying an exact numerical expression.
+    - Calculating the discriminant of a quadratic.
+    - Solving a symbolic equation.
+    - Substitute values in to a symbolic expression.
+
+    In preparation for your tutorial tomorrow please work through the second
+    chapter of the Python for mathematics book:
+    https://vknight.org/pfm/tools-for-mathematics/02-algebra/introduction/main.html
+
+    Please get in touch if I can assist with anything,
+    Vince