Physics and Maths, Studied this Week.

Okay, another week done and I still can't shake this virus / cold!

Anyway, I have concentrated, this week, on doing a lot of practice questions to consolidate some basic maths skills.  I often find, that by keeping the basic tools sharpened, such as algebraic manipulation, factorisation, handling logs, exponentials, roots, complex numbers and even practising my times tables; it takes a lot of strain out of dealing with complex pencil and paper exercises, that require lots of small mathematical steps, to achieve an answer.

An example of this, is the Open University TMA 1 part 2 questions for course MST121, Using Mathematics.  I have been writing my draft presentation of this marked piece of coursework.  The questions are based on defining a circle, with reference to 3 fixed points and also some manipulation of quadratics in working out where a circle and line meet.  There are lots of little steps (about 10), that must be done in order to solve the equations and I find that none of the steps, if practiced, are very difficult.  The skill actually comes, in working out what the question is asking you to do.

I do find this with maths questions, that they seem to sometimes throw at you, an equation that requires some moving about and re-arranging, before you can identify what  it is e.g. quadratic / equation of a circle / inverse function etc.  When you get one of these odd looking equations, the ability to quickly 'play around' with the expression, using pre-calculus skills, is extremely important.

I actually think that most people perhaps struggle with the basics and this leads them to think that they can't cope with higher maths courses.  Learning your times tables (up to 20 times table), allows you to glance at an expression and instantly recognise perfect squares, factors etc.  Learning how to manipulate fractions, allows you to instantly re-arrange numerical equations, to make them easier to work with.  There are many ways to make things easier for yourself, and I suspect, that practising the basics, is the key!

This weeks study:

Open University MST121


Functions!
Manipulation of functions
8hrs of self-made practice worksheets - Complex number manipulation / fractions / quadratics / factorisation / roots and exponentials / times tables.
Draft completion of question 1, TMA1 Part 2.

The Teaching Company Lectures, Calculus


Implicit differentiation and related rates


The Teaching Company Lectures, Cosmology


Cosmic acceleration

Audio book


The Modern Scholar: Astronomy I (Unabridged) (I'll post about this awesome series, later)

Entanglement: Amir D. Acze (quantum physics)

Total study time this week = 17hrs

I forgot to put on the total time for last week, which was 13hrs.

I am discovering more free study material, all the time, so I'll cover some of it, later.  I also have a theory about successful study, using different sources, which I'll expand on in another post.