Rory P ~ Maths on a Chalk Plain (@chalkplainmaths.co.uk) Bsky

SoME — Create and discover new math content The Summer of Math Exposition is an annual competition to foster the creation of excellent math content online.

Hello #ALevelMaths teachers. The Summer of Math Exposition some.3b1b.co competition has just entered judging and they are specifically looking for teachers' input this year! If anyone has the time, I'm sure your opinions would be much appreciated.

7 months ago 2 1 0 0

Quick note: This is a short and hopefully fun text written by, and aimed at high school calculus student(s), with a focus on intuition. It covers two topics in a way that I've endeavoured to make engaging. All JS graphics are by me. Please enjoy!

I had a lot of fun writing my submission for #SoME4 ! chalkplainmaths.co.uk/some4 . My submission is an article about Definite Integration and Euler's Constant (with a bit of a twist). All feedback is appreciated. Thanks to ‪@fred-crozatier.dev‬ and 3blue1brown for organising!

7 months ago 0 0 0 0

Welcome to my blog. I am an A Level (High School) student studying Maths, Further Maths, Chemistry and Physics in the UK. On this site, I hope to share my love for maths and its sister disciplines through a range of different articles. I recommend that you read my introductory post at some point. Otherwise, I hope you enjoy my work! Comments, queries, corrections and complaints are always welcome to rory@chalkplainmaths.co.uk.

Hello! It may be the weekend, but if you still fancy some #MathsToday, I've put the penultimate chapter from my series on partial fractions up at chalkplainmaths.co.uk/part_frac/4. This goes through the last section of my proof, slotting together the two previous sub-proofs.
Thanks!
#ALevelMaths

1 year ago 1 0 0 0

Previous to this, we made the first of the two puzzle pieces that we will soon slot together to form our proof. Prior to unification, however, we must create the second. Once again, we are dealing with two variables, however, rather than being the powers of the numerator and denominator, this time, they are both in the denominator, for we are going after the proof of our statement where there are two distinct factors beneath the fraction. Expressed in symbols, our aim is to prove that constant \(A,B\)s exist where \[ \frac{1}{(x+a)^n(x+b)^m}\equiv\sum_{r=1}^n\frac{A_r}{(x+a)^r}+\sum_{r=1}^m\frac{B_r}{(x+b)^r} \] \[ \textrm{where} \quad n,m\in\mathbb{N} \quad \textrm{and} \quad a\neq b \textrm{.} \] The \(\sum\) symbol means to sum together the expression inside for all values between those given on the top and bottom (inclusive). Note also that as \(n\) and \(m\) are natural numbers, they are nonzero, so both factors are to a power of at least one. Additionally, since \(a\neq b\) we know the factors are definitely different. This means we don't have to worry about edge cases where the form looks different to what is above.

For my #MathsToday, I've posted a new chapter on partial fractions: Fight of the factors! chalkplainmaths.co.uk/part_frac/3. This follows directly on from the preceding post and continues with our proof. Thanks!
#ALevelMaths

1 year ago 1 0 0 0

You’ve left the younger ones among us in suspense! What is it?

1 year ago 0 0 3 0

Thanks for having a look! Definitely a good idea to use binomial as then choose function would let you get a general formula for the constants. :)

1 year ago 1 0 0 0

In this chapter, we are going to tackle the first section of our proof, using a method known as 'Proof by Induction'. It allows us to induce the truth of a statement over all terms in a sequence having only proved that it holds for the first term, and that if it's true for any random term, it also holds for the next. Imagine a line of pillars out at sea, evenly spaced apart and stretching into the horizon. If I place you on the first pillar, and build you a portable bridge that spans the gap between one pillar and the next, it follows that you will be able to reach any pillar, even if the line is infinitely long!

Hello #ALevelMaths teachers, I ended up using induction pretty extensively in my proof of partial fractions. I’d love to hear your opinions on my explanation of it at chalkplainmaths.co.uk/part_frac/2/
#MathsToday

1 year ago 1 0 1 0

Hi, I'm Rory, an A Level Maths student.
I really like the subject and spend a fair bit of time playing around with it.
I am now writing up my findings into a blog.
I'd really appreciate anyone taking the time to read it.
Thanks!
chalkplainmaths.co.uk
#MathsToday #ALevelMaths

1 year ago 11 0 1 0

Posts by Rory P ~ Maths on a Chalk Plain