I already have this at least to gcse standard, though I do have to check formula as I am not memorising them at my age. I also a few years back tutored the child of an acquaintance to help her get her gcse maths.
Over the past couple of years I have realised that:-
Most problems have some sort of mathematics in them.
There is a big conflict in the maths community between conventional and baysian. Which I find amusing as while it is essentially guessing and modifying, that is what broke ww2 codes, and what makes your mobile work and enables self driving cars to drive.
There is immense beauty in the âharmonyâ of maths in life, most easily described I guess by mathematical patterns in nature.
Ultimately I am looking to gain better conceptual mathematical awareness (I will leave maths to mathematicians), as I am finding it quite exciting. But for the next year or two I think it necessary to get back to higher/a level standard.
I am no natural at maths, at School I did get a C at Higher (a level), but I remember the bit I enjoyed most was the proofs, those were âeasyâ marks.
I will say that the Leckie Scots student books are excellent.
Ah, apologies, I missed the bit about your experience.
Maths by iteration is quite complex and I donât think easy to get to grips with.
Likewise, turning natural phenomena into mathematical equations - once you get beyond the general ârule of sixâ for snowflakes for example, it gets very complex very quickly.
Personally, Iâm a very applied person, prefer to learn about stuff which might be useful and for which I have sufficient time; the above fits neither of those criteria
My Masters was called Modern Applications of Mathematics, and was basically industrial maths and mathematical biological modelling. Also included some parallel computer programming and more complex stats.
I did that after 4 years at PwC becoming a tax accountant! Getting back up to speed was a challenge, but as Cobbie says, it was a very personal approach that I just know fits with my own mind.
I definitely found the MSc more interesting, as it was giving some real world applications of maths. But it was also a lot harder. Undergrad was solving problems with clear solutions. The masters was half the time about figuring out if there even was a solution. I found that more challenging (I wasnât skilled enough to truly understand the fundamental underpinning of various tools weâd been provided with to understand how they might be potentially useful in different situations).
Likewise - i really enjoyed and was challenged by my BSc (Sport science), but the MSc was about application and practice (sport coaching) although my thesis were differentâŚ
Investigation into the benefits of a Natural Running Form training intervention in age group triathletes using high resolution MEMS accelerometers and video analysis technology to determine changes in running performance. - 82 %
DO AS I SAY, NOT AS I DO.
AN EXPLORATION OF THE TRAINING METHODS USED ON P COMPANY AND BY TRIATHLETES THROUGH THE LENS OF ATHLETE-CENTRED COACHING - 58%
Decades ago at school I loved the maths proofs as they were memorisable and easy marks. I now want to intuitively understand them.
Having come across my first easy proof re pythagorasâ theorem, using four triangles and squares, it is easy enough. However I am left a little dissatisfied, in that, while I know that the proof proves it, I am left with a feeling of âis that it/is that enoughâ.
Bear in mind that this is the first maths proof, from a N4 (first year gcse) book, I have looked at since school four decades ago.
I do have a book covering maths proofs in detail that I will be working through later this year once I have worked through the advanced higher/a level books. But donât want to get ahead of myself.
So mathematicians, do you have any tips on how to be âsatisfiedâ with proofs, so that I am set up correctly for moving forwards? Obviously working through them step by step. But having just done this for an easy visual proof, I am still left with âis that itâ.
Probably me being silly, but I sort of expected to feel more âyes thatâs it.â As opposed to âis that it.â
A proof is simply a method by which you can unequivocally show an equation or whatever holds in all cases, using base principles or axioms. Its also somewhat iterative in many cases, where proven knowledge of certain facts enables you to then determine additional concepts. There are a number of different methods by which proofs can be achieved, some elegant, some less so.
In the triangle case, youâre just using simple area equations for a triangle and a square and doing some algebra reorganisation. I donât actually think Iâve ever seen that proof before, likely because itâs so basic. Which is probably why youâre seeming unsatisfied.
I always liked proof by induction as a concept. It only works for the natural numbers, but there was something elegant about proving a statement held to infinity simply by demonstrating instance n+1 had to hold based on a supposition that instance n holds. That was lecture one, module one, of first year undergrad, so itâs not hugely complicated. I think some people had already done it in further maths A Level too
SS maybe proofs involving algebra will feel most satisfying?
Mentioned earlier my son is doing A level maths, as it happens one of his questions yesterday was âprove that difference between the squares of any two consecutive even numbers, is always divisible by 4â.
The way he answered it was to recognise that you can express âany 2 consecutive even numbersâ as:
2n
and
2n + 2
The squares of these numbers are:
4n^2
and
4n^2 + 8n + 4
The difference between these two squares is:
8n + 4
which can be written as:
4(2n+1)
And clearly 4 is a factor of this expression, which is the same as saying it is divisible by 4, so thatâs the proof.
I donât know how an actual mathematician would set that out, but he found it pretty satisfying to show that these logical steps proved the thing.
I did a pure maths A level in 1990 (applied maths and physics were boring me at the time) and I think I will dig out my old textbook later. Wouldnât mind doing those 2 A levels now, maybe I will give them a go at some point.
Yes to get there without simply guessing (my first guess was foolish btw, it really shouldâve been one guess) is a good demonstration of how to think!
Player A rolls one die. Player B rolls two dice. If A rolls a number greater or equal to the largest number rolled by B, then A wins, otherwise B wins. What is the probability that B wins?
