A-Level Further Maths: A1-01 Proof by Induction: An Introduction
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- čas přidán 28. 08. 2024
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As someone now in their 40s I recently had to re-learn some maths for my job - back in the day I regretfully dropped out of my maths A-level because I fell behind and could never catch up but watching these videos has really inspired me to pick up my old interest in this great subject again - thank you sir you are a legend
Really glad I could help!
Hi Jack, just wanna say thank you sooo much for your videos - i've just started y12 and had tests on core pure 1 (self learnt during holiday with your videos) and got A*. You're channel is honestly amazing
came back from a levels to do this in uni, thanks so much 🙏🏻
Hello. Something you said once has been playing on my mind...
You said once that you felt that proof by induction 'crept along' to the next number but I have always seen it as opposite - in that when I get to the point in the proof where K+1 behaves the same as K then I immediately imagine a super quick domino effect going off rapidly to infinity - knocking down all subsequent integers. Like going 'Brrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr..... See what I mean?
Wow, 649 videos! That's quite a lot but I will chunk it up and view all.
Just found out i wont be able to do further maths at college next year, tragic but i still want to try and learn it online, should i watch this along with the A level maths playlist? or does this contain everything i need for further maths
Hello sir! Do you perhaps have any paid/or free courses specially designed for caie a level further maths? This further maths series helped me out a lot as the syllabus is almost the same, but might there be any courses, like the curves one you created on udemy, specially targeted at cambridge students? Thank you! :)
So here is my usual conclusion so would this be correct to use?
As the statement is true for n=1, we can assume this is true for n=k. The statement is also true for n=k+1, so by induction, we can conclude that the statement must be true for all positive integers of n.
No because your first sentence says that you can assume it is true for n=k BECAUSE it is true for n=1. This isn't quite right. As it is true for n=1, and IF it is true for n=k it can be shown it is true for n=k+1, therefore it must be true for all n>=1 by induction.
Currently doing A Level Maths and Furthur Maths. Should I watch both of your playlists (A Level Maths and A Level Furthur Maths)? Or just this one?
Cheers laddie trying to help the girlfriend out with her further maths do not understand a word but it seems to be helping
can you pls start uploading further maths vectors videos , it will be a great help
That's section F and I'll be finishing section D soon. I've got no ETA on vectors I'm afraid.
Hi Jack, I had a little question here. Do you think it is mathematically sound/professional to, in the inductive step, to basically also manipulate the original statement with n = k+1 (the one we are trying to reach in the inductive step to show equivalency) in order to reach a point where both equations are same? It proves our point but I don't see it done anywhere. I see it to sometimes be a lot easier to meet half way then trying to reach the basis form with n=k+1.
Your judgement is appreciated.
It would be similar to proving a trig identity by working on both sides independently and getting the LHS = RHS. I would probably get as far as I could, then use the "target" to work backwards
@@TLMaths ok cool, yeh exactly like trig identity proving. Thanks for ur input.
hello sir, could you please do roots of polynomials for further MEI Pure?
I don't know if these would help: sites.google.com/site/tlmaths314/home/legacy-a-level-further-maths-2004/aqa/further-pure-1-fp1/01-roots-of-quadratics ?
Hello sir! it seems on your website there's the topics: proof, complex numbers and matrices. Are there supposed to be other topics like further calculus sir
You mean here? sites.google.com/view/tlmaths/home/a-level-further-maths/pure?authuser=0
I am a bit confused on where to begin learning as a a level further maths. According to TLMaths and as a level edexcel spec, it starts with Proof. But as I am going through proof, matrices and sum of series are coming up. Is there a certain order to begin learning as ?
I made the videos in specification order to make sure I covered all of the material. Unfortunately that's not really the best way to learn it, as you are discovering. You will find Teaching Order Year 1 and 2 on my website, but that is designed for my students who are studying OCR MEI and the options we cover. If you're not doing OCR MEI, then it won't be perfect, but may help.
www.tlmaths.com/home/a-level-further-maths
@@TLMaths Would it be okay to just go one by one using the edexcel spec and to skip proof and begin by learning complex numbers then matrices so on and so on... ?
Hi Jack, I’m currently teaching myself further maths, can you clarify that you go through all the content required for further maths for OCR MEI (B) I’m a little confused in what I will have to major and minor in based off of your website, is it okay if you let me know which topics I will select to major or minor in for my exams this year (12) and also next year would be helpful, thank you.
This is similar to「mathematical induction」in math B.
Do this cover「recurrence relation」too?
I'm thinking to do A Level Further Maths Edexcel on my own. Do you think that I can self teach it myself or not? Can I use your videos to do that?
You could but it would be challenging. My videos cover all the pure content in Edexcel Further Maths, but the applications will have differences as I teach OCR MEI
great video. love it
Hi Sir,
I'm currently studying the Pearson AS Further Maths with Descision 1 and Mechanics 1. I wanted to ask what videos should and shouldn't I watch just to be sure I don't learn any year 2 content by accident
You'll have to check with your specification document and/or your teacher
Did you cover Statistics, Mechanics and Decision in Further Maths video as well?
Yes - you can navigate everything from my website www.tlmaths.com/home/a-level-further-maths
Does your videos comply with Further Maths Syllabus?
That's what they're designed for
Which textbooks would you recommend for Edexcel Further Maths?
I've found these textbooks quite accessible: www.amazon.co.uk/Edexcel-level-Further-Mathematics-Textbook/dp/1292183330/ref=pd_bxgy_2/258-2646672-3883465?_encoding=UTF8&pd_rd_i=1292183330&pd_rd_r=f41a097a-29bf-4840-9954-01cb4b941787&pd_rd_w=mk6QL&pd_rd_wg=41gYv&pf_rd_p=dcf35746-0212-418b-a148-30395d107b2d&pf_rd_r=EH195F3DGM2W5VHXDJHW&psc=1&refRID=EH195F3DGM2W5VHXDJHW
Hello Good Sir ,
Does this whole ( A level Further Maths) playlist cover the further maths syllabus ?
with practice related to videos, would it be kind of same as doing further maths in class ? ( obviously there will be a lot of difference but if i can reach to some of that level)
Thank you ^
Could you recommend me a book to go with these videos so I can do further practice on them ? really thanks a lot.
Have you looked into your exam board's textbooks?
It will go through the whole compulsory Pure content (not applied). I haven't quite finished it, but it's almost there.
@@TLMaths Thank you Sir. I want to do this personally ( no exams just knowledge) , but i ll look into the exam boards textbook :)
Have you made any stats or mechanics vids? If not, are you planning on making any?
I want to make OCR MEI Statistics Minor videos, and then Mechanics Minor videos (that one's probably a little way off though)
@@TLMaths ok thank you
Have you done any videos on group theory?
Unfortunately not.
I utterly hate this, so I'm doing it once and for all
This looks easy but I still don't understand the maths behind it.
I'm doing city and guilds level 1 qualification and I somehow managed to book an A level maths and further maths private candidate exam because it seems easier than function skills because the lessons look easy based on the videos.
What's the jump between city and guilds functional skills maths and A level further maths like?
I got a 1 in my GCSE maths exam, then I decided to do functional skills maths, still can't pass it.
Is it possible for me to magically get A*A* in both A level maths and further maths after getting a 1 in GCSE maths and can't pass functional skills? I feel like I am committed to it.
I just want to be pass English and maths and pursue my career.
A 1 in GCSE Maths to an A* in A-Level Further Maths are many years apart. The City and Guilds qualification is level 1, GCSE is level 2, and A-Level is level 3. The entry requirement for A-Level Further Maths is generally a 7 or an 8 for GCSE Maths, and it's a two-year qualification in itself.
@@TLMaths A-Level Further Maths requires a 7 or an 8 in GCSE Maths?
I thought you needed a 9 in GCSE Maths to do A-Level Further Maths, and an 8 in GCSE Maths to do A-Level Maths.
Well at least in Harrow School and London Academy of Excellence (I've once considered both of them).
Do you need a grade 9 in GCSE Maths to do A Level Further Maths at your school?
@@evelynharris8666 Depends on the school or college as to what GCSE grade they want you to have. At the college I work at, you need at least a 7, but prefer an 8.