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Introduction to A-Level Mathematics

nick198929

Fellow Mathematicians :smile:

I've recently finished off Algebra and wish to teach myself Advanced Mathematics. I have a relatively old book, and one of the first things is differential equations.

I was wonder can anyone please tell me which topics I should learn in a specific order?

All comments are very much appreciated. Many thanks :smile:

Reply 1

Simplicity

17

If your applying A level material.

C1, C2 then FP1.

If your applying more then A level material.

Naive set theory, set theory then analysis.

Reply 2

kironkabir

12

Hey.

With A-level maths, it is all about practice, and learning how to use formulae.

Try these sites.
They offer revision/tutorials on all the major topics that need to be covered in Year 12 ( C1,C2,S1 and M1)

http://www.s-cool.co.uk/alevel/maths.html
http://www.mathsrevision.net/alevel/http://www.mathsrevision.net/alevel/

Reply 3

callum Honisett

13

If you haven't done any A-level Maths I'd advise you not to start with differential equations!

Reply 4

hamzab

12

I'm also starting AS, Im going Into A2 but didn't take Maths AS, I haven't done maths since GCSe at which I attained an A so just over a year ago... What's the best way I start? Look at my old GCSE text book A grade questions and then move onto The A level text book, Ive got it early so I can start over the Summer

Reply 5

jayshah31

14

callum Honisett

If you haven't done any A-level Maths I'd advise you not to start with differential equations!

Precisely.

I mean, if you can attack DE's already whoa that's great, but not likely to be honest. Learn basic integration, differentiation and where they come from.

Reply 6

impervious

15

All the trig stuff, cosec, cot, sec compound angle formula and harmonic functions should make a tidy start.

Reply 7

callum Honisett

13

jayshah31

Precisely.

I mean, if you can attack DE's already whoa that's great, but not likely to be honest. Learn basic integration, differentiation and where they come from.

Yeah, most definitely. DE's are probably the most advanced A2 topic along with vectors.

EDIT: Agreed that would be something special if you could do them already!

Reply 8

qgujxj39

17

This is Edexcel's specification: http://www.edexcel.com/migrationdocuments/GCE%20New%20GCE/spec-gce-mathematics.pdf

The core stuff starts on page 19, look under the stuff for C1. In particular, I'd advise learning how to perform simple differentiation and integration as a good introduction to AS maths. If you have an introductory book to differential equations, it should have that in; if it doesn't, it's probably much too advanced for you.

Reply 9

jayshah31

14

callum Honisett

Yeah, most definitely. DE's are probably the most advanced A2 topic along with vectors.

Vectors

DEs

They are just so unbelievably awesome.

Anyway, back to the topic in hand.

Go through a specification of an exam board if you want a gist of what you need to know. Look up "Pure 1", "Core 1" but don't mistake it for "Further Pure 1", that's Further Maths and you'll need to know the normal Pure's to take them on.

Edit: Looks like tommm beat me to it :sad:

Reply 10

callum Honisett

13

jayshah31

Vectors

DEs

They are just so unbelievably awesome.

Anyway, back to the topic in hand.

Go through a specification of an exam board if you want a gist of what you need to know. Look up "Pure 1", "Core 1" but don't mistake it for "Further Pure 1", that's Further Maths and you'll need to know the normal Pure's to take them on.

Edit: Looks like tommm beat me to it :sad:

I like vectors, but I have done M1 and M2 so that helps :biggrin:

But I like DE's much more. I'm currently looking at youtube stuff by 'patrickJMT' for solving second order DE's as I didn't do further Maths. Really wish I had, I'm currently looking at matrices and cross product etc. -also. Should be useful for uni'.

Reply 11

AnonyMatt

15

callum Honisett

I like vectors, but I have done M1 and M2 so that helps :biggrin:

But I like DE's much more. I'm currently looking at youtube stuff by 'patrickJMT' for solving second order DE's as I didn't do further Maths. Really wish I had, I'm currently looking at matrices and cross product etc. -also. Should be useful for uni'.

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Reply 12

callum Honisett

13

AnonyMatt

<33333333333333333333333333333333333333

He's absolutely amazing isn't he, explains things so clearly.

Reply 13

nick198929

OP

1

The first topic of the book in which I have been learning was on logical symbols and implications. Is learning this important?

Reply 14

stevencarrwork

What sort of symbols? Less than, More than?

Or things like 'iff' (if and only if), 'wlog' , 'without loss of generality'?

Or A|B (A given B)?

Does the rest of the book depend upon the symbols in the start? In which case they will be important if you are learning from that book.

Reply 15

Hedgeman49

17

nick198929

The first topic of the book in which I have been learning was on logical symbols and implications. Is learning this important?

No, not for a long time yet. If you learn the basic mathematical notation (x is a member of the reals, that kind of thing) then that will suffice. You won't need to know any of the advanced logical notation.

Reply 16

marshey

13

Just play around with fractals with pretty colours.

Reply 17

nick198929

OP

1

Hey

In regard to logical symbols, it gives an introduction to the various arrows and the terms 'imply' or 'implied'. The terms deduction and implication come to play.

Then there are several examples, then it leads to Sets and Boolean Algebra.

Reply 18

nick198929

OP

1

Could anyone please respond to my last post, above from this please.

Reply 19

majikthise

It's incredibly important in that it's implicitly used for pretty much everything, so you may as well learn it now even though you'd probably pick it up anyway. Don't be daunted though, it's not particularly difficult.

Introduction to A-Level Mathematics

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