Hey guys, long story short im doing business at university and decided i wanted to do maths becauses its the best i was originally going to do maths anyways but thats not the point of this post xD
So i've been accepted onto a maths course and just worrying about what i should study to refresh my skills and not go rusty..
Basically, i got an A* in my a level maths and i kinda worked through some further pure 1, but i dropped it because it wanted to concentrate on other things. Anyways what books would help towards maths at university, i already ordered core 3, 4 and fp1 to catch up .. should i be doing more further maths like fp2 n 3.. and are there any useful books or websites so i can try and get a head start on my course .. any help is much appreciated guys so thanks in advance
What should i study for university maths after a year off
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Which university are you going to? If it's one of the top ones then one recommendation I've seen is to look at past step papers.

I'd follow the advice of the previous poster and maybe work through Further Maths as well. A person I met at Oxford took a year off and did FM during his gap year to keep his mind sharp.

(Original post by ttoby)
Which university are you going to? If it's one of the top ones then one recommendation I've seen is to look at past step papers. 
(Original post by Bluefox91)
Im going to nottingham trent university, so its not really one of the more presitgious universities
'Algebra' could refer to lots of things in maths. As well as the x+y=z stuff you're used to, it can also refer to vectors&matrices stuff (this is called linear algebra) and it can also be something entirely new which is where you generalise the whole concepts of addition/multiplication and consider what happens e.g. when there are only finitely many numbers out there instead of infinitely many.
In the first year, the algebra would most likely be about vectors and matrices. Since they don't require further maths then this would probably mean going over the FP1 stuff again.
'Computational and numerical methods' would most likely be about getting an approximation to an answer when you can't solve it directly. This would probably include e.g. NewtonRaphson whixh would require your differentiation skills to be good.
'Foundations and Investigations in Mathematics' sounds like the type of course that would introduce you to university maths, covering lots of little topics and getting you used to proving things. If you've done induction then there would be more of that sort of stuff where you have to be quite formal/precise in your explanations.
'Mathematical Methods One'  I'm not entirely sure what this would involve.
'Statistics One'  This would most likely be covering similar stuff to the alevel stats modules, but with a more rigorous approach. Since none of the stats modules are core then they can't expect people to already know this stuff. However, there would probably be some differentiation/integration involved here so make sure you're strong on those.
'Vector Algebra and Calculus' would probably follow on from Algebra One and would involve differentiation/integration but with vectors.
Oh and also complex numbers would probably come up in some of these modules.
So overall, the most important thing would be to make sure your differentiation/integration skills are good. C3/C4 would be helpful here. If you're able to sit a past paper in each of those and get a B then you'll know you're good enough for the course.
Looking at FP1 (particularly stuff on matrices, complex numbers and induction) would be helpful but not essential. If you have time then you could always look at S1 but this isn't really necessary.
With regards to the other FP modules, although some of their content would probably overlap with what you do at uni it is quite a bit beyond the maths alevel material so they can't really expect you to know it. 
take stand alone maths and further maths units.

(Original post by ttoby)
These are the modules studied in the first year: http://www.ntu.ac.uk/apps/pss/course...=M&sl=2#course
'Algebra' could refer to lots of things in maths. As well as the x+y=z stuff you're used to, it can also refer to vectors&matrices stuff (this is called linear algebra) and it can also be something entirely new which is where you generalise the whole concepts of addition/multiplication and consider what happens e.g. when there are only finitely many numbers out there instead of infinitely many.
In the first year, the algebra would most likely be about vectors and matrices. Since they don't require further maths then this would probably mean going over the FP1 stuff again.
'Computational and numerical methods' would most likely be about getting an approximation to an answer when you can't solve it directly. This would probably include e.g. NewtonRaphson whixh would require your differentiation skills to be good.
'Foundations and Investigations in Mathematics' sounds like the type of course that would introduce you to university maths, covering lots of little topics and getting you used to proving things. If you've done induction then there would be more of that sort of stuff where you have to be quite formal/precise in your explanations.
'Mathematical Methods One'  I'm not entirely sure what this would involve.
'Statistics One'  This would most likely be covering similar stuff to the alevel stats modules, but with a more rigorous approach. Since none of the stats modules are core then they can't expect people to already know this stuff. However, there would probably be some differentiation/integration involved here so make sure you're strong on those.
'Vector Algebra and Calculus' would probably follow on from Algebra One and would involve differentiation/integration but with vectors.
Oh and also complex numbers would probably come up in some of these modules.
So overall, the most important thing would be to make sure your differentiation/integration skills are good. C3/C4 would be helpful here. If you're able to sit a past paper in each of those and get a B then you'll know you're good enough for the course.
Looking at FP1 (particularly stuff on matrices, complex numbers and induction) would be helpful but not essential. If you have time then you could always look at S1 but this isn't really necessary.
With regards to the other FP modules, although some of their content would probably overlap with what you do at uni it is quite a bit beyond the maths alevel material so they can't really expect you to know it. 
(Original post by ttoby)
These are the modules studied in the first year: http://www.ntu.ac.uk/apps/pss/course...=M&sl=2#course
'Algebra' could refer to lots of things in maths. As well as the x+y=z stuff you're used to, it can also refer to vectors&matrices stuff (this is called linear algebra) and it can also be something entirely new which is where you generalise the whole concepts of addition/multiplication and consider what happens e.g. when there are only finitely many numbers out there instead of infinitely many.
Often in mathematics at uni your professors will talk about the "algebraic" point of view vs the "analytic" point of view, without necessarily explaining what they mean. This seems to abound throughout mathematics, although another professor of mine said you should always be mindful that "there is only one mathematics". One example would be the famous trigonometric function, sine. The analytic point of view (in real analysis setting) would simply regard "sin" as a function. The algebraic point of view doesn't consider a function without specifying the domain and codomain. From the algebraic point of view anything else wouldn't make sense.
So (in higher/uni maths) there is algebra as a noun, which includes abstract algebra and linear algebra, and there is algebra as an adjective, "algebraic" which is sometimes contrasted with the adjective "analytic" that relates to "analysis".
(Original post by ttoby)
Looking at FP1 (particularly stuff on matrices, complex numbers and induction) would be helpful but not essential. If you have time then you could always look at S1 but this isn't really necessary.
With regards to the other FP modules, although some of their content would probably overlap with what you do at uni it is quite a bit beyond the maths alevel material so they can't really expect you to know it.
What's most important for university I would say is complex numbers, matrices and induction, and familiarity with the basic properties of various number systems. Calculus is in my opinion not as important, the main thing being basic knowledge of the properties of the famous functions, exp, log, sin, cos, tan, and their hyperbolic versions. 
(Original post by Raiden10)
"Algebra" tends to mean either the study of algebraic structures, which is new at university style mathematics, or to the same thing it means at Alevel  manipulation of expressions and the LHS and RHS of an equation, surds etc. But you're right algebra could refer to lots of things in undergraduate mathematics.
Often in mathematics at uni your professors will talk about the "algebraic" point of view vs the "analytic" point of view, without necessarily explaining what they mean. This seems to abound throughout mathematics, although another professor of mine said you should always be mindful that "there is only one mathematics". One example would be the famous trigonometric function, sine. The analytic point of view (in real analysis setting) would simply regard "sin" as a function. The algebraic point of view doesn't consider a function without specifying the domain and codomain. From the algebraic point of view anything else wouldn't make sense.
So (in higher/uni maths) there is algebra as a noun, which includes abstract algebra and linear algebra, and there is algebra as an adjective, "algebraic" which is sometimes contrasted with the adjective "analytic" that relates to "analysis".
It depends on the exam board but generally FP1, (stuff on matrices, complex numbers and induction) has a bigger importance for the pure mathematics at university, whereas the C1C4 material is pretty much focused on calculus and what will at university be called "mathematical methods".
What's most important for university I would say is complex numbers, matrices and induction, and familiarity with the basic properties of various number systems. Calculus is in my opinion not as important, the main thing being basic knowledge of the properties of the famous functions, exp, log, sin, cos, tan, and their hyperbolic versions. 
(Original post by ttoby)
I've certainly noticed that algebra and analysis are one of a few very broad topic areas that modules come under, but in my experience I haven't often seen this kind of distinction referred to in lectures. Regardless of the type of module, whenever a new function is introduced its domain and codomain would nearly always be specified (possible exceptions are when a course is taught by another department). And similarly we would be expected to specify these details ourselves when answering questions.
(Original post by ttoby)
I agree FP1 is very relevent to university maths, but the course doesn't ask for further maths Alevel so they can only assume knowlege of C1C4 and hence it's important to know the material there. 
If I had my summer again to revise for starting at uni, I would above all else ensure my integration and differentiation was tip top. I spent/spend a stupid amount of time staring at really simple examples and it means it's harder to focus on the parts that are actually new/difficult.
So yeah revise all the rules of integration and differentiation, I wouldn't worry about much else. The course will be designed to take you from your A Level standard up to university standard. 
(Original post by Bluefox91)
Hey guys, long story short im doing business at university and decided i wanted to do maths becauses its the best i was originally going to do maths anyways but thats not the point of this post xD
So i've been accepted onto a maths course and just worrying about what i should study to refresh my skills and not go rusty..
Basically, i got an A* in my a level maths and i kinda worked through some further pure 1, but i dropped it because it wanted to concentrate on other things. Anyways what books would help towards maths at university, i already ordered core 3, 4 and fp1 to catch up .. should i be doing more further maths like fp2 n 3.. and are there any useful books or websites so i can try and get a head start on my course .. any help is much appreciated guys so thanks in advance
If I had an extra year to prepare before university, I would actually go through each topic of the first year curriculum one after the other. A level further maths is useful but it's mainly computation. Definitely go through your A level maths again and if you can, FP13 is also useful.
At university, there is a lot of emphasis on proving things formally so try to go through the different proofs, I would also go through set theory, logic and limits (try to get accustomed with new notations that were not emphasised in A level.
But above all, try to enjoy your gap year! Have fun! Read fun books about mathematical curiosities before you get bombarded with problem sheets at uni. 
(Original post by Bluefox91)
Hey guys, long story short im doing business at university and decided i wanted to do maths becauses its the best i was originally going to do maths anyways but thats not the point of this post xD
So i've been accepted onto a maths course and just worrying about what i should study to refresh my skills and not go rusty..
Basically, i got an A* in my a level maths and i kinda worked through some further pure 1, but i dropped it because it wanted to concentrate on other things. Anyways what books would help towards maths at university, i already ordered core 3, 4 and fp1 to catch up .. should i be doing more further maths like fp2 n 3.. and are there any useful books or websites so i can try and get a head start on my course .. any help is much appreciated guys so thanks in advance 
(Original post by ttoby)
I've certainly noticed that algebra and analysis are one of a few very broad topic areas that modules come under, but in my experience I haven't often seen this kind of distinction referred to in lectures. Regardless of the type of module, whenever a new function is introduced its domain and codomain would nearly always be specified (possible exceptions are when a course is taught by another department). And similarly we would be expected to specify these details ourselves when answering questions.
Of course in any context, algebraic or analytic or whatever one needs to specify the domain and codomain of a function.
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