Calling all University Mathematicians!

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Hermione18
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#1
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#1
Hiya

I'm a maths offer holder with a firm and insurance choice of two prestigious russel group univesities.

I need advice on how to prepare for the degree during the summer - what things did you do that eased the transition/what do you wish you had done?

I'm looking to get a first in my first year.

Many thanks
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TheIrrational
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#2
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#2
Personally I did nothing over the summer between A levels and degree.

Analysis is the topic most people struggle with in first year, so I would highly recommend looking at some basic real analysis (sequence, series, differentiability etc). Failing that, some basic group theory or linear algebra.
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bijesh12
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#3
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#3
(Original post by TheIrrational)
Personally I did nothing over the summer between A levels and degree.

Analysis is the topic most people struggle with in first year, so I would highly recommend looking at some basic real analysis (sequence, series, differentiability etc). Failing that, some basic group theory or linear algebra.
I would agree... Analysis is a *****. But I would enjoy the summer.
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Maths degree
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#4
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#4
[QUOTE=TheIrrational;57855891]Personally I did nothing over the summer between A levels and degree.

Analysis is the topic most people struggle with in first year, so I would highly recommend looking at some basic real analysis (sequence, series, differentiability etc). Failing that, some basic group theory or linear algebra.[/QUOTE

Do you know where i can find like examples or practice questions on these ?
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Maths degree
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#5
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(Original post by TheIrrational)
Personally I did nothing over the summer between A levels and degree.

Analysis is the topic most people struggle with in first year, so I would highly recommend looking at some basic real analysis (sequence, series, differentiability etc). Failing that, some basic group theory or linear algebra.
Do you know where i can find like examples or practice questions on these ?
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qno2
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#6
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#6
Real Analysis is probably the most challenging topic you will encounter in your first year. Some people just get it while others (like me) still can't do it properly (I can still remember the Bolzano-Weierstrass word for word for some reason). You would be better off trying to learn and understand the basic definitions than trying questions like I'm guessing you have done in school. Stuff like sequences, subsequences, limits of sequences, functions, boundedness of functions, Differentiability, Integrability, series and power series.

You could also email the maths department at your uni and ask for suggestions. "A Concise Introduction to Pure Mathematics" by Martin Liebeck tends to be a recommended book for new undergraduates in maths.
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omegaSQU4RED
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#7
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#7
I would recommend reading up on analysis, group theory or linear algebra, as these most frequently come up in first year university courses and stand out as being very different from mathematics at school. There will be courses that are more a matter of doing calculations and applying methods (e.g. first year probability, statistics, multivariable/vector calculus) and these may be initially more comfortable to learn at first as this is more consistent with the style of maths you encounter at A-level. However, you will also come across a lot of pure mathematics, which you need to keep an open mind about as it is very different to anything you have seen before. So, for example, in an analysis course, you will study things that you have seen before, such as functions and sequences, although you will be studying their properties from first principles, learning definitions and proving results. Initially for a lot of undergraduate maths students this unfamiliar format can be very intimidating.

Unfortunately, at university (as a universal thing) the quality of the lecturing you get is pot luck - there are many lecturers who just "chalk and talk" and basically provide a monologue of mathematical content, theorems and proofs, and state them, without really attempting to engage with the students or showing them how the idea of the proof originates, etc. So part of it would be mental preparation for the fact that some lecturers may just be plain bad, and that in order to compensate you need to get into a habit of effective self-study and reading over the notes.

More importantly, I think that in order to best prepare for your degree, a good thing to do would be to look at the content you have already studied and think about it in a much more critical way - for example, how to prove certain results rather than just accepting them as true and then using them in routine calculations.

So to summarise:
  • Before you start, consider having a look at specific things to get you out of the comfort zone of learning things to syllabi and start linking mathematical concepts
  • Maths at university is about much more than just "doing the maths"
  • Maths at university is much more about proving things, and there will be a lot of lectures that are just "theorem, proof, theorem, proof, theorem, proof,..."
  • If you're given or have taken lecture notes, do read them regularly and make sure you engage with them to get the most out of them
  • Try and get out of the habit of revising solely based on past exam papers - maths at this level should be about more than just passing exams!
  • The quality of lecturing varies a lot
  • Typical first year topics include real analysis, linear algebra and group theory (pure maths)
  • Go in with an open mind!
If you want to read more about the framework of mathematical proof, logic, functions and set theory (also big in the first year) there is a book I highly recommend called How to Think Like a Mathematician by Kevin Houston.
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onimusha370
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#8
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#8
What's your firm and insurance?
Also what modules did you do at A level maths/further maths?
I did nothing in the summer before uni, still worked out ok
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Hermione18
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#9
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#9
UCL firm for Maths and Exeter Insurance
(Original post by onimusha370)
What's your firm and insurance?
Also what modules did you do at A level maths/further maths?
I did nothing in the summer before uni, still worked out ok
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TeeEm
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#10
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#10
(Original post by Hermione18)
Hiya

I'm a maths offer holder with a firm and insurance choice of two prestigious russel group univesities.

I need advice on how to prepare for the degree during the summer - what things did you do that eased the transition/what do you wish you had done?

I'm looking to get a first in my first year.

Many thanks
personally I would advise you to cover all the FP modules (if you have not covered already) and attempt STEP and AEA.

Analysis is impossible to self teach in my opinion
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tonasoso
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#11
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#11
First of all congrats on your offers!

I have completed my bsc last year, and the first thing I would advise you to do would be to have a look at the modules you will have next year at both of these universities. Find lecture notes on those ( there are usually plenty of ressources online for maths lecture notes ) and try and get familiar with their format. As people have said, maths at university is very different from a levels, and you will be confronted with very abstract concepts that will challenge your intuition. Getting comfortable with proofs is also quite a challenge, especially in modules like Analysis as people have already said.

I personally wouldn't attempt to solve exercises or questions yet, as I think being comfortable with the material will be your first challenge at university before actually tackling worksheets or exams. If you find a good set of lecture notes, you may use examples for practice but don't panic if you don't automatically know how to solve them. Being able to use theoretical knowledge at university level takes a lot more hard work than it does at a levels, as it relies less on methods or recipes.

The way you will revise your modules will also very much depend on the module. Some modules you might succeed in by relying on methods or doing a bunch of exam papers. I personally found that Differential Equations essentially required this type of approach, whereas a module like Real or Complex Analysis will force you to engage with theory ( which makes Analysis my favourite area of mathematics, although this opinion is not shared by many haha ).

However, I would also tell you to not panic or overthink it too much, universities are usually aware that maths at uni can be quite a big jump from a levels, and you probably will be confronted with nicer modules during your first term before tackling harder stuff. If you really enjoy mathematics and put in the work required, you should be fine!
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stillcrying
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#12
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#12
(Original post by tonasoso)
First of all congrats on your offers!

I have completed my bsc last year, and the first thing I would advise you to do would be to have a look at the modules you will have next year at both of these universities. Find lecture notes on those ( there are usually plenty of ressources online for maths lecture notes ) and try and get familiar with their format. As people have said, maths at university is very different from a levels, and you will be confronted with very abstract concepts that will challenge your intuition. Getting comfortable with proofs is also quite a challenge, especially in modules like Analysis as people have already said.

I personally wouldn't attempt to solve exercises or questions yet, as I think being comfortable with the material will be your first challenge at university before actually tackling worksheets or exams. If you find a good set of lecture notes, you may use examples for practice but don't panic if you don't automatically know how to solve them. Being able to use theoretical knowledge at university level takes a lot more hard work than it does at a levels, as it relies less on methods or recipes.

The way you will revise your modules will also very much depend on the module. Some modules you might succeed in by relying on methods or doing a bunch of exam papers. I personally found that Differential Equations essentially required this type of approach, whereas a module like Real or Complex Analysis will force you to engage with theory ( which makes Analysis my favourite area of mathematics, although this opinion is not shared by many haha ).

However, I would also tell you to not panic or overthink it too much, universities are usually aware that maths at uni can be quite a big jump from a levels, and you probably will be confronted with nicer modules during your first term before tackling harder stuff. If you really enjoy mathematics and put in the work required, you should be fine!
The original post is 5 years old... I have a feeling Hermione has finished university by now!
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tonasoso
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#13
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#13
(Original post by stillcrying)
The original post is 5 years old... I have a feeling Hermione has finished university by now!
Oops didn't notice that haha
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