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@RDKGames - MMath Mathematics (Fourth Year), University of Loughborough
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@astrotemp - BSc Physics and Applied Mathematics (graduate, 2018), UTAS
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@deathbySTEP- Maths (offer holder), University of Cambridge
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@peaerhead7997- Mathematics (First Year), University of Cambridge
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Linear Algebra - Expands upon what you've looked at with matrices in A-level further maths (or equivalent). You might generalise some of the calculations you've done with matrices (such as finding the determinant and inverse) to matrices of larger sizes, learning more computationally efficient ways to do these calculations, and applying to solving systems of linear equations among other things. You will expand upon this by studying more general objects called vector spaces, which you'll likely build upon in your second year. Tools of linear algebra turn out to be very important in further study of stats and mechanics!
•
Foundations - Warwick calls this module Foundations but it is called different things at other universities (for example, Numbers and Sets at Cambridge), but you will probably cover everything in here at some point. You will look at how the sets of numbers that you are familiar with (integers, rationals, building up to the real numbers) from scratch, and the challenges this brings. You'll look at some theory about sets and functions, building on what you've already looked at in A-level maths.
•
Analysis - Essentially here, you restart your study of calculus. (the current understanding you have is only really sufficient for use in applied fields) You will get a better understanding of infinity, studying concepts such as limits (which you may have encountered briefly before) and convergence. You'll move on to studying functions and their various properties. You'll revisit differentiation from first principles (which you may have already done at university). You may also look at integration from first principles, which is in general much trickier. (to summarise, you can split up the area under a curve into "infinitely many" rectangles that are "infinitely thin" and sum over these areas)
•
Differential Equations - This is where you get into your more immediately applicable maths. You'll expand on your study of differential equations from A-level here. The differential equations you'll have studied so far at A-level will be very nice, and will have solutions that you can (mostly) write nicely out. However, situations that may appear in the real world aren't exactly carefully crafted and so may be a little trickier. Then comes the need for more realistic approximations, as well as studying how we can analyse the solutions of a differential equation without explicitly finding them. You'll learn how to build up diagrams called phase portraits, which give us a very good idea of how solutions to a differential equation might behave. This has quite wide-reaching uses particularly in physics. You'll build upon this in later years, with a particular interesting application being the study of dynamical systems, which look at how a system, for example a population, grows and evolves over time.
•
Applied Maths - You will also probably study some more applied maths, such as statistics and classical mechanics, maybe some special relativity. In the first year at Warwick, you take a probability module as core. This essentially, consistent with other modules, goes back and defines probability in a much more general setting (with probability spaces), and goes from there. If you're into "puzzle style" maths, you'll probably enjoy some of the problems probability has to offer. (for example: if sweets are randomly distributed to children, what is the probability they all receive a sweet?) You may have the option to study some classical mechanics, which will probably be a far more mathematical approach than you've seen so far. I didn't take the mechanics option offered here so I can't offer much of an insight unfortunately!
•
Linear Algebra - Expands upon what you've looked at with matrices in A-level further maths (or equivalent). You might generalise some of the calculations you've done with matrices (such as finding the determinant and inverse) to matrices of larger sizes, learning more computationally efficient ways to do these calculations, and applying to solving systems of linear equations among other things. You will expand upon this by studying more general objects called vector spaces, which you'll likely build upon in your second year. Tools of linear algebra turn out to be very important in further study of stats and mechanics!
•
Foundations - Warwick calls this module Foundations but it is called different things at other universities (for example, Numbers and Sets at Cambridge), but you will probably cover everything in here at some point. You will look at how the sets of numbers that you are familiar with (integers, rationals, building up to the real numbers) from scratch, and the challenges this brings. You'll look at some theory about sets and functions, building on what you've already looked at in A-level maths.
•
Analysis - Essentially here, you restart your study of calculus. (the current understanding you have is only really sufficient for use in applied fields) You will get a better understanding of infinity, studying concepts such as limits (which you may have encountered briefly before) and convergence. You'll move on to studying functions and their various properties. You'll revisit differentiation from first principles (which you may have already done at university). You may also look at integration from first principles, which is in general much trickier. (to summarise, you can split up the area under a curve into "infinitely many" rectangles that are "infinitely thin" and sum over these areas)
•
Differential Equations - This is where you get into your more immediately applicable maths. You'll expand on your study of differential equations from A-level here. The differential equations you'll have studied so far at A-level will be very nice, and will have solutions that you can (mostly) write nicely out. However, situations that may appear in the real world aren't exactly carefully crafted and so may be a little trickier. Then comes the need for more realistic approximations, as well as studying how we can analyse the solutions of a differential equation without explicitly finding them. You'll learn how to build up diagrams called phase portraits, which give us a very good idea of how solutions to a differential equation might behave. This has quite wide-reaching uses particularly in physics. You'll build upon this in later years, with a particular interesting application being the study of dynamical systems, which look at how a system, for example a population, grows and evolves over time.
•
Applied Maths - You will also probably study some more applied maths, such as statistics and classical mechanics, maybe some special relativity. In the first year at Warwick, you take a probability module as core. This essentially, consistent with other modules, goes back and defines probability in a much more general setting (with probability spaces), and goes from there. If you're into "puzzle style" maths, you'll probably enjoy some of the problems probability has to offer. (for example: if sweets are randomly distributed to children, what is the probability they all receive a sweet?) You may have the option to study some classical mechanics, which will probably be a far more mathematical approach than you've seen so far. I didn't take the mechanics option offered here so I can't offer much of an insight unfortunately!
•
Linear Algebra - Expands upon what you've looked at with matrices in A-level further maths (or equivalent). You might generalise some of the calculations you've done with matrices (such as finding the determinant and inverse) to matrices of larger sizes, learning more computationally efficient ways to do these calculations, and applying to solving systems of linear equations among other things. You will expand upon this by studying more general objects called vector spaces, which you'll likely build upon in your second year. Tools of linear algebra turn out to be very important in further study of stats and mechanics!
•
Foundations - Warwick calls this module Foundations but it is called different things at other universities (for example, Numbers and Sets at Cambridge), but you will probably cover everything in here at some point. You will look at how the sets of numbers that you are familiar with (integers, rationals, building up to the real numbers) from scratch, and the challenges this brings. You'll look at some theory about sets and functions, building on what you've already looked at in A-level maths.
•
Analysis - Essentially here, you restart your study of calculus. (the current understanding you have is only really sufficient for use in applied fields) You will get a better understanding of infinity, studying concepts such as limits (which you may have encountered briefly before) and convergence. You'll move on to studying functions and their various properties. You'll revisit differentiation from first principles (which you may have already done at university). You may also look at integration from first principles, which is in general much trickier. (to summarise, you can split up the area under a curve into "infinitely many" rectangles that are "infinitely thin" and sum over these areas)
•
Differential Equations - This is where you get into your more immediately applicable maths. You'll expand on your study of differential equations from A-level here. The differential equations you'll have studied so far at A-level will be very nice, and will have solutions that you can (mostly) write nicely out. However, situations that may appear in the real world aren't exactly carefully crafted and so may be a little trickier. Then comes the need for more realistic approximations, as well as studying how we can analyse the solutions of a differential equation without explicitly finding them. You'll learn how to build up diagrams called phase portraits, which give us a very good idea of how solutions to a differential equation might behave. This has quite wide-reaching uses particularly in physics. You'll build upon this in later years, with a particular interesting application being the study of dynamical systems, which look at how a system, for example a population, grows and evolves over time.
•
Applied Maths - You will also probably study some more applied maths, such as statistics and classical mechanics, maybe some special relativity. In the first year at Warwick, you take a probability module as core. This essentially, consistent with other modules, goes back and defines probability in a much more general setting (with probability spaces), and goes from there. If you're into "puzzle style" maths, you'll probably enjoy some of the problems probability has to offer. (for example: if sweets are randomly distributed to children, what is the probability they all receive a sweet?) You may have the option to study some classical mechanics, which will probably be a far more mathematical approach than you've seen so far. I didn't take the mechanics option offered here so I can't offer much of an insight unfortunately!
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