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Metric Spaces - Lectures 13 & 14: Oxford Mathematics 2nd Year Student Lecture
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For the first time we are making a full Oxford Mathematics Undergraduate lecture course available. Ben Green's 2nd Year Metric Spaces course is the first half of the Metric Spaces and Complex Analysis course. This is the 7th of 11 videos.
The course is about the notion of distance. You may be familiar with the concept of the distance between two points in the plane or in space, but there are other notions of distance. For instance, one can measure how far apart two numbers are by counting the powers of 2 that divide their difference. Or one can measure the distance between two continuous functions f, g on [0,1] by calculating the integral of |f - g|.
All these notions of "distance" satisfy some basic axioms, most importantly the triangle inequality. This course explores what can be said about quite general notions of distance such as these examples. One of the main aims is to generalise concepts of analysis that you have already seen in particular cases.
You can watch all the lectures in the course here:
This is the latest lecture in the series of undergraduate lectures that we are making available to give an insight in to life in Oxford Mathematics. All first and second year lectures are followed by tutorials where students meet their tutor to go through the lecture and associated problem sheet and to talk and think more about the maths. Third and fourth year lectures are followed by classes.
The course is about the notion of distance. You may be familiar with the concept of the distance between two points in the plane or in space, but there are other notions of distance. For instance, one can measure how far apart two numbers are by counting the powers of 2 that divide their difference. Or one can measure the distance between two continuous functions f, g on [0,1] by calculating the integral of |f - g|.
All these notions of "distance" satisfy some basic axioms, most importantly the triangle inequality. This course explores what can be said about quite general notions of distance such as these examples. One of the main aims is to generalise concepts of analysis that you have already seen in particular cases.
You can watch all the lectures in the course here:
This is the latest lecture in the series of undergraduate lectures that we are making available to give an insight in to life in Oxford Mathematics. All first and second year lectures are followed by tutorials where students meet their tutor to go through the lecture and associated problem sheet and to talk and think more about the maths. Third and fourth year lectures are followed by classes.
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