Core Topics in University Mathematics: Recent Episodes
The University of Nottingham
This series of videos is aimed primarily at first-year undergraduate mathematics students. It covers some of the topics which students often find hard, but which are fundamental to success in university mathematics. One example of such a topic is curve sketching, which can reveal the qualitative behaviour of a function where perhaps the mathematical expression for the function is rather impenetrable. Proficiency with curve sketching comes with practice, and it is often hard to know where to begin. The videos in this series provide some useful tips. Another example of a core topic in university mathematics is the idea of proof. Rigorous proof allows us to establish the truth of mathematical statements. Videos in this series highlight two ways of proving mathematical statements: by induction and by contradiction. Further videos highlight the generalisation of a familiar pre-university mathematical concept (a vector) to a more abstract setting (vector spaces).
This video presents the answers to a quiz about sequences of real numbers and their properties.
This video shows some examples of sequences of real numbers and describes their properties.
This video describes how to use the ratio test to determine whether a series converges or diverges.
This video describes how to use the comparison test to determine whether a series converges or diverges.
This video establishes whether various sequences of real numbers converge, using the definition of convergence.
This video explains what it means for a sequence of real numbers to converge to a limit.
This video uses Proof by Induction to show that the sum of three consecutive cubes is divisible by nine.
This video describes some examples of curve sketching, for functions that can be written as a product of two other functions.
This video describes two examples of curve sketching, using symmetry, an examination of small and large values of the independent variable, and differentiation.
This video describes three ideas that are useful in curve sketching: symmetry, small and large values of the independent variable, and differentiation.
This video explains why curve sketching is so important and describes how to use transformations to extend the range of functions you can sketch.
This video proves that there are infinitely many prime numbers, using Proof by Contradiction.