Core Topics in University Mathematics

This video presents the answers to a quiz about sequences of real numbers and their properties.

This video presents 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 explains what it means for a series of real numbers to converge to a limit.

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.

This video discusses how to choose a function with specified properties.

This video shows the ABC of Vector Spaces, with examples.

This video describes the concept of a basis for a vector space.

This video tells us some things we never knew about the exponential function!

This video describes the induction step in Proof by Induction.

This video describes how Proof by Induction works and applies it to an example.