This course aims to introduce students to the idea of rigorous mathematical arguments and, in particular, to discuss the rigorous foundations of calculus.
An important feature of the course is the use of careful, rigorous proofs of the theorems used, and one of the aims of the course is to improve student's ability to understand such arguments and to develop such proofs for themselves.
A central concept in analysis is the idea of convergence, either of sequences, series or of functions. This course aims to discuss this concept rigorously, and provide the basic results which will be used in later courses.
Of course, we also discuss precise definitions of the derivative and the integral, and prove their basic properties. Everyone will be aware of these, but will probably not have seen rigorous proofs of them.
In addition, we describe methods for obtaining inequalities, and tests for convergence of series and power series.
Location: Edinburgh, Malaysia.
Further information: Syllabus, Number of lectures, Assessment, Learning Outcomes.
SCQF Level: 8.