Preface

This book has grown out of an undergraduate course that I have taught at the Australian National University (ANU) for over 20 years. The course is one-semester long, which means that it runs for a total of 12 weeks. In each week I teach two lectures, where a lecture is defined as a 100-minute class with a 5-minute break in the middle. This lecture format is common in Europe but can be implemented almost everywhere; for example, at the ANU—where a normal teaching period is 50 minutes—I simply reserve two consecutive periods for every lecture. A 12-week semester can in principle accommodate 24 lectures of this kind but the course material only occupies 21, with the remaining time spent on discussing assignments, review, etc. While I was transforming my lecture notes into a book, I decided to keep the splitting of the course material into 21 lectures. This approach is unusual as most authors would organise the content into chapters, with each chapter accommodating a particular topic. However, I find that dividing the material according to the way it is presented at the lectures has several advantages compared to the traditional topicbased book composition. Indeed, first of all, the lecture-based organisation ensures that the content is partitioned into (approximately) equal pieces, so that none of them stands out and looks intimidating to the students at least as far as the length is concerned. This issue becomes particularly important for those who wish to use the book for self-study and would like to keep a close eye on their overall progress. Secondly, the lecture-based format guarantees that the students get more training for the more advanced topics, which are spread over several lectures. Indeed, each lecture has its own unique set of exercises, and the students are strongly encouraged to do at least some of them before moving on. It is then automatic that the harder the topic, the more exercises one is expected to do to go through it. It should also be mentioned that some of the exercises for each lecture serve as a preparation for the following one. Thirdly, the lecture-based split-up gives clear teaching guidelines to the instructor, at the same time allowing for the possibility of re-arranging the material according to their own taste. As the book covers a one-semester course, it is shorter than most complex analysis texts (approximately 200 pages). It is well-known that many students are intimi-