The course is based on lecture notes and not on any textbook. This year's course will be based on the lecture notes which have developed during the last two years. Lecture notes

• Last update: 8.11
• Updated chapters: Chapter 1-7.

If you find typos or other mistakes in the notes, please contact Franz.

Mistakes and typos in the lecture notes will be corrected throughout the semester. Lecture notes+Changes (So far I have not gotten to mark all the changes, in particular in Chapter 1.)

Based on the diverse student body taking this course it is a difficult task to recommend books for the material. Below are some suggestions but I encourage you to visit the library and browse through the available literature and look if there are sources on the web that you find helpful.

• C. Heil: Metrics, Norms, Inner Products, and Operator Theory, Birkhäuser/Springer, Cham, 2018.

The book starts with an introduction to metric spaces and develops the theory of normed spaces and inner product spaces as particular cases which is not the way we are going to approach these topics, but the material is well-represented and large parts of the syllabus are covered in this well-written book.

• Vilmos Komornik: Topology, Calculus and Approximation, Springer Undergraduate Mathematics Series, 2017.

This book also starts with metric spaces and provides a thorough introduction into the topic and its applications. Browse through the parts that we are covering in the course.

• J. Michael Steele: The Cauchy-Schwarz Master Class. Cambridge Univ. Press, 2004.

The book covers the Cauchy-Schwarz inequality, Young's inequality, Minkowski's inequality and many more. The exposition is outstanding and quite in contrast to the other available sources on inequalities.

Both books are available free of charge if you access the Springer webpage via the NTNU network (use vpn client).