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Course material
The lecture notes will be updated and provided in PDF form. In addition, I suggest one or more of the following sources to aid you in your learning (please note that this only a suggestion—you could do well in the course without any books at all). The lectures will follow none of these books strictly, i.e., you will probably use them rather as reference books than as standard textbooks. The lecture notes is as close as you can come to the actual lectures.
- Friedberg et. al.: Linear Algebra, 4th ed, Pearson. ISBN 9780130084514.1)
Relevant chapters and sections: 1.1–1.6, 2.1–2.6, 3.1 (repetition), 3.2, 3.4, Chapter 4 (repetition), 5.1, 5.2, 5.4, 6.1–6.8, 7.1–7.2. Appendices: A,B.
This is a very thorough introduction to linear algebra, and both more abstract and rigorous than Strang (below).
- Kreyszig: Introductory Functional Analysis with Applications, John Wiley & Sons.
Selected material from this book will be available at the department office for a small fee.
Relevant chapters and sections: Chapter 1, 2.1–2.4, 2.6–2.10, 3.1–3.5, 3.8–3.10, Chapter 5, 7.1. Appendices: A.1.1–A.1.2, A.1.6.2)
The book by Kreyszig is very good for functional analysis and I do recommend it for anyone who is to continue with advanced mathematics. My suggestion is to first buy the accessible chapters from the departmental office to see what it is like.
- Young: An introduction to Hilbert space, Cambridge University Press. ISBN 9780521337175.
Relevant chapters and sections: Chapters 1–4 and 6–7.
A neat and short introduction to Hilbert spaces. At least those who are to continue with mathematics would benefit from it.
- Strang: Linear algebra and its applications.
Relevant chapters and sections: 1.2–1.6, 2.1–2.4, 2.6, 3.1, 3.3–3.4, Chapter 4 (repetition), 5.1–5.2, 5.5–5.6, 6.1–6.3. Appendix B.
This book is intended for students who are less familiar with matrices in particular, and with linear algebra in general. It is much more straightforward than Friedberg et al (above), but less precise and less abstract.