I’ve been working hard this week at learning more about measure theory. It’s a really interesting research subject and there are quite a few things that I didn’t know about it. In class, we are currently seeing the Lebesgue measure and topics. I’ve read up on the Borel, Haar, Radon, and Daniell measures.
I’ve got quite a few books in this area, including Paul Halmos’ Measure Theory¹ that I got for $6. The Measure and Integral² book that is used in my real analysis class is finally available. I have it photocopied, but I’d rather buy it. It’s a bit more expensive, but not that much. It’s $46. Einstein has it for $69.
The real analysis professor spends 3hrs a week copying that book onto the blackboard. It’s really strange. He doesn’t give any further examples and quite a few of my classmates abandoned the class after the first week.
As I mentioned before, the classes are what you make of them. At my level, having a great professor doesn’t really matter, unless he’s my thesis adviser. I’m actually lucky that 2 out of my 3 profs are good. Since I am going to specialize in analysis, probably abstract analysis and topology, the real analysis class is fundamental to my mathematical development, as it introduces all sorts of concepts that were probably not seen at an undergraduate level. We’ve started the Lebesgue integral and I hadn’t seen it before.
I picked up Paul R. Halmos’ A Hilbert Space Problem Book, 2nd edition from Springer Verlag vol 19 in their Graduate Texts in Mathematics. This is an original hardcover, which sells for $63 in the US. I got it for $6.18. I also got Halmos’ Measure Theory, vol 18 also at Springer Verlag, for $22. This is also an original hardcover.
I don’t know why these books are so cheap. Maybe someone ordered them and then decided not to buy them. The store was quite small and filled with undergrads trying to get their books. Maybe they don’t have enough space to store these books, that’s why they are bargain based. They have a limited appeal since they are books for graduate math students. Also, they are quite abstract and delving into pure mathematics, which some graduates might find unappealing with the trends in numerical analysis and education².
I also got Francis Hirsch’s and Gilles Lacombe’s Elements of Functional Analysis for $6.18. This was a softcover reprint of the origin vol 192 in Springer Verlag. The original hardcover sells for about $90³.
I had to order Thomas W. Hungerford’s Algebra, vol 73 in the same series at Springer Verlag. This was more expensive at $40. However, I found a softcover reprint for $35. That’s quite expensive for a math book in Taiwan. I ordered the hardcover since it was only $5 more.