An accessible, straightforward journey through the rise and fall of various theories at the heart of physics, from Newton's time to the early 20th cenAn accessible, straightforward journey through the rise and fall of various theories at the heart of physics, from Newton's time to the early 20th century era of Einstein and Infeld. Although "rise and fall" is not quite accurate; the authors stress that new theories tend to broaden the scope of the old theories rather than upending them entirely. Thus, for example, today we freely make use of Newtonian mechanics when dealing with non-relativistic speeds, or use Maxwell's equations when the electromagnetic field in question is large enough to obscure small-scale quantum effects.
This is a popular science book, and an extremely good one. The authors make heavy use of analogy and thought experiment, ideally chosen for both easy understanding and the way they accurately crystallize difficult concepts. Even if the reader has a firm grasp of the history of physics, this quick read also offers itself up to would-be science educators as the epitome of good pedagogy....more
Very spare, simple, unpretentious prose. There are no complex ideas and it's tied up a bit too tidy by the end, but on the whole I liked it as it remiVery spare, simple, unpretentious prose. There are no complex ideas and it's tied up a bit too tidy by the end, but on the whole I liked it as it reminded me of my own explorations into the woods as a child, as well as the lost childhood friendships that slowly fade to nothing.
A very good intro book for abstract algebra. It's short and sweet, but according to people who know more about the subject than I do, it has everythinA very good intro book for abstract algebra. It's short and sweet, but according to people who know more about the subject than I do, it has everything you should get in a first course. The style is conversational with lots of examples, but is not overly wordy. The theorems stand out visually from the page enough to find them, and a good amount of details are omitted as exercises. The problems are a good mix of difficulty. Comparing it to Lang I see now that they are a bit on the easy side, but still time-consuming and non-trivial, especially the later ones in the set. Almost all are proof-based....more
I picked up this book to fill in a hole in my math education in preparation for the GRE math subject test, and because it was far and away the cheapesI picked up this book to fill in a hole in my math education in preparation for the GRE math subject test, and because it was far and away the cheapest abstract algebra book I could find. I'm not particularly thrilled with it yet; it's better than an elementary approach I borrowed but I may just keep looking.
First, the text is a bit dated. It a corrected version of the 1966 printing. Some of the notation is not what is currently standard, which is a little inconvenient: "J" for the integers instead of "Z" (and without the mathbb font), etc. More irksome is the typography: the breaks between examples, lemmas, theorems, etc. are indistinguishable from equation line breaks, and so it's difficult to return to the statement of a theorem to verify something, or to notice at a glance where one one idea ends and another begins. The text is not overly cluttered with diagrams and simplistic explanations, which I like, but in areas such as Diophantine equations I feel it might benefit from a less dense approach. Theorems introduce 8 or 9 quantities by variable name only; even a bold typeface or subscripts or something might help certain subsets of variables stand apart from others in these cases.
The upside is that the text is pretty rigorous, and builds number systems and operations axiomatically all from the natural numbers. For someone who is already familiar with the properties of integers, the reals, etc., this is an interesting approach. The construction of the integers in particular was a new one for me....more
This is a concise, clear, well-researched and nuanced indictment of the legislative branch of the U.S. government. Lessig describes how the governmentThis is a concise, clear, well-researched and nuanced indictment of the legislative branch of the U.S. government. Lessig describes how the government has become dependent on special interest money, allowing big business to dictate policy, write special exemption into tax law, and generally strangle healthy free market competition. All the while government gets more bloated and incapable of solving problems. This systemic corruption is a far cry from the dramatic tit-for-tat bribery and swindling that occasionally makes headlines.
Because the corruption Lessig describes is less visible and less tangible, it's not as easy to build a movement against it. It's the same reason more people get up in arms against terrorism than pollution, or heart disease. One is a better story than the other. Yet this really should be the #1 issue of both the political left and right, because, while there are real issues that divide us, there are also plenty of non-issues that have widespread support but never get implemented, because of the stranglehold money has on our system. Big Business and Big Government in bed together.