Another post from the History Book Club. It seemed particularly appropriate for today (January 20th, Inauguration Day).
Science and the Founding Fathers: Science in the Political Thought of Thomas Jefferson, Benjamin Franklin, John Adams, and James Madison,
by I. Bernard Cohen, W.W. Norton & Company, 1995.
Filed under History Book Club, Reviews
Filed under History Book Club, Reviews
Hatcher’s Algebraic Topology unfortunately hadn’t been written when I studied the subject in grad school, but a few years ago I participated in a meetup that went through about half of it. I wrote up notes on things I puzzled over, or just observations I found helpful. Here they are. Besides the homology group mentioned in the title, some other tidbits: a figure to elucidate the calculation of the fundamental group of the complement of the Alexander Horned Sphere, and more details for the intuitive proof Hatcher sketches of Poincaré duality.
Filed under Topology
Filed under History Book Club, Reviews
The Death of Socrates, Jacques Louis David.
(From Wikimedia Commons)
Another post from the History Book Club. Continue reading
Filed under History Book Club, Reviews
Filed under History Book Club, Reviews
Every specialty has its tricks of the trade. They become second nature to practitioners, so they often don’t make it into the textbooks. Quantifiers rule in logic; here are some of the games we can play with them. I’ll start with tricks that apply in logic generally, then turn to those specific to Peano arithmetic.
Filed under Peano Arithmetic
Delacroix’s Liberty Leading the People
Another post from the History Book Club. Continue reading
Filed under History Book Club, Reviews
Substructures and extensions loom large in math: subgroups, subrings, extension fields, submanifolds, subspaces of topological spaces… So too in the model theory of PA.
Filed under Peano Arithmetic
MW: Indicators: we don’t need to discuss these, to prove the Paris-Harrington theorem. But I think they offer valuable insight.
Filed under Conversations, Peano Arithmetic
Diagonal Argument 