this article is an attempt to show that how the meanings of the words “philosophy” and “philosopher” change in plato’s phaedo in comparison with his early socratic dialogues. the phaedo is plato’s interpretation of socrates’ life, philosophy and death, in light of orphic and pythagorean eschatological doctrines. in this interpretation, plato reveals his problem of epistemological pessimism and ...

This paper deals with the 2-Peripatetic Salesman Problem for the case where costs respect the triangle inequality. The aim is to determine 2 edge disjoint Hamiltonian cycles of minimum total cost on a graph. We first present a straightforward 9/4 approximation algorithm based on the well known Christofides algorithm for the travelling salesman problem. Then we propose a 2(n−1)/n-approximation p...

These notes are based on lectures in algebraic topology taught by Peter May and Henry Chan at the 2016 University of Chicago Math REU. They are loosely chronological, having been reorganized for my benefit and significantly annotated by my personal exposition, plus solutions to in-class/HW exercises, plus content from readings (from May’s Finite Book), books (e.g. May’s Concise Course, Munkres’...