Jacob Davis

Teaching

Courses I have helped teach at CMU:

Semester	Course	Instructor
Fall 2010	21-300 & 600 Basic Logic	Peter Andrews
Spring 2011	21-260 Differential Equations	Irina Gheorghiciuc
Summer 2011	21-127 Concepts of Maths	me
Fall 2011	21-241 Matrices & Linear Transformations	Tim Flaherty
Spring 2012	21-260 Differential Equations	David Handron
Fall 2012	21-241 Matrices & Linear Transformations	Dana Mihai
Fall 2012	21-300 & 600 Basic Logic	Jose Iovino
Spring 2013	21-259 Calculus in 3D	Irina Gheorghiciuc
Fall 2013	21-242 Matrix Theory	Boris Bukh
Spring 2014	21-623 Complex Analysis	James Cummings
Fall 2014	21-127 Concepts of Maths	Tim Flaherty
Spring 2015	21-261 Introduction to ODEs	Jack Schaeffer
Fall 2015	21-127 Concepts of Maths	Irina Gheorghiciuc

I have written an online tool that teaches students logic by allowing them to write simple proofs and then providing helpful feedback on what they write. You can use it to learn propositional logic and then predicate logic. The code is available open source.

Based on my time at Cambridge I compiled some advice on how to lecture.

Research

Publications:

• The HOD Dichotomy, with Hugh Woodin and Daniel Rodriguez, Chapter 13 Appalachian Set Theory 2006-12, London Mathematical Society, Lecture Note Series 406. Published 2013 by Cambridge University Press. Based on an Appalachian Set Theory Workshop.
• Universal graphs at Aleph_(omega_1+1), to appear.

I have scanned notes for a large number of Cambridge courses, and would be happy to share them. I edit the lectured material significantly and take great care to fill any gaps in the presentation and ensure a fully rigorous development.

Part III Category Theory	2009-10 Prof. Johnstone	download	access online	Thanks to Guilherme Frederico for his help	errata
Part III Logic & Set Theory	2009-10 Dr Forster	download	access online	Thanks to Cong Chen for his help

Other

Ever wondered where your day goes? Find out by obsessively recording everything you do!

A report on performance in the Cambridge maths tripos results since 2002; it allows us to predict third and fourth year classes based on results in earlier years, and also compare the performances of different colleges. The (anonymised) original data is also available.