The Mandelbrot fractal
Schedule of topics and
Week 1: Survey of What is Ahead.
Viewing: Cartoon Logic.
Reading: Browse pages iii-xiii of the Hofstadter book.
Examples of Escher's art
Example of a canon (that is also a round)
The Crab Canon played on a Möbius strip (Mouse over the green rectangle, then click on the solid square in order to get into full-screen mode.)
Example of a fugue
Reading in Hofstadter: Introduction: A Musico-Logical Offering, pp. 3-28. The dialog: Three-Part Invention, pp. 29-32. The book's other dialogues are optional reading unless specifically mentioned in this Schedule of Readings.
Week 2-5: Formal Systems, Consistency, Completeness and Recursive Structures.
Learning Goals for each chapter of Gödel, Escher, Bach.
and the Nature of Mathematical Truth."
Reading: Chapter 1: The MU-puzzle. Chapter 2: Meaning and Form in Mathematics; Chapter 3: Figure and Ground. The dialogue Contracrostipunctus pp. 75-81. Chapter 4: Consistency, Completeness and Geometry. Chapter 5: Recursive Structures and Processes;
Chapter 7: The Propositional Calculus.
Weeks 6-9: Gödel's Incompleteness Theorems.
Reading: Hilbert attacks Poincare. Chapter 8: Number Theory (but skim pp. 217-220). Gödel's own lecture. Chapter 9: Mumon and Gödel, just pp. 260-272. The dialogue Aria with Diverse Variations, pp. 391-405. Expressibility vs. representability, on page 417. Primitive Recursive Predicates Are Represented in TNT, bottom of 417 and top line of 418. The Power of TNT on page 430. The dialogue Air on G's String, pp. 431-437. Chapter 14: On Formally Undecidable Propositions of TNT and Related Systems. A Very Brief History of Mathematical Logic (optional reading).
Week 10: Predicate Logic Symbolization and Semantics.
Reading: Chapters 7 and 8 of Hausman, Kahane, and Tidman.
Week 11: Relational Predicate Logic.
No class Nov. 11.
Reading: Chapter 10 of Hausman, Kahane, and Tidman, only sections 1-6, and 10.
Week 12: Identity and Philosophical Problems of Symbolic Logic.
Reading: Chapter 13 of Hausman, Kahane, and Tidman. The Logic of Binary Relations (optional reading).
Week 13: Axiom Systems.
Reading: Axiom Systems.
Week 14: Alternative Logics.
Guest speaker on Epistemic Logic, Liz Rard, U.C. Davis.
Reading: Alternative Logics, but skip section 7.
Week 15: Review.
Schedule changes:The above schedule of course topics and readings may be changed somewhat as we
progress through the semester, but these changes, if any, are not
expected to affect the schedule of
the homeworks and tests.
back to the main syllabus
Dec. 4, 2014