"No one will drive us from the paradise which Cantor created for us." -- Hilbert
"And we should call every truth false which was not accompanied by at least one laugh." -- Nietzsche
"Those with little intelligence view things as being existent or nonexistent. They do not see that what is to be seen
is perfect and utter peace." -- Nagarjuna
April 1: Introduction, Russel's paradox, "properties" (sections 1.1, 1.2)
April 3: Axioms (section 1.3)
April 6: Operations on sets (section 1.4)
April 8: Ordered pairs (section 2.1)
April 10: Relations (section 2.2)
April 13: Functions (section 2.3)
April 15: More on functions: index sets, products, and exponentiation (supplemental notes)
April 17: Equivalence relations and orderings (sections 2.4 and 2.5)
April 20: Equivalence relations "=" partitions, definition of A/E, sets of representatives (section 2.4)
April 22: Integers, isomorphisms of ordered sets, linear orderings (section 2.5)
April 24: Natural numbers are strictly ordered (section 3.1, 3.2)
April 27: Natural numbers are linearly-ordered and well-ordered (section 3.2)
April 29: Recursion theorem, examples of recursion (section 3.3)
May 1: Introduction to cardinals, Cantor-Bernstein Theorem (section 4.1)
May 4: Finite cardinals (section 4.2)
May 6: Countable sets (section 4.3)
May 8: Life of Georg Cantor, his diagonlization proof, the Cantor Set
May 11: (Exam)
May 13: Linear orderings (section 4.4)
May 15: Complete linear orderings (section 4.5)
May 18: Uncountable sets (section 4.6)
May 20: Axiom of choice (section 8.1)
May 22: More axiom of choice (section 8.2)
May 27: Well-ordered sets (section 6.1)
May 29: Ordinal numbers (section 6.2)
June 1: Axiom of replacement, transfinite induction and recursion, and ordinal arithmetic (sections 6.3-6.5)
June 3: The Banach-Tarski paradox
Supplemental materials available, for the essays:
"Nagarjuna and the Limits of Thought,", by Garfield and Priest, is available here. The following books have been placed
on reserve on the library, as of Friday 5/29:
Dauben, Joseph, "George Cantor: his mathematics and philosphy of the infinite"
Ferreiro, Dominguez Jose, "Labyrinth of thought: a history of set theory and its role in modern mathematics"
Khenpo Tsultrim Gyamtso, "The sun of wisdom: teachings on the noble Nagarjuna's Fundamental wisdom of the middle way"
Purket, Walther,"George Cantor, 1845-1918"
These books are available for two hour checkout. (You may check a book out overnight, if you pick it up two hours or less before the library closes and return it within one hour of opening.)
HW #1 (due Monday, 4/20, by 5pm)
p.11-12: # 3.1, 3.6
p.15: # 4.2, 4.4
p.18: # 1.1, 1.3, 1.6
p.22-23: # 2.2, 2.6
p.28: # 3.1, 3.2, 3.5, 3.9
HW #2 (due Monday, 5/4, by 5pm)
p.32: # 4.2, 4.3
p.37-38: # 5.6, 5.7, 5.8, 5.11
p.42: # 1.1
p.45-46: # 2.1, 2.7, 2.8
p.51-52: # 3.1, 3.6
HW #3 (due Wednesday, 5/20, by 5pm)
p. 68 # 1.3, 1.5, 1.6
p. 73 # 2.3, 2.5, 2.6
p. 78-79 # 3.2, 3.6
p. 84-85 # 4.1, 4.2, 4.3
p. 89-90 # 5.5, 5.7
p. 92 # 6.1, 6.2
HW #4 (due Wednesday, 6/3, by 5pm)
p. 143 # 1.2, 1.4, 1.7
p. 153 # 2.6, 2.8
p. 106 # 1.1, 1.2, 1.4
p. 110 # 2.1, 2.2, 2.7, 2.8