Week 1

Reading for Tuesday, February 9:

• Grimaldi:  1.1
• Try 1.1 #1,3,5,7 to see if you are understanding the section.
• Think about the rectangle problem

Additional data:

n	m	#boxes
3	3	36
2	4	30
3	4	60

Reading for Thursday, February 11:

• Grimaldi:  1.2

• Grimaldi:  1.3

Reading for Monday, February 15:

• 1.3 (binomial theorem), 1.4

Reading for Tuesday, February 16:

• Review counting

Reading for Thursday, February 18:

• Grimaldi:  2.1
• Pay particular attention to Example 2.2.  Express p ->q as an English sentence.  Use this expression to explain why p->q is true when p is false and q is true (row 2 of Table 2.2)
• How many rows are there in a truth table for a compound statement  made up of two primitive statements?  What if there are n primitive statements?
• What kind of statment is p /\ ~p?  p\/~p ?
• Try 1.2 #1,3

Reading for Friday, February 19:

• "Contrariwise," continued Tweedledee, "if it was so, it might be; and if it were so, it would be; but as it isn't, it ain't.  That's logic."  (Lewis Carroll, Through the Looking Glass)
• Grimaldi:  2.2
• Focus on showing logical equivalence using "Laws of Logic".  Duality and Substitution Rules are less important.
• What logical equivalences allow us to eliminate the connectives -> and <=> from compound statements?
• Negation of an implication:  express in English without beginning with the word "not".  (Ex. 2.13)
• What are the contrapositive, inverse and converse of the implication p->q?  Which are logically
         equivalent to p->q?
• Try 2.2  #5a, 7a, 9a

Reading for Monday, February 22:

• Grimaldi:  2.3  (Things to think about when you are reading the section)
• This section is a little overwhelming.  Focus on understanding how to demonstrate the validity of an argument.  Try not to get bogged down by all of the names of the rules.
• What does it mean to say that "p logically implies q"?
• How would you show that a rule of inference (say Syllogism) is valid using a truth table?
• Try 2.3 #5
• Why are the arguments given on p85 invalid?

Reading for Tuesday, February 23:

• "Reductio ad absurdum which Euclid loved so much, is one of a mathematician's finest weapons.  It is a far finer gambit than any chess gambit;  a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game."
• handout from class and solutions

Reading for Thursday, February 25:

• Grimaldi:  2.4
• How do you negate a statement that has universal or existential quantifiers?  (middle of page 109-110)
• Does order matter?  What is the difference between "for all x, there exists y, such that p(x,y)" and "there exists y, for all x, such that p(x,y)"?  Work through example 2.49 carefully.
• Try 2.4 #5,15

• Grimaldi:  2.4, 2.5
• How do the quantifiers interact with "and"  and "or" {/\, \/}?  Look at Table 2.22 on p108.
• Universal Specification and Univeral Generalization.  What's it all about? (p124 and p.128)

Reading for Monday, March 1:

• Grimaldi:  2.5

• Try 2-4 from Monday handout on proofs

• Grimaldi:  3.1
• What does it mean for two sets to be equal?
• What is the power set of A?  If |A| =n, how large is the power set of A?
• Try 3.1 #3.
• What is Russel's paradox?  (See Ex. 25, p156)

• Grimaldi:  3.2
• Hey, wait a minute, those membership tables look just like truth tables and the "Laws of Set Theory"(p160) look very similar to the "Laws of Logic" (p64-5).  What is the connection?   What differences are there?
• How do you prove things about sets?  What is an element argument?  (see proof of Thm 3.3, p158)
• Membership tables and Venn diagrams:  why can't we just use these?  Why do we have to prove things?
• Try 3.1 #1,11

Reading for Monday, March 8:

• Grimaldi:  3.3, 8.1

• Grimaldi:  4.1

• Grimaldi:  4.1

Week 6

Reading for Monday, March 15:

• Grimaldi:  4.1

• Grimaldi:  4.1 (False Proofs and Strong Induction)
• Find the Flaw

• Grimaldi:  4.2
• Fibonacci links:
• Fibonacci numbers, Golden section and Golden string (R. Knott in Surrey)
• The man
• Fibonacci Quarterly (in GAC library)

• Grimaldi 4.3

Reading for Monday, March 22:

• Grimaldi:  4.3

• Primes:
• Large Primes
• Great Internet Mersenne Prime Search
• Internet PrimeNet Server

• Grimaldi:  4.4
• How does the Euclidean algorithm work?  Why does it work?

• Modular arithmetic and a little cryptography
• RSA FAQ

Week 8

Tuesday, April 6:

• Finish decryption of linear functions

• Grimaldi:  5.1

• Grimaldi:  5.2

For Monday, April 12:

• Read Grimaldi:  5.3, 5.5

• Read Grimaldi:  5.6

• Read Grimaldi:  7.1

• Read Grimaldi:   7.2

For Monday, April 19:

• Read Grimaldi:  7.3

• Read Grimaldi:  7.3

For Friday, April 23:  Exam 2

For Monday, April 26:

• Read Grimaldi:  Lattices

• Read Grimaldi:  7.4 (Equivalence Relations)

• Read Grimaldi: 11.1,11.2

• Read Grimaldi: 11.2 (Graph isomorphism)

For Monday, May 3:

• Read Grimaldi: 11.3 (Euler paths and circuits)
• Paper topic and references due.

• Read Grimaldi:  11.4 (Planar graphs)

• Read Grimaldi:  11.5 (Hamilton paths and cycles)

• Read Grimaldi: 12.1 (trees)

For Monday, May 10:

• Read Grimaldi: 12.2
• Draft 1 due.

• Read Grimaldi:  12.3

• Read Grimaldi:  12.4
• Peer review due.

• Read Grimaldi:  13.2

For Monday, May 17:

• Read Grimaldi:  13.2
• Paper due.