SeLo: Sets and Logic [2009t,2008g]

Bonjour. Our Teaching Page has useful information for students in all of my classes. It has my schedule, LOR guidelines, and Usually Useful Pamphlets. One of them is the Checklist The checklist

(pdf) which gives pointers on what I consider to be good mathematical writing. Further information is at our class-archive URL (I email this private URL directly to students).

Computer	Time	Phone-list	Chalk
Marc	Sigrun	Cara	John

Individual-Project Home-E was due 1PM, Friday, 11Dec2009, carefully typed, but diagrams may be hand-drawn.
Quizzes so far, and potential problems (pdf).
I encourage you to post (emailing to our Archive) solns to all of the quiz problems.
Week-15: Mon, Wed (7 and 9 Dec) are the last two days of class. Schroeder-Bernstein theorem.
Week-14: Divisibility. Cardinality of sets, Cantor's diagonal argument. Project Home-E available Friday, 04Dec.
Week-13: Monday: Further discussion of divisibility, and how the Euclidean algorithm applies to polynomials. (Wed, canceled; Fri is Thanksgiving vacation).
Week-12:
The fascinating SeLo-D (pdf) got rave reviews; the Crowd Clamored for More! [Wed, 18Nov.]

Some examples of computer generated trimino tilings (txt).
Week-11: Examples of induction: Fibonacci numbers, and 2 base cases. Every posint factors as a product of primes irreducibles (existence). All horses have the some color. Trimino tiling.
Week-10: Defns of a lattice, a particular kind of poset (partially-ordered set). Strong/weak induction. Non-constructive proof: There exists positive irrational numbers B,E such that B^E is rational.
Week-9: Read 4.3.
We had the stimulating SeLo-C (pdf) in class on Wed, 28Oct.

Hopefully, Eager Mathematicians rush to post Solutions….
Week-8: Vacuous operations. What means the empty sum, empty product empty max empty gcd?
Week-7: Please finish reading sections 3.1–3.7. For 26Oct, have read 4.1, 4.2.
Indexed and non-indexed big-operators.

Decimal notation and repeated decimals .

Binomial and multinomial coeffs. Proof of Fermat's Little Thm by induction. Using a binomial coeff to count the number of ways of choosing N objects out of T distinguished types.

There was a makeup SeLo-B (pdf) for those with a legitimate reason for missing the original; please post solns.
Week-6: We continue in chapter 3. On Mon, 5Oct, we had extra classes, 9^th&10^th periods, in LIT127. We had our thought-provoking SeLo-B (pdf) on Wed, 7Oct., and here is a write-up of the congruence proof (pdf).
Week-5: More on quantification. Introduced the Powerset operator. Please finish reading chapter 2 by Friday, 2 Oct.
Week-4: Please cogitate deeply over iterated LBolt & linear congruences (pdf).
We: Started Quantifiers and reviewed Free variables and these functions: d(), sigma(), EulerPhi(), floor(), ceiling(). Discussed notations for tuples/sequences, gcd of tuple or set, relation between contrapositive, converse and inverse of a stmt.
Week-3:
We start Propositional logic (also called sentential logic ). Play with the Venn-diagram self test, noting that this page uses B' to mean the complement of B, which we generally write a B^c. [ASIDE: Please read our general terminology (pdf).]

We'll also look at the Euclidean Algorithm (i.e, the Lightning Bolt algorithm). The LBolt frame (pdf) has seven practice problems on page 1 [LBolt answers (txt) are available], and six make your own problem on page 2.

Please grok completely how to easily solve a linear congruence (pdf).
Week-2: Please print and read Mersenne primes and Even Perfect numbers (pdf).
We proved that Primes has arbitrarily long gaps. We proved Euclid's thm that there are infinitely many primes.

Having defined the arithmetic progression AP(s,G) := [s + GZ], we stated Dirichlet's thm for coprime APs. We noticed that Euclid's thm is the special case AP(0,1) of Dirichlet's. We proved Dirichlet's for AP(-1,4), and Prof. King gave an exercise to prove the same for AP(-1,3), and AP(-1,6).

We defined Modular arithmetic and proved that addition/subtraction and multiplication are preserved, mod N.
Week-1: Primes and Mersenne primes and perfect numbers.
Week-0:
David Gale's Game of chomp in Wikipedia. Doron Zeilberger's Three-rowed Chomp.

John posted some solns to our prerequisite mini-exam SeLo-A (pdf).

Author:	Daniel J. Velleman	ISBN-13:	978-0521675994
Year:	2006	Publisher:	Cambridge University Press

Author:	Keith Devlin	ISBN:	978-1584884491
Year:	2003	Publisher:	Chapman & Hall/CRC