LECTURE M-W-F 3:00 - 3:50
ET 202 (MAP:
BLDG #303)
DISCUSSION Tu-Th 5:00 - 5:50 SST 220B (MAP:
BLDG # 201)
INSTRUCTOR:
Martin Zeman, RH 410E
OFFICE
HOURS: Wednesday 11am - 1pm (I am coming from
the opposite side of the campus, so may be late few minutes.)
TA:
Nicole Fider, RH 440V
OFFICE
HOURS: Tuesday 10am - 1pm
COURSE INFORMATION AND POLICIES
GRADING UCI
Academic Honesty Policy UCI Student
Resources Page
BOOK By
Alessandra Pantano and Neil Donaldson will be used as the text for
this class.
MIDTERM INSTRUCTIONS
FINAL EXAM
INSTRUCTIONS
HOMEWORK ASSIGNMENTS HW1 HW2 HW3 HW4 HW5 HW6
COURSE PROGRESS PREVIOUS WEEKS
WEEK 10
W: Countability of Z×Z, N×N and Q. Cantor diagonal
argument: Uncountability of {0,1}N, non-existence of a
surjection f:A-->P(A).
M: Equinumerosity, cardinality of a set, finite
cardinality and finite sets, cardinality aleph-0 and countable
sets, uncountable sets, cardinality continuum. Examples of
bijections f:N-->Nu{0}, g:N-->Z, h:(-1,1)-->R.
Properties of relations: reflexivity, symmetricity,
transitivity. Equivalence relations. Examples of equivalence
relations: equality, congruence modulo 3. Equivalence class of
an element. Read Section 4.4 and 7.3
from the book. Recommended practice
problems.
WEEK 9
F: Injections, Surjections, Bijections. Calculating
images and preimages of sets under functions. Examples:
f_2:R-->R with f_2(x)=x2, f:R-->[0,\infty) with
f(x)=x2, g:N×N --> N with g((a,b))=g.c.d.(a,b),
computing Im(g), g[EVEN×ODD], g-1[{2}]. Function
F:P(U)-->{0,1}U where F(A)=the characteristic
function of A; proof of its injectivity and surjectivity.
Read Section 4.4 and 7.2 from the book.
Recommended practice
problems.
W: More examples of binary relations: membership
{(a,A)\in UxP(U) | a\in A} and subset: {(A,B)\in P(U)xP(U) |
A\subseteq B}. Inverse relation R-1 and examples of
computing the inverse on the ordering relation of N and on the
membership relation. Definition of a function as a binary
relation. Domain, codomain, image Im(f) of the function f. Image
f[X] of a set X and preimage (inverse image) f-1[Y]
of a set Y under f. Recommended
practice problems.
M: Complements and basic computing with complements. The
power set. Examples of power sets: Power set of the empty set,
one- two- and theree- element set. Ordered pairs and their basic
properties. Cartesian product and examples of cartesian product.
Binary relations, binary relations from A to B, binary relations
on A. Examples of binary relations on N: ordering,
divisibility. Read Section 6.1
(ignore Theorem 6.2 for the moment), Section 6.2 (ignore
Theorem 6.6 for the moment) and Section 7.1 from the book.
Recommended practice
problems.
WEEK 8
F: Basic identities concerning set operations:
commutativity, associativity, distributivity, de Morgan laws.
Three examples or proofs: A distributive law, a de Morgan law,
and the equality A\(A intersection B) = A\B. Complement. Read Section 4.3 from the book.
Recommended practice
problems.
W: Terminology fromt the book: roster notation, builder
notation. Inclusion. Theorem: equality of two sets is equivalent
to two inclusions. Basic properties of inclusions: empty set is
a subset of any set, a set is a subset of itself, transitivity
of inclusion. Basic set operations: intersection, union, set
difference. Read Section 4.2 from the
book but ignore everything about cardinalities. Also read
p.61. Recommended
practice problems.
M: An example of solving a linear Diophantine equation:
144x + 56y = 40. Sets: membership relation, extensionality
principle, the empty set. The example {x|x\notin x}. Review propositional logic and quantifiers.
Read Section 4.1 from the book but
ignore the notion of cardinality (Definition 4.2).
Recommended practice
problems.