YESYES means YES, even more so.
OF COURSE! means that no person who doesn't know that stuff shouldn't
even consider taking any CS course.

IN 456 means that it is a subject material of 456 and I do not assume
that they already know it, but it doesn't hurt if they have already seen it.

The answers given here a *spefically* for 456.  For example, everyone
should know elementary probability theory, but it's never used in 456.
For many sections, the answer would be "YES" for 477 even if it's "NO"
for 456.

#Chapter 1: Fundamentals of Discrete Mathematics
OF COURSE! #1.1 The rules of sum and product
OF COURSE! #1.2 Permuations  (That's spelled "permutations" in America.)
NO #1.3 Combinations: the binomial theorem
NO #1.4 Combinations with repition (Do you mean "repitition"?
NO #1.5 The catalan numbers (optional)

#Chapter 2: Fundamentals of Logic
COMMENT: Failure to understand this material is the greatest problem
         in 456.
YESYES #2.1 Basic connectives and truth tables
YESYES #2.2 Logical equivalence: the laws of logic
YES #2.3 Logical implication: rules of inference
YESYES #2.4 The use of quantifiers
YES  #2.5 Quantifiers, Definitions, and the proofs of theorems

#Chapter 3: Set Theory
OF COURSE! #3.1 Sets and Subsets
OF COURSE! #3.2 Set operations and the laws of set theory
OF COURSE! #3.3 Counting and venn diagrams
NO #3.4 A first word on probability
NO #3.5 The axioms of probability (optional)
NO #3.6 Conditional Probability: independenc3 (optional)
NO #3.7 Discrete random variables (optional)

#Chapter 4: Properties of the Integers: Mathematical Induction
NO #4.1 The well-ordering principle:
YES mathematical induction
IN 456 #4.2 Recursive definitions
NO #4.3 The division algorithm: prime numbers  (What do you mean?)
NO #4.4 The greatest common divisor: the euclidean algorithm
   (What do you mean?  Every grade school child knows what the gcd is.)
NO #4.5 The fundamental theorem of arithmetic
   But Ruth, in the 5th grade, is doing this in her homework.

#Chapter 5: Relations and Functions
YES #5.1 Cartesian products and relations
YES #5.2 Functions: plain and one-to-one
YES #5.3 Onto functions:
NO  stirling numbers of the second kind
NO  #5.4 Special functions
IN 456 #5.5 The pigeonhole principle
YES #5.6 Function composition and inverse function
YES #5.7 Compuational complexity (It is a main subject in 456)
NO #5.8 Analysis of algorithms

#Chapter 6: Languages: Finite State Machines
IN 456 6.1 Language: the set theory of strings
IN 456 #6.2 Finite state machines: a first encounter
NO  #6.3 Finite state machines: a second encounter

#Chapter 7: Relations: The Second Time Around
YES #7.1 Relations revisited: properties of relations
NO #7.2 Computer recognition: zero-one matrices and directed graphs
NO #7.3 Parial orders: hasse diagrams  (What's a parial order?)
YES #7.4 Equivalence relations and partitions
IN 456 #7.5 Finite state machines: the minimization process


#Part 2
#Further Topics in Enumeration

I spend time on the three kinds of enumeration:

1) A set is enumerable, i.e., countable.

2) A set is recursively enumerable, i.e., a machine can be built that
runs forever printing out all the members of the set.

3) A set is recursively enumerable in canonical order, i.e., a machine can
be built that runs forever printing out all the members of the set in
canonical order.

Every langauge us enumerable, but most are not recursively enumerable.
The halting problem is recursively enumerable but not recursively
enumerable in canonical order.
Recursively enumerable in canonical order is equivalent to decidable.

#Chapter 8: The Principle of Inclusion and Exclusion
NO  #8.1 The principle of inclusion and exclusion
NO  #8.2 Genearlizations of the principle
NO  #8.3 Derangements: nothing is in its right place
NO  #8.4 Rook polynomials
NO  #8.5 Arrangements with forbidden positions

#Chapter 9: Generating Functions
NO  #9.1 Introductory examples
NO  #9.2 Definition and examples: calculational techniques
NO  #9.3 Partitions of integers
NO  #9.4 The exponential generating function
NO  #9.5 The summation operator

#Chapter 10: Recurrence Relations
NO #10.1 The first-order linear recurrence relation
NO #10.2 The second-order linear homogeneous recurrence relation with
     constant coefficients
NO #10.3 The nonhomogeneous recurrence relations
NO #10.4 The method of generating functions
NO #10.5 A special kind of nonlinear recurrence relation (optional)
NO #10.6 Divide-and-conquer algorithms (optional)


#Part 3
#Graph Theory and Applications

YES #Chapter 11: An Introduction to Graph Theory
YES #11.1 Definitions and examples
NO #11.2 Subgraphs, complements, and graph isomorphism
NO #11.3 Vertex degree: euler trails and circuits
NO #11.4 Planar graphs
NO #11.5 Hamilton paths and cycles
NO #11.6 Graph coloring and chromatic polynomials

#Chapter 12: Trees
NO #12.1 Definitions, properties, and examples
NO #12.2 Rooted trees
NO #12.3 Trees and sorting
NO #12.4 Weighted trees and prefix codes
NO #12.5 Biconnected components and articulation points

#Chapter 13: Optimization and Matching
NO #13.1 Dijkstra's shortest path algorithm
NO #13.2 Minimal spanning trees: the algorithms of kruskal and prim
NO #13.3 Tranport networks: the max-flow min-cut theorem



#Part 4
#Modern Applied Algebra

#Chapter 14: Rings and modular arithmetic
NO #14.1 The ring structure: definitions and examples
NO #14.2 Ring properties and substructures
YES #14.3 The integer modulo n (They learned this in 135, didnt they?)
NO #14.4 Ring homomorphisms and isomorphisms

#Chapter 15: Boolean Algebra and Switching Functions
YES #15.1 Switching functions: disjunctive and conjuctive normal forms
NO #15.2 Gating networks: minimal sums of products: karnaugh maps
NO #15.3 Further applications: don't-care conditions
NO #15.4 The structure of boolean algebra (optional)

#Chapter 16: Groups, Coding Theory, and Polya's Method of Enumeration
NO #16.1 Definition, examples, and elementary properties
NO #16.2 Homomorphisms, isomorphisms, and cyclic groups
NO #16.3 Cosets and lagrange's theorem
NO #16.4 The RSA cryptosystem (optional)
   But this is the subject of an extra credit problem.  (Every 656 student
   is required to turn in one extra credit problem of his choice.)
NO #16.5 Elements of coding theory
NO #16.6 The Hamming metric
NO #16.7 The parity check and generator matrices
NO #16.8 Group codes: decoding with coset leaders
NO #16.9 Hamming matrices
NO #16.10 Counting and equivalence: burnside's theorem
NO #16.11 The cycle index
NO #16.12 The pattern inventory: polya's method of enumeration

#Chapter 17: Finite Fields and Combinatorial Designs
NO #17.1 Polynomial rings
NO #17.2 Irreducible polynomials: finite fields
NO #17.3 Latin squares
NO #17.4 Finite geometrics and affine planes
NO #17.5 Block designs and projective planes