Logic, Discrete Mathematical Structures

Fundamentals  -  Sets  and  subsets,  Operations  on  sets,  Sequences,  Division  in  the
integers, Mathematical structures
Logic    Propositions  and  Logical  operations,  Conditional  Statements,  Methods  of
proof, mathematical induction
Counting   Permutations,  Combinations,  The  pigeon  hole  principle,  elements  of
probability, recurrence relations
Relations and Digraphs  Product sets and partitions, relations and digraphs, paths
in  relations  and  digraphs,  properties  of  relations,  equivalence  relations,  computer
representation of relations and digraphs, manipulation of relations, Transitive closure
and Warshall;s algorithm
Functions    Functions  for  computer  science,  permutation  functions,  growth  of
functions
Graph  theory    Graphs,  Euler  paths  and  circuits,  Hamiltonian  paths  and  circuits,
coloring graphs
Order relations and structures  Partially ordered sets, External elements of partially
ordered  sets,  Lattices,  Finite  Boolean  algebra,  Functions  on  Boolean  algebra,
Boolean functions as Boolean polynomials
Trees  labeled trees, tree searching, Undirected trees, Minimal spanning trees
Semigroups and groups  Binary operations, semigroups, products and quotients of
semigroups, groups, Products and quotients of groups
Languages  and  finite  state  machines    Languages,  representation  of  special
languages  and  grammars,  Finite  state  machines,  Semi  groups  ,  machines  and
languages, machines and regular languages
Groups and coding  Coding of binary information and error detection
Decoding and error correction