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Math Topics for Discrete Math

Numbers in brackets indicate how many items pertain to that topic.

Logical Form & Equivalence   [11]
Statements
Logical connectives
Symbolic notation
Truth tables   [7]
Exclusive or   [1]
Logical equivalence
De Morgan's laws
Tautologies and contra.
Conditional Statements   [1]
Conditional statements
Negation of a conditional
Contrapositive
Converse and inverse
Only if and iff.
Necess. and suff. conds.
Proofs   [4]
Techs. of direct proof
Disproof by countereg.   [1]
Proof by contradiction
Proof by contraposition
Sequences   [4]
Terminology of sequences   [2]
Formula for a sequence   [4]
Summation notation   [2]
Telescoping sums
Change of variable
Product notation
Props. of sums & prods
Factorial notation   [1]
Mathematical Induction   [2]
Princip. of math. induct.
Strong Math. Induction
Set Theory: Basic Defns.   [3]
Definition of subset
Venn diagrams   [3]
Rels. among sets of nos.
Equal., union, intersect.
Diffs. and complements   [1]
Cartesian products
Properties of Sets   [1]
Basic set properties
Proving properties
Deriving set properties
Empty Set, Partits., Power
Counting   [1]
Counting lists, sublists
The multiplication rule   [1]
Counting possibilities   [3]
Permutations   [5]
Perms. of selected elements
R-permutations
Proving props. of P(n, r)
Counting Elements of Disj. Sets
The addition rule
Inclusion/exclusion rule
Gen'l inclusion/exclusion
Subsets and Combinations   [6]
R-combinations   [1]
Ordered and unordered   [1]
Permutations vs. combs.   [5]
Perms. w. repeated elements
Double counting
R-combs. with repetition
Combinatorial formulas   [1]
Pascal's triangle   [3]
The binomial theorem
 Functions Defined on Sets   [2]
Definition of a function
Equality of functions
Examples of functions
Well-defined functions
One-to-one and onto fcns.
One-to-one corresps.
Inverse functions
Pigeonhole principle
Applications   [1]
Composition of functions
Comp. of 1-1 & onto fcns.
Recursion   [3]
Recurrence relations   [11]
Recurs. def. sequences   [6]
The towers of Hanoi   [3]
The Fibonacci numbers
Solving Recurrence Rels.   [1]
Explicit formulas
Arith. & geom. sequences
Does seq. satisf formula?
2nd.order lin. rec. rels.
Technique for solving
Formula for Fib. seq.
Gambler's ruin
Gen'l recursive defns.
Graphs and Trees   [4]
Graphs, digraphs
Complete graphs
Bipartite graphs
Sub graphs
Degree
Degree vs. no. of edges
Paths and Circuits   [3]
Konigsberg bridges
Walks, paths, circuits   [3]
Connectedness
Euler's theorem
Constr. an Euler circuit   [2]
Hamiltonian circuits   [2]
Traveling salesperson   [1]
Matrix Reps. of Graphs   [2]
Matrix notation   [1]
Adjacency
Matrix multiplication   [1]
No. of walks of length n
Isomorphisms of Graphs   [2]
Definition
Finding noniso. graphs
Isomorphic invariants
Showing graphs noniso.
Trees   [1]
Definition and examples
Characterizations
Rooted trees
Binary trees
Spanning Trees   [1]
Definition
Existence
Finding minimal
Social Choice and Voting Theory   [1]
Fair division   [3]
Voting methods   [1]
Apportionment methods   [1]
Financial math   [1]


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