Mathematical Maturity
"Pattern Recognition"
Abstract Thinking, Abstractions
  Generalize and Particularize
  Deductive Reasoning - Debugging
Semantics vs. Syntax
Data Representation
  Number Systems - Computer Architecture
    Decimal
    Binary
      Signed
      Floating Point
        Limitations - cumulated error
    Hexadecimal
Digital Logic & Boolean Algebra
Relations
  Equivalence Relations and Partitions
Functions
  Partial Orders
  Graphs
    Trees
  Functional Notation
  Prefix, Infix, and Postfix Operators
Summations
Sequences
Asymptotic Notation
  Growth of Functions - Complexity of Algorithms
  Logarithms
  Polynomials
  Exponentials
Recursion - Lisp, Prolog
Recursively Defined Structures
Logical Reasoning 
  Propositional Logic
  DeMorgan's Laws - Rephrase (eg negate) selection and loop conditions
  Digital Logic
  Resolving Logic Expressions - Prolog
  Sequential Thinking
    Case Structure
    Iteration
  Instead of Hacking
Sets
Functional Dependencies - Databases
Proof Techniques
Formal Proofs - Complexity and Correctness of Algorithms
  Mathematical Induction (Strong) - P(1) ... P(N) => P(N+1)
  Mathematical Induction (Weak) - P(1), P(N) => P(N+1)
Combinatorics
Finite Probability
Expected Performance
Recurrence/Difference Equations - Complexity of algorithms (Tn=2Tn-1 + n)
  Finite Differences
Discrete Structures
  Arrays
  Linked Lists - Stacks, Queues, Trees, Graphs
  Matrices
Problem Modeling
Problem Solving Strategies - Divide and Conquer, Backtracking
Formal Systems - Grammars, Automata
Number Theory - Encryption
  Modular Arithmetic - Perpetual Calendar Problem
  Counting
  Enumeration
Assignment - Temporal effects
Cellular Automata - Life
Petrie Nets