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Math Behind Info Tech

Minimization

Procedure for minimizing a machine

Easy way to design a machine with a given behavior

Regular Expressions

Analyzing behaviors with regular expressions

Notation of regular expressions

Finite State Machines

Analyzing behaviors in words

Transition diagrams

Formal definition

Complexity

NP problems

Hamiltonian cycles

Eulerian paths

Graph Theory

Trees

Cycles

Paths

Graphs & directed graphs

Relations

Symmetric relations

Graphing relations

Relations as subsets of the Cartesian product

Combinatorics

Combinations

Permutations

Set Theory

Cartesian product

Number of subsets

Union, Intersection, Complement

Sets, subsets, empty set

Karnaugh Maps

Wrap around

Grouping blocks of 1's

2-, 3-, 4-variable Karnaugh maps

Realizing Behaviors

Half-adder

Designing networks from behaviors

Logic Gates

Cancellation laws

Logic networks

AND,OR, NOT gates

Logic

Analyzing logical expressions

Truth tables

Logical expressions

AND, OR, NOT

Statements

Hexadecimal & Binary

Converting between bases

Base 2

Binary addition

Binary counting

Base 16

Big Numbers

Metric prefixes

Calculating with big numbers

Floating point numbers

Scientific notation

Exponents

Powers of 2

Rules of exponents

Operations

Rational & real numbers

Properties

Subtration & division

Addition & multiplication

Counting

Natural numbers

Reset & Carry