Discrete Mathematics with Coding

Cover
Half Title
Series Page
Title Page
Copyright Page
Dedication
Contents
Preface
I. Essentials of VBA
1. Introduction
1.1. Modules, Subs, and Functions
1.2. Data Output and Input OutputExample, InputExample
1.3. Cell Characteristics CellAttributes
1.4. Number Formats NumberFormat
1.5. Passing Arguments SwitchIntegers
1.6. User-Defined Data Types
1.7. Command Buttons
1.8. Spin Buttons MixColors
1.9. Exercises
2. VBA Operators
2.1. Arithmetic Operators
2.2. Comparison Operators
2.3. Logical Operators
2.4. Exercises
3. Conditional Statements
3.1. The If Then Else Statement Grade
3.2. The Select Case Statement CycleEdges
3.3. Exercises
4. Loops
4.1. The For Next Statement
4.2. The Do While Loop ReduceFraction, NumberOfTerms
4.3. The Do Until Loop
4.4. Exit Statements
4.5. Finding the Zeros of a Function FindZero, FunctionVal
4.6. Exercises
5. Arrays
5.1. Declaring Arrays
5.2. First and Last Indices of an Array
5.3. Passing and Returning Arrays
5.4. Variants and the Array Function
5.5. Sorting Numeric Data NumericSort
5.6. Finding Nearest Numbers NearestNumbers
5.7. Stacks Push, Pop
5.8. Exercises
6. String Functions
6.1. The VBA Concatenation Operator
6.2. The VBA Extraction Function Mid
6.3. The VBA ASCII Functions Asc and Chr
6.4. VBA Data Conversion Functions CStr, CInt, CLng, CDbl
6.5. The VBA Function Replace
6.6. The VBA Function InStr
6.7. The VBA Operator Like
6.8. The VBA Functions Join and Split
6.9. Exercises
7. Grids
7.1. Setting up a Grid MakeGrid
7.2. The Grid as a Torus TorusPoint
7.3. Installing Coordinates in a Grid InstallCoord
7.4. Sieve of Erastothenes Sieve
7.5. A Changing Rectangle CollapseExpandRectangle, Delay
7.6. Table Sum Game TableSum
7.7. Finding the Nearest Cells NearestCells
7.8. A Growing Spiral Spiral
7.9. Billiard Ball BilliardBall
7.10. Exercises
8. Recursion
8.1. The Factorial Function FactRecursive
8.2. Binary Trees Binarytree
8.3. The Tower of Hanoi HanoiTower
*8.4. A Complex Arithmetic Calculator ComplexCalc
*8.5. A Polynomial Calculator PolyCalc
8.6. Exercises
9. Charts and Graphs
9.1. Frequency Charts LetterFreqency
9.2. Drawing Lines GraphPoly
9.3. Intersection of Two Lines LineIntersect
9.4. Projection of a Point onto a Line Point2Line
9.5. The Incenter of a Triangle Incenter
9.6. Function Graphs GraphFunction
9.7. Fitting a Line to Data Least Squares
9.8. Graphing Parametric Curves GraphCurve
9.9. A Fractal Game ChaosTriangleGame
9.10. Overlaying Graphs PredatorPrey
9.11. Bezier Curves Bezier
9.12. Exercises
10. Random Numbers
10.1. The VBA Function Rnd
10.2. A Nonsense Generator Nonsense
10.3. Area under a Curve AreaUnderCurve
10.4. A Simple Random Walk Random Walk
10.5. Spreading Disease SpreadOfDisease
10.6. Particle Swarm Optimization ParticleSwarmOpt
10.7. A Randomly Sprouting Plant SproutWither
10.8. Random Walk of a Rotating Pattern RotateAndMove
10.9. Random Tessellations RandomTess
10.10. Maxwell's Entropy Demon MaxwellsDemon
10.11. Multi-Random Walk RandomWalks
10.12. A Shedding Organism RandomWalkShed
10.13. A Splitting Organism RandomWalkSplit
10.14. Random Mazes Maze
10.15. Exercises
II. Linear Analysis
11. Linear Equations
11.1. Matrix Arrays MatrixIn, MatrixOut
11.2. Systems of Linear Equations
11.3. The Gauss Jordan Method
11.4. Row Operations with VBA RowOperations
11.5. Row Echelon Form with VBA RowEchelon
11.6. Exercises
12. Linear Programming
12.1. Linear Inequalities and Feasible Regions
12.2. Formulation of the General LP Problem
12.3. Graphic Solution for Two Dimensions
12.4. The Simplex Method
12.5. Standard Max Problem with VBA Simplex
12.6. Duality and the Standard LP Min Problem
12.7. Solving Nonstandard LP Problems
12.8. Exercises
13. Matrix Algebra
13.1. Matrix Scalar Multiplication ScalarMult
13.2. Matrix Addition and Substraction AddSubMat
13.3. Matrix Multiplication MultMat
13.4. Inverse of a Matrix MatrixInversion
13.5. Matrix Powers PowerMat
13.6. Input-Output Models IOModel
13.7. Polynomial of Best Fit PolyFitData
*13.8. The Barnsley Fern AffineIterations
*13.9. A Matrix Calculator MatrixCalculator
13.10. Exercises
14. Determinants
14.1. Definition and Properties
14.2. Determinants Using VBA DetEchelon, DetRecursive
14.3. Cramer's Rule CramersRule
14.4. Collinear and Coplanar Points Using Determinants
14.5. Areas and Volumes Using Determinants
14.6. Circumscribing a Triangle Circumcenter
14.7. Exercises
III. Logic
15. Propositional Logic
15.1. Compound Statements
15.2. Equivalent Statements and Laws of Logic
15.3. Truth Tables with VBA Stmt2TruthTable
15.4. Statement from a Truth Table TruthTable2DisjNormal
15.5. Valid Arguments
15.6. Exercises
16. Switching Circuits
16.1. Introduction
16.2. Series and Parallel Circuits
16.3. Equivalent Circuits
16.4. Circuit Expressions with VBA SwitchCircuitExpr
16.5. Exercises
17. Gates and Logic Circuits
17.1. The Gates NOT, AND, OR
17.2. The Gates XOR, NAND, NOR
17.3. Logic Circuit Expressions with VBA LogicCircuitExpr
17.4. Half Adders
17.5. VBA Simulation of a Half Adder
17.6. Full Adders
17.7. VBA Simulation of a 4-bit Adder FullAdder4
17.8. Exercises
IV. Combinatorics
18. Sets
18.1. Introduction
18.2. The Union of Two Sets Union
18.3. The Intersection of Two Sets Intersection, Card
18.4. The Complement of a Set Complement
18.5. Extensions to Three or More Sets
18.6. Calculating Sets with VBA SetCalculator
18.7. Venn Diagram Components with VBA VennParts
18.8. Laws of Set Equality
18.9. Laws of Set Inclusion
18.10. Cartesian Products, Relations, and Functions
18.11. Exercises
19. Counting
19.1. The Addition Principle
*19.2. Venn Solutions with VBA Venn3Solver
19.3. The Multiplication Principle
19.4. Permutations
19.5. Generating Permutations with VBA Permutations
19.6. Combinations
19.7. Generating Combinations with VBA Combinations
19.8. Traveling Salesman Problem TravelSales
*19.9. Permutation Algebra MultPerm, InvPerm, PowerPerm
*19.10. Permutation Cycles PermCycles
19.11. Exercises
V. Probability
20. Probability
20.1. Sample Spaces, Probabilities, and Events
20.2. Throwing a Pair of Fair Dice DiceRelativFreq
20.3. Poker Hands PokerHands
20.4. Drawing Balls from an Urn
20.5. Simulation of the Binomial Distribution GaltonsBoard
20.6. Conditional Probability
20.7. Bayes' Theorem
20.8. Disease Testing TruePosTrueNeg
20.9. Independence
20.10. Exercises
21. Random Variables
21.1. Examples of Random Variables
21.2. Expected Value of a Random Variable
21.3. Properties of Expectation
21.4. Variance and Standard Deviation of a Random Variable
21.5. The Law of Large Numbers
21.6. Central Limit Theorem
21.7. Exercises
22. Markov Chains
22.1. Transition Probabilities
22.2. Higher Order Transition Probabilities
22.3. The Initial Distribution of a Markov Chain
22.4. The Steady State Vector
22.5. Position Dependent Random Walk PositionRandWalk
22.6. Polya Urn Model PolyaUrn
22.7. Ehrenfest Diffusion Model EhrenfestUrns
22.8. Stepping Stone Model SteppingStone
22.9. Exercises
VI. Properties of Numbers
23. Divisibility and Prime Numbers
23.1. The Division Algorithm
23.2. Number Bases BaseToBase
*23.3. Wolfram's Binary Rules WolframRules
23.4. Greatest Common Divisor GCD
23.5. Prime Divisibility Property
23.6. The Fundamental Theorem of Arithmetic
23.7. Prime Decomposition with VBA PrimeDecomposition
23.8. Exercises
24. Congruence
24.1. Definition and Basic Properties
24.2. Congruence Arithmetic
24.3. Fermat's Little Theorem
24.4. Remainder of a Product ProductRmdr
24.5. Remainder of a Power PowerRmdr
24.6. Solving Congruence Equations CongruenceSolver
*24.7. Modular Arithmetic CongruenceTables
24.8. Exercises
25. Cryptography
25.1. Encoding the Alphabet
25.2. Caesar's Shift Cipher
25.3. Zigzag Cipher
25.4. Spiral Cipher SpiralCipher
25.5. Affine Cipher AffCipher
25.6. Permutation Cipher PermCipher
25.7. Vigenère Cipher VCipher
25.8. Four Square Cipher FourSquare
25.9. Matrix Cipher MatrixCipher
25.10. The RSA Algorithm RSACipher
25.11. Exercises
26. The Enigma Machine
26.1. Description
26.2. Implementation in VBA EnigmaCipher
26.3. A Closer Look at the Mathematics
27. Large Numbers
27.1. Arithmetic of Large Positive Integers
27.2. Arithmetic of Large Signed Integers
27.3. Arithmetic of Large Decimals
*27.4. A Large Scale Calculator LargeCalc
27.5. Exercises
Index