Discrete Mathematics with Coding image

Discrete Mathematics with Coding

7,210.00₹ 9,710.00₹

Buy Discrete Mathematics with Coding | New Arrivals, FOREIGN BOOKS , A Social Legal Perspective, ENGINEERING BOOKS

ABOUT THE BOOK

This book, for a first undergraduate course in Discrete Mathematics, systematically exploits the relationship between discrete mathematics and computer programming. Unlike most discrete mathematics texts focusing on one of the other, the book explores the rich and important connection between these two disciplines and shows how each discipline reinforces and enhances the other.

The mathematics in the book is self-contained, requiring only a good background in precalculus and some mathematical maturity. New mathematical topics are introduced as needed.

The coding language used is VBA Excel. The language is easy to learn, has intuitive commands, and the reader can develop interesting programs from the outset. Additionally, the spreadsheet platform in Excel makes for convenient and transparent data input and output and provides a powerful venue for complex data manipulation. Manipulating data is greatly simplified using spreadsheet features and visualizing the data can make programming and debugging easier.

The VBA language is seamlessly integrated into the spreadsheet environment with no other resources required. Furthermore, as some of the modules in the book show, intricate patterns, graphs, and animation in the form of moving cells is possible.

Features

  • Introduces coding in VBA Excel assuming no previous coding experience.

  • Develops programs in Linear Analysis, Logic, Combinatorics, Probability, and Number Theory.

  • Contains over 90 fully tested and debugged programs. The code for these is as well as the exercises is available on the author's website.

  • Contains numerous examples that gradually introduce the reader to coding techniques.

  • Includes programs that solve systems of linear equations, linear programming problems, combinatorial problems, Venn diagram problems and programs that produce truth tables from logic statements and logic statements from switching and gate circuits, encrypt and decrypt messages and simulate probability experiments.

TABLE OF CONTENTS

Introduction

1.1 Modules, Subs, and Functions

    1. Data Output and Input. OutputExample,InputExample

    2. Cell Characteristics. CellAttributes

    3. Number Formats. NumberFormat

    4. Passing Arguments. SwitchIntegers

    5. User Defined Data Types

    6. Command Buttons

    7. Spin Buttons. MixColors

    8. Exercises

    1. VBA Operators

      1. Arithmetic Operators

      2. Comparison Operators

      3. Logical Operators

      4. Exercises

    2. 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

　

　

    1. Variants and the Array Function

    2. Sorting Numeric Data. NumericSort

    3. Finding Nearest Numbers. NearestNumbers

    4. Stacks. Push, Pop

    5. Exercises

    1. String Functions

      1. The VBA Concatenation Operator &

        2. Duplicating Strings. DupString

      2. The VBA Extraction Function Mid

        3. Matching Symbols. IsMatch

        Inserting, Replacing a String. RemoveInsertString

        A Variation of Mid. Midd

      3. The VBA ASCII Functions Asc and Chr

        4. Boolean ASCII Functions. IsUpper,IsLower,IsLetter,IsDigit

      4. VBA Data Conversion Functions CStr, CInt, CLng, CDbl

      5. The VBA Function Replace

        6. Removing Spaces From a String. RemoveWhiteSpace

        Removing Duplicate Characters. RemoveDupChar

      6. The VBA Function InStr

      7. The VBA Operator Like

      8. The VBA Functions Join and Split

        9. Deleting Duplicate Strings. DeleteDupStr

      9. Exercises

    2. Grids

      1. Setting Up a Grid. MakeGrid

      2. The Grid As a Torus. TorusPoint

      3. Installing Coordinates in a Grid. InstallCoord

      4. Sieve of Erastothenes. Sieve

      5. A Changing Rectangle. CollapseExpandRectangle, Delay

      6. Table Sum Game. TableSum

      7. Finding the Nearest Cells. NearestCells

      8. A Growing Spiral. Spiral

      9. Billiard Ball. BilliardBall

      10. Exercises

    3. Recursion

      1. The Factorial Function. FactRecursive

      2. Binary Trees. Binarytree

      3. The Tower of Hanoi. HanoiTower

      *8.4 A Complex Arithmetic Calculator. ComplexCalc

      *8.5 A Polynomial Calculator. PolyCalc

      8.6 Exercises

    4. Charts and Graphs

    1. Frequency Charts. LetterFreqency

    2. Drawing Lines. GraphPoly

    3. Intersection of Two Lines. LineIntersect

    4. Projection of a Point onto a Line. Point2Line

    5. The Incenter of a Triangle. Incenter

    6. Function Graphs. GraphFunction

    7. Fitting a Line to Data. Least Squares

    8. Graphing Parametric Curves. GraphCurve

    9. A Fractal Game. ChaosTriangleGame

    10. Overlaying Graphs. PredatorPrey

    11. Bezier Curves. Bezier

    12. Exercises

  1. Random Numbers

    1. The VBA Function Rnd

      2. Random Decimals. RndDec

      Random Integers. RndInt

      Random Permutations. RndPerm

      Random Position. NextRndPos

      Probability Distributions. RndOut

    2. A Nonsense Generator. Nonsense

    3. Area Under a Curve. AreaUnderCurve

    4. A Simple Random Walk. Random Walk

    5. Spreading Disease. SpreadOfDisease

    6. Particle Swarm Optimization. ParticleSwarmOpt

    7. A Randomly Sprouting Plant. SproutWither

    8. Random Walk of a Rotating Pattern. RotateAndMove

    9. Random Tessellations. RandomTess

    10. Maxwell’s Entropy Demon. MaxwellsDemon

    11. Multi-Random Walk. RandomWalks

    12. A Shedding Organism. RandomWalkShed

    13. A Splitting Organism. RandomWalkSplit

    14. Random Mazes. Maze

    15. Exercises

    II Linear Analysis

  2. Linear Equations

    1. Matrix Arrays. MatrixIn, MatrixOut

    2. Systems of Linear Equations

    3. The Gauss Jordan Method

    4. Row Operations with VBA. RowOperations

    5. Row Echelon Form with VBA. RowEchelon

    6. Exercises

　

　

　

12 Linear Programming

12.1 Linear Inequalities and Feasible Regions

12.2 Formulation of the General LP Problem

The Standard LP Max Problem

The Standard LP Min Problem

Nonstandard LP Problems

    1. Graphic Solution for Two Dimensions

    2. The Simplex Method

    3. Standard Max Problem with VBA. Simplex

    4. Duality and the Standard LP Min Problem

    5. Solving Nonstandard LP Problems

    6. Exercises

    1. 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

    　

  1. Determinants

    1. Definition and Properties

    2. Determinants Using VBA. DetEchelon, DetRecursive

    3. Cramer’s Rule. CramersRule

    4. Collinear and Coplanar Points Using Determinants

    5. Areas and Volumes Using Determinants

    6. Circumscribing a Triangle. Circumcenter

    7. Exercises

　

　

III

Logic

15 Propositional Logic

　

15.1 Compound Statements

    1. Equivalent Statements and Laws of Logic

    2. Truth Tables with VBA. Stmt2TruthTable

    3. Statement from a Truth Table. TruthTable2DisjNormal

    4. Valid Arguments

    5. Exercises

    1. Switching Circuits

    1. Introduction

    2. Series and Parallel Circuits

    3. Equivalent Circuits

    4. Circuit Expressions With VBA. SwitchCircuitExpr

    5. Exercises

  1. Gates and Logic Circuits

    1. The Gates NOT, AND, OR

    2. The Gates XOR, NAND, NOR

    3. Logic Circuit Expressions with VBA. LogicCircuitExpr

    4. Half Adders

    5. VBA Simulation of a Half Adder

    6. Full Adders

    7. VBA Simulation of a 4-bit Adder. FullAdder4

    8. Exercises

    1. Combinatorics

    1. Sets

      1. Introduction

      2. The Union of Two Sets. Union

      3. The Intersection of Two Sets. Intersection, Card

      4. The Complement of a Set. Complement

      5. Extensions to Three or More Sets

      6. Calculating Sets with VBA. SetCalculator

      7. Venn Diagram Components with VBA. VennParts

      8. Laws of Set Equality

      9. Laws of Set Inclusion

      10. Cartesian Products, Relations, and Functions

      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

　

　

    1. Probability

    1. Probability

      1. Sample Spaces, Probabilities, and Events

      2. Throwing a Pair of Fair Dice. DiceRelativFreq

      3. Poker Hands. PokerHands

      4. Drawing Balls from an Urn

      5. Simulation of the Binomial Distribution. GaltonsBoard

      6. Conditional Probability

      7. Bayes’ Theorem

      8. Disease Testing. TruePosTrueNeg

      9. Independence

      10. Exercises

    2. Random Variables

      1. Examples of Random Variables

      2. Expected Value of a Random Variable

      3. Properties of Expectation

      4. Variance and Standard Deviation of a Random Variable

      5. The Law of Large Numbers

        6. Mean Time For Two Heads. MeanTimeForFirstHH

        Bernoulli-Laplace model. BernoulliLaplaceMeanTime

      6. Central Limit Theorem

        7. Write a review

        Please login or register to review