Fascinating World of Mathematics

Contents:

Preface • Acknowledgments

Introduction • What is Mathematics • Origin and Growth of Mathematics • Nature of Mathematics • Interaction with other Subjects • Dread of Mathematics

PART I: CHARM AND BEAUTY IN MATHEMATICS

Chapter 1: Counting and Number System • Introduction • Roman Numerals • Arabic Numerals • Natural Numbers • Cardinal and Oridinal Numbers • Addition and Substraction Operations • Multiplication and Division Operations • Fractions • Exponents • Order of Operations • Number Base • Binary Number System • Decimal Representation of Fractions • Rational and Irrational Numbers • Concept of Infinity • Arithmetic Operations with Zero and Infinity • Imaginary Numbers • Number Field • Some Interesting Paradoxes • Zeno's Paradoxes on Infinity • Mind Teasers

Chapter 2: Beauty in Numbers • Introduction • Surprising Number Patterns • Strange Cancellations • Generating all Natural Numbers from a Given Natural Number • Numbers with Interesting Properties • Special Types of Numbers • Prime Numbers • Factorial Loop • Results Involving Sums of Squares and Cubes • Very Large and Very Small Numbers • Some Well-Known Large Number Problems • Certain Unsolved Problems of Number System • Mind Teasers

Chapter 3: Numerical Computations? Introduction • Speed Computations • Vedic Mathematics • Arithmetic Computations in Vedic Mathematics • Computing Aids • Rapid Advances in Computing Aids • Exercises

Chapter 4: Mathematics & Logical Reasoning • Introduction • Examples of Logical Reasoning • What is Logically Wrong • How is it Possible • Pitfalls of Logic • Mind Teasers

Chapter 5: Algebra • Introduction • Algebraic Equations • Set & Operations on Sets • Sequences and Series • Series • Arithmetic, Geometric and Harmonic Means • Factorial Notation • Permutations • Binomial Theorem • Algebra as tool for solving problems • Pascal Triangle • Pythagorean Triplets • Algebra of the Golden Section • Concept of Limit • Algebraic Entertainments • Fallacies and Paradoxes • When Algebra May Not be so Helpful • Mind Teasers

Chapter 6: Geometry • Introduction • Two Dimensional Plane Geometry • Tracing a Plane Geometrical Figure without Raising Pencil • Seven Bridges Problem • Areas and Perimeters • Use of Algebra in Geometry • Circumference and Area of a Circle • Relating Concentric Circles • Relationship between the Number of Sides and Measures of Internal Angles of a Regular Polygon • Euclid's Plane Geometry • Some Impossible Constructions in Euclidean Geometry • Coordinate Geometry • Three Dimensional Geometry • Geometry on the Surface of a Sphere • A Peculiar Point in Earth's Surface • Celestial Sphere • Higher Dimensional Geometries • Topology • Mind Teasers

Chapter 7: Trigonometry • Introduction • Significance of Triangle • Trigonometric Ratios • Trigonometric Fallacies • Some Practical Applications • Applications in Astronomy • Spherical Trigonometry • Mind Teasers

Chapter 8: Probability and Statistics • Concept of Probability • Repeated trials • Expected returns • Separating Coins into Two Groups • Putting Letters in Right Envelopes • Do Men have More Sisters than Women • Is it a Fair Game • Complaint of a Daughter • To Switch or Not to Switch • Monty Hall Problem • How Much Money a Gambler Wins • Buffon's Needle Problem • Statistics • Statistical Parameters • Juggling with Statistics • Different Voting Schemes • A Child has No Time to Go to School • Effect of View Point • Paradoxes • Mind Teasers

Chapter 9: Calenders, Horoscope & Astrology • Introduction • Necessity of Keeping Record of the Passage of Time • Calenders • Gregorian Calendar • Finding the Day of Week on a Particular Date • Calender Peculiarities • Persons having Same Birthday • Friday the Thirteenth • Other Calendars • Horoscope • Observational Astronomy in India • Astrology • Mind Teasers

Chapter 10: Problem Solving • Introduction • Problem Solving • Problem Solving Techniques • Some Assorted Problems • Mind Teasers  

Chapter 11: Mathematics and Computers • Introduction • Contribution of Mathematics in Development of Computers • Use of Computers in Mathematics • Computer Games • Limitations of Computers • Dangers of lndiscriminate Use of Computers

PART II: MATHEMATICS BASED DIVERSIONS AND RECREATIONS 

Chapter 12: Games and Puzzles • Introduction • Single Person Games • Two Person Games • Puzzles • Mind Teasers  

Chapter 13: Sudoku • Introduction • Origin of Sudoku • How to Solve a Sudoku Puzzle • Level of Difficulty • Variation in the Size of Sudoku Puzzle • Designing a New Sudoku Puzzle • Samurai-Sudoku Puzzles • Mind Teasers

Chapter 14: Arithmetic Based Puzzles • Introduction • Finding Missing Digits in Arithmetic Operations • Mathdoku Puzzles • Alphanumeric Puzzles • Crypto-arithmetic Puzzles • Alphanumeric Equations • Mind Teasers

Chapter 15: Chessboard Related Problems • Introduction • Guarini's Problem • Knight's Tour Problem • Colouring of Chessboard • Open Knight Tour • Generating a Knight's Tour • Tours with Chess Pieces Other than Knight • Covering a Chessboard • Dominance Problem • Independence • Dissection Problem • Mind Teasers

Chapter 16: Magic Squares and Latin Squares • Introduction • Magic Squares • Different Types of Magic Squares • Magic Squares of Higher Order • Constructing a Magic Square • Magic Squares of Even Order and Semi-magic Squares • Latin Squares • Graeco-Latin (Eulerian) Squares • Orthogonal Latin Squares • Practical Applications of Latin Square • Mind Teasers

Hints & Answers

Suggested Collateral Readings

About the Author:

Prof. Chander Mohan obtained his B.A. (Hons.) (in 1957) and M.A. (in 1960) degrees in Mathematics from Punjab University and Ph.D. (in 1967) from Roorkee University. Since 1961 he has been actively engaged in teaching and research. He worked as a lecturer in Mathematics in M.M. Postgraduate college, Modinagar (U.P.) from 1961 to 1964. From 1964 to 2000, he worked as lecturer, reader and professor in Mathematics department at Roorkee University, Roorkee (now IIT Roorkee). He was head of the department from 1995-1999. During this period, he visited England and some European countries in 1973 under exchange of Young Scientists Programme of Commonwealth, and worked on deputation with Baghdad University in Iraq (1976-79). After retirement from Roorkee University in 2000, he worked as professor and dean, Amity School of Computer Science, Noida, till 2002. From 2002 to 2004, he worked as professor and head mathematics in IILM College of Engineering, Greater Noida. Since 2004, he is associated with Ambala College of Engineering and Applied Research, Devasthali, Ambala (Haryana), where he is currently Professor Emeritus in the department of Computer Science and Engineering. Prof. Mohan has guided several Ph.Ds. He has also authored several research papers and books. He is a member of a number of research societies, and his name appears in some of the well-known “Who's Who” of the world. Since childhood Prof. Mohan has a fascination for Mathematics and has been trying to make it appear interesting, exciting and popular, particularly among the young students.