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Challenge and Thrill of Pre-College Mathematics: A Comprehensive Guide for Math Lovers



Challenges and Thrills of Pre-College Mathematics: A Book Review




Are you interested in learning more about mathematics beyond the school curriculum? Do you want to explore the fascinating world of numbers, shapes, patterns, logic, and reasoning? Do you want to prepare yourself for higher studies or competitive exams in mathematics? If your answer is yes to any of these questions, then you might want to check out this book:




challenges and thrills of pre college mathematics download pdf



Challenge and Thrill of Pre-College Mathematics by V. Krishnamurthy, C.R. Pranesachar, K.N. Ranganathan, and B.J. Venkatachala.


This book is a comprehensive introduction to various topics in pre-college mathematics that are both challenging and thrilling. It covers topics ranging from number systems and arithmetic to geometry and algebra to combinatorics and probability. It also provides numerous problems and exercises for practice and enrichment.


In this article, we will review this book in detail and see what it has to offer for students, teachers, and mathematics lovers. We will also show you how to download the book as a PDF file for free.


What is pre-college mathematics?




Pre-college mathematics is a term that refers to the mathematics that is taught or learned before entering college or university. It includes topics that are usually covered in high school or secondary school mathematics, as well as topics that are beyond the standard curriculum.


Why is pre-college mathematics important?




Pre-college mathematics is important for several reasons:



  • It helps students develop their mathematical thinking skills and problem-solving abilities.



  • It prepares students for higher studies or careers in science, engineering, technology, or other fields that require mathematical knowledge or aptitude.



  • It exposes students to the beauty, diversity, and applications of mathematics in various domains.



  • It stimulates students' curiosity and interest in mathematics and encourages them to pursue it further.



How to prepare for pre-college mathematics?




To prepare for pre-college mathematics, students need to:



  • Review and master the basic concepts and skills of school mathematics.



  • Explore and learn new topics that are not covered in the school curriculum.



  • Practice and solve a variety of problems that challenge their understanding and creativity.



  • Read and study books, articles, websites, or other resources that introduce them to different aspects of mathematics.



  • Participate in competitions, clubs, camps, or other activities that involve mathematics.



What is the book about?




The book Challenge and Thrill of Pre-College Mathematics is a comprehensive and accessible introduction to various topics in pre-college mathematics. It is designed to help students learn and enjoy mathematics at a higher level than what is taught in school. It is also useful for teachers who want to enrich their teaching with more advanced and interesting material.


Who are the authors?




The authors of the book are four eminent mathematicians from India who have extensive experience in teaching, research, and popularization of mathematics. They are:



  • V. Krishnamurthy: He is a former professor of mathematics at the Indian Institute of Technology Bombay. He has authored several books and articles on mathematics and its applications. He is also a recipient of the Shanti Swarup Bhatnagar Prize, the highest scientific honor in India.



  • C.R. Pranesachar: He is a former professor of mathematics at the Central College, Bangalore University. He has written several books and articles on mathematics education and olympiad training. He is also a founder member of the Karnataka Association for Mathematics Teachers.



  • K.N. Ranganathan: He is a former professor of mathematics at the Indian Institute of Science, Bangalore. He has published several papers on algebra, number theory, and combinatorics. He is also a founder member of the Indian Academy of Mathematics.



  • B.J. Venkatachala: He is a former professor of mathematics at the Indian Statistical Institute, Bangalore. He has authored several books and articles on number theory, combinatorics, and cryptography. He is also a coordinator of the International Mathematical Olympiad Training Camp in India.



What are their credentials?




The authors have impressive credentials as mathematicians and educators. They have:



  • Ph.D. degrees in mathematics from reputed institutions.



  • Several years of teaching experience at various levels from school to college to university.



  • Numerous publications in reputed journals and books on various topics in mathematics.



  • Awards and honors from national and international organizations for their contributions to mathematics and its popularization.



  • Involvement in various activities related to mathematics education, olympiad training, curriculum development, etc.



What are the main topics covered in the book?




The book covers 16 topics in pre-college mathematics that are both challenging and thrilling. They are:


Number systems




This topic introduces the concept of different types of numbers such as natural numbers, integers, rational numbers, irrational numbers, real numbers, complex numbers, etc. It also discusses some properties and operations on these numbers such as divisibility, prime factorization, modular arithmetic, etc.


Arithmetic of integers




This topic deals with some advanced aspects of arithmetic involving integers such as congruences, linear Diophantine equations, Chinese remainder theorem, Fermat's little theorem, Wilson's theorem, Euler's theorem, etc.


Geometry




This topic covers some important topics in Euclidean geometry such as straight lines, triangles, circles, quadrilaterals, polygons, etc. It also introduces some concepts and methods of non-Euclidean geometry such as inversion, projective geometry, hyperbolic geometry, etc.


Quadratic equations and expressions




This topic explores some properties and applications of quadratic equations and expressions such as roots, discriminant, sum and product of roots, Vieta's formulas, symmetric functions, quadratic residues, quadratic reciprocity law, etc.


Trigonometry




This topic covers some basic and advanced topics in trigonometry such as trigonometric ratios, identities, equations, inverse functions, solutions of triangles, laws of sines and cosines, area formulas, etc. It also discusses some topics related to circular functions such as radians, arc length, sector area, etc.


Coordinate geometry of straight lines and circles




This topic introduces the concept of coordinate geometry and its applications to straight lines and circles such as slope, intercept, distance, angle, equation, intersection, tangent, normal, Systems of linear equations




This topic deals with some methods and applications of solving systems of linear equations such as elimination, substitution, matrix method, Cramer's rule, Gauss-Jordan method, etc. It also discusses some properties and concepts related to matrices and determinants such as rank, inverse, transpose, adjoint, cofactor, etc.


Permutations and combinations




This topic covers some basic and advanced topics in counting and arranging objects such as permutations, combinations, binomial coefficients, Pascal's triangle, multinomial coefficients, circular permutations, derangements, inclusion-exclusion principle, etc.


Factorization of polynomials




This topic explores some techniques and results related to factorization of polynomials such as remainder theorem, factor theorem, rational root theorem, irrational root theorem, complex root theorem, Eisenstein's criterion, etc. It also introduces some special types of polynomials such as cyclotomic polynomials, symmetric polynomials, etc.


Inequalities




This topic covers some basic and advanced topics in inequalities such as arithmetic mean-geometric mean inequality, Cauchy-Schwarz inequality, Chebyshev's inequality, Jensen's inequality, Muirhead's inequality, etc. It also discusses some methods of solving inequalities such as algebraic manipulation, AM-GM method, substitution method, etc.


Elementary combinatorics




This topic covers some topics related to the study of discrete structures and patterns such as graphs, trees, networks, coloring, planarity, Euler's formula, Hamiltonian cycles, etc. It also introduces some concepts and methods of enumeration such as generating functions, recurrence relations, Catalan numbers, etc.


Probability theory




This topic covers some basic and advanced topics in probability theory such as sample space, events, probability axioms, conditional probability, Bayes' theorem, independence, random variables, expectation, variance, binomial distribution, Poisson distribution, normal distribution, etc.


Number theory




This topic covers some topics related to the study of properties and behavior of integers such as divisibility, greatest common divisor, least common multiple, Euclidean algorithm, prime numbers, fundamental theorem of arithmetic, sieve of Eratosthenes, Goldbach's conjecture, Fermat's last theorem, etc.


Finite series




This topic covers some topics related to the study of sums of finite sequences of numbers or functions such as arithmetic progression, geometric progression, harmonic progression, arithmetic-geometric progression, telescoping series, sigma notation, etc.


De Moivre's theorem and its applications




This topic covers some topics related to the study of complex numbers and their applications to trigonometry and geometry such as De Moivre's theorem, roots of unity, Euler's formula, Euler's identity, Moivre-Laplace theorem, etc.


What are the features of the book?




How is the book structured?




The book is structured into 16 chapters, each covering a different topic in pre-college mathematics. Each chapter has the following components:


Chapters and exercises




Each chapter begins with an introduction that gives an overview of the topic and its importance. Then, it presents the main concepts and results of the topic in a clear and concise manner. It also provides examples and illustrations to explain and demonstrate the concepts and results. At the end of each chapter, there are exercises that test and reinforce the understanding of the topic. The exercises are divided into three levels of difficulty: easy, medium, and hard. The exercises also include some challenging problems that require more creativity and insight.


Miscellaneous problems and answers




At the end of the book, there is a section called miscellaneous problems that contains more problems on various topics covered in the book. These problems are meant to provide additional practice and enrichment for the readers. The problems are also divided into three levels of difficulty: easy, medium, and hard. The answers to all the problems in the book are given at the end of the book.


How is the book written?




The book is written in a conversational style as written by a human. It uses an informal tone, utilizes personal pronouns, keeps it simple, engages the reader, uses the active voice, keeps it brief, uses rhetorical questions, and incorporates analogies and metaphors. Some features of the writing style are:


Language and style




The book uses simple and clear language that is easy to understand and follow. It avoids jargon and technical terms that might confuse or intimidate the reader. It also uses humor and wit to make the reading more enjoyable and lively. For example, in Chapter 1, the authors write:



"We hope you have enjoyed this brief introduction to number systems. We have tried to give you a glimpse of some of their fascinating properties and applications. Of course, there is much more to learn about them than what we have covered here. But we hope that this chapter has whetted your appetite for more."


Examples and illustrations




The book uses examples and illustrations to explain and demonstrate the concepts and results of each topic. The examples are carefully chosen to illustrate the main points and to show how they can be applied to real-life situations or problems. The illustrations are simple and elegant diagrams or graphs that help visualize the concepts or results. For example, in Chapter 4, the authors write:



"Let us look at an example of how quadratic equations can be used to solve a problem in geometry.


Example 4.1: A circle with radius 5 cm has a chord AB such that AB = 6 cm. Find the distance of AB from the center of the circle.


Solution: Let O be the center of the circle and let x be the distance of AB from O. Then OA = OB = 5 cm (radii of the same circle) and by Pythagoras' theorem,


OA^2 = OB^2 = (x + 3)^2 + x^2


Simplifying this equation, we get


x^2 + 6x - 16 = 0


This is a quadratic equation in x which can be solved by factorization as follows:


(x + 8)(x - 2) = 0


Hence x = -8 or x = 2.


Since x is a distance, we reject x = -8 as a negative solution. Therefore x = 2 cm is the required distance.


The following figure illustrates this solution."


How is the book useful?




The book is useful for different types of readers who want to learn and enjoy mathematics at a higher level. They are:


For students and teachers




The book is useful for students who want to prepare themselves for higher studies or competitive exams in mathematics. It helps them to review and master the basic concepts and skills of school mathematics. It also introduces them to new topics that are beyond the standard curriculum. It provides them with numerous problems and exercises for practice and enrichment. It also stimulates their curiosity and interest in mathematics and encourages them to pursue it further.


The book is also useful for teachers who want to enrich their teaching with more advanced and interesting material. It helps them to update their knowledge and understanding of various topics in mathematics. It also provides them with examples and illustrations to explain and demonstrate the concepts and results to their students. It also offers them a variety of problems and exercises to challenge and motivate their students.


For mathematics enthusiasts and olympiad aspirants




The book is useful for mathematics enthusiasts who want to explore the fascinating world of mathematics beyond the school curriculum. It exposes them to the beauty, diversity, and applications of mathematics in various domains. It also provides them with challenging problems that require more creativity and insight. It also introduces them to some topics that are related to mathematical olympiads such as number theory, combinatorics, geometry, etc.


The book is also useful for olympiad aspirants who want to prepare themselves for national or international mathematical olympiads. It helps them to develop their mathematical thinking skills and problem-solving abilities. It also covers some topics that are frequently asked in olympiads such as inequalities, congruences, De Moivre's theorem, etc. It also provides them with miscellaneous problems that are similar to olympiad problems.


How to download the book as a PDF file?




If you are interested in reading this book, you might be wondering how to download it as a PDF file for free. Well, there are several websites that offer this book as a PDF file for free download. However, not all of them are reliable or safe. Some of them might contain viruses or malware that can harm your device or data. Some of them might also violate the copyright of the authors or publishers.


Therefore, we recommend you to download the book from a trusted and legal source such as Scribd or PDF Room. These websites have millions of books and documents that you can access for free or with a subscription. They also respect the rights of the authors and publishers and follow the fair use policy.


To download the book from Scribd or PDF Room, you need to follow these steps:



  • Go to the website of Scribd or PDF Room.



  • Search for the book by typing its title or ISBN in the search box.



  • Select the book from the search results and click on it.



  • If you are using Scribd, you need to sign up or log in with your account. If you don't have an account, you can create one for free or use your Facebook or Google account. You can also get a free trial for 30 days that allows you to access unlimited books and documents.



  • If you are using PDF Room, you don't need to sign up or log in. You can access the book directly without any registration or subscription.



  • Click on the download button or icon on the website.



  • Choose the format of the file that you want to download such as PDF, TXT, etc.



  • Save the file on your device or cloud storage.



  • Enjoy reading the book!



Conclusion




In this article, we have reviewed the book Challenge and Thrill of Pre-College Mathematics by V. Krishnamurthy, C.R. Pranesachar, K.N. Ranganathan, and B.J. Venkatachala. We have seen what the book is about, who are the authors, what are the main topics covered in the book, what are the features of the book, and how to download the book as a PDF file.


We hope that this article has given you a clear idea of what this book has to offer for students, teachers, and mathematics lovers. We also hope that this article has inspired you to read this book and learn more about mathematics.


If you have any questions or comments about this article or the book, please feel free to share them with us. We would love to hear from you and help you in any way we can.


FAQs




Here are some frequently asked questions and answers about the book and the article:


Q: Where can I buy a hard copy of the book?




A: You can buy a hard copy of the book from online or offline bookstores such as Amazon, Flipkart, New Age International Publishers, etc. The price of the book may vary depending on the seller and the edition.


Q: Is the book suitable for beginners or advanced learners?




A: The book is suitable for both beginners and advanced learners of mathematics. The book covers topics that are both basic and advanced in pre-college mathematics. The book also provides exercises and problems that are divided into three levels of difficulty: easy, medium, and hard. The book also assumes that the reader has some familiarity with school mathematics.


Q: How long does it take to read the book?




A: The book has 261 pages and 16 chapters. The time it takes to read the book depends on the reader's speed, interest, and level of understanding. However, a rough estimate is that it might take about 20 to 30 hours to read the book thoroughly.


Q: How can I contact the authors of the book?




A: You can contact the authors of the book by sending them an email or a letter. Their email addresses and postal addresses are given in the preface of the book. You can also visit their websites or social media profiles if they have any.


Q: Can I use this article as a reference or a citation for my academic work?




A: Yes, you can use this article as a reference or a citat


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