Books


Finally the page is (mostly) complete. :-)


In this page we’ll recommend you some books for Math Olympiad preparation, with book reviews and rating. As our main audience is the Bangladeshi students, we’ll try to write the comments in Bangla.

Problem solving books and books on different subject areas are listed separately, because before someone starts solving hard problems, they should consider reading at least one text book on each topic to LEARN math, as learning is the most important thing at the end of the day.


Before You Start:

Choosing the Correct Book: 

Before you start reading a book, you should judge your own level and you can search that book in Amazon. Most of the times you’ll find the product description and user comments to be helpful. We have reviewed the books on four criterions:

 

First, Difficulty: Though it is hard to judge the difficulty, as it mostly depends on personal choice, we have marked each book on a scale of 5. 1-2 means they are relatively easy, and in the reach of the beginners, 2-3 for the students who are already acquainted with Math Olympiads (probably the regional Math Olympiad winners), and 4-5 is the threshold for the advanced learners. We’ll advise the beginners to start from the easier books, and go to the advanced books after they have mastered the basics.

Then, the contents: Most of the books has excellent contents. However, in some cases they are not really written for high school students, and sometimes the problem choices are not as good as we expect. So, this rating is basically on the conciseness and the quality of the contents.

Type: This is mainly to differ the problem books from the texts. The following are the meaning of the codes.

a.      Problem book  

b.      Good balance between theory and problems

c.      Theoretical (Text book)

Problem Quality: This rating is mainly for the problem books. Most of the text might receive a low score, as they don’t usually contain hard or very interesting problems.


"বই কোথায় পাওয়া যায়?":

বইয়ের হার্ডকপির জন্য FAQ এর ৭ম প্রশ্নের উত্তর দেখুন

বই ডাউনলোড করতে চাইলে নিচের জিপ ফাইলটি দেখুন (লিস্ট.রার)। এর ভেতর একটি টেক্সট ফাইলে সব লিঙ্ক আছে। জিপ ফাইলের পাসওয়ার্ড: কেএমসিবিডি.ওআরজি (ইংরেজীতে ছোট হাতের অক্ষরে লিখতে হবে); আনজিপ করার সফটওয়্যার না থাকলে এখান থেকে ডাউনলোড করুন কোন ফাইল খুলতে সমস্যা হলে টেকস্ট ফাইলের ভেতরের নির্দেশিকা দেখুন।



The Book list:


Books for learning Problem solving:

Though problem solving can only be learnt through solving problems, here we enlist some books that will be useful for the students to hone their  problem solving skill.


  The Art and Craft of Problem Solving ***

Author:  Paul Zeitz

মন্তব্য:

 

Review:

1.      Difficulty: 2/5

2.      Content: 5/5

3.      Type: b

4.      Problem quality: 5/5

Amazon Description: The newly revised Second Edtion of this distinctive text uniquely blends interesting problems with strategies, tools, and techniques to develop mathematical skill and intuition necessary for problem solving. Readers are encouraged to do math rather than just study it. The author draws upon his experience as a coach for the International Mathematics Olympiad to give students an enhanced sense of mathematics and the ability to investigate and solve problems.


Mathematical Olympiad Challenges

Author:  Titu Andreescu, Razvan Gelca

মন্তব্য:

 

Review:

1.      Difficulty: 3/5

2.      Content: 4/5

3.      Type: a

4.      Problem quality: 4/5

Amazon Description: This significantly revised and expanded second edition of "Mathematical Olympiad Challenges" is a rich collection of problems put together by two experienced and well-known professors and coaches of the U.S. International Mathematical Olympiad Team. Hundreds of beautiful, challenging, and instructive problems from algebra, geometry, trigonometry, combinatorics, and number theory from numerous mathematical competitions and journals have been selected and updated. The problems are clustered by topic into self-contained sections with solutions provided separately. Historical insights and asides are presented to stimulate further inquiry. The emphasis throughout is on creative solutions to open-ended problems.With many new or expanded examples, problems, and solutions, this second edition includes completely rewritten discussions preceding each of the 30 units, as well as a more user-friendly style with more accessible and inviting examples. Featuring enhanced motivation for advanced high school and beginning college students, as well as instructors and Olympiad coaches, this text can be used for creative problem-solving courses, for professional teacher development seminars and workshops, for self-study, or as a resource for training for mathematical competitions.


Mathematical Olympiad Treasures

লেখক: Titu Andreescu, Bogdan Enescu,

মন্তব্য:

 

Review:

1.      Difficulty: 2/5

2.      Content: 3/5

3.      Type: a

4.      Problem quality: 3/5

Amazon Description: Mathematical Olympiad Treasures contains a stimulating collection of problems in geometry and trigonometry, algebra, number theory, and combinatorics. It encourages readers to think creatively about techniques and strategies for problem solving in the real world.

The problems are clustered by topic into self-contained chapters. The book begins with elementary facts, followed by carefully selected problems and detailed, step-by-step solutions, which then lead to more complicated, challenging problems and their solutions. Reflecting the experience of two professors and coaches of Mathematical Olympiads, the text will be valuable to teachers, students, and puzzle enthusiasts.


Problem-Solving Strategies (Problem Books in Mathematics)

লেখক: Arthur Engel

মন্তব্য:

 

Review:

1.      Difficulty: 3/5

2.      Content: 5/5

3.      Type: a

4.      Problem quality: 5/5

Amazon Description: PROBLEM SOLVING STRATEGIES is a unique collection of competition problems from over twenty major national and international mathematical competitions for high school students. The discussion of problem solving strategies is extensive. It is written for trainers and participants of contests of all levels up to the highest level: IMO, Tournament of the Towns, and the noncalculus parts of the Putnam Competition. It will appeal to high school teachers conducting a mathematics club who need a range of simple to complex problems and to those instructors wishing to pose a "problem of the week", "problem of the month", and "research problem of the year" to their students, thus bringing a creative atmosphere into their classrooms with continuous discussions of mathematical problems. This volume is a must-have for instructors wishing to enrich their teaching with some interesting non-routine problems and for individuals who are just interested in solving difficult and challenging problems. Each chapter starts with typical examples illustrating the central concepts and is followed by a number of carefully selected problems and their solutions. Most of the solutions are complete, but some merely point to the road leading to the final solution. Very few problems have no solutions. Readers interested in increasing the effectiveness of the book can do so by working on the examples in addition to the problems thereby increasing the number of problems to over 1300. In addition to being a valuable resource of mathematical problems and solution strategies, this volume is the most complete training book on the market.


Putnam and Beyond

লেখক: Razvan Gelca, Titu Andreescu

মন্তব্য:

 

Review:

1.      Difficulty: 4/5

2.      Content: 4/5

3.      Type: b

4.      Problem quality: 4/5

Amazon Description: Putnam and Beyond takes the reader on a journey through the world of college mathematics, focusing on some of the most important concepts and results in the theories of polynomials, linear algebra, real analysis in one and several variables, differential equations, coordinate geometry, trigonometry, elementary number theory, combinatorics, and probability. Using the W.L. Putnam Mathematical Competition for undergraduates as an inspiring symbol to build an appropriate math background for graduate studies in pure or applied mathematics, the reader is eased into transitioning from problem-solving at the high school level to the university and beyond, that is, to mathematical research.

Key features of Putnam and Beyond:

* Preliminary material provides an overview of common methods of proof: argument by contradiction, mathematical induction, pigeonhole principle, ordered sets, and invariants.

* Each chapter systematically presents a single subject within which problems are clustered in every section according to the specific topic.

* The exposition is driven by more than 1100 problems and examples chosen from numerous sources from around the world; many original contributions come from the authors.

* Complete solutions to all problems are given at the end of the book. The source, author, and historical background are cited whenever possible.

This work may be used as a study guide for the Putnam exam, as a text for many different problem-solving courses, and as a source of problems for standard courses in undergraduate mathematics. Putnam and Beyond is organized for self-study by undergraduate and graduate students, as well as teachers and researchers in the physical sciences who wish to to expand their mathematical horizons.


Problem Books:

These books mainly contain problem; and yes, a lot of problems. I hope that you'll have a great time solving them!


Five Hundred Mathematical Challenges

লেখক: Edward J. Barbeau, Murray S. Klamkin, William O. J. Moser

মন্তব্য:

 

Review:

1.      Difficulty: 1/5

2.      Content: 4/5

3.      Type: a

4.      Problem quality: 4/5

Amazon Description:
This book contains 500 problems that range over a wide spectrum of mathematics and of levels of difficulty. Some are simple mathematical puzzlers while others are serious problems at the Olympiad level. Students of all levels of interest and ability will be entertained by the book. For many problems, more than one solution is supplied so that students can compare the elegance and efficiency of different mathematical approaches. A special mathematical toolchest summarizes the results and techniques needed by competition-level students. Teachers will find the book useful, both for encouraging their students and for their own pleasure. Some of the problems can be used to provide a little spice in the regular curriculum by demonstrating the power of very basic techniques. The problems were first published as a series of problem booklets almost twenty years ago. They have stood the test of time and the demand for them has been steady. Their publication in book form is long overdue.


Junior Problem Seminar

লেখক: David A. Santos

মন্তব্য:

 

Freely available at: www.openmathtext.org/lecture_notes/junior_problem_seminar.pdf

Review:

1.      Difficulty: 2/5

2.      Content: 2/5

3.      Type: a

4.      Problem quality: 3/5

Description:  Problem solving seminar for high-school students, with answers, hints and solutions. This is a good book for beginners. A few of the topics covered are; the pigeonhole principle, parity, identities with squares and cubes, logarithms, complex numbers, the well-ordering principle, induction, inclusion-exclusion, Viéte's formulae and the rearrangement inequality.


Junior Balkan Mathematical Olympiads

লেখক: Dan Branzei, loan Serdean, Vasile Serdean  

মন্তব্য:

 

Review:

1.      Difficulty: 2/5

2.      Content: 4/5

3.      Type: a

4.      Problem quality: 4/5

Amazon Description: This book is intended to help students preparing to participate in mathematical Olympiads for juniors. An international competition for students up to 15 and 1/2 years is hosted annually in one of the Balkan countries since 1997. In the first chapter are presented the problems from this six Olympiads. Each Olympiad test consists in four problems, which are to be done in four hours. The book presents the tests used to select the Romanian team for the Junior Balkan Mathematical Olympiad. In addition, short-listed problems submitted to the Jury of JBMO, together with 20 training tests completes the content. Full solutions are provided for each of the 211 problems. It is our believe that students, teachers and all those who are mathematically incline will enjoy working these intriguing and challenging problems.


Problem Primer for the Olympiad, 2nd edition

লেখক: C. R. Pranesachar, B. J. Venkatachala, C. S. Yogananda

মন্তব্য:

 

Review:

1.      Difficulty: 2/5

2.      Content: 4/5

3.      Type: a

4.      Problem quality: 5/5

Description: The problems appearing in the Indian National Mathematical Olympaid (INMO) and the Regional Mathematical Olympias ( RMO) papers are of a very different nature from the problems students encounter in their school curriculum. This book is designed to help the students prepare for the INMO & RMO The problems have been classified into various sections- Number Theory, Algebra Geometry, Combinatorics and Miscellaneous problems. There is also a section containing important theorems and results from various topics generally not available in school text books, but which are of great help in solving the problems.


The IMO Compendium: A Collection of Problems Suggested for The International Mathematical Olympiads: 1959-2004

Author:  Dusan Djukic , Vladimir Jankovic , Ivan Matic, Nikola Petrovic

মন্তব্য:

 

Review:

1.      Difficulty: 5+/5

2.      Content: 5/5

3.      Type: a

4.      Problem quality: 5/5

Amazon Description: The International Mathematical Olympiad (IMO) has within its almost 50-year-old history become the most popular and prestigious competition for high-school students interested in mathematics. Only six students from each participating country are given the honor of participating in this competition every year. The IMO represents not only a great opportunity to tackle interesting and challenging mathematics problems, it also offers a way for high school students to measure up with students from the rest of the world. The IMO has sparked off a burst of creativity among enthusiasts in creating new and interesting mathematics problems. In an extremely stiff competition, only six problems are chosen each year to appear on the IMO. The total number of problems proposed for the IMOs up to this point is staggering and, as a whole, this collection of problems represents a valuable resource for all high school students preparing for the IMO. Until now it has been almost impossible to obtain a complete collection of the problems proposed at the IMO in book form. "The IMO Compendium" is the result of a two year long collaboration between four former IMO participants from Yugoslavia, now Serbia and Montenegro, to rescue these problems from old and scattered manuscripts, and produce the ultimate source of IMO practice problems. This book attempts to gather all the problems and solutions appearing on the IMO, as well as the so-called "short-lists", a total of 864 problems. In addition, the book contains 1036 problems from various "long-lists" over the years, for a grand total of 1900 problems. In short, "The IMO Compendium" is the ultimate collection of challenging high-school-level mathematics problems. It will be an invaluable resource, not only for high-school students preparing for mathematics competitions, but for anyone who loves and appreciates math.


Geometry:

Geometry Revisited

লেখক: H. S. M. Coxeter Samuel L. Greitzer

মন্তব্য:

 

Review:

1.      Difficulty: 2/5

2.      Content: 5/5

3.      Type: c

4.      Problem quality: 2/5

Amazon Description: Among the many beautiful and nontrivial theorems in geometry found in Geometry Revisited are the theorems of Ceva, Menelaus, Pappus, Desargues, Pascal, and Brianchon. A nice proof is given of Morley's remarkable theorem on angle trisectors. The transformational point of view is emphasized: reflections, rotations, translations, similarities, inversions, and affine and projective transformations. Many fascinating properties of circles, triangles, quadrilaterals, and conics are developed.


Plane Euclidean Geometry: Theory and Problems ***

লেখক: A.D. Gardiner C.J. Bradley

মন্তব্য: The best book for beginners and mid level Olympiad geometers. (Highly recommended)

 

Review:

1.      Difficulty: 2/5

2.      Content: 5/5

3.      Type: b

4.      Problem quality: 5/5


Amazon Description:
This geometry text offers beginning and advanced geometric problem solving tactics, as well as numerous practice problems. The book is most appropriate for experienced geometers who are learning how to take on more challenging geometry problems, such as those offered at the high school olympiad level.


103 Trigonometry Problems: From the Training of the USA IMO Team

লেখক: Titu Andreescu, Zuming Feng 

মন্তব্য:

 

Review:

1.      Difficulty: 2-4/5

2.      Content: 4/5

3.      Type: b

4.      Problem quality: 5/5


Amazon Description:
103 Trigonometry Problems contains highly-selected problems and solutions used in the training and testing of the USA International Mathematical Olympiad (IMO) team. Though many problems may initially appear impenetrable to the novice, most can be solved using only elementary high school mathematics techniques.

Key features:

  • Gradual progression in problem difficulty builds and strengthens mathematical skills and techniques
  • Basic topics include trigonometric formulas and identities, their applications in the geometry of the triangle, trigonometric equations and inequalities, and substitutions involving trigonometric functions
  • Problem-solving tactics and strategies, along with practical test-taking techniques, provide in-depth enrichment and preparation for possible participation in various mathematical competitions
  • Comprehensive introduction (first chapter) to trigonometric functions, their relations and functional properties, and their applications in the Euclidean plane and solid geometry expose advanced students to college level material
  • 103 Trigonometry Problems is a cogent problem-solving resource for advanced high school students, undergraduates, and mathematics teachers engaged in competition training.

Geometry Unbound

লেখক: Kiran S. Kedlaya

মন্তব্য:

 

Review:

1.      Difficulty: 3/5

2.      Content: 5/5

3.      Type: b

4.      Problem quality: 5/5

Description: The original text underlying this book was a set of notes I compiled, originally as a participant and later as an instructor, for the Math Olympiad Program (MOP), the annual summer program to prepare U.S. high school students for the International Mathematical Olympiad (IMO). Given the overt mission of the MOP, the notes as originally compiled were intended to bridge the gap between the knowledge of Euclidean geometry of American IMO prospects and that of their counterparts from other countries. To that end, they included a large number of challenging problems culled from Olympiad-level competitions from around the world. However, the resulting book you are now reading shares with the MOP a second mission, which is more covert and even a bit subversive. In revising it, I have attempted to usher the reader from the comfortable world of Euclidean geometry to the gates of “geometry” as the term is defined (in multiple ways) by modern mathematicians, using the solving of routine and nonroutine problems as the vehicle for discovery. In particular, I have aimed to deliver something more than “just another problems book”.


Episodes in Nineteenth and Twentieth Century Euclidean Geometry

লেখক: Ross Honsberger

মন্তব্য:

 

Review:

1.      Difficulty: 3/5

2.      Content: 5/5

3.      Type: b

4.      Problem quality: 5/5

Amazon Description: Professor Honsberger has succeeded in 'finding' and 'extricating' unexpected and little known properties of such fundamental figures as triangles, results that deserve to be better known. He has laid the foundations for his proofs with almost entirely synthetic methods easily accessible to students of Euclidean geometry early on. While in most of his other books Honsberger presents each of his gems, morsels, and plums, as self contained tidbits, in this volume he connects chapters with some deductive treads. He includes exercises and gives their solutions at the end of the book. In addition to appealing to lovers of synthetic geometry, this book will stimulate also those who, in this era of revitalizing geometry, will want to try their hands at deriving the results by analytic methods. Many of the incidence properties call to mind the duality principle; other results tempt the reader to prove them by vector methods, or by projective transformations, or complex numbers.

Problems in plane geometry

লেখক: Victor Prasolov, translated and edited by Dimitry Leites

মন্তব্য:

 

Review:

1.      Difficulty: 1-3/5

2.      Content: 5/5

3.      Type: b

4.      Problem quality: 5/5

Description: This is an excellent problem book for beginner to mid level geometers. You shall get an excellent collection of more than 1500 problems. Part 1 covers classical subjects of plane geometry. It contains nearly 1000 problems with complete solutions and over 100 problems to be solved on one’s own. Still more will be added for the English version of the book. Part 2 includes more recent topics, geometric transformations and problems more suitable for contests and for use in mathematical clubs. The problems cover cuttings, colorings, the pigeonhole (or Dirichlet’s) principle, induction, and so on.


College Geometry: An Introduction to the Modern Geometry of the Triangle and the Circle

লেখক: Nathan Altshiller-Court

মন্তব্য:

 

Review:

1.      Difficulty: 5/5

2.      Content: 5/5

3.      Type: b, c

4.      Problem quality: 5/5

Amazon Description: This is one of the two English books in print that give a fairly complete introduction to advanced Euclidean geometry, the other one being the comparable text by R A Johnson, Advanced Euclidean Geometry (Dover Books on Mathematics). The book contains all the classical theorems with full proofs, including many theorems that belong to the so called triangle geometry that was developed in the last quarter of the nineteenth century. Due to geometry software the subject is becoming popular again. The book also contains a treasure of exercises, but no solutions which could be a nuisance. But what use are the solutions? Problems should be solved and not looked up!. Many problems are about geometric constructions. If you prepare for a mathematical contest or if you are interested in a complete overview of the classical plane geometry (for instance after reading Ross Honsberger's "Episodes"), this is your book.


Geometric Transformations I

লেখক: I. M. Yaglom

মন্তব্য:

 

Review:

1.      Difficulty: 4/5

2.      Content: 5/5

3.      Type: b, c

4.      Problem quality: 4/5

Amazon Description: Almost everyoneis acquainted with plane Euclidean geometry as it is usually taught in high school. This book introduces the reader to a completely different way of looking at familiar geometrical facts. It is concerned with transformations of the plane that do not alter the shapes and sizes of geometric figures. Such transformations play a fundamental role in the group theoretic approach to geometry.

The treatment is direct and simple. The reader is introduced to new ideas and then is urged to solve problems using these ideas. The problems form an essential part of this book and the solutions are given in detail in the second half of the book.

 

Geometric Transformations II

লেখক: I. M. Yaglom

মন্তব্য:

 

Review:

1.      Difficulty: 4/5

2.      Content: 5/5

3.      Type: b, c

4.      Problem quality: 4/5


Amazon Description: This book is the sequel to Geometric Transformations I which appeared in this series in 1962. Part I treas length-preserving transformations, this volume treats shape-preserving transformations; and Part III treats affine and protective transformations. These classes of transformations play a fundamental role in the group-theoretic approach to geometry.


Number Theory:

Theory of Numbers: A Text and Source Book of Problems 

Author: Andrew Adler and John E. Cloury

মন্তব্য:

 

Review:

1.      Difficulty: 2/5

2.      Content: 5/5

3.      Type: b, c

4.      Problem quality: 5/5

Amazon Decsription: This text presents the principal ideas of classical number theory emphasizing the historical development of these results and the important figures who worked on them. It is intended to introduce third or fourth-year undergraduates to mathematical proofs by presenting them in a clear and simple way and by providing complete, step-by-step solutions to the problems with as much detail as students would be expected to provide themselves. This is the only book in number theory that provides detailed solutions to 800 problems, with complete references to the results used so that the student can follow each step of the argument.


Elementary Number Theory

Author: David M. Burton 

মন্তব্য:

 

Review:

1.      Difficulty: 2/5

2.      Content: 4/5

3.      Type: c

4.      Problem quality: 2/5

Amazon Description: Elementary Number Theory is designed for the one-semester junior- or senior-level number theory course usually taken by mathematics majors who plan to teach mathematics in high school or college. In this new edition all numerical information has been updated and recent developments in number theory are indicated where appropriate. --This text refers to an out of print or unavailable edition of this title.


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An Introduction to Diophantine Equations: A Problem-Based Approach

Author: Titu Andreescu, Dorin Andrica, and Ion Cucurezeanu

মন্তব্য:

 

Review:

1.      Difficulty: 3/5

2.      Content: 5/5

3.      Type: b

4.      Problem quality: 5/5

Amazon Description: This problem-solving book is an introduction to the study of Diophantine equations, a class of equations in which only integer solutions are allowed. The presentation features some classical Diophantine equations, including linear, Pythagorean, and some higher degree equations, as well as exponential Diophantine equations. Many of the selected exercises and problems are original or are presented with original solutions. An Introduction to Diophantine Equations: A Problem-Based Approach is intended for undergraduates, advanced high school students and teachers, mathematical contest participants — including Olympiad and Putnam competitors — as well as readers interested in essential mathematics. The work uniquely presents unconventional and non-routine examples, ideas, and techniques.



Combinatorics:

Principles and Techniques in Combinatorics

লেখক: Chen Chuan-Chong and Koh Khee-Meng

মন্তব্য:

 

Review:

1.      Difficulty: 2/5

2.      Content: 5/5

3.      Type: b

4.      Problem quality: 4/5

Amazon Description: "This book should be a must for all mathematicians who are involved in the training of Mathematical Olympiad teams, but it will also be a valuable source of problems for university courses." Mathematical Reviews

A textbook suitable for undergraduate courses, the materials in this book are presented very explicitly so that students will find it easy to read and also find a wide range of examples. A number of combinatorial problems taken from mathematical competitions and exercises are also included.


Combinatorics: A Problem Oriented Approach

লেখক: Daniel A. Marcus

মন্তব্য:

 

Review:

1.      Difficulty: 2/5

2.      Content: 3/5

3.      Type: a, b

4.      Problem quality: 3/5

Amazon Description: The format of this book is unique in that it combines features of a traditional text with those of a problem book. The material is presented through a series of problems, about 250 in all, with connecting text; this is supplemented by a further 250 problems suitable for homework assignment. The problems are structured in order to introduce concepts in a logical order, and in a thought-provoking way. The first four sections of the book deal with basic combinatorial entities; the last four cover special counting methods. Many applications to probability are included along the way. Students from a wide range of backgrounds, mathematics, computer science or engineering will appreciate this appealing introduction.


A Path to Combinatorics for Undergraduates: Counting Strategies

লেখক: Titu Andreescu and Zuming Feng

মন্তব্য:

 

Review:

1.      Difficulty: 4-5/5

2.      Content: 5/5

3.      Type: a, b

4.      Problem quality: 5/5

Amazon Description: This unique approach to combinatorics is centered around challenging examples, fully-worked solutions, and hundreds of problems---many from Olympiads and other competitions, and many original to the authors. Each chapter highlights a particular aspect of the subject and casts combinatorial concepts in the guise of questions, illustrations, and exercises that are designed to encourage creativity, improve problem-solving techniques, and widen the reader's mathematical horizons.

Topics encompass permutations and combinations, binomial coefficients and their applications, recursion, bijections, inclusions and exclusions, and generating functions. The work is replete with a broad range of useful methods and results, such as Sperner's Theorem, Catalan paths, integer partitions and Young's diagrams, and Lucas' and Kummer's Theorems on divisibility. Strong emphasis is placed on connections between combinatorial and graph-theoretic reasoning and on links between algebra and geometry.

The authors' previous text, 102 Combinatorial Problems, makes a fine companion volume to the present work, which is ideal for Olympiad participants and coaches, advanced high school students, undergraduates, and college instructors. The book's unusual problems and examples will stimulate seasoned mathematicians as well. A Path to Combinatorics for Undergraduates is a lively introduction not only to combinatorics, but to mathematical ingenuity, rigor, and the joy of solving puzzles.


102 Combinatorial Problems

লেখক: Titu Andreescu and Zuming Feng

মন্তব্য:

 

Review:

1.      Difficulty: 3-5/5

2.      Content: 4/5

3.      Type: a

4.      Problem quality: 5/5

Amazon Description: "Combinatorial Problems" consists of 102 carefully selected problems that have been used in the training and testing of the USA International Mathematical Olympiad (IMO) team.

Key features: * Provides in-depth enrichment in the important areas of combinatorics by reorganizing and enhancing problem-solving tactics and strategies * Topics include: combinatorial arguments and identities, generating functions, graph theory, recursive relations, sums and products, probability, number theory, polynomials, theory of equations, complex numbers in geometry, algorithmic proofs, combinatorial and advanced geometry, functional equations and classical inequalities

The book is systematically organized, gradually building combinatorial skills and techniques and broadening the student's view of mathematics. Aside from its practical use in training teachers and students engaged in mathematical competitions, it is a source of enrichment that is bound to stimulate interest in a variety of mathematical areas that are tangential to combinatorics.


Proofs that Really Count: The Art of Combinatorial Proof

লেখক: Arthur T. Benjamin, Jennifer Quinn

মন্তব্য: Excellent book for honing your intuition!

 

Review:

1.      Difficulty: 4-5/5

2.      Content: 5/5

3.      Type: a

4.      Problem quality: 5/5

Amazon Description: Mathematics is the science of patterns, and mathematicians attempt to understand these patterns and discover new ones using a variety of tools. In Proofs That Really Count, award-winning math professors Arthur Benjamin and Jennifer Quinn demonstrate that many number patterns, even very complex ones, can be understood by simple counting arguments. The book emphasizes numbers that are often not thought of as numbers that count: Fibonacci Numbers, Lucas Numbers, Continued Fractions, and Harmonic Numbers, to name a few. Numerous hints and references are given for all chapter exercises and many chapters end with a list of identities in need of combinatorial proof. The extensive appendix of identities will be a valuable resource. This book should appeal to readers of all levels, from high school math students to professional mathematicians.


Algebra:

101 Problems in Algebra From the Training of the USA IMO Team

লেখক: Titu Andreescu, Zuming Feng  

মন্তব্য:

 

Review:

1.      Difficulty: 3-5/5

2.      Content: 4/5

3.      Type: a

4.      Problem quality: 4/5

Amazon Description: This book contains 101 highly rated problems used in training and testing the USA IMO Team. It gradually builds students algebraic skills and techniques and aims to broaden students views of mathematics and better prepare them for participation in mathematics competitions. It provides in-depth enrichment in important areas of algebra by reorganizing and enhancing studentsproblem-solving tactics and stimulates interest for future study of mathematics. The problems are carefully graded, ranging from quite accessible towards quite challenging. The problems have been well developed and are highly recommended to any student aspiring to participate at National or International Mathematical Olympiads.


Inequalities: A Mathematical Olympiad Approach 

Author: Radmila Bulajich Manfrino, José Antonio Gómez Ortega, and Rogelio Valdez Delgado

মন্তব্য:

 

Review:

1.      Difficulty: 2/5

2.      Content: 5/5

3.      Type: b, c

4.      Problem quality: 5/5

Amazon Description: This book presents classical inequalities and specific inequalities which are particularly useful for attacking and solving optimization problems. Most of the examples, exercises and problems that appear in the book originate from Mathematical Olympiad contests around the world. The material is divided into four chapters. In Chapter 1 algebraic inequalities are presented, starting with the basic ones and ending with more sophisticated techniques; Chapter 2 deals with geometric inequalities and Chapter 3 comprises a comprehensive list of recent problems that appeared in those contests during the last 14 years. Finally, hints and solutions to all exercises and problems are given in Chapter 4.


Polynomials (Problem Books in Mathematics)

Author: E. J. Barbeau

মন্তব্য:

 

Review:

1.      Difficulty: 2/5

2.      Content: 3/5

3.      Type: c

4.      Problem quality: 3/5

Amazon Description: The book extends the high school curriculum and provides a backdrop for later study in calculus, modern algebra, numerical analysis, and complex variable theory. Exercises introduce many techniques and topics in the theory of equations, such as evolution and factorization of polynomials, solution of equations, interpolation, approximation, and congruences. The theory is not treated formally, but rather illustrated through examples. Over 300 problems drawn from journals, contests, and examinations test understanding, ingenuity, and skill. Each chapter ends with a list of hints; there are answers to many of the exercises and solutions to all of the problems. In addition, 69 'explorations' invite the reader to investigate research problems and related topics.


Functional Equations and How to Solve

লেখক: Christopher G. Small

মন্তব্য:

 

Review:

1.      Difficulty: 3/5

2.      Content: 3/5

3.      Type: b

4.      Problem quality: 3/5

Amazon Description: "This book is devoted to functional equations of a special type, namely to those appearing in competitions … . The book contains many solved examples and problems at the end of each chapter. … The book has 130 pages, 5 chapters and an appendix, a Hints/Solutions section, a short bibliography and an index. … The book will be valuable for instructors working with young gifted students in problem solving seminars." (EMS Newsletter, June, 2008)

Over the years, a number of books have been written on the theory of functional equations. However, very little has been published which helps readers to solve functional equations in mathematics competitions and mathematical problem solving. This book fills that gap. The student who encounters a functional equation on a mathematics contest will need to investigate solutions to the equation by finding all solutions, or by showing that all solutions have a particular property. The emphasis here will be on the development of those tools which are most useful in assigning a family of solutions to each functional equation in explicit form.

At the end of each chapter, readers will find a list of problems associated with the material in that chapter. The problems vary greatly, with the easiest problems being accessible to any high school student who has read the chapter carefully. The most difficult problems will be a reasonable challenge to advanced students studying for the International Mathematical Olympiad at the high school level or the William Lowell Putnam Competition for university undergraduates. The book ends with an appendix containing topics that provide a springboard for further investigation of the concepts of limits, infinite series and continuity.


Secrets in Inequalities

লেখক: Pham Kim Hung

মন্তব্য:

 

Review:

1.      Difficulty: 4/5

2.      Content: 5/5

3.      Type: b

4.      Problem quality: 5/5

Description: This book contains many beautiful and hard inequalities. The chapters in this book cover basic inequalities from an advanced standpoint.

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