**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:

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:

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.*

*%%%Telang NT*

**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.