Иностранная литература, посвященная олимпиадной тематике

[mpl]

Иностранная литература, посвященная олимпиадной тематике

Большинство книг можно найти на сайте gen.lib.rus.ec.

• Andreescu T., Kedlaya K., Zeitz P. Mathematical contests 1995-1996: Olympiad problems and solutions from around the world - MAA, 1997, 202 p.
• Andreescu T., Kedlaya K. Mathematical olympiads 1996-1997: Olympiad problems and solutions from around the world - MAA, 1998, 182 p.
• Andreescu T., Kedlaya K. Mathematical Olympiads 1997-1998: Problems and Solutions from Around the World - AMC, 1999
• Andreescu T., Cirtoaje V., Dospinescu G., Lascu M. Old and New Inequalities - GIL, 2000, 125 p.
• Andreescu T., Feng Z. Mathematical Olympiads 1999-2000: Problems and Solutions from around the World - MAA, 2001, 344 p.
• Andreescu T., Feng Z., Lee Jr G. Mathematical Olympiads 2000-2001: Problems and Solutions from around the World - MAA, 2002, 271 p.
• Andreescu T., Feng Z. 102 Combinatorial Problems from the training of USA IMO team - Birkhäuser, 2003, p. 115
• Andreescu T., Andrica D. 360 Problems for Mathematical Contests - 2003, GIL Publishing house, 2003, 280 p.
• Andreescu T., Feng Z. USA & International Mathematical Olympiads 2003 - MAA, 2004, 101 p.
• Andreescu T., Feng Z. A path to combinatorics for undergraduates: counting strategies - Birkhäuser, 2004, 228 p
• Andreescu T., Mushkarov O., Stoyanov L. Geometric Problems on Maxima and Minima - Birkhauser, 2005
• Andreescu T., Feng Z. 103 Trigonometry Problems. From the Training of the USA IMO Team - Birkhäuser, 2005 - 214 pp
• Andreescu T., Feng Z., Loh P. USA and International Mathematical Olympiads 2004 - MAA, 2005, 61 p.
• Andreescu T., Andrica D., Feng Z. 104 Number Theory Problems. From the Training of the USA IMO Team - Birkhäuser, 2007 - 204 pp
• Andreescu T., Boreico I. Functional Equations (Electronic Edition) - 2007, 140 p.
• Andreescu T., Gelca R. Putnam and Beyond - Springer, 2007, 815 p.
• Andreescu T., Gelca R. Mathematical Olympiad Challenges (2nd) - Birkhäuser, 2008, 291 p.
• Andreescu T., Dospinescu G. Problems from the book [2nd Edition ed.] - XYZ Press, 2008, 554 p.
• Andreescu T., Andrica D. Number theory: Structures, examples, and problems - Birkhäuser, 2009, 412 p.
• Andreescu T., Andrica D., Cucurezeanu I. An introduction to Diophantine equations: A problem-based approach - Birkhauser, 2010, 345 p.
• Andreescu T., Enescu B. Mathematical Olympiad Treasures (2nd) - Birkhäuser, 2011, 262 p.

• Djukic D., Jankovic V., Matic I., Petrovic N. The Imo Compendium: A Collection of Problems Suggested for the International Mathematical Olympiads: 1959-2004 [1 ed.] (Problem Books in Mathematics) - Springer, 2006, 755 pp
• Djukic D., Jankovic V., Matic I., Petrovic N. The IMO Compendium: A Collection of Problems Suggested for The International Mathematical Olympiads: 1959-2009 [2 ed.] (Problem Books in Mathematics) - Springer, Berlin, 2011, 825 pp

• Gronau H.-D. 50th IMO - 50 Years of International Mathematical Olympiads - Springer, 2011, 241 pp

• Jiagu X. Lecture Notes on Mathematical Olympiad Courses: For Junior Section Vol. 1 (Mathematical Olympiad Series Vol. 6) - World Scientific Publishing Company, 2010, 184 pp,
• Jiagu X. Lecture Notes on Mathematical Olympiad Courses: For Junior Section, Vol. 2 (Mathematical Olympiad Series Vol. 6) - World Scientific Publishing Company, 2010, 192 pp,

• Liu A. Chinese Mathematics Competitions and Olympiads, Book 1: 1981-1993 (Enrichment Series, Volume 13) - AMT Publishing, 1998, 194 pp
• Liu A. Chinese Mathematics Competitions and Olympiads, Book 2: 1993-2001 (Enrichment Series, Volume 22) - AMT Publishing, 2005, 174 pp

• Manfrino R.B. Inequalities: A Mathematical Olympiad Approach - Birkhauser, 2009

• Posamentier A.S., Salkind C.T. Challenging Problems in Geometry - Dover Books on Mathematics, 1996
• Posamentier A.S., Salkind C.T. Challenging Problems in Algebra - Dover Books on Mathematics, 1996

• Sahoo P. K. , Kannappan P. Introduction to Functional Equations - Chapman and Hall/CRC, 2011, 465 Pages
• Slinko A. USSR Mathematical Olympiads 1989-1992 (Enrichment Series, Volume 11) - 1997

• Xiong B., Lee P.Y. Mathematical Olympiad in China: Problems and Solutions - World Scientific Publishing Company, 2007, 276 pp
• Xiong B., Lee P.Y. Mathematical Olympiad in China (2007-2008): Problems and Solutions - World Scientific Publishing Company, 2009, 194 pp

---

Дополнительно
КНИЖНЫЕ ПОЛКИ СООБЩЕСТВА EEK.DIARY, в том числе:
Литература по подготовке к математическим олимпиадам (часть I)
Литература по подготовке к математическим олимпиадам (часть II)

---

Топики, посвященные олимпиадам разных стран:
Математическая олимпиада Аргентины
Математические соревнования в Германии
Греческая математическая олимпиада
Конкурс Georg Mohr (Дания)
Всеукраинская математическая олимпиада
Математический конкурс Франции
Испанская математическая олимпиада
Математическая олимпиада в Италии
Математическая олимпиада в Хорватии
Шведские математические соревнования
Польская математическая олимпиада
Математическая олимпиада Чехии и Словакии
Математические состязания в Бельгии
Математические олимпиады в Бангладеш
Математическая олимпиада Мексики
Олимпиада Португалии по математике
Scottish Mathematical Challenge
Ирландская математическая олимпиада
Niels Henrik Abel Mathematics Contest (Норвегия)
Математическая олимпиада в Голландии
Математическая олимпиада в Румынии
Математическая олимпиада в Сербии
Математические соревнования в Венгрии
Математическая олимпиада в Сирии
Математическая олимпиада в Великобритании
Олимпиада в Перу
Таиландская олимпиада
Математическая олимпиада в Бразилии

Comments

[mpl]

Andreescu T., Andrica D., Cucurezeanu I. An introduction to Diophantine equations: A problem-based approach - Birkhauser, 2010, 345 p. Скачать ifolder.ru/31380780

Preface
Diophantus, the “father of algebra,” is best known for his book Arithmetica, a work on the solution of algebraic equations and the theory of numbers. However, essentially nothing is known of his life, and there has been much debate regarding precisely the years in which he lived.
Diophantus did his work in the great city of Alexandria. At this time, Alexandria was the center of mathematical learning. The period from 250 bce to 350 ce in Alexandria is known as the Silver Age, also the Later Alexandrian Age. This was a time when mathematicians were discovering many ideas that led to our current conception of mathematics. The era is considered silver because it came after the Golden Age, a time of great development in the field of mathematics. This Golden Age encompasses the lifetime of Euclid.
The quality of mathematics from this period was an inspiration for the axiomatic methods of today’s mathematics. While it is known that Diophantus lived in the Silver Age, it is hard to pinpoint the exact years in which he lived. While many references to the work of Diophantus have been made, Diophantus himself made few references to other mathematicians’ work, thus making the process of determining the time that he lived more difficult.
Diophantus did quote the definition of a polygonal number from the work of Hypsicles, who was active before 150 bce, so we can conclude that Diophantus lived after that date. From the other end, Theon, a mathematician also from Alexandria, quoted the work of Diophantus in 350 ce. Most historians believe that Diophantus did most of his work around 250 ce. The greatest amount of information about Diophantus’s life comes from the possibly fictitious collection of riddles written by Metrodorus around 500 ce. One of these is as follows:
His boyhood lasted 1/6 of his life; he married after 1/7
more; his beard grew after 1/12 more, and his son was
born five years later; the son lived to half his father’s
age, and the father died four years after the son.
Diophantus was the first to employ symbols in Greek algebra. He used a symbol (arithmos) for an unknown quantity, as well as symbols for algebraic operations and for powers. Arithmetica is also significant for its results in the theory of numbers, such as the fact that no integer of the form 8n+7 can be written as the sum of three squares.
Arithmetica is a collection of 150 problems that give approximate solutions to equations up to degree three. Arithmetica also contains equations that deal with indeterminate equations. These equations deal with the theory of numbers. The original Arithmetica is believed to have comprised 13 books, but the surviving Greek manuscripts contain only six. The others are considered lost works. It is possible that these books were lost in a fire that occurred not long after Diophantus finished Arithmetica.
In what follows, we call a Diophantine equation an equation of the form
`f(x1, x2, . . . , xn) = 0`, (1)
where f is an n-variable function with n ≥ 2. If f is a polynomial with integral coefficients, then (1) is an algebraic Diophantine equation.
An n-uple `(x_1^0, x_2^0, . . . , x_n^0) in ZZ^n` satisfying (1) is called a solution to equation (1). An equation having one or more solutions is called solvable.
Concerning a Diophantine equation three basic problems arise:
Problem 1. Is the equation solvable?
Problem 2. If it is solvable, is the number of its solutions finite or infinite?
Problem 3. If it is solvable, determine all of its solutions.
Diophantus’s work on equations of type (1) was continued by Chinese mathematicians (third century), Arabs (eight through twelfth centuries) and taken to a deeper level by Fermat, Euler, Lagrange, Gauss, and many others. This topic remains of great importance in contemporary mathematics.
This book is organized in two parts. The first contains three chapters. Chapter 1 introduces the reader to the main elementary methods in solving Diophantine equations, such as decomposition, modular arithmetic, mathematical induction, and Fermat’s infinite descent. Chapter 2 presents classical Diophantine equations, including linear, Pythagorean, higher-degree, and exponential equations, such as Catalan’s. Chapter 3 focuses on Pell-type equations, serving again as an introduction to this special class of quadratic Diophantine equations. Chapter 4 contains some advanced methods involving Gaussian integers, quadratic rings, divisors of certain forms, and quadratic reciprocity. Throughout Part I, each of the sections contains representative examples that illustrate the theory. Part II contains complete solutions to all exercises in Part I. For several problems, multiple solutions are presented, along with useful comments and remarks. Many of the selected exercises and problems are original or have been given original solutions by the authors.
The book is intended for undergraduates, high school students and teachers, mathematical contest (including Olympiad and Putnam) participants, as well as any person interested in mathematics.
We would like to thank Richard Stong for his careful reading of the manuscript. His pertinent suggestions have been very useful in improving the text.

Contents
Preface v
I Diophantine Equations 1
I.1 Elementary Methods for Solving Diophantine
Equations 3
1.1 The Factoring Method . . . . . . . . . . . . . . . . 3
1.2 Solving Diophantine Equations Using Inequalities . 13
1.3 The ParametricMethod . . . . . . . . . . . . . . . . 20
1.4 TheModular ArithmeticMethod . . . . . . . . . . 29
1.5 The Method of Mathematical Induction . . . . . . . 36
1.6 Fermat’s Method of Infinite Descent (FMID) . . . . 47
1.7 Miscellaneous Diophantine Equations . . . . . . . . 58
I.2 Some Classical Diophantine Equations 67
2.1 Linear Diophantine Equations . . . . . . . . . . . . 67
2.2 Pythagorean Triples and Related Problems . . . . . 76
2.3 Other Remarkable Equations . . . . . . . . . . . . . 88
I.3 Pell-Type Equations 117
3.1 Pell’s Equation: History and Motivation . . . . . . . 118
3.2 Solving Pell’s Equation . . . . . . . . . . . . . . . . 121
3.3 The Equation `ax^2 - by^2 =1` . . . . . . . . . . . . . 135
3.4 The Negative Pell’s Equation . . . . . . . . . . . . . 140
I.4 Some Advanced Methods for Solving Diophantine Equations 147
4.1 The Ring Z[i] of Gaussian Integers . . . . . . . . . . 151
4.2 The Ring of Integers of Q[√d] . . . . . . . . . . . . 162
4.3 Quadratic Reciprocity and Diophantine Equations . 178
4.4 Divisors of Certain Forms . . . . . . . . . . . . . . . 181
4.4.1 Divisors of `a^2 + b^2` . . . . . . . . . . . . . . . 182
4.4.2 Divisors of `a^2 + 2b^2` . . . . . . . . . . . . . . 186
4.4.3 Divisors of `a^2 - 2b^2` . . . . . . . . . . . . . . 188
II Solutions to Exercises and Problems 191
II.1 Solutions to Elementary Methods for Solving
Diophantine Equations 193
1.1 The Factoring Method . . . . . . . . . . . . . . . . 193
1.2 Solving Diophantine Equations Using Inequalities . 202
1.3 The ParametricMethod . . . . . . . . . . . . . . . . 213
1.4 TheModular ArithmeticMethod . . . . . . . . . . 219
1.5 The Method of Mathematical Induction . . . . . . . 229
1.6 Fermat’s Method of Infinite Descent (FMID) . . . . 239
1.7 Miscellaneous Diophantine Equations . . . . . . . . 253
II.2 Solutions to Some Classical Diophantine
Equations 265
2.1 Linear Diophantine Equations . . . . . . . . . . . . 265
2.2 Pythagorean Triples and Related Problems . . . . . 273
2.3 Other Remarkable Equations . . . . . . . . . . . . . 278
II.3 Solutions to Pell-Type Equations 289
3.1 Solving Pell’s Equation by Elementary Methods . . 289
3.2 The Equation `ax^2 - by^2 =1` . . . . . . . . . . . . . 298
3.3 The Negative Pell’s Equation . . . . . . . . . . . . . 301
II.4 Solutions to Some Advanced Methods in Solving Diophantine Equations 309
4.1 The Ring Z[i] of Gaussian Integers . . . . . . . . . . 309
4.2 The Ring of Integers of Q[√d] . . . . . . . . . . . . 314
4.3 Quadratic Reciprocity and Diophantine Equations . 322
4.4 Divisors of Certain Forms . . . . . . . . . . . . . . . 324
References 327
Glossary 331
Index 341

[mpl]

Andreescu T., Enescu B. Mathematical Olympiad Treasures (2nd) - Birkhäuser, 2011, 262 p. Скачать

Preface
Mathematical Olympiads have a tradition longer than one hundred years. The first mathematical competitions were organized in Eastern Europe (Hungary and Romania) by the end of the 19th century. In 1959 the first International Mathematical Olympiad was held in Romania. Seven countries, with a total of 52 students, attended that contest. In 2010, the IMO was held in Kazakhstan. The number of participating countries was 97, and the number of students 517.
Obviously, the number of young students interested in mathematics and mathematical competitions is nowadays greater than ever. It is sufficient to visit some mathematical forums on the net to see that there are tens of thousands registered users and millions of posts.
When we were thinking about writing this book, we asked ourselves to whom it will be addressed. Should it be the beginner student, who is making the first steps in discovering the beauty of mathematical problems, or, maybe, the more advanced reader, already trained in competitions. Or, why not, the teacher who wants to use a good set of problems in helping his/her students prepare for mathematical contests.
We have decided to take the hard way and have in mind all these potential readers.
Thus, we have selected Olympiad problems of various levels of difficulty. Some are rather easy, but definitely not exercises; some are quite difficult, being a challenge even for Olympiad experts.
Most of the problems come from various mathematical competitions (the International Mathematical Olympiad, The Tournament of the Towns, national Olympiads, regional Olympiads). Some problems were created by the authors and some are folklore.
The problems are grouped in three chapters: Algebra, Geometry and Trigonometry, and Number Theory and Combinatorics. This is the way problems are classified at the International Mathematical Olympiad.
In each chapter, the problems are clustered by topic into self-contained sections.
Each section begins with elementary facts, followed by a number of carefully selected problems and an extensive discussion of their solutions. At the end of each section the reader will find a number of proposed problems, whose complete solutions are presented in the second part of the book.
We encourage the beginning reader to carefully examine the problems solved at the beginning of each section and try to solve the proposed problems before examining the solutions provided at the end of the book. As for the advanced reader, our advice is to try finding alternative solutions and generalizations of the proposed problems.
In the second edition of the book, we added two new sections in Chaps. 1 and 3, and more than 60 new problems with complete solutions.

Contents
Part I Problems
1 Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1 An Algebraic Identity . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Cauchy–Schwarz Revisited . . . . . . . . . . . . . . . . . . . . . 7
1.3 Easy Ways Through Absolute Values . . . . . . . . . . . . . . . . 11
1.4 Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.5 Take theConjugate! . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.6 Inequalities with Convex Functions . . . . . . . . . . . . . . . . . 20
1.7 Induction at Work . . . . . . . . . . . . . . . . . . . . . . . . . . 24
1.8 Roots andCoefficients . . . . . . . . . . . . . . . . . . . . . . . . 27
1.9 The Rearrangements Inequality . . . . . . . . . . . . . . . . . . . 31
2 Geometry and Trigonometry . . . . . . . . . . . . . . . . . . . . . . 37
2.1 Geometric Inequalities . . . . . . . . . . . . . . . . . . . . . . . . 37
2.2 An Interesting Locus . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.3 Cyclic Quads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.4 Equiangular Polygons . . . . . . . . . . . . . . . . . . . . . . . . 50
2.5 More on Equilateral Triangles . . . . . . . . . . . . . . . . . . . . 54
2.6 The “Carpets” Theorem . . . . . . . . . . . . . . . . . . . . . . . 58
2.7 Quadrilaterals with an Inscribed Circle . . . . . . . . . . . . . . . 62
2.8 Dr.TrigLearnsComplexNumbers . . . . . . . . . . . . . . . . . 66
3 Number Theory and Combinatorics . . . . . . . . . . . . . . . . . . 71
3.1 ArraysofNumbers . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.2 Functions Defined on Sets of Points . . . . . . . . . . . . . . . . . 74
3.3 Count Twice! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.4 Sequences of Integers . . . . . . . . . . . . . . . . . . . . . . . . 81
3.5 EquationswithInfinitelyManySolutions . . . . . . . . . . . . . . 85
3.6 EquationswithNoSolutions . . . . . . . . . . . . . . . . . . . . 88
3.7 Powersof2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
3.8 Progressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
3.9 TheMarriageLemma . . . . . . . . . . . . . . . . . . . . . . . . 96
Part II Solutions
4 Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.1 An Algebraic Identity . . . . . . . . . . . . . . . . . . . . . . . . 101
4.2 Cauchy–Schwarz Revisited . . . . . . . . . . . . . . . . . . . . . 109
4.3 Easy Ways Through Absolute Values . . . . . . . . . . . . . . . . 116
4.4 Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
4.5 Take theConjugate! . . . . . . . . . . . . . . . . . . . . . . . . . 124
4.6 Inequalities with Convex Functions . . . . . . . . . . . . . . . . . 130
4.7 Induction at Work . . . . . . . . . . . . . . . . . . . . . . . . . . 134
4.8 Roots andCoefficients . . . . . . . . . . . . . . . . . . . . . . . . 138
4.9 The Rearrangements Inequality . . . . . . . . . . . . . . . . . . . 144
5 Geometry and Trigonometry . . . . . . . . . . . . . . . . . . . . . . 149
5.1 Geometric Inequalities . . . . . . . . . . . . . . . . . . . . . . . . 149
5.2 An Interesting Locus . . . . . . . . . . . . . . . . . . . . . . . . . 156
5.3 Cyclic Quads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
5.4 Equiangular Polygons . . . . . . . . . . . . . . . . . . . . . . . . 171
5.5 More on Equilateral Triangles . . . . . . . . . . . . . . . . . . . . 176
5.6 The “Carpets” Theorem . . . . . . . . . . . . . . . . . . . . . . . 181
5.7 Quadrilaterals with an Inscribed Circle . . . . . . . . . . . . . . . 185
5.8 Dr.TrigLearnsComplexNumbers . . . . . . . . . . . . . . . . . 193
6 Number Theory and Combinatorics . . . . . . . . . . . . . . . . . . 197
6.1 ArraysofNumbers . . . . . . . . . . . . . . . . . . . . . . . . . . 197
6.2 Functions Defined on Sets of Points . . . . . . . . . . . . . . . . . 201
6.3 Count Twice! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
6.4 Sequences of Integers . . . . . . . . . . . . . . . . . . . . . . . . 213
6.5 EquationswithInfinitelyManySolutions . . . . . . . . . . . . . . 219
6.6 EquationswithNoSolutions . . . . . . . . . . . . . . . . . . . . 224
6.7 Powersof2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
6.8 Progressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237
6.9 TheMarriageLemma . . . . . . . . . . . . . . . . . . . . . . . . 244
Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249
Index of Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
Index to the Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253

[mpl]

Andreescu T., Feng Z. A path to combinatorics for undergraduates: counting strategies - Birkhäuser, 2004, 228 p Скачать ifolder.ru/31381014

Contents
• Preface . vii
• Introduction ........................................... ix
• Acknowled.gements .................................... xv
• Abbreviations and Notation .......................... xvii
• 1. Addition or Multiplication? . . . . . . . . . . . . . . .... . . . . . . . . 1
• 2. Combinations . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
• 3. Properties of Binomial Coefficients . . . . . . . . . . . . . .. . . . 43
• 4. Bijections . . . . . . . . ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
• 5. Recursions . .. ..... . .. . .. . . .. . .. . .. . . .. .. .. .. .. ,. ............................... 91
• 6. Inclusion and Exclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
• 7. Calculating in Two Ways: Fubini's Principle . . . . . . . 143
• 8. Generating Functions . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . 165
• 9. Review Exercises . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . 195
• Glossary . . . . . . . . . . . . . .. .. . . . . . . . . . . . . . . . . .. . . . . . . . . . . 213
• Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
• Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
• Afterword . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . .. . . . .. ... 227

Preface
The main goal of the two authors is to help undergraduate students understand the concepts and ideas of combinatorics, an important realm of mathematics, and to enable them to ultimately achieve excellence in this field. This goal is accomplished by familiarizing students with typical examples illustrating central mathematical facts, and by challenging students with a number of carefully selected problems. It is essential that the student works through the exercises in order to build a bridge between ordinary high school permutation and combination exercises and more sophisticated, intricate, and abstract concepts and problems in undergraduate combinatorics. The extensive discussions of the solutions are a key part of the learning process.
The concepts are not stacked at the beginning of each section in a blue box, as in many undergraduate textbooks. Instead, the key mathematical ideas are carefully worked into organized, challenging, and instructive examples. The authors are proud of their strength, their collection of beautiful problems, which they have accumulated through years of work preparing students for the International Mathematics Olympiads and other competitions.
A good foundation in combinatorics is provided in the first six chapters of this book. While most of the problems in the first six chapters are real counting problems, it is in chapters seven and eight where readers are introduced to essay-type proofs. This is the place to develop significant problem-solving experience, and to learn when and how to use available skills to complete the proofs.

[Гость]

Пишет  kostyaknop:

11.04.2012 в 22:29

Prasanna K. Sahoo, Palaniappan Kannappan Introduction to Functional Equations - Chapman and Hall/CRC, 2011, 465 Pages Introduction to Functional Equations grew out of a set of class notes from an introductory graduate level course at the University of Louisville. This introductory text communicates an elementary exposition of valued functional equations where the unknown functions take on real or complex values. In order to make the presentation as manageable as possible for students from a variety of disciplines, the book chooses not to focus on functional equations where the unknown functions take on values on algebraic structures such as groups, rings, or fields. However, each chapter includes sections highlighting various developments of the main equations treated in that chapter. For advanced students, the book introduces functional equations in abstract domains like semigroups, groups, and Banach spaces. Functional equations covered include: Cauchy Functional Equations and Applications, The Jensen Functional Equation, Pexider's Functional Equation, Quadratic Functional Equation, D'Alembert Functional Equation, Trigonometric Functional Equations, Pompeiu Functional Equation, Hosszu Functional Equation, Davison Functional Equation, Abel Functional Equation, Mean Value Type Functional Equations, Functional Equations for Distance Measures The innovation of solving functional equations lies in finding the right tricks for a particular equation. Accessible and rooted in current theory, methods, and research, this book sharpens mathematical competency and prepares students of mathematics and engineering for further work in advanced functional equations. Скачать (pdf, 4 Мб) libgen

URL комментария

[Гость]

Владелец дневника видит IP-адреса пользователей, оставивших комментарии!

[Гость]

mpl,

[Гость]

Гость,

[Гость]

Владелец дневника видит IP-адреса пользователей, оставивших комментарии!

[kostyaknop]

gen.lib.rus.ec/book/index.php?md5=E6B60841CFD16...
Студентськi математичнi олiмпiади. Збiрник задач Булдигiн В.В., Кушнiревич В.А., Шкабара О.С.

[Гость]

Владелец дневника видит IP-адреса пользователей, оставивших комментарии!

[Гость]

Владелец дневника видит IP-адреса пользователей, оставивших комментарии!

[Гость]

Владелец дневника видит IP-адреса пользователей, оставивших комментарии!

[Гость]

Владелец дневника видит IP-адреса пользователей, оставивших комментарии!

[Гость]

Владелец дневника видит IP-адреса пользователей, оставивших комментарии!

[Гость]

Владелец дневника видит IP-адреса пользователей, оставивших комментарии!

[Гость]

Владелец дневника видит IP-адреса пользователей, оставивших комментарии!

[Гость]

Владелец дневника видит IP-адреса пользователей, оставивших комментарии!