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Mathematical buffet
- 9Introduction
- PART I Basic ideas and facts
- 115CHAPTER 1 General advice
- 1.116Tiny mathematical plays
- 1.220The importance of make-up
- 1.325Looking for bridges
- 1.427Finding weak points
- 1.529On the other side of the river
- 1.631Complete the picture!
- 1.733Reversing the theorems
- 1.839The art of listening
- 1.942The inertia of thinking
- 1.1047To know and to understand
- 1.1150To see the difference
- 1.1255Finding the invariants
- 1.1357Do the opposite!
- 1.1462Exercises
- 1.1564Hints
- 265CHAPTER 2 The Numbers
- 2.165Natural numbers and integers
- 2.270Arithmetic in Zm
- 2.375Diophantine equations
- 2.476Rational and irrational numbers
- 2.580Real numbers
- 2.682Complex numbers
- 2.793Exercises
- 2.896Hints
- 397CHAPTER 3 Algebra
- 3.197Identities and factorization
- 3.299Polynomials in one variable
- 3.3105Symmetric polynomials
- 3.4108Summing up
- 3.5112Inequalities: basic properties
- 3.6121Proving inequalities
- 3.7135Exercises
- 3.8138Hints
- 4139CHAPTER 4 Geometry
- 4.1139The anatomy of a triangle
- 4.2145The degree of freedom
- 4.3151How to remember trigonometry
- 4.4157Angle chasing
- 4.5168Centre of gravity and barycentric coordinates
- 4.6175When are the points collinear?
- 4.7182Equal sizes in a triangle
- 4.8189Exercises
- 4.9190Hints
- 5191CHAPTER 5 Geometric transformations
- 5.1191Reflection
- 5.2196Homothety
- 5.3200Exercises
- 5.4202Hints
- 6203CHAPTER 6 Combinatorics
- 6.1203Enumerating the objects
- 6.2207Elements of graph theory
- 6.3212The pigeonhole principle
- 6.4216Colouring the problem
- 6.5216Exercises
- 6.6218Hints
- 7219CHAPTER 7 Functions and functional equations
- 7.1219Functions and permutations
- 7.2226Functional equations
- 7.3233Exercises
- 7.4234Hints
- PART II Advanced tools
- 8237CHAPTER 8 Number Theory
- 8.1237Order and primitive elements
- 8.2239Quadratic equations in Z p and the Legendre symbol
- 8.3242Continuous fractions and Pell’s equation
- 9249CHAPTER 9 Elements of linear algebra
- 9.1249Matrices
- 9.2259Vector algebra
- 9.3262Real numbers as a rational vector space
- 9.4264Finite-dimensional vector spaces inside of R
- 10269CHAPTER 10 Real functions
- 10.1269Lagrange’s Mean Value Theorem
- 10.2270Some elements of topology
- 10.3274Completeness and Baire’s theorem
- 10.4277Fixpoints
- 10.5280Trigonometric polynomials
- 10.6282Infinite sums
- 11285CHAPTER 11 Algebraic constructions
- 11.1285Formal series
- 11.2290Combinatorics on words
- 11.3294More about sequences
- 12297CHAPTER 12 Advanced geometry
- 12.1297Identities and inequalities in triangles
- 12.2300Directed angles
- 12.3302Inversion
- 12.4311Affine and projective maps
- 12.5317Geometry in Figures
- 13319CHAPTER 13 Combinatorial arguments
- 13.1319König’s lemma
- 13.2320Ramsey’s theorem
- 13.3325Playing games
- 13.4328Combinatorial geometry
- PART III Problems
- 14335CHAPTER 14 Papers
- 14.1335Paper 1
- 14.2336Paper 2
- 14.3337Paper 3
- 14.4338Paper 4
- 14.5339Paper 5
- 14.6340Paper 6
- 14.7341Paper 7
- 14.8342Paper 8
- 14.9343Paper 9
- 14.10344Paper 10
- 14.11345Paper 11
- 14.12346Paper 12
- 14.13347Paper 13
- 14.14348Paper 14
- 14.15349Paper 15
- 14.16350Paper 16
- 14.17351Paper 17
- 14.18352Paper 18
- 14.19353Paper 19
- 14.20354Paper 20
- PART IV Solutions
- 15357CHAPTER 15 Solutions to all papers
- 16487CHAPTER 16 Sources
- 489Bibliography
- 493Index
Information
- Författare:
- Victor Ufnarovski Jana Madjarova Frank Wikström
- Språk:
- Engelska
- ISBN:
- 9789144111032
- Utgivningsår:
- 2016
- Artikelnummer:
- 39120-01
- Upplaga:
- Första
- Sidantal:
- 498