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Tao T. Ч Solving Mathematical Problems: A Personal Perspective
Tao T. Ч Solving Mathematical Problems: A Personal Perspective

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Ќазвание: Solving Mathematical Problems: A Personal Perspective

јвтор: Tao T.

јннотаци€:

Authored by a leading name in mathematics, this engaging and clearly presented text leads the reader through the various tactics involved in solving mathematical problems at the Mathematical Olympiad level. Covering number theory, algebra, analysis, Euclidean geometry, and analytic geometry, Solving Mathematical Problems includes numerous exercises and model solutions throughout. Assuming only a basic level of mathematics, the text is ideal for students of 14 years and above in pure mathematics.


язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 2006

 оличество страниц: 103

ƒобавлена в каталог: 01.04.2008

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
(mod n) notation      10
18, multiples of      12Ч13
2, powers of      14Ч18
9, multiples of      9 11Ч13
Algebra      35
Algebra, examination marks problem      86Ч89
Algebra, polynomials      41Ч47
Ami-symmetry      25 26 30
Analysis of functions      36Ч40
Analytic geometry, line segments      77Ч79
Analytic geometry, partitioning of rectangles      74Ч77
Analytic geometry, square swimming pool problem      79Ч82
Analytic geometry, vector arithmetic      69Ч74
Angles in circles      50Ч51
Angles of triangles      50Ч54
Angles, notation      51
Angles, proof of equality      58 66Ч68
Areas of triangles      58
Arithmetic progression, lengths of triangle      1 2Ч7
Bernoulli polynomials      24
Chains, partitioning of rectangle      76Ч77
Chameleon colour combinations      83Ч85
Chessboard problem      84
Chocolate-breaking game      90Ч93
Chords, subtended angles      51 67
Circle theorems      49Ч50 57 67
Circles, angles in      50Ч51
Colour combinations, chameleons      83Ч85
Concurrence, perpendicular bisectors of triangle      ix
Conjectures      4
Consequences, proof of      4
Constant polynomials      42
Constructions      58Ч61
Contradiction, proof by      65Ч66 76Ч77
Coordinate geometry      55 58
Coordinate geometry, use in constructions      59
Coprime numbers      10
Cosine rule      3 53
Cubes, sum of      35
Cubic polynomials      42
Cyclic manoeuvres      85
Cyclic quadrilaterals      58
Data, omitting it from problem      5
Data, recording it      3
Data, understanding it      2
Degree of a polynomial (n)      41 42
Degrees of freedom, polynomials      46
Diagonals, lengths of      69Ч74
Diagrams      3 4
Diameter, angle subtended by (ThalesТ theorem)      49Ч50 57 67
Digits, rearrangement      14Ч19
Digits, summing      10Ч14
Digits, summing, powers of 2      16Ч18
Diophantmc equations      19Ч22
Direct (forward) approach      54Ч55
Divisibility, sums of powers      23Ч26
Divisibility, sums of reciprocals      27Ч33
Division system, price of penknife      95Ч97
Elegance of solutions      ix
Elimination of variables      61
Equations, use of      3Ч4
Equilateral triangles, construction      58Ч60
Euclidean geometry      49Ч50
Euclidean geometry, angles in circles      50Ч51
Euclidean geometry, angles of triangles      51Ч54
Euclidean geometry, constructions      58Ч61
Euclidean geometry, equating angles      66Ч68
Euclidean geometry, ratios      55Ч58
Euclidean geometry, squares and rectangles      62Ч66
Examination marks problem      86Ч89
Exponent variables      20Ч22
Factorization techniques, Diophantine equations      21
Factors      87
Factors of polynomials      42 44 45Ч47
Factors of polynomials, roots of      43
FermatТs Last Theorem      20
Finite problems, simplification      13
Formulae, use of      3Ч4
Forward (direct) approach      54Ч55
Functions, analysis      36Ч40
Functions, polynomials      41Ч47
Generalization      4 15
Geometry      see УAnalytic geometryФ УEuclidean
guessing      14 80Ч82
HeronТs formula      3 4 6Ч7
Homogeneous polynomials      42
Induction approach      92
Induction, proof by      37Ч38 40
Inequalities      88
Inequalities in analysis of functions      36Ч40
Inequalities in Euclidean geometry      65Ч66
Infinite products      28
Integer lengths, rectangles      74Ч77
Irreducible polynomials      42
Isosceles triangles      52
LagrangeТs Theorem      9
Levels of difficulty      viii
Line segments, analytic geometry      77Ч79
Matrix algebra      35
Modification of problems      4Ч5
Modular arithmetic      9 10
Modular arithmetic, Diophantine equations      21Ч22
Modular arithmetic, powers of 2      17Ч18
Modular arithmetic, squares      96
Modular arithmetic, sums of powers      23 24Ч26
Modular arithmetic, sums of reciprocals      28Ч33
Modular arithmetic, vectors      85
Multiples of 9      9 11Ч13
Natural numbers      10
NIM      91
Notation      3
Notation, vectors      84 90
Number theory      9Ч10
Number theory, digit rearrangement      14Ч19
Number theory, digit summing      10Ч14 16
Number theory, Diophantine equations      19Ч22
Number theory, sums of powers      23Ч26
Number theory, sums of reciprocals      27Ч33
Numerators, reduced      27Ч28
Objectives of problems      2
p-adics      9
Pairwise cancelling      25 26 30 32
Parallel lines      58Ч60
Parameterization      44
Partitioning of rectangle      74Ч77
periodicity      23Ч24
physical constraints      3
Polygons, lengths of line segments      69Ч74
Polynomials      41Ч43
Polynomials and reciprocals      43Ч44
Polynomials, factorization      44 45Ч47
Powers of 2, digit rearrangement      14Ч19
Powers of 2, digit sums      16Ч18
Powers, sums of      23Ч26
Prime numbers      10
Problem types      1Ч2
Proof by contradiction      65Ч66 76Ч77
Proof by induction      37Ч38
Proof by induction, strong induction      40
Proving results      6
Pseudo-coordinate geometry      58
PythagorasТ theorem      57
Quadnlaterals, midpoints of sides      50
Quadratic formula      20 42
Quadratic polynomials      42
Ratios, Euclidean geometry      55Ч58
Rearrangement of digits      14Ч19
Reciprocals and polynomials      43Ч41
Reciprocals, sums of      27Ч33
Rectangles, chocolate-breaking game      90Ч93
Rectangles, in a square      62Ч66
Rectangles, partitioning      74Ч77
Reduced numerators      27Ч28
Reformulation of problems      4
Representation of data and objectives      3
Reversal of problems      5
Roots of factors of polynomials      43
Roots of polynomials      42 44 46
Rotations      60
Similar triangles      56 57
Simplification of problems      4 5 6 13 19 91Ч92
Sine rule      3 53 54
Skill games      93
Special cases      4Ч5
Special cases in geometry problems      58
Square roots      20
Square swimming pool problem      79Ч82
Squares (Euclidean geometry)      62Ч66
Squares, modular arithmetic      96
SteinerТs theorem of parallel axes      74
Steps in problem-solving      1
Strong induction      40
Sums of cubes      35
Sums of digits      10Ч14
Sums of lengths of line segments      79
Sums of powers      23Ч26
Sums of powers, powers of 2      16Ч18
Sums of reciprocals      27Ч33
Symmetry      30 32 73Ч74
Tables      89
Tangents to circle      57
ThalesТ Theorem      49Ч50 57 67
Triangle inequality      3 79
Triangles, angles of      50Ч54
Triangles, areas of      58
Triangles, concurrence of perpendicular bisectors      ix
Triangles, lengths in arithmetic progression      1 2Ч7
Triangles, similar      56 57
Trigonometry      53Ч54
Trivial polynomials      42
Variables      3
Variables, elimination of      61
Variables, exponent      20Ч22
Vector geometry      55 69 73Ч74
Vectors, chameleon colour combinations      84Ч85
Vectors, chocolate-breaking game      90
WilsonТs Theorem      9
УEvaluate...Ф problems      1Ч2
УFind a...Ф/УFind all...Ф problems      1 2
УIs there a...Ф questions      1 2
УPocket mathematicsФ      36
УShow thar...Ф problems      1Ч2
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