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Moskowitz M.A. — Adventures in mathematics
Moskowitz M.A. — Adventures in mathematics

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Название: Adventures in mathematics

Автор: Moskowitz M.A.

Аннотация:

Our purpose here is to present mathematics as it really is: a vast panorama of ideas, whose history reflects some of the most noble thoughts of mankind. This book represents an attempt, although on a limited scale, to convey some of this to the reader who perhaps has little technical or mathematical background, but who is truly interested in ideas and understanding certain aspects of the world around us. The material would also be appropriate to high school or community college teachers who seek an overview of mathematics so they can see through the formalities of the standard curriculum and, in turn, convey to their students some of the real scope and power to be found in mathematical ideas. Selections from the subject matter presented here would also be very suitable for a college pre-calculus course. Indeed, one of our objectives is to try to find and to understand some real mathematics without the reader needing to have a knowledge of calculus...


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2004

Количество страниц: 108

Добавлена в каталог: 15.12.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
2-point transitivity      85
Abelian group      47
Action, transitive      54
Affine motion      80
Algebra on a dial      46
Algebraic numbers      44
Antipodal      93
Archimedian property      23
Area of circle      19
Area of triangle      19
Argument      33
Arithmetic mean      23
Arithmetic progress      4 5
Automorphism      53
Axioms      49
Bijective      50
Binary operation      49
Binomial theorem      6 8
Bolyai      65
Brouwer fixed point theorem      102
Cantor      24
Cauchy — Schwartz inequality      67
Center      53
Chinese remainder theorem      45
Closed under addition      3
Coefficient      14
Combinatorial properties      97
Commutative      7
Commutative ring with identity      7 47
Completing the square      37
complex numbers      32
Congruent      81
Conjugacy class      54
conjugate      33
Conjugate pairs      42
Conjugate, subgroups      55
Continuous vector field      102
coordinates      33
Countable      24
Cyclic subgroup      51
Decimal expansion      23
Degree      14
DeMoivre’s Theorem      34
Descartes      65
Diagonal process      24
Dilation      80
Dirichlet      27
Discriminant      37
Distribution law      4 8
Division algorithm      25
Elliptic geometry      65
Enumerable      24
Enumerated      24
Equivalence, G-equivariant      55
Erlangen      49
Euclidean      65
Euclidean algorithm      25
Euler      43
Euler characteristic      97
Exact      53
Excess      92
Fermat      43
Fermat’s theorem      58
Field      13
Finite order      51
Fundamental theorem of algebra      35 42 100
Fundamental Theorem of Arithmetic      26
G-invariant      54
Gauss      5 65
Gaussian integers      42
Geometric mean      23
Geometric progression      39
Geometric series      39
Geometry, elliptic      65
Geometry, Eucludean      65
Geometry, hyperbolic      65
Geometry, non — Euclidean      65
Golden mean      38
Greatest common divisor      27
Group      49
Group action      53
Group, abelian      50
Group, commutative      50
Group, orthogonal      64
Homeomorphic      96
Homeomorphism      96
Homomorphism      52
Hyperbolic geometry      65
Ideal      56
INDEX      101
Index of a subgroup      51
Indirect proof      4
Inequality, Cauchy — Schwartz      67
Infinite series      39
Inner automorphism      53
Integer part      23
Integers      3
Intersection      viii
Invertible      47 63
Irrational numbers      15
Isometry      80
Isometry group      81
Isomorphism      52
Isomorphism theorem, first      52
Isomorphism, G-equivariant      55
Kant      87
Klein      49
Klein’s Erlangen Program      53
Lagrange      51
Lagrange, Theorem      51
Law of Cosines      68
Left coset      51
Length      66
Linear algebra      60
linear combination      62
Linear transformation      62
Linear transformations, invertible      63
Liouville      41
Little Fermat theorem      57
Lobachevski      65
Long division      41
Matrix      62
Method of exhaustion      20
Modulus      34
Multiplicity      26
Non — Euclidean      65
Norm      66
Normal subgroup      52 84
Orbit      54
Ordered field      21
Ordering      21
Origin      60
Orthogonal group      64
Parallel postulate      73
Parallelogram law      33
Pascal’s triangle      9
Periodic decimal expansion      40
Permutation      6
Platonic solids      99
Poincar$\acute{e}$      104
Polar decomposition      33 35
Polyhedron      96
Polynomial equation      14
Prime factorization      26
Prime number      25
Prime polynomial      41
primitive      36
Principle of continuity      17
Principle of Induction      4
Proof by contradiction      4
Pure imaginary      33
Pythagorean Theorem      68
Pythagorean triple      8
Quadratic equation      37
Quotient ring      56
Radius of the earth      79
Rational numbers      10
Real number field      16
Real numbers      14
Relatively prime      27
Remainder      25
Riemann      65
Ring homomorphism      56
Root of units      35
Similar      86
Singularity      102
Squeezing principle      19
Stabilizer      55
Subfield      33
Subgroup      51
Subring      56
Subset      vii
Systems of linear equation      13
Tangent vector field      103
Transformation group      53
Transitivity, 2-point      85
Translation      81
Triangle inequality      22
Triangulated      97
union      viii
Vector      60
Vector field      102 103
Vector space      60
Vectors      33
Weil      49
Wilson’s Theorem      57
Zero-divisors      47
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