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Farmer D.W. — Groups and symmetry: A guide to discovering mathematics
Farmer D.W. — Groups and symmetry: A guide to discovering mathematics

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Название: Groups and symmetry: A guide to discovering mathematics

Автор: Farmer D.W.


In most mathematics textbooks, the most exciting part of mathematics - the process of invention and discovery - is completely hidden from the reader. The aim of Groups and Symmetry is to change all that. By means of a series of carefully selected tasks, this book leads readers to discover some real mathematics. There are no formulas to memorize; no procedures to follow. The book is a guide: Its job is to start you in the right direction and to bring you back if you stray too far. Discovery is left to you. Suitable for a one-semester course at the beginning undergraduate level, there are no prerequisites for understanding the text. Any college student interested in discovering the beauty of mathematics will enjoy a course taught from this book. The book has also been used successfully with nonscience students who want to fulfill a science requirement.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: AMS

Год издания: 1995

Количество страниц: 112

Добавлена в каталог: 15.11.2013

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Предметный указатель
$A_{N}$, alternating group      90
$C_{N}$, cyclic group      61
$C_{N}$, symmetry type      36
$D_{N}$, dihedral group      61
$D_{N}$, symmetry type      37
$n$-gon      30
$r$, smallest rotation symmetry      32
$S_{N}$, symmetric group      68
1 stands for do-nothing      32
15-puzzle      90
2-cycle      71
Addition mod $n$      63
Alternating group      90
Associative operation      53
Basic unit      8 49
Bilateral symmetry      38
Cayley diagram      73
Cayley, Arthur      67
Closed path      93
Conway, John H      42
Crystallographic restriction      52
CYCLE      68
Cyclic group, $C_{N}$      61
Dihedral group, $D_{N}$      61
Do-nothing, denoted by one      32
Do-nothing, is a rotation and a translation      25
Do-nothing, is always a symmetry      27
Dual      95
Equivalent mirror lines      47
Equivalent rotocenter      44
Escher, M.C.      48
Even permutation      90
Exponents, rules of      32
Fedorov, E.S.      48
Finite figure      28
Fixed point      23
footprints      42
Fundamental domain      11
Generator      73 92
Glide line      22
Glide reflection      22
Glide reflection, phantom figure      22
Group      51 53
Group, $A_{N}$, alternating group      90
Group, $C_{N}$, cyclic group      61
Group, $D_{N}$, dihedral group      61
Group, $S_{N}$, symmetric group      68
Group, generators      73
Group, presentation      92
Group, relation      92
Identity matrix      92
Inverse      35 38
Isomorphism      71
Kali      53 98
Lloyd, Sam      91
Magic square      96
Matrix      91
Mirror      19
Mirror line      19
MOD      63
Modular addition      63
Modular arithmetic      91
Modular multiplication      65
Modulo, see mod multiplication mod $n$      65
Multiplication table of a triangle      35
Odd permutation      90
Order of a rotation      46
P$\grave{o}$lya, George      48
Penrose tiles      53
Pentagon, easy way to make one      31
Pentagon, regular      29
Permutation      67
Permutation, even or odd      90
Phantom figure      22
Polygon, symmetries of      33
Presentation      92
QuasiTiler      53 19
Reflection      19
Regular polygon      29
Regular polygon, symmetries of      30
Regular solid      95
Relation      92
Rigid motion of the plane      15
Rigid motion, glide reflection      22
Rigid motion, reflection      19
Rigid motion, rotation      16
Rigid motion, rotation, measured counterclockwise      28
Rigid motion, translation      15
Rotation      16
Rotation, measured counterclockwise      28
Rotation, rotocenter      16
Rotocenter      16
Rotocenter, equivalent      44
Rules of exponents      32
Silly walks      42
Spokes of a wheel      17
Square, symmetries of      29 33
Strip pattern      39
Subgroup      61
Symmetric group      68
Symmetries of a polygon      33
Symmetries of a square      29 33
Symmetry      27
Symmetry type      36 71
Symmetry type, $C_{N}$, cyclic      36
Symmetry type, $D_{N}$, dihedral      37
Timbanidis, Nicolas      34
Translation      15
Transposition      71 90
Triangle, multiplication table      35
Trivial symmetry      27
Wallpaper pattern      see “Wallpattern”
Wallpattern      43 19
Я      19
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