Algebra a Lykeiou- Sxoliko Biblio 2011-New

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  • -

  • . .. 2

    . .. 2

    . .

    . .

    . .

    , . . , . . , . .

    : 1991

    : 1992, 1993, 1994, 1995, 1996, 1997, 1998

    .

  • . . /

    : / /

    : /

    :

    :

  • .

    (2010)

    , .

    , . , . , . . . -

    :

    .

    (2010)

    . , . . -

    .

    (2010),

    . , . , . , . . .

    :

    1 .

    .

    ,

    .

    2 ,

    .

    3 ,

    1 2 .

    , , 1 2 .

    4 1 2

    , , 1 2 .

    5 ,

    -

    (pattern) .

    6 . -

  • .

    7 ,

    . -

    .

  • . 1 92 13

    1: 1.1 - 201.2 29

    2: 2.1 432.2 542.3 612.4 69

    3: 3.1 1 793.2 863.3 2 88

    4: 4.1 1 1014.2 2 1064.3 & 115

    5: 5.1 1215.2 1255.3 1325.4 - 141

    6: 6.1 1456.2 152

    6.3 (x) = x + 1596.4 - 1686.5 -- 175

    7: 7.1 : (x) = x2 1887.2 : (x) = 1947.3 : (x) = x2+x+ 199

    207

    - 213

    x

  • .1

    , , , , . - . . : , .

    : , 2 2 .

    2 2 : 2 2a a . : P Q , , P Q , P Q P Q .

    P Q P, Q. P , Q (1). (1) , , .

    . , , P Q - P . , P Q , P Q - . , .

  • 10 10

    : 2 2 (1) (2), , . : 9 , .

    2 2 , 2 23 3 , 3 3 z .

    9 , , . , , :

    :

    . P Q , , P, Q Q, P, P Q , , P Q P Q .

    P Q P Q. : , .

    , 0 0 . ,

    0 0 0

  • - 11 11

    P Q , P Q .

    P Q P Q .

    2 2 1 0x x x , 2x x

    2 1x , , : 2 20 1 0x x x .

    : 9 1x , 9 0x 1x -

    .

    :

    -, -.

    0 z 0 z ,

    0 0 z z 0 z

    P Q , P Q .

    P Q P Q . ,

    ( 1) 0x x ( 1)( 1) 0x x x , - 1x .

  • 12 12

    I. , - . .

    1. 2 9 3

    2. 2 1

    3. 2 1 z z

    4. 22 4 z z

    5. 22 4 ! !

    6. 22 4

    7. 2 4 2

    8. 2 4 2 ! !

    9. 2 3 6

    II. .

    1 2 0x x 0 2x xz z 2 2 0x x z 2x 3 2 4x 2 2x x

    4 2 4 0x x 0x

    5 2 0 1 0x x x x 0 2x x 6 2 4 0x x ! 2x

  • - 13 13

    .2

    , .. , , , , . , .. , - , . - , .. -, . , - , , - . Cantor:

    , , .

    , , .

    , , . . - . , , - . 1000000, .

    , , . : 9 ` , 9 ] , 9 _ 9 \ .

  • 14 14

    x , x x , x x x .

    35` , 3

    5_ , 2 ] , 2_ , 2 \ .

    :

    ) , , . .., 2, 4 6, :

    ^ ` 2, 4, 6 , - , -. 1 100

    ^ ` 1, 2, 3, ... , 100 , 1

    v, , -

    : 1 1 1

    = 1, , , , ... 2 3 4

    - . ) - , , :

    ^ `0x x !\ x\ , 0x ! .

    ^ ` x x]

  • - 15 15

    , , , :

    ^ ` x x x: , x . - . :

    ^ ` 1, 2 ^ `= ( 1)( 2) 0 x x x \ ( 1)( 2) 0x x 1 2, . - .

    , . : , - . =.

    ^ `= 1, 2, 3, ... , 15 ^ `= 1, 2, 3, ... , 100 - . .

    , .

    . : i) , . ii) , . iii) , = .

  • 16 16

    ^ `2 1x x \ . , 2 1x . , , { }. :

    . .

    Venn Venn. x ,

    . , , ,` ] _ - =\ . - , - .

    x , .

    ^ ` 1,2,3,...,10 :

    ^ ` 1,2,3,4 ^ ` 3,4,5,6 . x ^ `1,2,3,4,5,6 ,

    , - .

  • - 17 17

    :

    , - - .

    :

    ^ ` x x x

    x ^ `3,4 .

    :

    , - - ,

    :

    ^ ` x x x , - , .

    x ^ `5,6,7,8,9,10 , .

    :

    .

    :

    ^ ` x x

  • 18 18

    I. 1. - .

    2. - ;

    3. Venn - ` , ] , _ \ .

    3,5 0 10 135

    2,3 205

    100 5 ` ] _

    II. . 1. ^ `= 16x x` ^ `= 24x x` ,:

    ) =............................ ) =................ 2.

    ^ `= x x ^ `= x x . : ) =....... ) =...... ) =...... ) B=......

    III. . 1. . : ) ) ) )

    2. . : ) ) ) )

    IV. . 1. , .: ) = ) = ) () = ..

    2. . ) ) = .

  • 1

    . - Pascal Fermat 17 . - , - , , , 16 17 .. ' - , , . . 18 Bernoulli, Moivre, Laplace Gauss. Laplace . Laplace - , . , - Gauss. - , -

  • 20 1.

    . , 19 , , . , (Chebyshev, Markov, Von Mises, Kolmogorov .., . . - , , , , , , . . - . -, .

    1.1-

    , 100 , 760 mm Hg, . , , t. - (deterministic) . , (- ) . - (random experiment). , - ,

  • 1.1- 21

    . :1. .2. .3.

    .4.

    .5. .6. .7. , 5 ..,

    -.8.

    1.

    9. .

    . - (sample space) .

    1, 2,...,

    , :

    = {1, 2,...,}.

    , , , = {, }. , 1, 2, 3, 4, 5, 6. , ={1,2,3,4,5,6}.

    - (event) . , = {2,4,6}, B = {1,3,5} = {6} .

  • 22 1.

    , 6. - . . , , . , - , . - . , , = {2,4,6} , - 2 4 6. -, , . . . . (). , = {1,2,3,4,5,6} = {2,4,6} () = 3, () = 6 (} = 0.

    , . -, - , . , , :

    , , .

  • 1.1- 23

    , - , , .

    ', -, . ' - .

    _, - -, . _ = '.

    . - , - .

    -

    ' ( )

    ( )' - ( ')

  • 24 1.

    , = {1,2,3,4} = {2,4,6}. 1, , , - , ' , ', , ( )', ( - ), .

    - - , = {2,4,6} = {1,3,5}. - , - . . :

    , = . - .

    1 . i) . ii)

    : 1: 2: 2 3: 2 4: 5: iii) '3, 5 2, 5 4.

    i) ,