Existence of Mathematics

TRICK 1
http://www.youtube.com/watch?v=pWtF94cTZ6k

The mathematics behind is
STEP 1 The piles are 
Pile 1 : 10
Pile 2 : 15
Pile 3 : 15
9

STEP 2 
(Pile 1)+1(+x from Pile2)
(Pile 2)=y+1+(x’ from Pile3)
(Pile 3)=y’+1+9

STEP 3
Now, the whole deck becomes
Deck = (10+1)+(x+y+1)+(x’+y’+1)+9

Since, x+y =15(Pile2) and x'+y' =15(Pile3)
Deck = (10+1)+(15+1)+(15+1)+9
Deck = 11(position1)+16(position2)+16(position3)+9

From the bottom, positions of selected cards is,
(11, 27, 43) => (38, 22, 6) from the top.

Adding 4 cards to the bottom, positions of selected cards become
(15, 31, 47)

STEP 4
Uping and Downing, causes the cards to be left at even position ie the Downs, with following positions :
(15, 31, 47)
(  8, 16, 24),
(  4,   8, 12),­
(  2,   4,   6),
(  1,   2,   3)

TRICK 2

References
http://www.youtube.com/results?search_query=mathematics+card+trick&oq=mathematics+card+&gs_l=youtube.3.0.0l2j0i10l3j0i5i10l5.7781.20275.0.22316.17.16.1.0.0.0.457.3182.1j8j6j0j1.16.0...0.0...1ac.1.11.youtube.Chhz7mOAxu4