Gauss Hypergeometric Equation
This famous differential equation is
x(1 x) y + [c (a + b + 1) x] y aby = 0,
where a, b, and c are constants. The coefficients
of this equation may look rather strange, but we
shall find that they are perfectly adapted to the

LAPLACE TRANSFORMS
L[ f ( x)]:= e
px
f ( x)dx = F ( p); p
0
L
is a linear
operator, that is;
L[ f + g ] = L[ f ] + L[ g ].
Laplace transforms of certain
functions
L[1] = e
px
0
L[ x ] = e
n
px
0
L[e ] = e
ax
0
1
dx =
p
n!
x dx = n +1
p
n
1
e dx =
;p>a

Jonathan Bergknoff
Herstein Solutions
Chapters 1 and 2
Throughout, G is a group and p is a prime integer unless otherwise stated. A B denotes that A is a
subgroup of B while A E B denotes that A is a normal subgroup of B.
H 1.3.14* (Fermats Little Theorem

A Bit of Fun: Fun with Bits
By bmerry TopCoder Member
Discuss this article in the forums
Introduction
Most of the optimizations that go into TopCoder challenges are high-level; that is, they
affect the algorithm rather than the implementation. However, on

Computational Complexity: Section 2
By misof topcoder member
read Section 1
In this part of the article we will focus on estimating the time complexity for recursive
programs. In essence, this will lead to finding the order of growth for solutions of
recu

Tutorial 1
Tutorial1
Supposepostaldepartmentprints
only 5 and 9 cent stamps prove that
only5and9centstampsprovethat
itispossibletomakeupanypostage
ofncentsusingonly5
f
i
l
and9
d cent
stampsforn=>35
p
Fibonacci Sequence
FibonacciSequence
Defn:F(0)
Defn:
F

Gennady Korotkevich
Apart from interesting problems and breathtaking competition, the algorithm contests
have their own astonishing personalities. Let me introduce the today's hero: Gennady
Korotkevich. His name is also spelled Henadzi Karatkevich sometim

Representation of Integers and Reals: Section 2
By misof TopCoder Member
read Section 1
Rumor: Floating point variables can store not only numbers but also some strange
values.
Validity: True.
As stated in the previous answer, the standard reserves both t

Computational Complexity: Section 1
By misof topcoder member
Discuss this article in the forums
In this article Ill try to introduce you to the area of computation complexity. The article
will be a bit long before we get to the actual formal definitions b

Representation of Integers and Reals: Section 1
By misof TopCoder Member
Discuss this article in the forums
Choosing the correct data type for your variables can often be the only difference
between a faulty solution and a correct one. Especially when the

Birla Institute of Technology & Science- Pilani, K K Birla Goa Campus
Discrete Structures for Computer Science (CS/IS F222), Test - I
Semester I, Year: 2012-2013
Date: 13-09-2012, Duration: One hour, Total Marks: 75, Closed Book
Note:
Different parts of t