Indian Institute of Technology Madras
Department of Mathematics
MA 2130 Basic Graph Theory
Assignment-I
Notations and Definitions:
(1) (G) = mincfw_d(v) : v V (G), 4(G) = maxcfw_d(v) : v V (G).
(2) If G has vertices v1 , v2 , . . . , vn , the sequence (d(

MH2814 Probability & Statistics
Continuous Probability Distribution
Dr Tan Geok Choo
Division of Mathematical Sciences
School of Physical and Mathematical Sciences
Nanyang Technological University
Dr Tan Geok Choo (Division of Mathematical Sciences
MH2814

Nanyang Technological University
SPMS/Division of Mathematical Sciences
2016/2017 Semester 1
MH2814 Probability & Statistics
Assignment 1
Name &
Matriculation Number
Score:
IMPORTANT NOTE
1. Each assignment is allocated 10 points. If you do not score full

Nanyang Technological University
SPMS/Division of Mathematical Sciences
MH2814 Probability & Statistics
Tutorial 7
.
Topics: Geometric distribution and Poisson distribution; Poisson Approximation.
.
1. The probability that a student pilot passes the writt

MH2814 Probability & Statistics
Joint Probability Distribution
Dr Tan Geok Choo
Division of Mathematical Sciences
School of Physical and Mathematical Sciences
Nanyang Technological University
Dr Tan Geok Choo (Division of Mathematical Sciences
MH2814
Scho

MH2814 Probability & Statistics
Conditional Probability & Independent Events
Dr Tan Geok Choo
Division of Mathematical Sciences
School of Physical and Mathematical Sciences
Nanyang Technological University
Dr Tan Geok Choo (Division of Mathematical Scienc

MH2814 Probability & Statistics
Basic Probability Theory
Dr Tan Geok Choo
Division of Mathematical Sciences
School of Physical and Mathematical Sciences
Nanyang Technological University
Dr Tan Geok Choo (Division of Mathematical Sciences
MH2814
SchoolProb

MH2814 Probability & Statistics
Discrete Probability Distribution
Dr Tan Geok Choo
Division of Mathematical Sciences
School of Physical and Mathematical Sciences
Nanyang Technological University
Dr Tan Geok Choo (Division of Mathematical Sciences
MH2814
S

Classnotes - MA2030
Linear Algebra
Arindama Singh
Department of Mathematics
Indian Institute of Technology Madras
This is a modified version of the classnotes of A. V. Jayanthan and A. Singh
Contents
1
2
3
4
5
Vector Spaces
1.1 What is a vector space?
1.2

Indian Institute of Technology Madras
Department of Mathematics
MA 2130 Basic Graph Theory
Assignment-5
1. Write a proof of the fact that every tree is planar.
2. Draw a planar graph in which every vertex has degree exactly 5.
3. Suppose that e is a bridg

Matching Theory
Matching:
Let G = (V , E) be a simple graph. A subset M of E is called a
matching in G if no pair of edges e1 and e2 of M share a
common vertex.
Matching Theory
Matching:
Let G = (V , E) be a simple graph. A subset M of E is called a
match

MH2814 Probability & Statistics
Population & Samples
Dr Tan Geok Choo
Division of Mathematical Sciences
School of Physical and Mathematical Sciences
Nanyang Technological University
Dr Tan Geok Choo (Division of Mathematical Sciences
MH2814
SchoolProbabil

Nanyang Technological University
SPMS/Division of Mathematical Sciences
2016/2017 Semester 1
MH2814 Probability & Statistics
Assignment 2
Name &
Matriculation Number
Score:
IMPORTANT NOTE
Submission week: 29th August 2016 -2nd September 2016. (Week for Tu

Indian Institute of Technology Madras
Department of Mathematics
MA 2130 Basic Graph Theory
Assignment-2
Notations: n is the number of vertices and m is the number of edges in a graph G = (V, E).
(1) If G = (V, E) is a simple, connected, incomplete and n 3

MH2814 Probability & Statistics
Discrete Probability Distribution
Dr Tan Geok Choo
Division of Mathematical Sciences
School of Physical and Mathematical Sciences
Nanyang Technological University
Dr Tan Geok Choo (Division of Mathematical Sciences
MH2814
S

Nanyang Technological University
SPMS/Division of Mathematical Sciences
MH2814 Probability & Statistics
Tutorial 3
.
Topics: Bayes Rule. Random variables (Discrete , Continuous), Discrete Probability
distribution functions, Cumulative distribution functio

MH2814 Probability & Statistics
Expectation & Variance
Dr Tan Geok Choo
Division of Mathematical Sciences
School of Physical and Mathematical Sciences
Nanyang Technological University
Dr Tan Geok Choo (Division of Mathematical Sciences
MH2814
SchoolProbab

Nanyang Technological University
SPMS/Division of Mathematical Sciences
MH2814 Probability & Statistics
Tutorial 7
.
Topics: Geometric Distribution and Poisson distribution; Poisson Approximation.
.
1. The probability that a student pilot passes the writt

Selected Solutions
Math 420
Homework 2
1/20/12
1.5.8 Let
C11 C12
C=
C21 C22
be a 2 2 matrix. We inquire when it is possible to find 2 2 matrices A and B such that
C = AB BA. Prove that such matrices can be found if and only if C11 + C22 = 0.
It is easy to

Nanyang Technological University
SPMS/Division of Mathematical Sciences
MH2814 Probability & Statistics
Tutorial 1
.
MH2814 Assessments:
1. Final Examination (60%): 2-Hour.
2. Common Tests (30%): TWO 40-min common tests, each contributes 15%.
Dates: 16/9/

Nanyang Technological University
SPMS/Division of Mathematical Sciences
MH2814 Probability & Statistics
Tutorial 1
.
1. A construction company has five categories of employees as follows:
Category:
1
2
3
4
5
Salary ($ /month) : 600 700 800 900 1000
No. of

Nanyang Technological University
SPMS/Division of Mathematical Sciences
MH2814 Probability & Statistics
Tutorial 3
.
Topics: Bayes Rule. Random variables (Discrete , Continuous), Discrete Probability
distribution functions, Cumulative distribution functio

MH2814 Probability & Statistics
Sample Space
Dr Tan Geok Choo
Division of Mathematical Sciences
School of Physical and Mathematical Sciences
Nanyang Technological University
Dr Tan Geok Choo (Division of Mathematical Sciences
MH2814
SchoolProbability
of P

MA2130: Basic Graph Theory
Planar Graphs
Dr. S. Mishra, Department of Mathematics, I.I.T. Madras
November 7, 2016
Planar Graphs
Definition : A graph G = (V , E) is called a planar graph if it
can be drawn in the plane in such a way that every pair of
edge