Study Materials
Click on the item to get full text in pdf format.
A) Some class notes regarding Real Analysis (Countable Set and Elements of Point Set Theory)
Definition and concept of countable set; Some important theorems related to countable set; countability of Rational number system and Real numbers in (0, 1)
Some important problems and their solutions on Rational and Real numbers system
Definitions and concepts of point set theory; Interior, Limit and Adherent points; Open, Closed and derived sets
Important theorems regarding point set theory
Definitions, concepts and theorems regarding cover, covering and compact set; Bolzano-Weierstrass theorem for set; Heine-Borel property
B) Some class notes regarding advanced group theory
Homomorphism, Automorphism, Inner automorphism and Group of automorphism and corresponding theorems
Group of automorphism of finite and infinite cyclic group and some important theorem
Understanding of Commutator subgroups and corresponding some theorem
Concept Characteristic subgroup and some important theorems
Concept and properties of External direct products and corresponding theorems
Understanding Internal direct product and some important theorems
More discussions and theorems on External and Internal direct products
Some problems on External and Internal direct products
Class equation and Conjugacy relation
C) Numerical Analysis
Numerical solution of equations and concept of Tabular and Bisection method
Concept of Fixed-point iteration method
Concept of Newton-Raphson
Regula Falsi Method and Secant Method
D) Computer programming in C
Computer's fundamentals and introduction to the programming language C
Structure of C program, Library functions and some examples if simple programs
Relational operators, Looping, Decision making and some examples
Arrays, User defined functions, and example of simple programs
F) Cardinality of sets
Discussion about equipotent sets, Cardinality, countable set, Peano's Axioms, Well ordering principle and Principle of Mathematical induction.