over view of syllabus of this course

Natural Number, Whole Number, Integers
Even number, Odd Number, Properties of Divisibility.
· Prime Numbers and Composite Numbers and their properties.
Rational Numbers, their properties and representation.
H.C.F or G.C.D. and L.C.M, Co-Prime and Twin Prime numbers and Their properties.
Method to Convert decimal to Rational and Vise-versa, Irrational Number.
Real Numbers, their representation and properties.
Tree form of Different types of Real Numbers.
Important Symbols (Part 1) such as "infinity, number line, implies, iff"
Important Symbols (Part 2) such as "min, max, <, >, <=, >=, "
Important Symbol (Part 3) Such as "Modulo, Factorial, congruent, for all"
Sigma, Pie, Summation, Permutation, Vers(x), Covers(x)
Combination (nCr), exp(x), symbol(e)
fast calculation in Mathematics
Double factorial and their representation

Definition of set, form of representation (Roster and set builder form)
Types of sets, conversion of forms
pair set, subset, equal set and their properties
super set, Proper subset, Finite and infinite set, equivalent set.
Venn diagram, power set, Universal set, some operations on sets.
Union, intersection, compliment of sets, difference of 2 set.
Problems based on set theory.

Definition of interval, types (open interval, closed, open-closed, closed-open)
Graphical and set builder notation of different intervals.
Intersection and Union of interval, Problems based on intervals.

Definition of inequality and examples, operation on inequality
Properties of inequality, reciprocal of number, Some definition (solution set)
Solution of single and double inequality
System of inequality, inequality of the form a.b and a/b is positive or negative
Properties of inequality, solution of inequality of the form (x-a) *(x-b)> or >=
Properties of inequality, solution of inequality of the form (x-a) *(x-b) < or <
double inequality of the form f(x) <g(x)< h(x), operation of inequality
squaring of inequality, and some important results using inequality.

Definition of modulus, their representation and geometrical meaning of modulus
Properties of Modulus with suitable examples
Properties of Modulus with suitable examples (|x| < or > a when a>0)
Properties of Modulus with suitable examples (|x| < or > a when a<0 and a=0)
max, min in term of modulus, steps to solve inequality involved modulus
problems based on equality involving modulus.
problems based on Multiple modulus with equality
problems based on inequality involving modulus.
Square root, Multiple modulus involving inequality
Relation between Square root and Modulus with suitable examples.

Quadratic express (definition and their standard and their sign scheme)
Sign scheme of quadratic expressions when D=0.
problems based on sign scheme of quadratic expressions.
Problem Based on Quadratic Expression

Definition and Examples of Monomial, Polynomial and rational function
Definition and Examples of Monomial, Polynomial and rational function
Wavy curve method to find sign scheme of rational function
Solving inequality using wavy curve method
Solution of Inequality involving Modulus using Wavy curve method
Min and Max Value of Quadratic Expression and factorization of Quadratic express