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• The student will learn all basic concept of mathematics, which help them to understand higher mathematics.
• Students of Foundation course or 2 year program.
• Master the Fundamentals of Math is organized into the following sections: Numbers and negative numbers Factors and multiples Decimals Fractions Mixed numbers Ratio and proportion Exponents Radicals Scientific notation
• 1. Introduction
• 2. Natural Number • 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
• 3. Set Theory • 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.
• 4. Interval • 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.
• 5. Inequality • 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 >=0 • Properties of inequality, solution of inequality of the form (x-a) *(x-b) < or <=0 • double inequality of the form f(x)
• 6. Modulus • 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
• 7. Monomial, Polynomial and Rational Function • Definition and Examples of Monomial, Polynomial and rational function