Applied Mathematics

Unit I: Numbers, Quantification and Numerical Applications

• Prime Numbers, Encryptions using Prime Numbers
• Binary Numbers
• Complex Numbers (Preliminary idea only)
• Indices, Logarithm and Antilogarithm
• Laws and properties of logarithms
• Simple applications of logarithm and antilogarithm
• Numerical problems on averages, calendar, clock, time, work and distance, mensuration, seating arrangement

Unit II: Algebra

• Sets
• Types of sets
• Venn diagram
• De Morgan's laws
• Problem solving using Venn diagram
• Relations and types of relations
• Introduction of Sequences, Series
• Arithmetic and Geometric progression
• Relationship between AM and GM
• Basic concepts of Permutations and Combinations
• Permutations, Circular Permutations, Permutations with restrictions
• Combinations with standard results

Unit III: Mathematical and Logical Reasoning

• Mathematically acceptable statements
• Connecting words/ phrases in Mathematical statement consolidating the understanding of "if and only if (necessary and sufficient) condition", "implies", "and/or", "implied by", "and", "or", "there exists" and their use through variety of examples related to real life and Mathematics
• Problems based on logical reasoning (coding-decoding, odd man out, blood relation, syllogism etc)

Unit IV: Calculus

• Introducing functions
• Domain and Range of a function
• Types of functions (Polynomial function; Rational function; Composite function; Logarithm function; Exponential function; Modulus function; Greatest Integer function, Signum function)
• Graphical representation of functions
• Concept of limits and continuity of a function
• Instantaneous rates of change
• Differentiation as a process of finding derivative
• Derivatives of algebraic functions using Chain rule
• Tangent line and equations of tangents

Unit V: Probability

• Random experiment, sample space, events, mutually exclusive events
• Independent and Dependent Events
• Law of Total Probability
• Bayes’ Theorem

Unit VI: Descriptive Statistics

• Types of data (raw data, univariate data, bivariate and multi-variate data)
• Data on various scales (nominal, ordinal, interval and ratio scale)
• Data representation and visualization
• Data interpretation (central tendency, dispersion, deviation, variance, skewness and kurtosis)
• Percentile rank and quartile rank
• Correlation (Pearson and Spearman method of correlation)
• Applications of descriptive statistics using real time data

Unit VII: Basics of Financial Mathematics

• Interest and interest rate
• Accumulation with simple and compound interest
• Simple and compound interest rates with equivalency
• Effective rate of interest
• Present value, net present value and future value
• Annuities, calculating value of regular annuity
• Simple applications of regular annuities (up to 3 period)
• Tax, calculation of tax and simple applications of tax calculation in Goods and service tax, Income Tax
• Bills, tariff rates, fixed charge, surcharge, service charge
• Calculation and interpretation of electricity bill, water supply bill and other supply bills

(Comparing interest rates on various types of savings; calculating income tax; electricity bills, water bill; service surcharge using realistic data)

Unit VIII: Coordinate Geometry

• Straight Line
• Circles
• Parabola

(only standard forms and graphical representation on two-dimensional plane)