# DR.SOURAV SIR'S CLASSES

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## ISI BSDS

## ABOUT THE

COURSE

## The programme of Statistical Data Science focuses on statistical methodologies, with emphasis on statistical machine learning, computational statistics and data analytics.

## The programme of Statistical Data Science focuses on statistical methodologies, with emphasis on statistical machine learning, computational statistics and data analytics.

## LIVE SESSIONS

## MOCK TEST SERIES

1.Online/Offline Classes

2.Comprehensive mock test series

3. Solutions to past years' entrance questions

4. Topic-wise analysis

5. Provision of complete study materials

6. Special doubt-clearing sessions

7. Recordings of every live class, ensuring you won't miss any session even if you can't attend live (24*7)

1. Complete Mock Tests on any topic you like

2. You can give the exams from your home using a phone or laptop or pc or a tablet.

3. After every exam complete solutions with marks will be provided to you.

4. Any doubts with any part you are free to ask us via what's app/email/call.

5. Segment wise preparation

6.Full length mock test

7.Checking by experts

## SYLLABUS

## Sets, relations and functions

Sets and their representations; Union, intersection, difference and complement of sets and their algebraic properties; Power set. Types of relations and equivalence relations. Functions as maps; One-one, into and onto functions; Essential real-valued functions such as polynomials, rational, trigonometric, logarithmic, and exponential functions; Equations involving polynomials, exponential and logarithmic functions; Inverse functions; Transformation of functions; Composition of functions; Graphs of simple functions.

## Complex number system

Different representations of complex numbers; Conjugate, modulus and argument of a complex number; Powers of complex numbers; Roots of unity; Quadratic equations and their solutions; Fundamental theorem of algebra.

## Sequence and series

## Basics of combinatorics

Permutation and combination; Fundamental principles of counting; Binomial theorem and its applications; Principle of mathematical induction and its applications.

## Limits, continuity and differentiability of functions

Definition of limit, continuity and differentiability; Properties of continuous functions and differentiable functions; Chain rule of differentiation; Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite, and implicit functions; Rolle’s theorem and mean-value theorem and their applications; Maxima and minima of functions of one variable.

Arithmetic and geometric progressions and their combinations; Convergence of infinite series; Sums of integer powers of natural numbers; Relationship between arithmetic and geometric means.

## Trigonometry

Trigonometric functions and their inverses; Trigonometric identities and equations; applications to measuring heights, computation of distances and areas.

Each candidate applying for admission to this programme has to take a selection test of duration 2 hours comprising 30 objective type questions in Mathematics at the Higher Secondary level (10+2 years programme). The level of the test will to be similar to the JEE Mathematics test. Sample questions will be released on the webpage. A single merit list will be released and candidates will be allowed to choose their preferred centres in that order.

## Integral calculus

Integrals as limits of sums; Properties of indefinite integrals; Fundamental theorem of calculus and its simple applications; Fundamental integral involving algebraic, trigonometric, exponential, and logarithmic functions. Integration by substitution and by parts; Definite integrals, their properties, and applications to determining areas of regions bounded by simple and standard curves.

## Coordinate geometry

## Basics of differential equations

Ordinary differential equations, their order and degree; First order linear differential equations; Solving differential equations by methods of separation of variables and substitution; Solution of homogeneous and first order linear differential equations.

## Vector algebra

Vectors and scalars; Addition of vectors; Components of a vector in two dimensions and three dimensional space; Scalar (dot) and vector (cross) products; Scalar and vector triple products; Simple properties and applications: Directions ratios, and direction cosines; Angle between two straight lines and skew lines; Point of intersection of two straight lines and shortest distance between two straight lines.

Algebra of matrices; Types of matrices; Matrices of order two and three; Evaluation of determinants; Adjoint and determinant of a matrix; Evaluation of the inverse of a nonsingular matrix; Properties of matrix inverses; Elementary transformations of a matrix; Rank of a matrix; Test of consistency and solution of simultaneous linear equations in two or three variables using matrices

Cartesian system and locus of a point; Straight lines and their intersections; Angles between straight lines and distance between a point and a straight line; Equation of a circle, its radius and centre; Equations of conic sections (parabola, ellipse, and hyperbola) in standard forms and in parametric forms; Tangent and normal at a point on a circle and on conics

## 3-dimensional geometry

Coordinates of points in 3D space; Angles between straight lines and planes; Intersec-on formulas

## Introductory statistics and probability

Measures of centrality and dispersion; Mean, median, mode, variance and standard deviation for grouped and ungrouped data. Probability of an event; Fundamental rules of probability calculation; Probability distribution; Binomial distribution; Bayes’ theorem.

In order to be eligible for admission, a student should have successfully completed 10+2 years of Higher Secondary Education (or its equivalent) with Mathematics and English as subjects of study.