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IIMC Math Syllabus Overview

The document outlines the syllabus for a mathematics qualifying exam, including 10 topics: 1) set theory, 2) functions, 3) differentiation, 4) partial differentiation, 5) integration, 6) differential equations, 7) combinatorial analysis, 8) linear algebra, 9) coordinate geometry, and 10) progressions. It provides a brief overview of the concepts covered within each topic, such as basic set operations, types of functions, derivatives of commonly used functions, integration techniques, matrices, and arithmetic, geometric and harmonic progressions.

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Mukul Mathur
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210 views2 pages

IIMC Math Syllabus Overview

The document outlines the syllabus for a mathematics qualifying exam, including 10 topics: 1) set theory, 2) functions, 3) differentiation, 4) partial differentiation, 5) integration, 6) differential equations, 7) combinatorial analysis, 8) linear algebra, 9) coordinate geometry, and 10) progressions. It provides a brief overview of the concepts covered within each topic, such as basic set operations, types of functions, derivatives of commonly used functions, integration techniques, matrices, and arithmetic, geometric and harmonic progressions.

Uploaded by

Mukul Mathur
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Indian Institute of Management Calcutta

Syllabus for Mathematics (Qualifying) (OM 100)


1. Set Theory: Definition, Notation, Membership, Subsets, Supersets, Cardinality,
Countable Sets, Uncountable Sets, Finite Sets, Infinite Sets, Cartesian Product,
Commonly used Sets, Basic Set Operations, and Venn Diagrams.
2. Functions: Definition, Linear Functions, Quadratic Functions, Cubic Functions,
Plotting the graphs of functions using horizontal and vertical shift, Asymptotes,
Rational Functions, Exponential and Logarithmic Functions. One to one, Many to
one, Into and Onto functions, Inverse of a function (if exists), Zeros of a function.
Limits, continuity and differentiability of a function.
3. Differentiation: Introduction to Derivatives, Derivatives of some commonly
used Functions, Chain Rule, Derivatives of sum/difference/product of two
functions, Derivatives of Rational Functions, Higher Order Derivatives,
Applications and Interpretation of Derivatives, Determining maxima, minima,
points of inflection of a function, Determining the curvature (convex/concave) of
a function
4. Partial Differentiation: Differentiation of functions of more than one variable.
5. Integration: Introduction, Integration by Substitution, Integration by partial
fraction, Integration by parts, Introduction to Definite Integration and its
properties. Applications of definite integration to determine the area under a
simple curve and the area enclosed between two curves
6. Differential Equations: Order and degree of differential equations, Solving first
order linear differential equations
7. Combinatorial Analysis: Permutations and combinations, Binomial theorem for
a positive integral index, properties of binomial coefficients.
8. Linear Algebra: Introduction to Matrices, Addition, Subtraction, Scalar and
Matrix Multiplication, Transpose of a matrix, Matrices with special characteristics
such as Diagonal matrix, Scalar matrix, Identity matrix, Symmetric and Skew-
symmetric matrix, Determinants, Properties of Determinants, Solving Systems of
Simultaneous Linear Equations using Cramers Rule, Gaussian Elimination
method, Gauss Jordan Elimination method.
9. Co-ordinate Geometry: Cartesian coordinates, distance between two points, shift
of origin. Equation of a straight line in various forms, distance of a point from a
line, Lines through the point of intersection of two given lines, equation of the
bisector of the angle between two lines, Equation of a circle.
10. Progression: Arithmetic, geometric and harmonic progressions, arithmetic,
geometric and harmonic means, sums of finite arithmetic and geometric
progressions, infinite geometric series, sums of squares and cubes of the first n
natural numbers

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