Subject Matter Expert

Job Description

**Job Description**:
Subject Matter Expert - Mathematics

Location: Delhi, India.

The Role

What you’ll do
- Authoring Solutions for advanced questions from Mathematics textbooks.
- Online answering of Mathematics questions posted by students globally on Chegg Website.
- Quality review of solutions submitted by external answerers.
- Content feedback fixing
- Practice Content creation & review
- Video Content Reviews
- Work on the domain specific Ad-hoc Projects.

**Requirements**:

- M. Sc Mathematics/Applied Mathematics.
- Excellent in communication skills, both oral and written.
- Willing to work in rotational shifts.

SME Hiring - Mathematics Syllabus

Calculus:
Functions; Limits and Continuity, Transcendental Functions; Curve Sketching, Derivatives, Application of the Derivatives, Integration; Application of Integration, Integration Techniques; Sequence and Infinite Series; Power Series, Parametric Equations and Polar Coordinates, Differential Equations.

Functions of Several Variable; Vectors and 3d Geometry, Partial Derivatives; Multiple Integrals and Their Applications, Change of Variables, Polar, Spherical and Cylindrical Coordinates, Line Integrals, Flux, Green’ Theorem, Surface Integrals in 3d space. Vector Calculus.

Ordinary and Partial Differential Equations:
First-Order Differential Equations; higher-Order Linear Equations; Applications of Higher-Order Linear Equations; System of Linear Differential Equations; Laplace Transform; Series Solutions; System of Nonlinear Differential Equations

Wave, Heat Equations-Separation of variables and Fourier series: 1D and 2D-Laplace’s equation (in Cylindrical and Spherical Coordinates.)-Poisson’s Formula-Canonical forms, Nonlinear PDEs

Numerical Analysis:
Solutions of Equations in one variable, Interpolation and polynomial approximation, Numerical differentiation and integration Initial value problems for ordinary differential equations, iterative techniques in Matrix algebra. Euler Methods, Runge-Kutta Methods, Multistep Methods, Higher order Equations and systems, Second order Boundary value problems.

Discrete Structures:
Logic, Sets, and Functions, Algorithms, the Integers, and Matrices, Counting and Advanced Counting Techniques, Mathematical Reasoning, Recursive Definitions, Discrete Probability, Relations, Equivalence Relations and Partial Ordering, Graphs and Trees, Chromatic Number, Plane and Planar Graphs, A Five-Color Theorem, Independence Number and Clique Number, Matching Number, Connectivity, Digraphs and Networks.

Real Analysis:
Sets and functions, Mathematical induction, the real numbers, Sequence and series, limits, continuous functions, differentiation, Riemann integral, sequence of functions, Infinite series

Linear Algebra:
Systems of linear equations, Row reduction and echelon forms, Matrix operations, including inverses, Block matrices, Linear dependence and independence, Subspaces and bases and dimensions, Orthogonal bases and orthogonal projections, Gram-Schmidt process, Linear models and least-squares problems, Determinants and their properties, Cramer's Rule, Eigenvalues and eigenvectors, Diagonalization of a matrix, Symmetric matrices, Positive definite matrices, Similar matrices, Linear transformations, Singular Value Decomposition

Topology:
Countable uncountable sets, Topological spaces, connectedness and compactness, closed sets, and limit points, The countability axioms, separation axioms, The Tychonoff theorem, Metric space.

Complex Analysis:
Complex Number, Harmonic functions, Continuity and Differentiability, Complex Integration, Analytic function, Cauchy-Green's Formula, Power series, Radius of convergence, Conformal Mapping, Residues and Poles, Riemann Sphere, Singularity, Mobius Transformation.

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