MathematicsAlgebra
Euclidean And Analytical Geometry
Probability 
Introduction to Matrices  Part I Introduction to Matrices. Theory, definitions. What a Matrix is, order of a matrix, equality of matrices, different kind of matrices: row matrix, column matrix, square matrix, diagonal, identity and triangular matrices. Definitions of Trace, Minor, Cofactors, Adjoint, Inverse, Transpose of a matrix. Addition, subtraction, scalar multiplication, multiplication of matrices. Defining special types of matrices like Symmetric, Skew Symmetric, Idempotent, Involuntary, Nilpotent, Singular, NonSingular, Unitary matrices. 
Introduction to Matrices  Part II Problems
and solved examples based on the subtopics mentioned above. Some of
the problems in this part demonstrate finding the rank, inverse or
characteristic equations of matrices. Representing real life problems in
matrix form. 
Determinants Introduction to determinants. Second and third order determinants, minors and cofactors. Properties of determinants and how it remains altered or unaltered based on simple transformations is matrices. Expanding the determinant. Solved problems related to determinants.  Simultaneous linear equations in multiple variables Representing a system of linear equations in multiple variables in matrix form. Using determinants to solve these systems of equations. Meaning of consistent, homogeneous and nonhomogeneous systems of equations. Theorems relating to consistency of systems of equations. Application of Cramer rule. Solved problems demonstrating how to solve linear equations using matrix and determinant related methods. 
Basic concepts in Linear Algebra and Vector spaces Theory and definitions. Closure, commutative, associative, distributive laws. Defining Vector space, subspaces, linear dependence, dimension and bias. A few introductory problems proving certain sets to be vector spaces. 
Introductory problems related to Vector Spaces 
Problems demonstrating the concepts introduced in the previous
tutorial. Checking or proving something to be a subspace, demonstrating
that something is not a subspace of something else, verifying linear
independence; problems relating to dimension and basis; inverting
matrices and echelon matrices. 
More concepts related to Vector Spaces
Defining and explaining the norm of a vector, inner product,
GrahamSchmidt process, coordinate vectors, linear transformation and
its kernel. Introductory problems related to these. 
Problems related to linear transformation, linear maps and operators  Solved examples and problems related to linear transformation, linear maps and operators and other concepts discussed theoretically in the previous tutorial. 
Definitions of Rank, Eigen Values, Eigen Vectors, Cayley Hamilton Theorem Eigenvalues, eigenvectors, Cayley Hamilton Theorem 
More Problems related to Simultaneous Equations; problems related to eigenvalues and eigenvectors Demonstrating the Crammer rule, using eigenvalue methods to solve vector space problems, verifying Cayley Hamilton Theorem, advanced problems related to systems of equations. Solving a system of differential equations . 
A few closing problems in Linear Algebra Solving a recurrence relation, some more of system of equations. 
Vectors
Vectors 1a ( Theory and Definitions: Introduction to Vectors; Vector, Scalar and Triple Products) Introducing a vector, position vectors, direction cosines, different types of vectors, addition and subtraction of vectors. Vector and Scalar products. Scalar Triple product and Vector triple product and their properties. Components and projections of vectors. 
Vectors 1b ( Solved Problem Sets: Introduction to Vectors; Vector, Scalar and Triple Products ) Solved examples and problem sets based on the above concepts. 
Vectors 2a ( Theory and Definitions: Vectors and Geometry ) Vectors and geometry. Parametric
vectorial equations of lines and planes. Angles between lines and
planes. Coplanar and collinear points. Cartesian equations for lines
and planes in 3D. 
Vectors 2b ( Solved Problem Sets: Vectors and Geometry ) Solved examples and problem sets based on the above concepts. 

Vectors 3b ( Solved Problem Sets: Vector Differential and Integral Calculus )  Solved examples and problem sets based on the above concepts. 
Trigonometry 1a ( Introduction to Trigonometry  Definitions, Formulas ) Introducing trigonometric ratios, plots of trigonometric functions, compound angle formulas. Domains and ranges of trigonometric functions, monotonicity of trigonometric functions quadrant wise. Formulas for double and triple angle ratios. 
Trigonometry 1b ( Tutorial with solved problems based on Trigonometric ratios ) Problems based on the concepts introduced above. 
Trigonometry 2a ( Basic concepts related to Heights and Distances ) Applying trigonometry to problems involving heights and distances. Angles of elevation and depression. Sine and Cosine rule, half angle formulas. Circumradius, inradius and escribed radius. Circumcentre, incentre, centroid and median of a triangle. 
Trigonometry 2b ( Tutorial with solved problems related to Heights and Distances and other applications of Trigonometry )  Problems based on the concepts introduced above. 
Trigonometry 3a ( Introducing Inverse Trigonometric Ratios) Inverse trigonometric ratios  their domains, ranges and plots. 
Trigonometry 3b ( Tutorial with solved problems related to inverse trigonometric ratios ) Problems related to inverse trigonometric ratios. 
Trigonometry 4 ( A tutorial on solving trigonometric equations ) Solving trigonometric equations. Methods and transformations frequently used in solving such equations. 
Single Variable Calculus
Quick and introductory definitions related to Funtions, Limits and Continuity  Defining the domain and range of a function, the meaning of continuity, limits, left and right hand limits, properties of limits and the "lim" operator; some common limits; defining the L'Hospital rule, intermediate and extreme value theorems. 
Functions, Limits and Continuity  Solved Problem Set I  The Domain, Range, Plots and Graphs of Functions; L'Hospital's Rule  Solved
problems demonstrating how to compute the domain and range of
functions, drawing the graphs of functions, the mod function, deciding
if a function is invertible or not; calculating limits for some
elementary examples, solving 0/0 forms, applying L'Hospital rule. 
More advanced cases of evaluating limits, conditions for continuity of functions, common approximations used while evaluating limits for ln ( 1 + x ), sin (x); continuity related problems for more advanced functions than the ones in the first group of problems (in the last tutorial). 
Functions, Limits and Continuity  Solved Problem Set III  Continuity and Intermediate Value Theorems  Problems related to Continuity, intermediate value theorem. 
Introductory
concepts and definitions related to Differentiation  Basic formulas,
Successive Differentiation, Leibnitz, Rolle and Lagrange Theorems,
Maxima , Minima, Convexity, Concavity, etc  Theory and
definitions introducing differentiability, basic differentiation
formulas of common algebraic and trigonometric functions , successive
differentiation, Leibnitz Theorem, Rolle's Theorem, Lagrange's Mean
Value Theorem, Increasing and decreasing functions, Maxima and Minima;
Concavity, convexity and inflexion, implicit differentiation. 
Differential Calculus  Solved Problem Set I  Common Exponential, Log , trigonometric and polynomial functions  Examples and solved problems  differentiation of common algebraic, exponential, logarithmic, trigonometric and polynomial functions and terms; problems related to differentiability . 
Differential
Calculus  Solved Problem Set II  Derivability and continuity of
functins  Change of Indepndent Variables  Finding Nth Derivatives  
Differential Calculus  Solved Problems Set III Maximia, Minima, Extreme Values, Rolle's Theorem  
Differential Calculus  Solved Problems Set IV  Points of Inflexion, Radius of Curvature, Curve Sketching  
Differential Calculus  Solved Problems Set V  Curve Sketching, Parametric Curves  More examples of investigating and sketching curves, parametric representation of curves 
Introducing Integral Calculus  Definite and Indefinite Integrals  using Substitution , Integration By Parts, ILATE rule  Theory and definitions. What integration means, the integral and the integrand. Indefinite integrals, integrals of common functions. Definite integration and properties of definite integrals; Integration by substitution, integration by parts, the LIATE rule, Integral as the limit of a sum. Important forms encountered in integration. 
Integral Calculus  Solved Problems Set I  Basic examples of polynomials and trigonometric functions, area under curves  Examples
and solved problems  elementary examples of integration involving
trigonometric functions, polynomials; integration by parts; area under
curves. 
Integral Calculus  Solved Problems Set II  More integrals, functions involving trigonometric and inverse trigonometric ratios  Examples and solved problems  integration by substitution, definite integrals, integration involving trigonometric and inverse trigonometric ratios. 
Integral Calculus  Solved Problems Set III  Reduction Formulas, Using Partial FractionsI Examples and solved problems  Reduction formulas, reducing the integrand to partial fractions, more of definite integrals 
Integral Calculus  Solved Problems Set IV  More of integration using partial fractions, more complex substitutions and transformations  Examples and solved problems  More of integrals involving partial fractions, more complex substitutions and transformations 
Integral Calculus  Solved Problems Set V Integration as a summation of a series  Examples
and solved problems  More complex examples of integration, examples of
integration as the limit of a summation of a series 
Introduction
to Differential Equations and Solved Problems  Set I  Order and
Degree, Linear and NonLinear Differential Equations, Homogeneous
Equations, Integrating Factor  
Differential Equations  Solved Problems  Set II  D operator, auxillary equation, General Solution  Examples
and solved problems  Solving linear differential equations, the D
operator, auxiliary equations. Finding the general solution ( CF + PI ) 
Differential Equations  Solved Problems  Set III  More Differential Equations  More complex cases of differential equations. 
Differential Equations  Solved Problems  Set IV  
Multiple Variable Calculus
Applied Mathematics : An Introduction to Game Theory

Applied Mathematics : An Introduction to Operations Research
Introduction to Operations Research 