### Mathematics Course Description

#### Mathematics

**Level I – Semester I**

**MAT111β: Vector Analysis (30 lecture hrs + 15 tutorial hrs) -(Credit value 2.5)**

Vector Algebra: Definition of a Vector, Addition and Subtraction, Components, Physical examples.

Vector Products:Scalar and Vector products including a brief introduction to determinants, triple products, Geometrical applica-tions. Differentiation and Integration of a Vector functions.

Vector Analysis:Scalar and Vector fields, grad, div, curl, Manipulation with combinations of these operators acting on combinations of fields.

Integral transformations: Line, Surface and Volume integrals, the divergence theorem, conservative and solenoidal fields, Greens theorem, Stokes theorem (3-D) form.

General Co-ordinates: Unit vectors in orthogonal curvilinear co-ordinates, elementary arc length and volume, curl, div, grad in curvilinear co-ordinates.

Method of assessment: end of semester examination

**MAT112δ: Differential Equations (15 lecture hrs + 7 tutorial hrs) -( Credit Value 1.25)**

Introduction, Equations of first order and first degree, Orthogonal trajectories, Clairant’s form, Linear equations, Theory of operators, Euler’s form, Simultaneous equations.

Method of assessment: end of semester examination

**MAT113δ: Introductory Statistics (15 lecture hrs + 8 tutorial hrs) -( Credit Value 1.25)**

Definition of Probability, Conditional Probability and the Independence of events, , The Law of Total Probability and Bayes’ Rule, Definition of random variables, Cumulative distribution function, Density functions for discrete random variables and continuous random variables, Expectations, Mean, Variance, standard deviation, Expected value of a function of a random variable, Moments, Central Moments, Moment Generating function, Bernoulli and Binomial Distributions, Hypergeometric Distribution, Poisson Distribution, Geometric Distribution, Uniform Distribution, Normal Distribution, Exponential and Gamma Distribution, Approximation: Binomial and Poisson by Normal.

Method of assessment: end of semester examination

**MAT1142: Mathematics for Biology (30 lecture hrs) Only for students following Biological Science Stream -( Credit Value 2 – Not counted for the Degree)**

Basic Algebra (including Complex Numbers), Logarithms, Trigonometric functions, Limits, The principle of Dif- ferentiation, Differentiation of a Product, Quotient and a function of a function, Maxima and Minima, Partial Differentiation, Total Differentiation, Homogeneous Functions and Eulers Theorem on Homogeneous functions, Integration as the converse of Differentiation, Integration by parts, Exact Differential equations, Definite Integral, Vectors, Determinants, Matrices, Introduction to Group Theory, Statistics for Chemistry( permutations, Configurations and Microstates, Molecular Assemblies, The importance of , W=W!/na! nb! ,The Boltzman Distribution.)

Method of assessment: end of semester examination

**Level I – Semester II**

**MAT121β : Algebra (30 lecture hrs + 15 tutorial hrs) -( Credit Value 2.5)**

Elementary set theory, Relations, mappings and functions, theory of polynomial equations in one variable including the statement of the fundamental theory, Newton’s relations between roots, solution of cubic and biquadratic equations, determinants, solution of equations using determinants nth roots of unity, factors of x^{n} − a^{n }, x^{n} + a^{n} ,x^{2n} − 2x^{n}a^{n} cos(nx) + a^{2n} , elementary group theory, rings and fields, complex theory approach through fields.

Method of assessment: end of semester examination

**MAT122β: Calculus (Real Analysis) (30 lecture hrs + 15 tutorial hrs) -( Credit Value 2.5)**

Classical Logic, Set theory, Field axioms, Real number system as a field, Functions and its properties, Real sequences, Continuity and Limits of functions, Differentiability.

Method of assessment: end of semester examination