I enable to find syllabus for m.sc. maths of entrace exam

Hello.
M.Sc. Mathematics is a postgraduate programme oftwo years,subdivided intofour semesters. The main objective of this course is to give first-hand knowledge in advanced applied mathematics and forefront research experience.

Colleges likeLOYOLA COLLEGE,CHENNAI,,IIT KANPUR,IIT DELHI conducts entrance test for taking admissions into M.Sc. Mathematics course. Students selected through entrance test would further have to go through a personal interview before final selection.

The entrance test consists of objective type questions and the syllabus for the same is usually from:

Real Analysis

Linear and Abstract Algebra

Calculus

Topology

REAL ANALYSIS : Basic topology,sequences and series, continuity, The Lebesgue Integral, Simple and Step Functions, Lebesgue integral of step functions, Upper Functions, Lebesgue integral of upper functions.

LINEAR AMD ABSTRACT ALGEBRA :

Permutations and combinations,Sylow theorems,groups of order p square, pq , polynomial rings, matrix rings

NUMBER THEORY :

Divisibility,Euclidean theorem, Eulers theorem,Arithmetic functions, roots and indices.

TOPOLOGY :

Orer of topology, base for a topology, connected spaces,compact space of the real line, countability axioms

PROBABILITY THEORY :
Nature of data and methods of compilation, representation of data,measures of central tendency,measuring variability of data, tools of interpreting numerical data, like mean, median,quartiles, standard deviation,skewness and kurtosis and correlation analysis

DIFFERENTIAL GEOMETRY :

Tensors,crves with torsion,envelopes and developable surfaces, involutes,tangent planes and funcdamental magnitudes.

LINEAR PROGRAMMING :

Convex sets,opened and closed half-spaces , sensitivity analysis,parametric programming, transportation problems.

COMPLEX ANALYSIS :

Geometric representation of numbers,complex valued functions,power series,trigonometric functions, Cauchys theorem for rectangle, in a disk and its general form.

GEOMETRY OF NUMBERS :

Lattices,Hermites theory on minima of positive definite quadratic forms.

ELASTICITY :

Analysis of strain, analysis of stress, Equations of Elasticity, Inverse and semi-inverse methods of solution, General Equations of the plane problems in polar co ordinates

VECTOR ANALYSIS :

Scalar and vector point functions,Greens and Stokes theorems, Curi-linear coordinates,the equation of motion and first integral.

FIELD THEORY :

Fields,theorem of Galois theory,Cyclotomic extensions,Lagranges theorem on primitive elements, degree field extensions and all other forms and applications of fields, and solvability of polynomials by radicals


M.Sc. Mathematics makes sure to provide advanced research skills and provide in-depth knowledge of reasoning and problem-solving skills. It incorporates foundation of mathematical thinking and teaches both pure and applied mathematics to the core. Students will be taught core mathematical subjects which includes probability theory, theoretical computer science, algebra, number theory, algebraic geometry, global analysis, dynamical systems, differential equations and many more.

FIELDS OF WORK

Students in this field can get work inthe government sector, financial sector in private firms and Universities. Work profile can be ofActuarial professional, Teacher, Database Manager, and External Auditor. Average starting salary after doing this course can be around4-5 lakhper annum and can go up after gaining some experience.

GOOD LUCK.