Entrance Exam for MSc Mathematics in Mysore University

Is there any entrance exam for MSc Mathematics from Mysore University, can you please provide me information about it ?

[Kiran Chandar]

Yes Mysore University conduct entrance exam for taking admission in MSc Mathematics.

For you here I am giving you eligibility criteria of entrance exam and syllabus of this exam for doing preparation.

Eligibility criteria for entrance exam:
Candidates who are appearing or have appeared for Final semester/Year of B.Sc./B.Sc. Ed. (RIE) course with
Mathematics as Major/Optional subject are eligible to write the entrance exam.

Eligibility criteria for Admission:
Candidates must have 45% of marks for admission.
For SC, ST and Cat. I candidates must have 40% marks for admission, after deducting 3% for each extra year over normal duration of the course.

Syllabus of entrance exam:
Analytical Geometry:
Cartesian coordinates in three dimensional space – Relation between cartesian coordinates
and position vector – Distance formula (cartesian and vector form) –
Division formula (cartesian and vector form) – Direction cosines – Direction ratios
– Projection on a straight line – Angle between two lines – Area of triangle –
volume of a tetrahedron.
Straight line – Equations of straight lines (cartesian and vector form) - Planes –
Equations of planes (cartesian and vector form) - Normal form – Angle between
planes – Coaxial planes – Parallel and perpendicular planes – length of a
perpendicular form a point to a plane – Bisectors of angles between two planes –
Mutual position of a lines and planes – Shortest distances between two skew lines.
Quadric Curves:
Translation and rotation of cartesian axes in a plane – Curves of second degree –
Discriminant and trace - theorem on discriminant and trace – removing the mixed
term – removing linear terms – proof of the theorem. The set of points   y x,
satisfying equation 0 2 2 2      F Ey Cy Bxy Ax is either empty or a point or
consists of one or two lines or is a parabola, an ellipse or a hyperbola – problems
there on – Polar equations of a conic – problems there on – Quadratic Surfaces –
Sphere – Cylinder – Cone - Ellipsoid – Hyperboloids – Paraboloids - Ruled
Surfaces.
UNIT - II
Differential Calculus:
Real Numbers – Inequalities – Absolute Value – Intervals – Functions – Graphs –
Limit of a function – Left hand and right hand limits –   definition of
continuity of a function - problems. Differentiation – Linear approximation
theorem – derivatives of higher order – Leibnitz’s theorem – Monotone functions -
Maxima and Minima – Concavity, Convexity and points of inflection. Polar
coordinates- angel between the radius vector and the tangent at a point on a curve –
angle of intersection between two cnurves – Pedal equations – Derivative of arc
length in cartesian, parametric and polar coordinates, curvature – radius of
curvature – circle of curvature – evolutes.
Differentiability and its applications:
Differentiability- Theorems – Rolle’s theorem – Lagranges’s Mean valve theorem
– Cauchy’s mean value theorem – Taylor’s theorem – Maclaurin’s theorem –
Generalized mean value theorem – Taylor’s infinite series and power series
expansion – Maclaurin’s infinite series – Indeterminate forms.
Asymptotes – Envelopes – Singular points – Multiple points – cusp, nodes and
conjugate points – Tracing of standard curves with Cartesian and polar equations.
Partial Derivatives:
Functions of two or more variables – Explicit and implicit functions – The
neighborhood of a point – The limit of a function – Continuity – Partial derivatives
– Differentiable functions – Linear approximation theorem – Homogeneous
functions – Euler’s theorem – Chain rule – Change of variables – Directional
derivatives – Partial derivatives of higher order – Taylor’s theorem – Derivatives
of implicit functions – Jacobian – Some illustrative examples.
UNIT - III
Theory of Numbers:
Division Algorithm - Divisibility - Prime and composite numbers - Proving the
existence and uniqueness of GCD and the Euclidean Algorithm - Fundamental
theorem of Arithmetic - The least common multiple – congruences - linear
congruences - Wilson’s theorem - Simultaneous congruences - Theorem of
Euler, Fermat and Lagrange.
Theory of Equations:
Theory of Equations – Euclid’s algorithm - Polynomials with integral coefficients
– Remainder theorem – Factor theorem – Fundamental theorem of algebra
(statement only) – Irrational and complex roots occur in conjugate pairs – Relation
between roots and coefficients of a polynomial equation – symmetric functions –
Transformations – Reciprocal equations – Descartes rule of signs – Multiple roots
- Solving cubic equations by Cardon’s method – solving quartic equations by
Descarte’s and Ferrari’s Method.
Group Theory:
Definition and examples of groups – Some general properties of Groups
Permutations - group of permutations, cyclic permutations, Even and odd
permutations. Powers of an element of a group – Subgroups – Cyclic groups, n Z
and Z . Cosets, Index of a group, Lagrange’s theorem consequences. Normal
subgroups, Quotient groups – Homomorphism, Isomorphism, Automorphism.
Fundamental theorem of homomorphism – Isomomorphism – Direct product of groups – Cayley’s theorem.

For full syllabus I am uploading a pdf file which is free to download: