Thiagarajar college (autonomous), madurai – 9




НазваниеThiagarajar college (autonomous), madurai – 9
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Unit

Chapter/Section

I

Chapter 2 : 2.1 to 2.5 , 2.7

II

Chapter 3 : 3.1 to 3.4

III

Chapter 4 : 4.2 to 4.6

IV

Chapter 5 : 5.2,5.3 Chapter 6: 6.1,6.2

V

Chapter 7 : 7.1,7.2 Chapter 8: 8.1 to 8.4




Reference Book : An Introduction to Formal Languages and Automata - Peter Linz

– 4th edition, Jones and Bartlett – 2006


THIAGARAJAR COLLEGE (AUTONOMOUS), MADURAI – 625 009

(Re- Accredited with 'A' Grade by NAAC)

Department of Mathematics

(From 2011 – 2013 batch onwards)

Course : M.Sc. Code No. :

Semester : III No. of hours allotted : 6

Paper : Elective I or II No. of credits : 5

Title of the Paper : Differential Geometry


Course objective : To introduce the curve in space, to find geodesics curvature, torsion of a curve and various applications in differential geometry

Unit - I (18 Hours)

The Theory of space curves : Definition - Arc length - Tangent and normal, binormal – curvature and Torsion of a curve – contact between curves and surfaces – involutes and evolutes – intrinsic eqns.


Unit – II (18 Hours)

The metric and local intrinsic properties of surfaces : Definition – curves on a surfaces – surface of revolution – Helicoids – metric- intrinsic properties – Geodesic – canonical geodesic equation normal property of Geodesic eqns. – existence theorem – Geodesic curvature – Gauss – Bonnet theorem – Gaussian curvature.


Unit - III (18 Hours)

The second fundamental form : Definition – principle of curvature - lines of curvature - developable – developable associated with space curves - minimal surface – ruled surface – fundamental existence theorem for surfaces.


Unit - IV (18 Hours)

Differential geometry of surface in the large : Compact surfaces whose points are umbilics – Hilberts Lemma – complete surfaces – complete surfaces of Gaussian Curvature – characteristics of the complete surface – Hilberts theorem – conjugate points on geodesic


Unit - V (18 Hours)

Tenser algebra: Vector spaces – dual spaces – Tenser product of vector space – transformation formula – inner product


Text Book: An introduction to Differential Geometry - T.J. Willmore, 2001


Unit

Chapter/Section

I

I(I.2 to I.5, I.7 to I.9)

II

II(II.1 to II.5, II.7 to II.11, II.13 to II.16)

III

III( III.1 to III.5, III.7, III.8, III.11)

IV

IV(IV.1 to IV.5, IV.7, IV.8)

V

V(V.1 to V.5, V.7)



Reference Book: Differential Geometry – Mittal and Agarwal,

Krishnaprakasam Publishers, Meerut, 1998

THIAGARAJAR COLLEGE (AUTONOMOUS), MADURAI – 625 009

(Re- Accredited with 'A' Grade by NAAC)

Department of Mathematics

(From 2011 – 2013 batch onwards)

Course : M.Sc. Code No. :

Semester : III No. of hours allotted : 6

Paper : Elective I or II No. of credits : 5

Title of the Paper : Combinatorics


Course objective: To introduce combinatorial techniques for solving enumeration problems.

Unit – I (18 Hours)

Permutations and Combinations: Introduction- rules of sum and product- Permutations and Combinations- Distributions of Distinct Objects- distributions of non distinct objects.
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