Metric and Vector Space
Paper Code:
MAT602
Credits:
3
Contact Hours:
45.00
Max. Marks:
100.00
Objective:
o To improve basics in mathematics.
o To improve analytical skill.
Unit I:
I
9.00
Metric Space: Definition with examples, Bounded set, Open set, Closed set, Neighbourhoods, Boundary points, Limit points and Exterior point, Closure of a set, Metric Subspace.
Unit II:
II
9.00
Continuous mappings, Sequence in a Metric Space, Cauchy Sequence, Subsequence, Completeness of Metric Space.
Unit III:
III
9.00
Separable Space, Contraction Mapping, Banach’s contraction Mapping, Compact spaces and Compact sets, Connected Spaces and Connected sets, Bolzano’s Theorem, Product Spaces
Unit IV:
IV
9.00
Vector space: Definition with Examples, Sub-space, Linear combination of vectors, Linear Span.
Unit V:
V
9.00
Linearly dependent and independent vectors and their simple properties, Bases and dimension.
Essential Readings:
- K. C. Sarangi, Real Analysis and Metric Space, RBD, Jaipur.
- P.B. Bhattacharya, S.K.Jain and S.R. Nagpaul, Basic Abstract Algebra , Cambridge University Press.
- G. C. Sharma, Modern Algebra, Shivlal Agarwal & Co. Agra.
References:
- Deepak Chatterjee,Abstract Algebra.PHI. Ltd., New Delhi.
- I.N. Herstein, Topics in Algebra , Wiley Eastern Ltd., New Delhi
- Malcolm Birkoff, Abstract Algebra , Cambridge University Press.
Academic Year:
