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