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Metric and Vector Space [1]

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: 
  1. K. C. Sarangi, Real Analysis and Metric Space, RBD, Jaipur.
  2. P.B. Bhattacharya, S.K.Jain and S.R. Nagpaul, Basic Abstract Algebra , Cambridge University Press.
  3. G. C. Sharma, Modern Algebra, Shivlal Agarwal & Co. Agra.
References: 
  1. Deepak Chatterjee,Abstract Algebra.PHI. Ltd., New Delhi.
  2. I.N. Herstein, Topics in Algebra , Wiley Eastern Ltd., New Delhi
  3. Malcolm Birkoff, Abstract Algebra , Cambridge University Press.
Academic Year: 
2014-2015 [2]

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Links:
[1] https://maths.iisuniv.ac.in/courses/subjects/metric-and-vector-space-2
[2] https://maths.iisuniv.ac.in/academic-year/2014-2015