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COs  Course outcomes  Mapping Cos with POs (High3, Medium2, Low1) 
CO1  Understand the Euclidean distance function on R^{n} and appreciate its properties, and state and use the Triangle and Reverse Triangle Inequalities for the Euclidean distance function on R^{n}

PO1(3), PO2(2) 
CO2  Explain the definition of continuity for functions from R^{n} to R^{m} and determine whether a given function from R^{n} to R^{m} is continuous

PO2(2) 
CO3  Explain the geometric meaning of each of the metric space properties and be able to verify whether a given distance function is a metric

PO9(2) 
CO4  Distinguish between open and closed balls in a metric space and be able to determine them for given metric spaces
Define convergence for sequences in a metric space and determine whether a given sequence in a metric space converges

PO4(3) 
ModuleI (T5hr P0hr P6hr)
Metric Spaces: Definition and examples, open and closed spheres,
Project1: Write a report on applications of metric spaces.
Project2: Show that the class denote a set of all bounded sequence of real numbers is a metric space.
Project3: Show that the class of all sequences is a metric space.
ModuleII (T3hr P0hr P4hr)
Neighbourhoods, Interior points. Open set
Project4: Write a report on relation between boundary points, limit points. And their applications.
Project5(Flip class): Prove theorems on Neighbourhoods, Interior points
ModuleIII (T5hr P0hr P6hr)
Closed set, boundary points, limit points and isolated points, closure of a set, dense sets.
Project6: Write a report on difference between open set closed set and limit point , interior point with appropriate examples.
Project7: Write the difference between boundary points, limit points and isolated points explain through examples.
Project8 (Flip class): Prove theorems on closed set and dense sets.
ModuleIV (T4hr P0hr P6hr)
Separable metric spaces, sequences in metric space, convergent sequences, Cauchy sequences
Project9: Write a report on applications of convergent sequences and Cauchy sequences.
Project10: Every convergent sequence is bounded. Is the reverse true? Justify your answer with suitable example.
Project11(Flip class): Prove theorems on convergent sequences and Cauchy sequences.
ModuleV (T4hr P0hr P4hr)
Complete metric space, subspace, Cantor’s theorem. Continuous functions,
Project 12(Flip class): Prove theorems on Complete metric space, subspace.
Project13(Flip class): : Prove that addition, subtraction, multiplication and division (with condition) of continuous functions are continuous.
ModuleVI (T4hr P0hr P6hr)
Uniform continuity, Connectedness, connected subsets of separated sets.
Project14(Flip class): Prove theorems on Uniform continuity and Connectedness.
Project 15: Write the difference between continuity and uniform continuity and explain through a proper example..
Project16 (Flip class): Prove theorems on connected subsets of separated sets.
ModuleVII (T5hr P0hr P4hr)
Disconnected sets, contraction mappings, Banach fixed point theorem.
Project 17(Flip class): Geometrical interpretation of connected and disconnected sets.
Project18: Write some applications of Banach fixed point theorem.
Text Books:
Reference Books:
Introduction
PPT link: https://www.slideshare.net/NaliniSPatil/metricspace151515844
Study Material: Introduction to Metric spaces with examples
youtube link: https://youtu.be/6CLl5xx5XY
Examples on Metric Spaces
Study Material: http://more examples
Youtube link: https://youtu.be/etP21xln8iQ
Project1: Write a report on applications of metric spaces.
Theorems on Metric Spaces.
Study Material: Theorems on metric space
youtube link: https://youtu.be/Af03P1xVNSs?list=PLbMVogVj5nJSxFihVec4A3z_FOGPRCo
Project2: Show that the class denote a set of all bounded sequence of real numbers is a metric space.
Project3: Show that the class of all sequences is a metric space.
Project4: Write a report on relation between boundary points, limit points. And their applications
Project5(Flip class): Prove theorems on Neighbourhoods, Interior points
Project6: Write a report on difference between open set closed set and limit point , interior point with appropriate examples.
Project7: Write the difference between boundary points, limit points and isolated points explain through examples
Project8 (Flip class): Prove theorems on closed set and dense sets.
sequences in metric space
PPT link: https://www.slideshare.net/VishangSingh/analysissequencesandboundedsequences
convergent sequences
youtube link: https://youtu.be/DZT8o7Y08Mw
youtube link: https://youtu.be/FgRslqEYTJI
Project9: Write a report on applications of convergent sequences and Cauchy sequences
Project10: Every convergent sequence is bounded. Is the reverse true? Justify your answer with suitable example.
Project11(Flip class): Prove theorems on convergent sequences and Cauchy sequences.
Project12(Flip class): Prove theorems on Complete metric space, subspace.
Continuous functions
PPT link: https://www.slideshare.net/sumanmathews/continuousfunctions
youtubelink : https://youtu.be/hXkQqCBLRp8
Project 13: Prove that addition, subtraction, multiplication and division (with condition) of continuous functions are continuous.
Theorems on Continuous functions
PPT link: https://www.slideshare.net/VishveshJasani/continuityofafunction
Project14(Flip class): Prove theorems on Uniform continuity and Connectedness.
Project 15: Write the difference between continuity and uniform continuity and explain through a proper example
Project16 (Flip class): Prove theorems on connected subsets of separated sets.
Project 17(Flip class): Geometrical interpretation of connected and disconnected sets.
Project18: Write some applications of Banach fixed point theorem.
My Self Dr.Bhairaba Kumar Majhi,M,Sc,B.Ed,M.Tech(CSE),Ph.D(Mathematics ) ,Asst.Professor And HOD Department of Mathematics School Of Applied Sciences,Presently working at CUTM,Bolangir Campus.I have 16 Years of Experience in Teaching at Different Levels Of UG,PG & Engineering Mathematics.