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Download MTTS Expository Articles

The articles are prepared by Prof. S Kumaresan, the MTTS Programme Director and usually gets distributed to the MTTS/ Mini MTTS/ PTMT participants.

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Sl No Title Description Targeted Audience MTTS Level Downloads
11 Every compact metric space is a continuous image of the cantor set Proves that any compact metric space is a continuous image of the Cantor's middle thirds set. A good illustration of the principle of reducing to simpler problems and building from them.
M.Sc. 2 883 downloads so far.
Last downloaded on: 20-04-2019 11:38 PM
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12 Complex Analysis: Handout-2 (Results on Power Series) Results on power series
867 downloads so far.
Last downloaded on: 21-04-2019 01:39 AM
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13 Inverse Mapping Theorem Gives a proof of Inverse Function theorem (in the context of any complete normed linear space, in particular $\R^n) and its geometric meaning. It avoids contraction principle and gives a direct proof.
M.Sc. 2 854 downloads so far.
Last downloaded on: 12-04-2019 11:43 PM
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14 Completeness of R Gives perhaps the simplest proof of Cauchy completeness of $\R$. Does not use anything other than the definitions of convergence and Cauchy sequences and LUB property of $\R$. This needs wider publicity. Included in out book on Real analsyis.
2nd year B.Sc O,1 792 downloads so far.
Last downloaded on: 21-04-2019 01:39 AM
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15 Cardinality and Countability A quick review of cardinality, countability and uncountability via problems. Readers are asked to refer to Munkres for details. Hints are given to some where our proofs are different from those in Munkres. Some explicit bijections are given so as to train a student in the art of setting up such functions.
1st/2nd year B.Sc O,1 776 downloads so far.
Last downloaded on: 16-04-2019 08:24 PM
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16 Outline of a Topology Course Outline of a topology course given at University of Mumbai (very brief outline)
M.Sc. 2 770 downloads so far.
Last downloaded on: 19-04-2019 02:59 PM
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17 Exercises on Inverse images Has a good set of exercises which are meaningful in mathematics to make the studenst deal with the concept confidently. This is a problem area all over.
O O 750 downloads so far.
Last downloaded on: 16-04-2019 07:30 PM
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18 Properties Equivalent to the LUB Property of Ordered Fields Properties equivalent to LUB property. Almost similar to the article ?complete1.pdf? but contains an example of complete non-Archimedean field.
Final year B.Sc,, M.Sc. 1,2 748 downloads so far.
Last downloaded on: 20-04-2019 12:57 AM
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19 Implicit Function Theorem The aim of this article is bring out the geometric content of the implicit function theorem of two variables. To make it self-contained, I have included a proof of the theorem. The exposition is aimed at students of mathematics from final year B.Sc.\ or first year M.Sc. It also brings out the geometric meaning of the Lagrange multiplier method.
B.Sc./M.Sc 1,2 700 downloads so far.
Last downloaded on: 19-04-2019 01:30 AM
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20 Summary of Real Analysis 2 Semester 2 (2009-10) Calculus of several variables up to Taylor's theorem and maxima-minima
Final year B.Sc, M.Sc 1,2 675 downloads so far.
Last downloaded on: 18-04-2019 05:28 AM
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