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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 The Role of LUB Axiom in Real Analysis Brings out the role of LUB property (order completeness) of $\R$. Gives a unified view of many of the crucial results in a first course in real analysis
likely to be best for a review of basic real analysis. B.Sc. 541 downloads so far.
Last downloaded on: 14-08-2018 10:07 AM
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12 Summary of Differential Geometry (January-April 2008) A summary of the course on differential geometry of curves and surface as it unfolded. More was covered and we used other articles on these themes.
Senior undergraduates, M.Sc 525 downloads so far.
Last downloaded on: 13-08-2018 05:20 PM
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13 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,1 509 downloads so far.
Last downloaded on: 14-08-2018 08:57 AM
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14 Outline of a Topology Course Outline of a topology course given at University of Mumbai (very brief outline)
M.Sc. 2 472 downloads so far.
Last downloaded on: 14-08-2018 03:48 AM
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15 A Diagnostic Quiz in Complex Analysis A diagnostic quiz in complex analysis.
M.Sc. 2 461 downloads so far.
Last downloaded on: 13-08-2018 05:21 PM
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16 Limit Inferior and Limit Superior A thorough treatment of limsup and liminf. This topic is a source of concern for many students.
B.Sc 1,2 454 downloads so far.
Last downloaded on: 13-08-2018 07:14 PM
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17 Group Actions Gives the definition, some interesting examples and exercises. Good way to master group actions, as students learn only the left/right and conjugacy actions in a typical algebra course.
B.Sc./M.Sc 1,2 446 downloads so far.
Last downloaded on: 13-08-2018 05:21 PM
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18 Arithmetic-Geometric Mean Inequality Proof by Induction and Calculus A proof of the classic inequality on AM-GM using calculus and induction.
2nd /final year BSc O 440 downloads so far.
Last downloaded on: 14-08-2018 10:34 AM
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19 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 1,2 427 downloads so far.
Last downloaded on: 13-08-2018 05:21 PM
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20 Simple and Direct Proofs of Some Results in the Theory of Compact Spaces Simple and direct proofs of some results in the theory of compact spaces.
Final year B.Sc, M.Sc 1,2 401 downloads so far.
Last downloaded on: 14-08-2018 12:06 AM
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