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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 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,1 772 downloads so far.
Last downloaded on: 20-02-2019 06:21 AM
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12 Limit Inferior and Limit Superior A thorough treatment of limsup and liminf. This topic is a source of concern for many students.
B.Sc 1,2 757 downloads so far.
Last downloaded on: 20-02-2019 08:06 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,1 731 downloads so far.
Last downloaded on: 20-02-2019 06:53 AM
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14 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 716 downloads so far.
Last downloaded on: 20-02-2019 09:32 AM
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15 Outline of a Topology Course Outline of a topology course given at University of Mumbai (very brief outline)
M.Sc. 2 706 downloads so far.
Last downloaded on: 20-02-2019 12:30 AM
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16 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 1,2 639 downloads so far.
Last downloaded on: 20-02-2019 02:54 AM
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17 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 618 downloads so far.
Last downloaded on: 17-02-2019 02:39 AM
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18 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 1,2 607 downloads so far.
Last downloaded on: 18-02-2019 09:34 PM
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19 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. 1,2 600 downloads so far.
Last downloaded on: 19-02-2019 07:27 AM
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20 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 1,2 570 downloads so far.
Last downloaded on: 18-02-2019 02:48 AM
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