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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 Functional Analysis (2011) Summary of Lectures An outline of a course in functional analysis given at University of Hyderabad. Contains a lot of concrete examples, spaces of functions and good exercises. Prepares the students for future use of functional analysis in other parts of mathematics. Goes up to the spectral theom for compact self-adjoint operators, Riesz-Schauder theory of compact operators, their applications to integral equations.
M.Sc. 2 291 downloads so far.
Last downloaded on: 22-09-2017 08:22 PM
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12 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 1,2 276 downloads so far.
Last downloaded on: 22-09-2017 08:22 PM
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13 Structure of Linear Maps Gives a motivated and clutter free proofs of many theorems about the structure of linear maps. Proves Jordan canonical form, spectral theorems for self-adjoint,normal, unitary and orthogonal maps, singular value decompositions, triangular forms.
Final year B.Sc, M.Sc 1,2 265 downloads so far.
Last downloaded on: 22-09-2017 08:22 PM
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14 Limit Inferior and Limit Superior A thorough treatment of limsup and liminf. This topic is a source of concern for many students.
B.Sc 1,2 263 downloads so far.
Last downloaded on: 22-09-2017 08:23 PM
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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,1 252 downloads so far.
Last downloaded on: 22-09-2017 08:23 PM
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16 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 250 downloads so far.
Last downloaded on: 22-09-2017 08:24 PM
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17 Problems in Algebraic Topology Assignments in a first course in algebraic topology. A good set of exercises to face your pre-Ph.D.exams.
2nd year M.Sc. 230 downloads so far.
Last downloaded on: 22-09-2017 08:24 PM
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18 Complex Analysis: Handout-3 (Cauchy-Riemann Equations) Cauchy-Riemann equations
it also brings out the `geometric' meaning of C-R equations. A must read for students who like geometry. Final 227 downloads so far.
Last downloaded on: 22-09-2017 08:25 PM
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19 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 1,2 222 downloads so far.
Last downloaded on: 22-09-2017 08:25 PM
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20 The Fundamental Theorem of Algebra Offers many simple proofs of the fundamental theorem of algebra
B.Sc./M.Sc 1,2 221 downloads so far.
Last downloaded on: 22-09-2017 08:25 PM
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