Expository articles
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Found total 224 results. Displaying results from 141 to 160.
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141
Plane Geometries
Give a pedestrian approach to the classical Euclidean, elliptical and hyperbolic geometries with a minimal (incomplete) set of axioms. Included in our book ``A Course in Geometry?.
Keywords :
B.Sc
MTTS Level :
MTTS Level :
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(Downloaded 470 times last on 18 January 2025, 04:30 am
(Downloaded 470 times last on 18 January 2025, 04:30 am
142
An Example of a Prime Ideal
Gives a simple example of a prime ideal in the polynomial ring of two variables, namely the example of a parabola.
Keywords :
M.Sc.
MTTS Level :
MTTS Level :
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(Downloaded 576 times last on 18 January 2025, 04:29 am
(Downloaded 576 times last on 18 January 2025, 04:29 am
143
A topological Proof of the Infinitutde of Primes
Topological proof of the infinitude of primes
Keywords :
included in the topology notes.
MTTS Level :
MTTS Level :
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(Downloaded 619 times last on 19 January 2025, 04:27 am
(Downloaded 619 times last on 19 January 2025, 04:27 am
144
Topics in Measure Theory
This hand-out deals with the notion of product measures, proved Fubini and Tonelli theorems, gives proofs of Radon-Nikodym theorem and a simple proof of a lemma needed in the study of complex measures.
Keywords :
M.Sc.
MTTS Level :
MTTS Level :
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(Downloaded 938 times last on 22 January 2025, 01:41 pm
(Downloaded 938 times last on 22 January 2025, 01:41 pm
145
Proper Maps
Gives all the basic results of proper maps within contexts. An important concept in modern topology but rarely found in textbooks on topology.
Keywords :
M.Sc.
MTTS Level :
MTTS Level :
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(Downloaded 918 times last on 22 January 2025, 06:58 am
(Downloaded 918 times last on 22 January 2025, 06:58 am
146
Maps into the Punctured Plane
It takes an analytic approach to the problem of determining the fundamental group of the circle by looking at homotopy classes of maps into $C^*$, the punctured plane.
Keywords :
M.Sc./Ph.D
MTTS Level :
MTTS Level :
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(Downloaded 633 times last on 18 January 2025, 04:29 am
(Downloaded 633 times last on 18 January 2025, 04:29 am
147
Examples of Cosets and Quotient Groups
Lists examples of quotient groups for practice. Details may be found in ``Outline of Group Theory?
Keywords :
B.Sc
MTTS Level :
MTTS Level :
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(Downloaded 1086 times last on 21 January 2025, 11:40 pm
(Downloaded 1086 times last on 21 January 2025, 11:40 pm
148
How to work with quotient rings?
It teaches you how to work with quotient rings.
Keywords :
M.Sc.
MTTS Level :
MTTS Level :
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(Downloaded 1319 times last on 22 January 2025, 02:05 pm
(Downloaded 1319 times last on 22 January 2025, 02:05 pm
149
Quotient Topology
Will make you comfortable with the notion of quotient spaces with lots of examples with rigorous proofs.
Keywords :
M.Sc.
MTTS Level :
MTTS Level :
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(Downloaded 2859 times last on 22 January 2025, 10:27 pm
(Downloaded 2859 times last on 22 January 2025, 10:27 pm
150
Raleigh Quotients and Spectral Theorems
Uses the method of Raleigh quotients to deduce the spectral theorem for symmetric maps and an orthogonal maps.
Keywords :
Final year B.Sc, M.Sc
MTTS Level :
MTTS Level :
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(Downloaded 480 times last on 18 January 2025, 04:29 am
(Downloaded 480 times last on 18 January 2025, 04:29 am
151
Rank Theorem
Rank theorem (of differential calculus) is proved here.
Keywords :
M.Sc.
MTTS Level :
MTTS Level :
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(Downloaded 838 times last on 21 January 2025, 07:39 pm
(Downloaded 838 times last on 21 January 2025, 07:39 pm
152
Summary of Real Analysis — Batch B (2007–08)
Daily sheet of a course in real analysis up to continuity. This is perhaps what we do in Level O of MTTS camps.
Keywords :
B.Sc
MTTS Level :
MTTS Level :
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(Downloaded 2665 times last on 18 January 2025, 04:29 am
(Downloaded 2665 times last on 18 January 2025, 04:29 am
153
Summary of Real Analysis — Semester 1 (2008)
Actual summary of the course as it unfolded, a subset of real_analysis_2008.pdf.
Keywords :
2nd Year B.Sc onwards up to First year M.Sc
MTTS Level :
MTTS Level :
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(Downloaded 1159 times last on 18 January 2025, 04:29 am
(Downloaded 1159 times last on 18 January 2025, 04:29 am
154
An Outline of Real Analysis
An outline of real analysis ; one of the trio (2008, 2010, 2012). Our book ?A Basic course in Real Analysis? is based on these.
Keywords :
MTTS Level :
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(Downloaded 2353 times last on 22 January 2025, 11:50 pm
(Downloaded 2353 times last on 22 January 2025, 11:50 pm
155
Summary of Real Analysis 2 – Semester 2 (2009-10)
Integration in $R^n$ a terse treatment with a complete proof of the change of variable formula in $R^n$.
Keywords :
M.Sc.
MTTS Level :
MTTS Level :
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(Downloaded 667 times last on 18 January 2025, 04:30 am
(Downloaded 667 times last on 18 January 2025, 04:30 am
156
Summary of Real Analysis 2 – Semester 2 (2009-10)
Calculus of several variables up to Taylor's theorem and maxima-minima
Keywords :
Final year B.Sc, M.Sc
MTTS Level :
MTTS Level :
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(Downloaded 1602 times last on 21 January 2025, 11:28 am
(Downloaded 1602 times last on 21 January 2025, 11:28 am
157
Reduction modulo p
Irreducibility of polynomials using reduction modulo a prime (to be done yet!)
Keywords : Polynomials, Irreducibility criteria, Reduction modulo a prime
MSc
MTTS Level : 2
MTTS Level : 2
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(Downloaded 540 times last on 18 January 2025, 04:30 am
(Downloaded 540 times last on 18 January 2025, 04:30 am
158
Riesz-Fredholm-Schauder Theory
Gives a direct proof of Fredhohlm alternative theorem without using spectral theorem for compact operators.
Keywords :
M.Sc.
MTTS Level :
MTTS Level :
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(Downloaded 443 times last on 18 January 2025, 04:30 am
(Downloaded 443 times last on 18 January 2025, 04:30 am
159
Riesz-Markov Representation Theorem
It proves Riesz representation theorem for positive linear functionals on the space of continuous functions with compact support on a locally compact space. While it closely follows the treatment found in Rudin's Real and complex analysis, it makes use of the fact that students at this level would be familiar with Lebesgue measure theory and hence provides a simpler argument.
Keywords :
M.Sc./Ph.D.
MTTS Level :
MTTS Level :
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(Downloaded 1514 times last on 22 January 2025, 08:59 pm
(Downloaded 1514 times last on 22 January 2025, 08:59 pm
160
Continuity of the Roots of a Polynomial
It gives three proofs of the continuity of roots of polynomials as dependents on the coeeficients. Needs to write a perspective (pun intended!) of the third proof!
Keywords :
M.Sc./Ph.D
MTTS Level :
MTTS Level :
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(Downloaded 672 times last on 23 January 2025, 01:22 am
(Downloaded 672 times last on 23 January 2025, 01:22 am