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Found total 224 results. Displaying results from 181 to 200.

 
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181
Tangents

This article gives you a gentle introduction to the notion of tangents so as to make your journey through Differential Geometry enjoyable.

Keywords :

M.Sc.
MTTS Level :
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(Downloaded 1149 times last on 05 March 2025, 03:04 am
182
Taylor's Theorem

Gives proofs of Taylor's theorem of single variable calculus with all important forms of the remainder. As an application, we establish the convergence of the binomial series of any index. A good place to learn some hard analysis.

Keywords :

Final year B.Sc, M.Sc
MTTS Level :
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(Downloaded 779 times last on 03 March 2025, 03:25 am
183
Existence of Continuous Functions

Starts with the existence of real valued continuous functions on a metric space, Urysohn's lemma and Tietze extension theorem in the context of metric spaces and then proceeds to prove them in the case of normal spaces.

Keywords :

M.Sc.
MTTS Level :
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(Downloaded 765 times last on 06 March 2025, 01:21 pm
184
Generating Topologies— A Unified View ofSubspace, Product and Quotient Topologies

Unifies the principles underlying the construction of subspace, product and quotient topologies; also brings out the importance of universal mapping properties of these constructions.

Keywords :

M.Sc.
MTTS Level :
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(Downloaded 865 times last on 05 March 2025, 03:01 pm
185
R m is homeomorphic to R n iff m = n

Starting with a definition of topological dimension, the article gives a self-contained elementary proof of the fact that $R^m$ is homeomorphic to R^n$ iff $m=n$.

Keywords :

M.Sc./Ph.D
MTTS Level :
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(Downloaded 775 times last on 06 March 2025, 07:01 pm
186
Topological Groups — via Problems

Basic notions, examples and results about topological groups via graded exercises.

Keywords :

M.Sc.
MTTS Level :
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(Downloaded 1183 times last on 07 March 2025, 12:41 am
187
Outline of a Topology Course

Outline of a topology course given at University of Mumbai (very brief outline)

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M.Sc.
MTTS Level :
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(Downloaded 3181 times last on 06 March 2025, 04:08 am
188

Outline of a topology course

Keywords :

a shorter version of the next.
MTTS Level :
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(Downloaded 1679 times last on 03 March 2025, 09:47 am
189

Outline of a topology course

Keywords :

contains many of my articles on topology as appendices. Only one of the three may be released in the Expository section.
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(Downloaded 3222 times last on 06 March 2025, 08:21 pm
190
Structure Theorems for Linear Maps

This is graded exercise version of the article ?Structure_linear_maps.pdf?; If you wish to have a quick idea and ready to work out the details, you may read this; if you want details to be spelt out, go to the other article.

Keywords :

M.Sc.
MTTS Level :
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(Downloaded 1001 times last on 07 March 2025, 08:04 am
191

Gives a complete straightforward proof of Tyknoff's theorem about the compactness of arbitrary products of compact spaces.

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M.Sc.
MTTS Level :
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(Downloaded 626 times last on 07 March 2025, 03:11 am
192
Uncountability of R

Gives 3 proofs, one uses LUB, another nested interval and the third the decimal expansion and diagonal trick. The 1st proof needs more details.

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B.Sc
MTTS Level :
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(Downloaded 1023 times last on 03 March 2025, 03:26 am
193
Extension of Uniformy Continuus Functions

Gives a excruciatingly detailed proof of the result on extensions of uniformly continuous functions to a complete metric space. This may also be found in my book on metric spaces.

Keywords :

Final year B.Sc, M.Sc
MTTS Level :
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(Downloaded 641 times last on 03 March 2025, 03:26 am
194
Vector Product on R 3

This is part of Frenet.pdf, but is of independent interest. Gives the geometric meaning of the vector product and the identities involved with this concept.

Keywords :

B.Sc
MTTS Level :
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(Downloaded 509 times last on 03 March 2025, 03:26 am
195
Vector Analysis

A very brief summary with sketches of ideas underlying the classical theorems of vector analysis. Can at best be a pointer to the theme.

Keywords :

Final year B.Sc, M.Sc
MTTS Level :
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(Downloaded 674 times last on 03 March 2025, 03:26 am
196
Vector Fields on Spheres

Vector fields on $S^2$ and ends up with Milnor's proof of hairy ball theorem

Keywords :

M.Sc./Ph.D
MTTS Level :
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(Downloaded 1176 times last on 06 March 2025, 01:03 am
197
Volterra’s Proof of Nonexistence of a Function

Volterra's elementary proof of the non-existence of a function which is continuous at all rationals and discontinuous at irrationals. This is usually proved using the topological nature of the set of discontinuities of a function and baire category theorem.

Keywords :

Final year B.Sc, M.Sc
MTTS Level :
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(Downloaded 660 times last on 01 March 2025, 07:56 pm
198
Every Real Sequence has a Monotone Subsequence

Gives a (nemonic/geometric) proof of the fact that any real sequence has a monotone subsequence.

Keywords :

B.Sc
MTTS Level :
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(Downloaded 957 times last on 03 March 2025, 03:26 am
199
An Elementary Proof of Weierstrass Approximation Theorem

Elementary proof of Weierstrass approximation theorem. May be compared with elem_wat.pdf

Keywords :

Final year B.Sc, M.Sc
MTTS Level :
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(Downloaded 743 times last on 03 March 2025, 03:26 am
200
Weyl’s Integral and Character Formulas for U (n)

Weyl integral and character formula for $U(n)$. Includes Braching law for $U(n)$. This was a handout to a 700 level course at Indiana University, Bloomington during the year 1983-84. There is complete set of handouts for the 2 semester course. I plan to type all of them as and when I find time.

Keywords :

Ph.D.
MTTS Level :
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(Downloaded 598 times last on 02 March 2025, 01:50 pm