## Axiom of Choice

Dear readers, Below are some useful you tube videos on Axiom of Choice.

## Infinitesimals

Dear readers, Below is series of quite informative you tube lectures by Derek Owens on the "infinitesimals".

## Equivalence relation and partition

Dear readers, Below is an elementary  youtube lecture on Equivalence relation and partition.

## Epsilon-motivation for studying "Abstract Algebra"

Dear readers, Below are some links that may provide  motivation to study "Abstract Algebra". . Why do we need to study abstract algebra? What are some real-life applications of abstract algebra?  Reasons why Abstract Algebra is valuable to math ed majors (and math majors).

## For people who think Topology & Geometry is a difficult subject.

Dear readers, The below is a link of a series of you tube lectures given by Dr Tadashi Tokieda on Topology & Geometry for the people who think topology/Geometry is a difficult subject. I bet you will really change your mind after watching these lectures. Topology & Geometry Video Lectures

## Good way of describing Subspaces of Metric Spaces

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Dear readers I am sharing a good you tube link by Ben Garside teaching what it is meant by a subspace of a metric space. subspace of a metric space.

## Riemann Lebesgue Theorem

Dear readers, here is shared a link to Riemann Lebesgue Theorem based on the book An Introduction to Analysis, Second Edition, by James R. Kirkwood, Boston: PWS Publishing (1995).

## Closure of a Linear Operator

Dear readers, I am posting a link found via Google about the Closure of a Linear Operator. The author  characterises the existence of  the closure of a linear operator. The proof of the characterization is clear, if some one is unclear about the proof, he/she can discuss me. Closure of a Linear Operator

## Visualizing Linear Algebra with Maple

Dear readers, here is a link for visualizing Linear Algebra: visualizing linear algebra with maple.

## Video Lectures in Mathematical Analysis II

Dear readers, I am posting a very rare link for video lectures on Mathematical Analysis II. It contains almost all the topics found in standard undergraduate texts in Mathematical Analysis II. For rest of the lectures click Here

## Video Lectures in Modern Analysis I

Below is link for video lectures in Modern Analysis I or Real Analysis I. It contains almost all the topics found in standard undergraduate texts in Mathematical Analysis I. For rest of the lectures click Here

## Video Lectures in Complex Analysis

Dear readers, I am posting a very rare link for video lectures on Complex Analysis. It contains almost all the topics found in standard undergraduate texts in Complex Analysis. For rest of the lectures click Here

## Video Lectures in Partial differential Equation (pde)

Dear readers, I am posting a very rare link for video lectures in partial differential equation. It contains almost all the topics found in standard texts in partial differential equations. For rest of the lectures click Here

## Video Lectures in Fourier Transform and its Applications

I am posting a link on "Video Lectures in Fourier Transform and its Applications". Click the link below to view the lectures.

## MIT Video Lectures in Differential Equations

I am posting a link on Video Lectures in Differential Equations at MIT.

## Permutations and Combinations

Below is a link for a very good video about Permutations and Combinations.

## The Use of the Linear Algebra by Web Search Engines

Read the article.......The Use of the Linear Algebra by Web Search Engines

## Proof: Natural Number Addition and Multiplication is Closed.

The proof is given using successor function S defined in the Peano axioms. The proof of these two facts are given in 2.1 and 2.2 for the addition and multiplication case respectively in the link below.... http://en.wikipedia.org/wiki/Peano_axioms#Addition

## Proof: Natural Number Addition and Multiplication is Associative.

For the proof for addition case click below..... http://www.proofwiki.org/wiki/Natural_Number_Addition_is_Commutative For the proof for addition case click below........ http://www.proofwiki.org/wiki/Natural_Number_Multiplication_is_Commutative

## Proof: Natural Number Multiplication is Associative.

For the proof click on the link below.... http://www.proofwiki.org/wiki/Natural_Number_Multiplication_is_Associative/Proof_2

## importing latex into Maple

SnuggleTeX (1.2.2) is a very useful software to import latex into maple. http://www2.ph.ed.ac.uk/snuggletex/UpConversionDemo

## How to check whether a polynomial has roots in the group of integers modulo n?

Dear readers, I am writing this post on a question put by my student. Download the solution for details. Solution

## Video Lectures in Finite Element Methods

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The link below contains video Lectures on Finite Element Method. To see the lectures Click

## On Teaching Mathematics

On Teaching Mathematics is a provocative article by Vladimir Arnold.

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## How to write Math in Gmail?

To write mathematics in your gmail account use GmailTeX. I have checked that it efficiently works in Google Chrome. To download GmailTex Click

## SONG: Finite Simple Group (of Order Two)

For Video Click below Finite Simple Group (of Order Two) The path of love is never smooth But mine’s continuous for you You’re the upper bound in the chains of my heart You’re my Axiom of Choice, you know it’s true But lately our relation’s not so well-defined And I just can’t function without you

## Prove that each term in the lower central series of a group G is characteristic in G.

To see the proof Click

## Prove that each term in the upper central series of a group G is characteristic in G.

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To see the proof Click

## Best treatise of Free Books in Mathematics

Library.nu which was first known as gigapedia.org is a best treatise of free books in mathematics. to see this website Click

## Every Boolean ring is commutative.

To see the proof Click

## Characteristic subgroups and its properties

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A subgroup of a group is called characteristic in , denoted char , if every automorphism of maps to itself, i.e., for all .  Results concerning characteristic subgroups which we shall use later (and whose proofs are relegated to the exercises) are (1) characteristic subgroups are normal, (2) if is the unique subgroup of of a given

## PlUS MAGAZINE...living Mathematics

Plus is an internet magazine which aims to introduce readers to the beauty and the practical applications of mathematics. A lot of people don't have a very clear idea what "real" maths consists of....... Read more

## Video Lectures in Partial Differential Equations

In the link below there are given 32 hours video lectures in Partial Differential Equations. Click If you are not able to view these files, then download Quick Player

## Characteristic of a ring and some of its basic properties

In the link below find the definition and basic properties of characteristic of a ring. Click

## Proof: characteristic of an integral domain is 0 or prime.

In the link below it is given a very nice proof the fact that: The characteristic of an integral domain is 0 or prime. For proof Click

## Computation of "CENTER OF A DIHEDRAL GROUP"

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In the link below, the center of Dihedral group D_n for any positive integer n is computed. It is proved that the Center of , if n is odd & Center of , if n is even For proof click

## Video Lectures in Modern Algebra

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The link below contains video lectures in Abstract Algebra. Click

## Proof: group of order 4 is abelian

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In the link below there is very nice proof of the fact that "The group of order 4 is abelian" Click

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