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Operating as usual

04/03/2024
04/03/2024

Evaluate the limit

03/03/2024

Founder of Set Theory
Set theory, branch of Mathematics that deals with the properties of well-defined collections of distinct objects.
The German Mathematician George Cantor had established the theory of Sets.
Now, applications of Set theory are made in Modern Science, Technology, Business, Economics, Higher Algebra, Calculus, Probability, etc.
Definition: A set is a collection of well-defined distinct objects.
Mathematically we write as A = { 1,2,3,4,5}.
Mathematically a set is identified as Capital letters, elements are enclosed within braces. Here 1,2,3,4,5 are called elements of A.
Set Representation :
1.Roster Form or Tabular Form: e.g. A = {2,3,5,7}.
2. Set- Builder Form or Property Method: E.g. A ={ x: x is prime number between 1 and 10}
Or A ={ x | x is a prime number less than 10}
Types of Sets:
1) Finite Sets
2) Infinite Sets
3) Cardinal Number
4) Equivalent Sets
5) Equal Sets
6) Empty Set or Null Set or Void Set
7) Universal Set
8) Subset
9) Proper Subset
10) Power Set

03/03/2024

Math Meme from the group of Math Memes

03/03/2024

A one sentence proof

Photos from Mathematics Learning 's post 01/03/2024

Some great mathematician born in second month of the year in February

28/02/2024

THOMAS FULLER - The mental calculator.

Thomas Fuller died on 29th Dec 1790. He was an African slave known for his skills in mathematics.
He was captured in Africa by White Slave Traders and shipped to the USA in 1724 when he was only 14years.

28/02/2024

A goat problem:
Consider a fenced circular field of radius R with a goat tied to a point on the exterior of the fence by means of a tether of length L, how long should the rope be for the goat to graze 1/2 of the field?

27/02/2024

IQ challenge

24/02/2024

Jamal Nazrul Islam
Born
in Jhenaidah, British Indian Ocean Territory
February 24, 1939
Died
March 16, 2013
Jamal Nazrul Islam (Bengali : জামাল নজরুল ইসলাম) was a Bangladeshi mathematical physicist and cosmologist. He was a professor at University of Chittagong. He also served as the director of the Research Center for Mathematical and Physical Sciences (RCMPS) at the University of Chittagong.

He received a BSc degree from St. Xavier's College at the University of Calcutta. In 1959, he got his Honors in Functional Mathematics and Theoretical Physics from Cambridge University. He completed his Masters in 1960. A student of the Trinity College, he finished the Mathematical Tripos. Islam obtained his PhD in applied mathematics and theoretical physics from Trinity College, Cambridge in 1968, followed by a DSc in 1982.

Islam worked in the Institute of Theoretical Astronomy (later amalgamated to Institute of Astronomy, Cambridge) from 1967 until 1971. Later he worked as a researcher in California Institute of Technology and University of Washington. During 1973-1974 he served as the faculty of Applied Mathematics of King's College London. In 1978 he then joined the faculty of City University London until he returned to Chittagong in 1984. Until his death he served as Professor Emeritus at the University of Chittagong.

His research areas include Applied Mathematics, Theoretical Physics, Mathematical Physics, theory of Gravitation, General Relativity, Mathematical Cosmology and Quantum Field Theory. Islam authored/coauthored/edited more than 50 scientific articles, books and some popular articles published in various scientific journals. Besides this he has also written books in Bengali. Particularly noteworthy are Black Hole, published from the Bangla Academy, “The Mother Tongue, Scientific Research and other Articles” and “Art, Literature and Society”. The latter two are compilations.
1. “If all astronomical processes cease, how will the passage of time manifest itself? It is doubtful if vacuum fluctuations can provide a clock for the recording of time. Will time itself come to a stop? Is this a meaningful question? Such questions are difficult to answer.”
― Jamal Nazrul Islam, The Ultimate Fate Of The Universe
2. “It is clear that there is a very great deal to be learnt about the universe and the endless subtleties of its various manifestations. What about the moral side of man, or what people with a religious bent of mind would prefer to call the spiritual nature of man? How will this develop in the endless aeons of the future? Perhaps in most of these questions like Newton we are still standing on the shore while the great ocean of knowledge lies ahead. It is significant that after more than two centuries of the acquisition of knowledge eminent men of science still have similar feelings.”
― Jamal Nazrul Islam, The Ultimate Fate Of The Universe
3. “Why should one bother about the ultimate fate of the universe? One answer to this question is similar to the answer to the question about climbing Mount Everest: because the problem exists. It is in the nature of the human mind to seek incessantly new frontiers of knowledge to explore.”
― Jamal Nazrul Islam, The Ultimate Fate Of The Universe
4. “The study of the universe as a whole is a unique enterprise. At least in one sense one is seeking to understand the totality of things. We, as thinking beings, are as much a part of the universe as are neutron stars and white dwarfs and our destiny is inextricably bound up with that of the universe.”
― Jamal Nazrul Islam, The Ultimate Fate Of The Universe
5. “It is irrelevant whether or not there are other forms of life in the Galaxy or in other galaxies. The fact that we are here provides an 'existence proof as it is called in mathematics. To say that we are an accident of nature is to miss the point. The laws of nature are presumably eternal and immutable. They do not change in mid-stream and suddenly acquire the ability to create a pretty toy if circumstances arise.”
― Jamal Nazrul Islam, The Ultimate Fate Of The Universe
6. “One of the most intriguing things about the universe, which probably cannot be explained by scientific investigations, is that it exists and we, who are a part of the universe, are able to contemplate and study it.”
― Jamal Nazrul Islam, The Ultimate Fate Of The Universe
7. “It is possible that those strange sentient beings of the far-future cold universe will find contemplating a warm universe such as ours not very pleasant, much as a nocturnal creature shuns daylight. But the more speculative amongst them may look back to our universe and to the Earth as an ideal world full of sunshine and a supply of adequate energy to last for billions of years, a dream world which will have passed away never to return. And what do we human beings do with this ideal dream world of ours? We oppress each other, build nuclear weapons for each other's destruction, and plunder the resources of the Earth!”
― Jamal Nazrul Islam, The Ultimate Fate Of The Universe
8. “Doubtless there is a desire in human beings to exist everywhere in space, but there seems to be a much stronger desire to exist everywhere in time, or at least in future time.”
― Jamal Nazrul Islam, The Ultimate Fate Of The Universe
9. “The steady state theory is aesthetically and philosophically pleasing to many people, to whom it is a matter of regret that observations indicate that it is not the correct model.”
― Jamal Nazrul Islam, The Ultimate Fate Of The Universe
10. “The precise structure and description of the Galaxy is quite complicated with many unsolved problems. However, from the point of view of the large-scale structure of the universe, the detailed structure of the Galaxy is not very important.”
― Jamal Nazrul Islam
11. “The human mind has a different attitude towards 'time' and 'space' as regards the survival of the human race.”
― Jamal Nazrul Islam, The Ultimate Fate Of The Universe
12. “If the standard model is correct, the universe started in a state of high density and temperature, with all matter and radiation forming one great continuous mass. It is very remarkable that this undifferentiated soup should have the intrinsic property that in due course of time it develops into galaxies of which at least one creates life with such staggering complexity, subtlety and diversity and often such stunning beauty. It also creates thinking and feeling beings which in turn can contemplate the universe and study its properties and which can love and hate.”
― Jamal Nazrul Islam, The Ultimate Fate Of The Universe
13. “There is very little hope for life of any kind surviving the big crunch in a closed universe. However, one cannot be dogmatic about this as one does not know the limits of human ingenuity. If indeed the universe is closed, we probably have tens of billions of years to think about how to survive the big crunch, if it is not against the laws of nature that something should survive.”
― Jamal Nazrul Islam, The Ultimate Fate Of The Universe
14. “One way in which a recurrence of life can occur is in the event that the cycle of the big bang and final collapse is repeated, and if galaxies are born again and again conditions for the existence of life may develop in some regions. Whether or not this can happen (assuming that the universe is closed) is, of course, not known.”
― Jamal Nazrul Islam, The Ultimate Fate Of The Universe
15. “Indeed, it is not clear whether it is meaningful to talk about 'after' the big crunch, just as it is not clear whether it is meaningful to talk about what happened 'before' the big bang. These questions are not necessarily meaningless, but the fact is we simply do not know.”
― Jamal Nazrul Islam, The Ultimate Fate Of The Universe
16. “Some people, including Hawking, think that we may be able to understand the big bang or the big crunch (in particular, whether time has a beginning or an end at these events) when we have a satisfactory quantum theory of gravitation.”
― Jamal Nazrul Islam, The Ultimate Fate Of The Universe
17. “Supposing a new era begins after the big crunch, will the number of protons (or baryons) be the same in the next cycle? Will the protons retain a memory of their previous life in the earlier epoch of the universe when deciding to decay or not to decay? Will there be subsequent cycles of big bangs and big crunches? If so, will proton decay affect the cycles of the far future? There exist no answers to such questions at present.”
― Jamal Nazrul Islam, The Ultimate Fate Of The Universe
18. “One of the most intriguing problems is to understand the precise nature of time, especially with regard to the big bang, the big crunch and the long-term future of an open universe.”
― Jamal Nazrul Islam, The Ultimate Fate Of The Universe
19. “The urge is irresistible to ask, are we an essential part of the plan and architecture of the universe? Is there a purpose to the universe? Of course one can immediately counter such questions by asking what one means by 'essential part' and 'purpose'. Perhaps such questions are improperly posed and should not be asked, but it cannot be denied that these questions arise in the mind.”
― Jamal Nazrul Islam, The Ultimate Fate Of The Universe
20. “It is perhaps worth noticing that we have arrived 'on the scene' at a fairly early date. By this I mean that the time scale that it has taken nature to create us is of the same order of magnitude as the age of the universe. The universe is about 10-15 billion years old, and the Earth about 4.5 billion years old. Life is supposed to have begun on Earth about 3 billion years ago. It would not have been possible to evolve life, because of the hostile conditions, in the first few billion years after the big bang. Thus we have been created almost as soon as the universe was in a position to create us. It is an interesting question how long the universe will continue to create entirely new forms of life, assuming that it is open.”
― Jamal Nazrul Islam, The Ultimate Fate Of The Universe
21. “It is possibly true that intelligent life with a sophisticated technology is needed for the eventual survival of life. Dinosaurs and many other species became extinct because they could not adapt themselves to changes in the environment. Of course many other species have lived through many crises. But it is doubtful that any species, other than human beings (or atany rate, intelligent beings) can survive.”
― Jamal Nazrul Islam, The Ultimate Fate Of The Universe
22. “Could the emergence of intelligent beings like us be one of nature's plans for the eventual survival of life through various extreme conditions?”
― Jamal Nazrul Islam, The Ultimate Fate Of The Universe

24/02/2024

Happy birthday to Jamal Nazrul Islam
Jamal Nazrul Islam was a Bangladeshi mathematician and academic who made significant contributions to the fields of algebra and algebraic geometry. He was born in 1943 in the town of Barisal, in what was then British India. After completing his undergraduate studies at the University of Dhaka, Islam went on to earn a PhD in mathematics from the University of Chicago in the United States.
Throughout his career, Islam conducted research on a wide range of topics related to algebra and algebraic geometry, including group theory, representation theory, and the theory of Lie algebras. He also made important contributions to the development of the theory of quantum groups, which are a type of mathematical structure that has applications in various areas of physics and mathematics.
In addition to his research, Islam was also an accomplished academic and teacher. He served as a professor at several universities in Bangladesh and around the world, including the University of Dhaka, the University of Chicago, and the University of California, Berkeley. He also served as the head of the Department of Mathematics at the University of Dhaka and as the Dean of the Faculty of Science at the University of Chittagong.
Islam's contributions to algebra and algebraic geometry and his dedication to teaching and academia earned him numerous accolades and awards during his career, including the Bangladesh Academy of Sciences Gold Medal in 1992. He passed away in 2015 at the age of 71.

24/02/2024

By Edwin Sampang

23/02/2024

𝐌𝐚𝐭𝐡𝐞𝐦𝐚𝐭𝐢𝐜𝐢𝐚𝐧
Carl Friedrich Gauss
Gauss made significant contributions to a wide range of mathematical fields, including number theory, algebra, analysis, geometry, and statistics. He is perhaps best known for his work in number theory, where he made groundbreaking discoveries in the study of prime numbers, modular arithmetic, and quadratic forms.
Gauss also made important contributions to the development of the theory of electromagnetism and invented the method of least squares, which is widely used in statistical analysis and regression analysis. Additionally, he made significant contributions to the study of astronomy, including the prediction of the orbit of the asteroid Ceres.
Here are some of his most notable contributions:
Number Theory: Gauss made groundbreaking discoveries in the study of prime numbers, modular arithmetic, and quadratic forms. His Disquisitiones Arithmeticae, published in 1801, is considered a landmark work in the field of number theory.
Method of Least Squares: Gauss invented the method of least squares, a statistical technique used to find the line of best fit for a set of data. This method is widely used in regression analysis and data modeling.
Differential Geometry: Gauss made significant contributions to the field of differential geometry, including the development of the Gauss-Bonnet theorem and the concept of curvature.
Electromagnetism: Gauss contributed to the development of the theory of electromagnetism, including the discovery of Gauss's law, which relates the distribution of electric charge to the resulting electric field.
Astronomy: Gauss made significant contributions to the study of astronomy, including the prediction of the orbit of the asteroid Ceres and the development of the method of least squares to analyze astronomical data.
Overall, Gauss's contributions to mathematics and science have had a profound impact on the development of these fields, and his work continues to be studied and celebrated to this day .
May be an image of text that says "Karl Friedrich Gauß."

22/02/2024

MIT integration bee- 2024

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