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Theorem
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Fermat’s Last Theorem
‘I have a truly marvellous demonstration of this proposition which this margin is too narrow to contain.’ It was with these words, written in the 1630s, that Pierre de Fermat intrigued and infuriated the mathematics community.For over 350 years, proving Fermat’s Last Theorem was the most notorious unsolved mathematical problem, a puzzle whose basics most children could grasp but whose solution eluded the greatest minds in the world.In 1993, after years of secret toil, Englishman Andrew Wiles announced to an astounded audience that he had cracked Fermat’s Last Theorem.He had no idea of the nightmare that lay ahead. In ‘Fermat’s Last Theorem’ Simon Singh has crafted a remarkable tale of intellectual endeavour spanning three centuries, and a moving testament to the obsession, sacrifice and extraordinary determination of Andrew Wiles: one man against all the odds.
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Pythagorean Theorem
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Emmy Noether's Wonderful Theorem
"In the judgment of the most competent living mathematicians, Fraulein Noether was the most significant creative mathematical genius thus far produced since the higher education of women began."-Albert Einstein The year was 1915, and the young mathematician Emmy Noether had just settled into Gottingen University when Albert Einstein visited to lecture on his nearly finished general theory of relativity.Two leading mathematicians of the day, David Hilbert and Felix Klein, dug into the new theory with gusto, but had difficulty reconciling it with what was known about the conservation of energy.Knowing of her expertise in invariance theory, they requested Noether's help.To solve the problem, she developed a novel theorem, applicable across all of physics, which relates conservation laws to continuous symmetries-one of the most important pieces of mathematical reasoning ever developed. Noether's "first" and "second" theorem was published in 1918.The first theorem relates symmetries under global spacetime transformations to the conservation of energy and momentum, and symmetry under global gauge transformations to charge conservation. In continuum mechanics and field theories, these conservation laws are expressed as equations of continuity.The second theorem, an extension of the first, allows transformations with local gauge invariance, and the equations of continuity acquire the covariant derivative characteristic of coupled matter-field systems.General relativity, it turns out, exhibits local gauge invariance.Noether's theorem also laid the foundation for later generations to apply local gauge invariance to theories of elementary particle interactions.In Dwight E. Neuenschwander's new edition of Emmy Noether's Wonderful Theorem, readers will encounter an updated explanation of Noether's "first" theorem.The discussion of local gauge invariance has been expanded into a detailed presentation of the motivation, proof, and applications of the "second" theorem, including Noether's resolution of concerns about general relativity.Other refinements in the new edition include an enlarged biography of Emmy Noether's life and work, parallels drawn between the present approach and Noether's original 1918 paper, and a summary of the logic behind Noether's theorem.
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What is the difference between web development and software development?
Web development primarily focuses on creating websites and web applications that are accessed through a web browser, using technologies such as HTML, CSS, and JavaScript. Software development, on the other hand, involves creating applications that can run on various platforms, including desktop computers, mobile devices, and servers. While web development is a subset of software development, software development encompasses a broader range of applications beyond just web-based ones.
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What training opportunities are available for IT specialists to specialize in web development and general programming, such as software development?
There are various training opportunities available for IT specialists looking to specialize in web development and general programming. Online platforms like Coursera, Udemy, and Codecademy offer courses and certifications in programming languages such as Python, Java, and JavaScript. Additionally, coding bootcamps like General Assembly and Flatiron School provide intensive, hands-on training in software development. IT specialists can also pursue advanced degrees in computer science or related fields to deepen their knowledge and skills in web development and programming.
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What training options are available for IT specialists to specialize in web development and general programming, such as software development?
IT specialists looking to specialize in web development and general programming have a variety of training options available to them. They can pursue formal education through degree programs in computer science or related fields, attend coding bootcamps that offer intensive training in programming languages and frameworks, or take online courses and tutorials to learn specific skills. Additionally, IT specialists can participate in workshops, seminars, and conferences to stay updated on the latest trends and technologies in web development and software development. Continuous learning and practice are essential for IT specialists to excel in these specialized areas.
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Is learning programming and software development very challenging?
Learning programming and software development can be challenging for some people, as it requires logical thinking, problem-solving skills, and attention to detail. However, with dedication, practice, and the right resources, it is definitely achievable. Breaking down complex concepts into smaller, more manageable parts and seeking help from online tutorials, courses, and communities can make the learning process easier and more enjoyable. Ultimately, the level of challenge will vary depending on the individual's background, experience, and learning style.
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Godel's Theorem : A Very Short Introduction
Very Short Introductions: Brilliant, Sharp, Inspiring Kurt Gödel first published his celebrated theorem, showing that no axiomatization can determine the whole truth and nothing but the truth concerning arithmetic, nearly a century ago.The theorem challenged prevalent presuppositions about the nature of mathematics and was consequently of considerable mathematical interest, while also raising various deep philosophical questions.Gödel's Theorem has since established itself as a landmark intellectual achievement, having a profound impact on today's mathematical ideas.Gödel and his theorem have attracted something of a cult following, though his theorem is often misunderstood. This Very Short Introduction places the theorem in its intellectual and historical context, and explains the key concepts as well as common misunderstandings of what it actually states.A. W. Moore provides a clear statement of the theorem, presenting two proofs, each of which has something distinctive to teach about its content.Moore also discusses the most important philosophical implications of the theorem.In particular, Moore addresses the famous question of whether the theorem shows the human mind to have mathematical powers beyond those of any possible computerABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area.These pocket-sized books are the perfect way to get ahead in a new subject quickly.Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.
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Pythagorean Theorem for Babies
Set the children in your life on a lifelong path to learning with the next installment of the Baby University board book series.Full of scientific information, this is the perfect book to teach complex concepts in a simple, engaging way.Pythagorean Theorem for Babies is a colorfully simple introduction for youngsters (and grownups!) to what the Pythagorean Theorem is and how we can go about proving it.It's never too early to become a scientist!
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Notes on the Brown-Douglas-Fillmore Theorem
Suitable for both postgraduate students and researchers in the field of operator theory, this book is an excellent resource providing the complete proof of the Brown-Douglas-Fillmore theorem.The book starts with a rapid introduction to the standard preparatory material in basic operator theory taught at the first year graduate level course.To quickly get to the main points of the proof of the theorem, several topics that aid in the understanding of the proof are included in the appendices.These topics serve the purpose of providing familiarity with a large variety of tools used in the proof and adds to the flexibility of reading them independently.
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Birth of a Theorem : A Mathematical Adventure
“This man could plainly do for mathematics what Brian Cox has done for physics” — Sunday TimesHow does a genius see the world?Where and how does inspiration strike?Cédric Villani takes us on a mesmerising adventure as he wrestles with the Boltzmann equation – a new theorem that will eventually win him the most coveted prize in mathematics and a place in the mathematical history books.Along the way he encounters obstacles and setbacks, losses of faith and even brushes with madness. His story is one of courage and partnership, doubt and anxiety, elation and despair.Of ordinary family life blurring with the abstract world of mathematical physics, of theories and equations that haunt your dreams and seeking the elusive inspiration found only in a locked, darkened room. Blending science with history, biography with myth, Villani conjures up an inimitable cast: the omnipresent Einstein, mad genius Kurt Godel, and Villani’s personal hero, John Nash. Step inside the magical world of Cédric Villani…
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Which programming languages are used in software development?
There are many programming languages used in software development, including popular languages such as Java, Python, C++, JavaScript, and Ruby. Each language has its own strengths and is used for different purposes in software development. For example, Java is commonly used for building enterprise-level applications, while Python is known for its simplicity and versatility. C++ is often used for system software and game development, while JavaScript is essential for web development. Overall, the choice of programming language depends on the specific requirements of the software being developed.
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What is the Pythagorean theorem and the cathetus theorem?
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In mathematical terms, it can be written as a^2 + b^2 = c^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides, called catheti. The cathetus theorem, also known as the converse of the Pythagorean theorem, states that if the square of the length of the longest side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right-angled triangle. In other words, if a^2 + b^2 = c^2, then the triangle is a right-angled triangle, where c is the longest side (hypotenuse) and a and b are
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What is the Pythagorean theorem and the altitude theorem?
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed as a^2 + b^2 = c^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides. The altitude theorem, also known as the geometric mean theorem, states that in a right-angled triangle, the altitude (the perpendicular line from the right angle to the hypotenuse) is the geometric mean between the two segments of the hypotenuse. This can be expressed as h^2 = p * q, where h is the length of the altitude, and p and q are the lengths of the two segments of the hypotenuse.
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What is the difference between software development and programming?
Software development is a broader term that encompasses the entire process of creating software, including planning, designing, testing, and maintaining software applications. Programming, on the other hand, refers specifically to the act of writing code to instruct a computer to perform certain tasks. While programming is a key component of software development, software development involves a more comprehensive approach that includes various stages beyond just writing code.
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