A Journey Through The Realm of Numbers

A Journey Through The Realm of Numbers

Author: Menny Aka

Publisher: Springer Nature

Published: 2020-10-03

Total Pages: 344

ISBN-13: 3030552330

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This book takes the reader on a journey from familiar high school mathematics to undergraduate algebra and number theory. The journey starts with the basic idea that new number systems arise from solving different equations, leading to (abstract) algebra. Along this journey, the reader will be exposed to important ideas of mathematics, and will learn a little about how mathematics is really done. Starting at an elementary level, the book gradually eases the reader into the complexities of higher mathematics; in particular, the formal structure of mathematical writing (definitions, theorems and proofs) is introduced in simple terms. The book covers a range of topics, from the very foundations (numbers, set theory) to basic abstract algebra (groups, rings, fields), driven throughout by the need to understand concrete equations and problems, such as determining which numbers are sums of squares. Some topics usually reserved for a more advanced audience, such as Eisenstein integers or quadratic reciprocity, are lucidly presented in an accessible way. The book also introduces the reader to open source software for computations, to enhance understanding of the material and nurture basic programming skills. For the more adventurous, a number of Outlooks included in the text offer a glimpse of possible mathematical excursions. This book supports readers in transition from high school to university mathematics, and will also benefit university students keen to explore the beginnings of algebraic number theory. It can be read either on its own or as a supporting text for first courses in algebra or number theory, and can also be used for a topics course on Diophantine equations.


Book Synopsis A Journey Through The Realm of Numbers by : Menny Aka

Download or read book A Journey Through The Realm of Numbers written by Menny Aka and published by Springer Nature. This book was released on 2020-10-03 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book takes the reader on a journey from familiar high school mathematics to undergraduate algebra and number theory. The journey starts with the basic idea that new number systems arise from solving different equations, leading to (abstract) algebra. Along this journey, the reader will be exposed to important ideas of mathematics, and will learn a little about how mathematics is really done. Starting at an elementary level, the book gradually eases the reader into the complexities of higher mathematics; in particular, the formal structure of mathematical writing (definitions, theorems and proofs) is introduced in simple terms. The book covers a range of topics, from the very foundations (numbers, set theory) to basic abstract algebra (groups, rings, fields), driven throughout by the need to understand concrete equations and problems, such as determining which numbers are sums of squares. Some topics usually reserved for a more advanced audience, such as Eisenstein integers or quadratic reciprocity, are lucidly presented in an accessible way. The book also introduces the reader to open source software for computations, to enhance understanding of the material and nurture basic programming skills. For the more adventurous, a number of Outlooks included in the text offer a glimpse of possible mathematical excursions. This book supports readers in transition from high school to university mathematics, and will also benefit university students keen to explore the beginnings of algebraic number theory. It can be read either on its own or as a supporting text for first courses in algebra or number theory, and can also be used for a topics course on Diophantine equations.

How Numbers Work

How Numbers Work

Author: New Scientist

Publisher: Nicholas Brealey

Published: 2018-05-01

Total Pages: 224

ISBN-13: 1473670365

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Think of a number between one and ten No, hang on, let's make this interesting. Between zero and infinity. Even if you stick to the whole numbers, there are a lot to choose from - an infinite number in fact. Throw in decimal fractions and infinity suddenly gets an awful lot bigger (is that even possible?) And then there are the negative numbers, the imaginary numbers, the irrational numbers like p which never end. It literally never ends. The world of numbers is indeed strange and beautiful. Among its inhabitants are some really notable characters - pi, e, the square root of minus two and the famous golden ratio to name just a few. Prime numbers occupy a special status. Zero is very odd indeed. And even some apparently common-or-garden integers such as 37 have special properties. Adventures In Mathematics takes a tour of this mind-blowing but beautiful world of numbers and the mathematical rules that connect them. Find out mathematicians' favourite numbers, and the ones they are afraid of (spoiler: it isn't 13). Discover the incredible connection between numbers and the rules of nature. And learn some amazing mathematical tricks that will keep you amused for hours.


Book Synopsis How Numbers Work by : New Scientist

Download or read book How Numbers Work written by New Scientist and published by Nicholas Brealey. This book was released on 2018-05-01 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: Think of a number between one and ten No, hang on, let's make this interesting. Between zero and infinity. Even if you stick to the whole numbers, there are a lot to choose from - an infinite number in fact. Throw in decimal fractions and infinity suddenly gets an awful lot bigger (is that even possible?) And then there are the negative numbers, the imaginary numbers, the irrational numbers like p which never end. It literally never ends. The world of numbers is indeed strange and beautiful. Among its inhabitants are some really notable characters - pi, e, the square root of minus two and the famous golden ratio to name just a few. Prime numbers occupy a special status. Zero is very odd indeed. And even some apparently common-or-garden integers such as 37 have special properties. Adventures In Mathematics takes a tour of this mind-blowing but beautiful world of numbers and the mathematical rules that connect them. Find out mathematicians' favourite numbers, and the ones they are afraid of (spoiler: it isn't 13). Discover the incredible connection between numbers and the rules of nature. And learn some amazing mathematical tricks that will keep you amused for hours.

A Journey Through the Realm of Numbers

A Journey Through the Realm of Numbers

Author: Menny Aka

Publisher:

Published: 2020

Total Pages: 0

ISBN-13: 9788303055231

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This book takes the reader on a journey from familiar high school mathematics to undergraduate algebra and number theory. The journey starts with the basic idea that new number systems arise from solving different equations, leading to (abstract) algebra. Along this journey, the reader will be exposed to important ideas of mathematics, and will learn a little about how mathematics is really done. Starting at an elementary level, the book gradually eases the reader into the complexities of higher mathematics; in particular, the formal structure of mathematical writing (definitions, theorems and proofs) is introduced in simple terms. The book covers a range of topics, from the very foundations (numbers, set theory) to basic abstract algebra (groups, rings, fields), driven throughout by the need to understand concrete equations and problems, such as determining which numbers are sums of squares. Some topics usually reserved for a more advanced audience, such as Eisenstein integers or quadratic reciprocity, are lucidly presented in an accessible way. The book also introduces the reader to open source software for computations, to enhance understanding of the material and nurture basic programming skills. For the more adventurous, a number of Outlooks included in the text offer a glimpse of possible mathematical excursions. This book supports readers in transition from high school to university mathematics, and will also benefit university students keen to explore the beginnings of algebraic number theory. It can be read either on its own or as a supporting text for first courses in algebra or number theory, and can also be used for a topics course on Diophantine equations.


Book Synopsis A Journey Through the Realm of Numbers by : Menny Aka

Download or read book A Journey Through the Realm of Numbers written by Menny Aka and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book takes the reader on a journey from familiar high school mathematics to undergraduate algebra and number theory. The journey starts with the basic idea that new number systems arise from solving different equations, leading to (abstract) algebra. Along this journey, the reader will be exposed to important ideas of mathematics, and will learn a little about how mathematics is really done. Starting at an elementary level, the book gradually eases the reader into the complexities of higher mathematics; in particular, the formal structure of mathematical writing (definitions, theorems and proofs) is introduced in simple terms. The book covers a range of topics, from the very foundations (numbers, set theory) to basic abstract algebra (groups, rings, fields), driven throughout by the need to understand concrete equations and problems, such as determining which numbers are sums of squares. Some topics usually reserved for a more advanced audience, such as Eisenstein integers or quadratic reciprocity, are lucidly presented in an accessible way. The book also introduces the reader to open source software for computations, to enhance understanding of the material and nurture basic programming skills. For the more adventurous, a number of Outlooks included in the text offer a glimpse of possible mathematical excursions. This book supports readers in transition from high school to university mathematics, and will also benefit university students keen to explore the beginnings of algebraic number theory. It can be read either on its own or as a supporting text for first courses in algebra or number theory, and can also be used for a topics course on Diophantine equations.

Fantastic Numbers and Where to Find Them

Fantastic Numbers and Where to Find Them

Author: Antonio Padilla

Publisher: Farrar, Straus and Giroux

Published: 2022-07-26

Total Pages: 211

ISBN-13: 0374600570

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A fun, dazzling exploration of the strange numbers that illuminate the ultimate nature of reality. For particularly brilliant theoretical physicists like James Clerk Maxwell, Paul Dirac, or Albert Einstein, the search for mathematical truths led to strange new understandings of the ultimate nature of reality. But what are these truths? What are the mysterious numbers that explain the universe? In Fantastic Numbers and Where to Find Them, the leading theoretical physicist and YouTube star Antonio Padilla takes us on an irreverent cosmic tour of nine of the most extraordinary numbers in physics, offering a startling picture of how the universe works. These strange numbers include Graham’s number, which is so large that if you thought about it in the wrong way, your head would collapse into a singularity; TREE(3), whose finite nature can never be definitively proved, because to do so would take so much time that the universe would experience a Poincaré Recurrence—resetting to precisely the state it currently holds, down to the arrangement of individual atoms; and 10^{-120}, measuring the desperately unlikely balance of energy needed to allow the universe to exist for more than just a moment, to extend beyond the size of a single atom—in other words, the mystery of our unexpected universe. Leading us down the rabbit hole to a deeper understanding of reality, Padilla explains how these unusual numbers are the key to understanding such mind-boggling phenomena as black holes, relativity, and the problem of the cosmological constant—that the two best and most rigorously tested ways of understanding the universe contradict one another. Fantastic Numbers and Where to Find Them is a combination of popular and cutting-edge science—and a lively, entertaining, and even funny exploration of the most fundamental truths about the universe.


Book Synopsis Fantastic Numbers and Where to Find Them by : Antonio Padilla

Download or read book Fantastic Numbers and Where to Find Them written by Antonio Padilla and published by Farrar, Straus and Giroux. This book was released on 2022-07-26 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: A fun, dazzling exploration of the strange numbers that illuminate the ultimate nature of reality. For particularly brilliant theoretical physicists like James Clerk Maxwell, Paul Dirac, or Albert Einstein, the search for mathematical truths led to strange new understandings of the ultimate nature of reality. But what are these truths? What are the mysterious numbers that explain the universe? In Fantastic Numbers and Where to Find Them, the leading theoretical physicist and YouTube star Antonio Padilla takes us on an irreverent cosmic tour of nine of the most extraordinary numbers in physics, offering a startling picture of how the universe works. These strange numbers include Graham’s number, which is so large that if you thought about it in the wrong way, your head would collapse into a singularity; TREE(3), whose finite nature can never be definitively proved, because to do so would take so much time that the universe would experience a Poincaré Recurrence—resetting to precisely the state it currently holds, down to the arrangement of individual atoms; and 10^{-120}, measuring the desperately unlikely balance of energy needed to allow the universe to exist for more than just a moment, to extend beyond the size of a single atom—in other words, the mystery of our unexpected universe. Leading us down the rabbit hole to a deeper understanding of reality, Padilla explains how these unusual numbers are the key to understanding such mind-boggling phenomena as black holes, relativity, and the problem of the cosmological constant—that the two best and most rigorously tested ways of understanding the universe contradict one another. Fantastic Numbers and Where to Find Them is a combination of popular and cutting-edge science—and a lively, entertaining, and even funny exploration of the most fundamental truths about the universe.

A Journey Through the Realm of Theoretical Chemistry

A Journey Through the Realm of Theoretical Chemistry

Author: Fereydoon Milani-nejad, PhD

Publisher: Xlibris Corporation

Published: 2015-11-24

Total Pages: 108

ISBN-13: 1514411008

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The main goal of this book is to show how human behavior could be explained in terms of chemical laws. Chapter 1, “Overview,” is devoted to this task; subjects such as chemistry of mutual feelings, connection and its stability, love at first sight, fate and will, uplifting of the soul, dual personality, excited universe, and more are explained qualitatively on terms of chemical laws in this chapter. These concepts show that theoretical chemistry is readily and smoothly applicable to other disciplines, such as sociology, psychology, philosophy, social sciences, and even theology. As an example consider the following paragraph from chapter 3. There is a Beginning and there is an End. There exist an infinite number of pathways between the Beginning and the End. No matter what route one chooses, the End will be the same. Among the infinite number of pathways there is one pathway, called reversible pathway (Heavenly way) with maximum efficiency. There is another pathway for which the efficiency is zero (Hell way). All other pathways are combinations of these two extreme cases. The closer the chosen path is to the ideal path, the more rewarding the journey will be.


Book Synopsis A Journey Through the Realm of Theoretical Chemistry by : Fereydoon Milani-nejad, PhD

Download or read book A Journey Through the Realm of Theoretical Chemistry written by Fereydoon Milani-nejad, PhD and published by Xlibris Corporation. This book was released on 2015-11-24 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main goal of this book is to show how human behavior could be explained in terms of chemical laws. Chapter 1, “Overview,” is devoted to this task; subjects such as chemistry of mutual feelings, connection and its stability, love at first sight, fate and will, uplifting of the soul, dual personality, excited universe, and more are explained qualitatively on terms of chemical laws in this chapter. These concepts show that theoretical chemistry is readily and smoothly applicable to other disciplines, such as sociology, psychology, philosophy, social sciences, and even theology. As an example consider the following paragraph from chapter 3. There is a Beginning and there is an End. There exist an infinite number of pathways between the Beginning and the End. No matter what route one chooses, the End will be the same. Among the infinite number of pathways there is one pathway, called reversible pathway (Heavenly way) with maximum efficiency. There is another pathway for which the efficiency is zero (Hell way). All other pathways are combinations of these two extreme cases. The closer the chosen path is to the ideal path, the more rewarding the journey will be.

The Mystery of Numbers: Revealed Through Their Digital Root

The Mystery of Numbers: Revealed Through Their Digital Root

Author: Talal Ghannam

Publisher: Talal Ghannam

Published: 2012-07-04

Total Pages: 319

ISBN-13: 1477678417

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What is it that brings all these different things together? The subatomic particles and the Vedic square. The hydrogen atom and the golden section. Fibonacci numbers, consciousness, and alchemy. Nikola Tesla, music, and the ether. Electromagnetism, gravity, and the fourth dimension. The procession of the equinox, the Mayan dooms day, the Hindu Brahma cycle, and Atlantis. It is Numbers, or more precisely; their Digital Root. In this book the author examines the amazing world of numbers, particularly those which have intrigued and fascinated ancient and modern mathematicians alike. However, he does it from a very novel point of view; by implementing the digital root operation, in which the individual digits of any of these numbers are summed up until a single digit is left over. The author will show that when applying this simple operation to magical numbers, and to many other groups of numbers, an amazing world of hidden interconnections; repetition cycles; numerical symmetries; and geometrical patterns emerge. Especially when the geometrical (the circle) and the numerical aspects of the digital root world are combined together. It is in this circular/numerical world where numbers, individually and collectively, exist in their most basic, yet perfect and symmetrical states, and where the basic nine numbers are differentiated into three groups of amazing properties, which will be shown to underlie the essence of the whole universe; from the atom and its forces to the solar system and its geometry. This book will take us on a numerical and spiritual journey: starting from prime and figurate numbers; to Fibonacci sequence and the golden section; to alchemy and the Mayan calendar; to the atoms and its forces, along with the ether and the fourth dimension. In addition, the author will show how these new revelations of the digital root world are corroborating the numerological and mystical qualities that have been attributed to numbers by philosophers and mystics throughout the ages. This book will paint a so holistic and meaningful image of the world that will forever change our perception, not only towards numbers, but towards the whole universe as well.


Book Synopsis The Mystery of Numbers: Revealed Through Their Digital Root by : Talal Ghannam

Download or read book The Mystery of Numbers: Revealed Through Their Digital Root written by Talal Ghannam and published by Talal Ghannam. This book was released on 2012-07-04 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: What is it that brings all these different things together? The subatomic particles and the Vedic square. The hydrogen atom and the golden section. Fibonacci numbers, consciousness, and alchemy. Nikola Tesla, music, and the ether. Electromagnetism, gravity, and the fourth dimension. The procession of the equinox, the Mayan dooms day, the Hindu Brahma cycle, and Atlantis. It is Numbers, or more precisely; their Digital Root. In this book the author examines the amazing world of numbers, particularly those which have intrigued and fascinated ancient and modern mathematicians alike. However, he does it from a very novel point of view; by implementing the digital root operation, in which the individual digits of any of these numbers are summed up until a single digit is left over. The author will show that when applying this simple operation to magical numbers, and to many other groups of numbers, an amazing world of hidden interconnections; repetition cycles; numerical symmetries; and geometrical patterns emerge. Especially when the geometrical (the circle) and the numerical aspects of the digital root world are combined together. It is in this circular/numerical world where numbers, individually and collectively, exist in their most basic, yet perfect and symmetrical states, and where the basic nine numbers are differentiated into three groups of amazing properties, which will be shown to underlie the essence of the whole universe; from the atom and its forces to the solar system and its geometry. This book will take us on a numerical and spiritual journey: starting from prime and figurate numbers; to Fibonacci sequence and the golden section; to alchemy and the Mayan calendar; to the atoms and its forces, along with the ether and the fourth dimension. In addition, the author will show how these new revelations of the digital root world are corroborating the numerological and mystical qualities that have been attributed to numbers by philosophers and mystics throughout the ages. This book will paint a so holistic and meaningful image of the world that will forever change our perception, not only towards numbers, but towards the whole universe as well.

Learn Your Colors

Learn Your Colors

Author: IglooBooks

Publisher: Igloo Books

Published: 2021-09-07

Total Pages: 18

ISBN-13: 9781800228153

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Learn all about colors with this chunky board book. With bright, colorful pages and super cute pictures, this book is the perfect introduction to colors for little ones.


Book Synopsis Learn Your Colors by : IglooBooks

Download or read book Learn Your Colors written by IglooBooks and published by Igloo Books. This book was released on 2021-09-07 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: Learn all about colors with this chunky board book. With bright, colorful pages and super cute pictures, this book is the perfect introduction to colors for little ones.

e: The Story of a Number

e: The Story of a Number

Author: Eli Maor

Publisher: Princeton University Press

Published: 2011-10-12

Total Pages: 242

ISBN-13: 1400832349

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The interest earned on a bank account, the arrangement of seeds in a sunflower, and the shape of the Gateway Arch in St. Louis are all intimately connected with the mysterious number e. In this informal and engaging history, Eli Maor portrays the curious characters and the elegant mathematics that lie behind the number. Designed for a reader with only a modest mathematical background, this biography brings out the central importance of e to mathematics and illuminates a golden era in the age of science.


Book Synopsis e: The Story of a Number by : Eli Maor

Download or read book e: The Story of a Number written by Eli Maor and published by Princeton University Press. This book was released on 2011-10-12 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: The interest earned on a bank account, the arrangement of seeds in a sunflower, and the shape of the Gateway Arch in St. Louis are all intimately connected with the mysterious number e. In this informal and engaging history, Eli Maor portrays the curious characters and the elegant mathematics that lie behind the number. Designed for a reader with only a modest mathematical background, this biography brings out the central importance of e to mathematics and illuminates a golden era in the age of science.

Thinking in Numbers

Thinking in Numbers

Author: Daniel Tammet

Publisher:

Published: 2014-07-01

Total Pages: 139

ISBN-13: 9780316250795

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The book that Daniel Tammet, bestselling author and mathematical savant, was born to write. In Tammet's world, numbers are beautiful and mathematics illuminates our lives and minds. Using anecdotes, everyday examples, and ruminations on history, literature, and more, Tammet allows us to share his unique insights and delight in the way numbers, fractions, and equations underpin all our lives. His idiosyncratic worldview gives us new perspecttives on the universal questions of what it is to be human and how we make meaning. This book will change the way you think about math and fire your imagination to see the world with fresh eyes.--From publisher description.


Book Synopsis Thinking in Numbers by : Daniel Tammet

Download or read book Thinking in Numbers written by Daniel Tammet and published by . This book was released on 2014-07-01 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book that Daniel Tammet, bestselling author and mathematical savant, was born to write. In Tammet's world, numbers are beautiful and mathematics illuminates our lives and minds. Using anecdotes, everyday examples, and ruminations on history, literature, and more, Tammet allows us to share his unique insights and delight in the way numbers, fractions, and equations underpin all our lives. His idiosyncratic worldview gives us new perspecttives on the universal questions of what it is to be human and how we make meaning. This book will change the way you think about math and fire your imagination to see the world with fresh eyes.--From publisher description.

Math with Bad Drawings

Math with Bad Drawings

Author: Ben Orlin

Publisher: Black Dog & Leventhal

Published: 2018-09-18

Total Pages: 556

ISBN-13: 0316509027

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A hilarious reeducation in mathematics-full of joy, jokes, and stick figures-that sheds light on the countless practical and wonderful ways that math structures and shapes our world. In Math With Bad Drawings, Ben Orlin reveals to us what math actually is; its myriad uses, its strange symbols, and the wild leaps of logic and faith that define the usually impenetrable work of the mathematician. Truth and knowledge come in multiple forms: colorful drawings, encouraging jokes, and the stories and insights of an empathetic teacher who believes that math should belong to everyone. Orlin shows us how to think like a mathematician by teaching us a brand-new game of tic-tac-toe, how to understand an economic crises by rolling a pair of dice, and the mathematical headache that ensues when attempting to build a spherical Death Star. Every discussion in the book is illustrated with Orlin's trademark "bad drawings," which convey his message and insights with perfect pitch and clarity. With 24 chapters covering topics from the electoral college to human genetics to the reasons not to trust statistics, Math with Bad Drawings is a life-changing book for the math-estranged and math-enamored alike.


Book Synopsis Math with Bad Drawings by : Ben Orlin

Download or read book Math with Bad Drawings written by Ben Orlin and published by Black Dog & Leventhal. This book was released on 2018-09-18 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: A hilarious reeducation in mathematics-full of joy, jokes, and stick figures-that sheds light on the countless practical and wonderful ways that math structures and shapes our world. In Math With Bad Drawings, Ben Orlin reveals to us what math actually is; its myriad uses, its strange symbols, and the wild leaps of logic and faith that define the usually impenetrable work of the mathematician. Truth and knowledge come in multiple forms: colorful drawings, encouraging jokes, and the stories and insights of an empathetic teacher who believes that math should belong to everyone. Orlin shows us how to think like a mathematician by teaching us a brand-new game of tic-tac-toe, how to understand an economic crises by rolling a pair of dice, and the mathematical headache that ensues when attempting to build a spherical Death Star. Every discussion in the book is illustrated with Orlin's trademark "bad drawings," which convey his message and insights with perfect pitch and clarity. With 24 chapters covering topics from the electoral college to human genetics to the reasons not to trust statistics, Math with Bad Drawings is a life-changing book for the math-estranged and math-enamored alike.