A Computational Introduction to Number Theory and Algebra

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About the Book

All of the mathematics required beyond basic calculus is developed “from scratch.” Moreover, the book generally alternates between “theory” and “applications”: one or two chapters on a particular set of purely mathematical concepts are followed by one or two chapters on algorithms and applications; the mathematics provides the theoretical underpinnings for the applications, while the applications both motivate and illustrate the mathematics. Of course, this dichotomy between theory and applications is not perfectly maintained: the chapters that focus mainly on applications include the development of some of the mathematics that is specific to a particular application, and very occasionally, some of the chapters that focus mainly on mathematics include a discussion of related algorithmic ideas as well.

The mathematical material covered includes the basics of number theory (including unique factorization, congruences, the distribution of primes, and quadratic reciprocity) and of abstract algebra (including groups, rings, fields, and vector spaces). It also includes an introduction to discrete probability theory—this material is needed to properly treat the topics of probabilistic algorithms and cryptographic applications. The treatment of all these topics is more or less standard, except that the text only deals with commutative structures (i.e., abelian groups and commutative rings with unity) — this is all that is really needed for the purposes of this text, and the theory of these structures is much simpler and more transparent than that of more general, non-commutative structures.

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A Complete French Grammar for Reference and Practice

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This comprehensive manual thoroughly covers every aspect of French grammar, from the basic to the most advanced level, and illustrates the grammatical structures with useful, practical and interesting examples. Up-to-date language and usage both on the formal and on the informal level is paired with cultural information about France, making the study of grammar a pleasant experience. The book offers its users clear and detailed explanations, as well as the opportunity to practice their reading, writing and speaking skills in numerous oral and written exercises, which include translations, suggestions for communicative activities with a partner, and topics for written composition. A Complete French Grammar for Reference and Practice can be used as a classroom text in intermediate and advanced courses, as well as for reference and self-study. It is a reliable source of information for teachers and students alike, and addresses all those learners who want to speak and write French correctly.

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How to Write an Essay

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Description

If you’re at high school, college or university, you’ll almost certainly need to write essays. More and more students are being asked to produce written assignments, even in physics and mathematics.

Writing an essay means more than finding and recording facts. It means thinking critically: analysing material and reaching a conclusion. It means showing that you understand the material you’ve been studying. Above all, it means presenting a coherent argument.

Learning to write essays also prepares us for life beyond college. In the real world, more and more of us need to be able to express ideas clearly, with good grammar and a flexible style. Essay writing gives us the skills to become more effective citizens.

And yet, all too often, students are not offered the skills and techniques to write effective essays.

How do you start? What kind of words should you use? Are you entitled to offer your own views on a subject?

How to Write an Essay will make life easier for you. It will help you produce an essay that your tutor will appreciate, and that will do you credit.

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The Miracle of Adam and Jesus

Miraculously, the name of Jesus, PBUH, is repeated in the holy Qur’an 25 …

Allah, the almighty says in the holy Qur’an:

“The similitude of Jesus before Allah is as that of Adam; He created him from dust, then said to him: "Be". And he was.” Al-i-Imran: 3: 59

Miraculously, the name of Jesus, PBUH, is repeated in the holy Qur’an 25 times and the name of Adam, PBUH, is repeated 25 times as well. It’s worth noting here that the seventh Qur’anic verse in which the name of Jesus, PBUH, is mentioned is exactly the same verse in which the name of Adam, PBUH, is mentioned. Besides, the nineteenth verse (out of 25 verses) in which the name of Adam, PBUH, is mentioned is in chapter 19,Mariam (Mary), and the name of Jesus, PBUH, is also mentioned for the nineteenth time in the same chapter, Mary. The question that needs be answered here is whether this is a mere coincidence or a miracle?

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By: Abduldaem Al-Kaheel

www.kaheel7.com/eng

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The Spherical Earth

A picture of the earth that shows its spherical shape and shows the day and night, God be He exalted says: (He has created the heavens and the earth with truth. He makes the night to go in the day and makes the day to go in the night. And He has subjected the sun and the moon, each running (on a fixed course) for an appointed term. Verily, He is the All-Mighty, the Oft-Forgiving) [Surat Al-Zumar, verse: 5].And today we aren't suspicious of the spherical shape of the earth as we see it in front of us in the real pictures.

 

The holy verse:

God be He exalted says: (He has created the heavens and the earth with truth. He makes the night to go in the day and makes the day to go in the night. And He has subjected the sun and the moon, each running (on a fixed course) for an appointed term. Verily, He is the All-Mighty, the Oft-Forgiving) [Surat Al-Zumar, verse: 5].

 

The explanation of the verse: 

God be He blessed and exalted talks about His countless graces, so He tells us about the creation of the heavens and the earth, He also makes the night goes in the day and the day goes in the night (their succession). He also subjected the sun and the moon, each running to a certain day.

And here we can deduce an important scientific sign that the shape of the succession of the day and night is a spherical shape as they interfere with each other.

 

Scientific fact:

The spherical shape of the earth has become one of the definite facts and this is shown in the pictures that have been taken to the earth from the outer space. In 1968, the spaceship Apollo has taken the first picture to the earth and after that thousands of pictures have been taken to the earth; all of them have shown the earth like a ball that floats in the darkness.

The point of inimitability:

From this holy verse and especially in His Almighty saying: "He makes the night to go in the day and makes the day to go in the night" we can notice that the day and night moves in a spherical system and interfere with each other and this doesn't occur unless the earth is like a sphere and this is what has been actually found by scientists.

The question here: If Mohammad peace be upon him wasn't a messenger from Almighty God, then from where has this expression come "He makes the night to go in the day and makes the day to go in the night" and how did he know that the earth is like a sphere? This is from the signs of the prophecy of Mohammad peace be upon him.

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By: Abduldaem Al-Kaheel

www.kaheel7.com/eng 

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Mountains of Clouds

The above picture which was taken by scientists represents a several-km-height …

The above picture which was taken by scientists represents a several-km-height cloud while the lower picture is a mountain that’s also several-km-height. It might be surprising to realise that the holy Qur'an talks about mountains of clouds; Allah, the almighty says in the holy Qur'an:

“Seest thou not that Allah makes the clouds move gently, then joins them together, then makes them into a heap? - then wilt thou see rain issue forth from their midst. And He sends down from the sky mountain masses (of clouds) wherein is hail: He strikes therewith whom He pleases and He turns it away from whom He pleases, the vivid flash of His lightning well-nigh blinds the sight.” Nur or Light: 24: 43

The holy Qur’an talked about the mountains of clouds fourteen centuries before scientists took photos of them, a proof of the inimitability of the holy Qur'an. We can't but glorify Allah, the exalted.

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By: Abduldaem Al-Kaheel

www.kaheel7.com/eng

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New study 2014 unveiled the secret of lying.

New study 2014 unveiled the secret of lying.. Let’s read and discover …

Did you know?

Study finds truth and lies

decided by areas of prefrontal

cortex.

Researchers at the

Virginia Tech Carilion

Research Institute conducted

a study that confirmed the

parts of the brain that make

the decision to lie.

Study

shows region in front of brain

becomes active over lying.

Allah says: 

(A lying, sinning forelock)

[96/16]. Subhan Allah!!

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By: Abduldaem Al-Kaheel

www.kaheel7.com/eng

Study suggests region in front of brain exerts control over lying impulses, http://www.dailycal.org/2014/09/10/study-suggests-region-front-brain-exerts-control-lying-impulses/

http://ticker.baruchconnect.com/article/study-finds-truth-and-lies-decided-by-areas-of-prefrontal-cortex/

http://newscenter.berkeley.edu/2014/09/08/study-links-honesty-to-prefrontal-region-of-the-brain/

http://www.nature.com/neuro/journal/v17/n10/full/nn.3798.html

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The Earth’s Water

he radius of the earth is Talmost 6,400 km and its medial crustal thickening is 30 km below the continents and mountains …

he radius of the earth is Talmost 6,400 km and its medial crustal thickening is 30 km below the continents and mountains, but it becomes around 5 km below sea beds and oceans. Such layer is thin and breakable and that’s why the earth’s crust is divided into 12 plates or more. Enormous masses of seas, therefore, slip from the bottom of oceans and dive under the ground. Scientists are concerned about the loss of quantities of fresh water deep under the ground and the inability of people to make use of it. All glory to Allah, the almighty for the holy Qur’an warns against such a phenomenon and talks about the possibility of disappearance of water under the layers of the earth. Allah, the exalted says in the holy Qur’an:

“And We send down water from the sky according to (due) measure, and We cause it to soak in the soil; and We certainly are able to drain it off (with ease).” Mu’minun or the Believers: 23: 18

Allah also says in the holy Qur’an:

“Say: "See ye?- If your stream be some morning lost (in the underground earth), who then can supply you with clear-flowing water?"” Mulk: 67: 30

Shall we then return to the path of Allah, the exalted!

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By: Abduldaem Al-Kaheel

www.kaheel7.com/eng

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The Cosmic Bridge

This is a picture of a 10-million-light year cosmic bridge that joins between two groupings of galaxies …

This is a picture of a 10-million-light year cosmic bridge that joins between two groupings of galaxies. Scientists affirm that the universe is rich in giant structures such as bridges and walls and they are made of galaxies and form solid cosmic buildings. All glory to Allah, the almighty who talks about such structures in the holy Qur’an using a wonderful expression which is zodiac. Allah, the exalted says in the holy Qur’an:

It is We Who have set out the zodiacal signs in the heavens, and made them fair-seeming to (all) beholders;” Hijr or the Rocky Tract: 15: 16

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By: Abduldaem Al-Kaheel

www.kaheel7.com/eng

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