Like masterpieces of art, music, and literature, great mathematical theorems are creative milestones, works of genius destined to last forever. Now William Dunham gives them the attention they deserve.

Dunham places each theorem within its historical context and explores the very human and often turbulent life of the creator — from Archimedes, the absentminded theoretician whose absorption in his work often precluded eating or bathing, to Gerolamo Cardano, the sixteenth-century mathematician whose accomplishments flourished despite a bizarre array of misadventures, to the paranoid genius of modern times, Georg Cantor. He also provides step-by-step proofs for the theorems, each easily accessible to readers with no more than a knowledge of high school mathematics. A rare combination of the historical, biographical, and mathematical, Journey Through Genius is a fascinating introduction to a neglected field of human creativity.

“It is mathematics presented as a series of works of art; a fascinating lingering over individual examples of ingenuity and insight. It is mathematics by lightning flash.” —Isaac Asimov 

تهدف هذه السلسلة إلى توفير مادة علمية ثرية للمساعدة على المشاركة في مجال مسابقات الرياضيات الدولية، وتحتوي هذه الكتب على محتوى علمي وشروح وأمثلة تتخطى فروع الرياضيات لترسم طريقاً نحو التميز، وتقدم مصدرًا ثريًّا ومعينًا على التفكير الرياضي، وهي مادة مناسبة لجميع المستويات.

A Guided Tour of Math, from One to Infinity:

 forget the Pythagorean theorem again!"--Scientific American

Many people take math in high school and promptly forget much of it. But math plays a part in all of our lives all of the time, whether we know it or not. In The Joy of x, Steven Strogatz expands on his hit New York Times series to explain the big ideas of math gently and clearly, with wit, insight, and brilliant illustrations.

Whether he is illuminating how often you should flip your mattress to get the maximum lifespan from it, explaining just how Google searches the internet, or determining how many people you should date before settling down, Strogatz shows how math connects to every aspect of life. Discussing pop culture, medicine, law, philosophy, art, and business, Strogatz is the math teacher you wish you'd had. Whether you aced integral calculus or aren't sure what an integer is, you'll find profound wisdom and persistent delight in The Joy of x.

تهدف هذه السلسلة إلى توفير مادة علمية ثرية للمساعدة على المشاركة في مجال مسابقات الرياضيات الدولية، وتحتوي هذه الكتب على محتوى علمي وشروح وأمثلة تتخطى فروع الرياضيات لترسم طريقاً نحو التميز، وتقدم مصدرًا ثريًّا ومعينًا على التفكير الرياضي، وهي مادة مناسبة لجميع المستويات.

تهدف هذه السلسلة إلى توفير مادة علمية ثرية للمساعدة على المشاركة في مجال مسابقات الرياضيات الدولية، وتحتوي هذه الكتب على محتوى علمي وشروح وأمثلة تتخطى فروع الرياضيات لترسم طريقاً نحو التميز، وتقدم مصدرًا ثريًّا ومعينًا على التفكير الرياضي، وهي مادة مناسبة لجميع المستويات.

What is math? How exactly does it work? And what do three siblings trying to share a cake have to do with it? In How to Bake Pi, math professor Eugenia Cheng provides an accessible introduction to the logic and beauty of mathematics, powered, unexpectedly, by insights from the kitchen: we learn, for example, how the béchamel in a lasagna can be a lot like the number 5, and why making a good custard proves that math is easy but life is hard. Of course, it’s not all cooking; we’ll also run the New York and Chicago marathons, pay visits to Cinderella and Lewis Carroll, and even get to the bottom of a tomato’s identity as a vegetable. This is not the math of our high school classes: mathematics, Cheng shows us, is less about numbers and formulas and more about how we know, believe, and understand anything, including whether our brother took too much cake. 

تهدف هذه السلسلة إلى توفير مادة علمية ثرية للمساعدة على المشاركة في مجال مسابقات الرياضيات الدولية، وتحتوي هذه الكتب على محتوى علمي وشروح وأمثلة تتخطى فروع الرياضيات لترسم طريقاً نحو التميز، وتقدم مصدرًا ثريًّا ومعينًا على التفكير الرياضي، وهي مادة مناسبة لجميع المستويات.

تحت عنوانه الطريف" "جسور إلى اللانهاية" يَنطلقُ المؤلف Michael Guillen ليعبُر بنا أنهاراً وطُرقاً وَعرة في ساحات الرياضيات القديمة، ومَسالكها الحديثة حتى نَصل إلى فهم بسيط وواضح لكثير من جوانب الرياضيات، وهو يفعل ذلك دون أن يستخدم الرموز الرياضية الغامضة والمعادلات المعقدَّة، بل يلجأ إلى لُغة سهلة، ويستعين بأمثلة عملية مباشرة، تقرّب إلى أذهاننا وإلى خيالنا آفاق عالم الرياضيات، ويَجعلنا نعيش تلك الآفاق البعيدة ونحسّ بها حتى وكأننا فيها أو هي فينا، بعد أن ننتهي من قراءة الكتاب، سوف ينتابنا إحساسٌ عميق بأننا قد أصبحنا أكثر وعياً وفهماً وعلماً لكثير من جوانب الحياة نفسها، لأنّ الرياضيات قد دخلت الآن عمليّاً في فهم كثير من جوانب الحياة، ولمْ تعد مجرّد أعداد ورموز ومعادلات جامدة باردة غريبة، فهو لا يتحدث إلينا عن الحساب والجبر والهندسة، بل يتحدَّث عن الأرض الزراعية وعن الصناعة والتجارة والبنوك والاقتصاد، ويتطرَّق إلى دور الرياضيات في ألعابنا وتسليتنا وحروبنا وسلامنا ومشاعرنا وكثير مما نُحبّ ونَكره، نعم لقد تخلّلت الرياضيات الآن دقائق الحياة اليومية العادية للإنسان المعاصر، وأصبح من المحتم علينا أنْ نحاول فهمها واستيعابها، وأن نسعى إلى تجاوز الرَّهبة والقلق والتوتر الذي يَنتابُنا عندما نَقترب من دراستها.

Like its bestselling predecessors Cabinet of Mathematical Curiosities and Hoard of Mathematical Treasures, Professor Stewart's Casebook of Mathematical Mysteries is aimed at everyone from mathematical aficionados to novices. Join Professor Stewart's intrepid investigators to uncover:

Calculus is the key to much of modern science and engineering. It is the mathematical method for the analysis of things that change, and since in the natural world we are surrounded by change, the development of calculus was a huge breakthrough in the history of mathematics. But it is also something of a mathematical adventure, largely because of the way infinity enters at virtually every twist and turn...In The Calculus Story David Acheson presents a wide-ranging picture of calculus and its applications, from ancient Greece right up to the present day. Drawing on their original writings, he introduces the people who helped to build our understanding of calculus. With a step by step treatment, he demonstrates how to start doing calculus, from the very beginning. 

Internationally famous expositor discusses such topics as differential equations, matrices, groups, sets, transformations, mathematical logic and other important modern mathematics, as well as use in physics, astrophysics, and similar fields. Superb explanations for both lay readers and specialists.  

The Golden Ratio examines the presence of this divine number in art and architecture throughout history, as well as its ubiquity among plants, animals, and even the cosmos. This gorgeous book—with layflat dimensions that closely approximate the golden ratio—features clear, enlightening, and entertaining commentary alongside stunning full-color illustrations by Venezuelan artist and architect Rafael Araujo.

From the pyramids of Giza, to quasicrystals, to the proportions of the human face, the golden ratio has an infinite capacity to generate shapes with exquisite properties. This book invites you to take a new look at this timeless topic, with a compilation of research and information worthy of a text book, accompanied by over 200 beautiful color illustrations that transform this into the ultimate coffee table book.

Author Gary Meisner shares the results of his twenty-year investigation and collaboration with thousands of people across the globe in dozens of professions and walks of life. The evidence will close the gaps of understanding related to many claims of the golden ratio’s appearances and applications, and present new findings to take our knowledge further yet.

Whoever you are, and whatever you may know about this topic, you’ll find something new, interesting, and informative in this book, and may find yourself challenged to see, apply, and share this unique number of mathematics and science in new ways. 

The companion book to COURSERA®'s wildly popular massive open online course "Learning How to Learn"

Whether you are a student struggling to fulfill a math or science requirement, or you are embarking on a career change that requires a new skill set, A Mind for Numbers offers the tools you need to get a better grasp of that intimidating material. Engineering professor Barbara Oakley knows firsthand how it feels to struggle with math. She flunked her way through high school math and science courses, before enlisting in the army immediately after graduation. When she saw how her lack of mathematical and technical savvy severely limited her options—both to rise in the military and to explore other careers—she returned to school with a newfound determination to re-tool her brain to master the very subjects that had given her so much trouble throughout her entire life. 

A perennial bestseller by eminent mathematician G. Polya, How to Solve It will show anyone in any field how to think straight. In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be "reasoned" out―from building a bridge to winning a game of anagrams. Generations of readers have relished Polya's deft―indeed, brilliant―instructions on stripping away irrelevancies and going straight to the heart of the problem. 

This little book makes serious math simple!

• Over 120 concepts including laws, principles, equations, paradoxes, and theorems

• Simplifies mathematics, providing fascinating answers to intriguing questions

• Jargon-free text provides accessible explanations for famous principles such as chaos theory, Fibonacci numbers, Euclid's Elements, Zeno's paradoxes, and more

• The perfect gift for students, scholars, deep thinkers, armchair intellectuals, and anyone who is interested in math

The Little Book of Mathematical Principles provides simple, clear explanations for over 120 principles, equations, paradoxes, laws, and theorems that form the basis of modern mathematics.

Making serious math simple, this book explains Fibonacci numbers, Euclid's Elements, and Zeno's paradoxes, as well as other fundamental principles such as chaos theory, game theory, and the game of life.

This book brings together everything you need to know for the SAT math section. Unlike most other test prep books, this one is truly geared towards the student aiming for the perfect score. It leaves no stones unturned.

Inside, You'll Find:

• Clear explanations of the tested math concepts, from the simplest to the most obscure

• Hundreds of examples to illustrate all the question types and the different ways they can show up

• Over 500 practice questions and explanations to help you master each topic

• The most common mistakes students make (so you don’t)

One of the most important milestones in mathematics in the twentieth century was the development of topology as an independent field of study and the subsequent systematic application of topological ideas to other fields of mathematics.

While there are many other works on introductory topology, this volume employs a methodology somewhat different from other texts. Metric space and point-set topology material is treated in the first two chapters; algebraic topological material in the remaining two. The authors lead readers through a number of nontrivial applications of metric space topology to analysis, clearly establishing the relevance of topology to analysis. Second, the treatment of topics from elementary algebraic topology concentrates on results with concrete geometric meaning and presents relatively little algebraic formalism; at the same time, this treatment provides proof of some highly nontrivial results. By presenting homotopy theory without considering homology theory, important applications become immediately evident without the necessity of a large formal program.

Prerequisites are familiarity with real numbers and some basic set theory. Carefully chosen exercises are integrated into the text (the authors have provided solutions to selected exercises for the Dover edition), while a list of notations and bibliographical references appear at the end of the book. 

Combining stories of great writers and philosophers with quotations and riddles, this original text for first courses in mathematical logic examines problems related to proofs, propositional logic and first-order logic, undecidability, and other topics. 2014 edition.

 How Simple Questions Lead Us to Mathematics’ Deepest Truths

point of algebra? Is maths even real? From imaginary numbers to the perplexing order of operations we all had drilled into us, Eugenia Cheng - mathematician, writer and woman on a mission to rid the world of maths phobia - brings us maths as we've never seen it before, revealing how profound insights can emerge from seemingly unlikely sources. Written with intelligence and passion, Is Maths Real? is a celebration of the true, curious spirit of the discipline.

This textbook is designed for students. Rather than the typical definition-theorem-proof-repeat style, this text includes much more commentary, motivation and explanation. The proofs are not terse, and aim for understanding over economy.

 Although mathematics majors are usually conversant with number theory by the time they have completed a course in abstract algebra, other undergraduates, especially those in education and the liberal arts, often need a more basic introduction to the topic.

In this book the author solves the problem of maintaining the interest of students at both levels by offering a combinatorial approach to elementary number theory. In studying number theory from such a perspective, mathematics majors are spared repetition and provided with new insights, while other students benefit from the consequent simplicity of the proofs for many theorems.

Among the topics covered in this accessible, carefully designed introduction are multiplicativity-divisibility, including the fundamental theorem of arithmetic, combinatorial and computational number theory, congruences, arithmetic functions, primitive roots and prime numbers. Later chapters offer lucid treatments of quadratic congruences, additivity (including partition theory) and geometric number theory.

Of particular importance in this text is the author's emphasis on the value of numerical examples in number theory and the role of computers in obtaining such examples. Exercises provide opportunities for constructing numerical tables with or without a computer. Students can then derive conjectures from such numerical tables, after which relevant theorems will seem natural and well-motivated.. 

The author, Chris McMullen, Ph.D., has over twenty years of experience teaching math skills to physics students. He prepared this comprehensive workbook (with full solutions to every problem) to share his strategies for mastering calculus. This workbook covers a variety of essential calculus skills, including:

• derivatives of polynomials, trig functions, exponentials, and logarithms

• the chain rule, product rule, and quotient rule

• second derivatives

• how to find the extreme values of a function

• limits, including l'Hopital's rule

• antiderivatives of polynomials, trig functions, exponentials, and logarithms

• definite and indefinite integrals

• techniques of integration, including substitution, trig sub, and integration by parts

• multiple integrals

The goal of this workbook isn't to cover every possible topic from calculus, but to focus on the most essential skills needed to apply calculus to other subjects, such as physics or engineering 

From preeminent math personality and author of The Joy of x, a brilliant and endlessly appealing explanation of calculus--how it works and why it makes our lives immeasurably better.

Without calculus, we wouldn't have cell phones, TV, GPS, or ultrasound. We wouldn't have unraveled DNA or discovered Neptune or figured out how to put 5,000 songs in your pocket.

Though many of us were scared away from this essential, engrossing subject in high school and college, Steven Strogatz's brilliantly creative, down-to-earth history shows that calculus is not about complexity; it's about simplicity. It harnesses an unreal number--infinity--to tackle real-world problems, breaking them down into easier ones and then reassembling the answers into solutions that feel miraculous.

Infinite Powers recounts how calculus tantalized and thrilled its inventors, starting with its first glimmers in ancient Greece and bringing us right up to the discovery of gravitational waves (a phenomenon predicted by calculus). Strogatz reveals how this form of math rose to the challenges of each age: how to determine the area of a circle with only sand and a stick; how to explain why Mars goes "backwards" sometimes; how to make electricity with magnets; how to ensure your rocket doesn't miss the moon; how to turn the tide in the fight against AIDS.

As Strogatz proves, calculus is truly the language of the universe. By unveiling the principles of that language, Infinite Powers makes us marvel at the world anew

Proofs play a central role in advanced mathematics and theoretical computer science, yet many students struggle the first time they take a course in which proofs play a significant role. This bestselling text's third edition helps students transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. Featuring over 150 new exercises and a new chapter on number theory, this new edition introduces students to the world of advanced mathematics through the mastery of proofs. The book begins with the basic concepts of logic and set theory to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for an analysis of techniques that can be used to build up complex proofs step by step, using detailed 'scratch work' sections to expose the machinery of proofs about numbers, sets, relations, and functions. Assuming no background beyond standard high school mathematics, this book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and, of course, mathematicians.

This best-selling textbook for a second course in linear algebra is aimed at undergrad math majors and graduate students. The novel approach taken here banishes determinants to the end of the book. The text focuses on the central goal of linear algebra: understanding the structure of linear operators on finite-dimensional vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. The third edition contains major improvements and revisions throughout the book. More than 300 new exercises have been added since the previous edition. Many new examples have been added to illustrate the key ideas of linear algebra. New topics covered in the book include product spaces, quotient spaces, and dual spaces. Beautiful new formatting creates pages with an unusually pleasant appearance in both print and electronic versions. No prerequisites are assumed other than the usual demand for suitable mathematical maturity. Thus the text starts by discussing vector spaces, linear independence, span, basis, and dimension. The book then deals with linear maps, eigenvalues, and eigenvectors. Inner-product spaces are introduced, leading to the finite-dimensional spectral theorem and its consequences. Generalized eigenvectors are then used to provide insight into the structure of a linear operator.

مئة ألف لماذا هي مجموعة من الكتب العلمية في جميع مجالات العلوم، وهذا الكتاب الخاص بالرياضيات يقدم مواضيع ممتعة للقراءة ويسهم في نشر المعرفة وتعزيز المفاهيم الرياضية.