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Elliptic Curves
This book uses the beautiful theory of elliptic curves to introduce the reader to some of the deeper aspects of number theory.It assumes only a knowledge of the basic algebra, complex analysis, and topology usually taught in first-year graduate courses.An elliptic curve is a plane curve defined by a cubic polynomial.Although the problem of finding the rational points on an elliptic curve has fascinated mathematicians since ancient times, it was not until 1922 that Mordell proved that the points form a finitely generated group.There is still no proven algorithm for finding the rank of the group, but in one of the earliest important applications of computers to mathematics, Birch and Swinnerton-Dyer discovered a relation between the rank and the numbers of points on the curve computed modulo a prime. Chapter IV of the book proves Mordell's theorem and explains the conjecture of Birch and Swinnerton-Dyer.Every elliptic curve over the rational numbers has an L-series attached to it.Hasse conjectured that this L-series satisfies a functional equation, and in 1955 Taniyama suggested that Hasse's conjecture could be proved by showing that the L-series arises from a modular form.This was shown to be correct by Wiles (and others) in the 1990s, and, as a consequence, one obtains a proof of Fermat's Last Theorem.Chapter V of the book is devoted to explaining this work.The first three chapters develop the basic theory of elliptic curves.For this edition, the text has been completely revised and updated.
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Curves Mallorca
Everybody has their own ideas about the most popular mediterranean holiday island.Whether you dream of sunbathing at a scenic bay, or of joining a group of cyclists to cycle up mountains, or of enjoying the winding mountain roads in an open-top sportscar, Mallorca has all of that and more.Unfortunately, most people know about the island's advantages so you will never be alone.Never?Volume 10 of the successful Curves series conveys exactly that: the experience of being alone.Beaches without sunburned tourists, roads without coaches, cyclists, or hired cars, photographed by Stefan Bogner with his unique touch.How he does it remains a secret. What we know for sure is that he captures highlight after highlight: Palma de Mallorca, Port d'Andratx, Pollenca, Can Picafort, Cap de Formentor,Lean back, fasten your seatbelt, browse - and enjoy!Text in English and German.
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Elliptic curves and functions
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Curves: Portugal : Band 14
Did Curves join the surfer community? Or the community of Fado lovers? Will there be a huge soulful-driving mural in Lisbon, the vibrant capital of street art?Will we do a few rounds in Estoril, the country’s famous race track?Who knows? But what we do know: Curves No. 14 goes to Portugal!It goes without saying that this country offers great opportunities for sophisticated curve chasers.The mix of mountains, rolling hinterlands and coast is extremely rich in variety.Densely populated regions alternate with almost uninhabited areas. And no matter whether you wish for high waves or prefer to enjoy Vinho Verde, grilled sardines and pastel de nata - Portugal has lots of off-road highlights to offer. Rediscover Portugal with Curves!Text in English and German.
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Cars & Curves Vol.2
Following on from Cars & Curves Volume 1, Volume 2 gathers an exquisite selection of the best and rarest Porsche models, including the 908, 962, 718 Spyder, and Carrera Abarth, and follows them through awe-inspiring terrain.The action-packed photos, often taken from helicopters, are accompanied by powerfully written texts by Ben Winter, which complement the fascinating images and make the impressive routes feel like the real thing - as if you were at the wheel.What are you waiting for? Leaf through, buckle up and drive off!Text in English and German.
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Curves: Norway : Number 17
Norway has long been an insider tip among road lovers.The Trollstigen is often mentioned in the same breath as legendary passes all over the world.It's important to know that whether you move on two wheels or four, there is so much more to discover here.Curves has set out in search of the absolute highlights and presents exactly that here: breath-taking views, endless winding roads, and gastronomic highlights - all combined to create a travel guide of a very special kind.Norway is presented here as you certainly don't know it - yet!Text in English and German. Also available:Curves: Germany's Coastline | Denmark ISBN 9783667110909
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Lita/Dangerous Curves: Digitally Remastered
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Differential Geometry of Plane Curves
This book features plane curves—the simplest objects in differential geometry—to illustrate many deep and inspiring results in the field in an elementary and accessible way.After an introduction to the basic properties of plane curves, the authors introduce a number of complex and beautiful topics, including the rotation number (with a proof of the fundamental theorem of algebra), rotation index, Jordan curve theorem, isoperimetric inequality, convex curves, curves of constant width, and the four-vertex theorem.The last chapter connects the classical with the modern by giving an introduction to the curve-shortening flow that is based on original articles but requires a minimum of previous knowledge. Over 200 figures and more than 100 exercises illustrate the beauty of plane curves and test the reader's skills.Prerequisites are courses in standard one variable calculus and analytic geometry on the plane.
Price: 52.00 £ | Shipping*: 0.00 £
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What is spatial visualization ability?
Spatial visualization ability refers to the capacity to mentally manipulate and comprehend spatial relationships between objects. Individuals with strong spatial visualization skills can easily visualize and understand how objects relate to each other in space, such as rotating or manipulating shapes in their mind. This ability is crucial in various fields such as engineering, architecture, and mathematics, as it allows individuals to solve complex problems and understand spatial concepts more effectively. Improving spatial visualization ability can enhance problem-solving skills and overall cognitive performance.
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Is spatial visualization important for engineers?
Yes, spatial visualization is important for engineers as it allows them to mentally manipulate and understand complex 3D objects and structures. Engineers often need to design and analyze various components and systems, and spatial visualization skills help them to conceptualize and communicate their ideas effectively. Whether it's designing a new product, creating blueprints for a building, or solving complex problems, spatial visualization is a crucial skill that allows engineers to think critically and innovate in their field.
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Are curves really positive?
Curves can be positive in various contexts. In mathematics, curves can represent beautiful and intricate shapes that inspire creativity and exploration. In art and design, curves are often used to create visually appealing and dynamic compositions. However, the perception of curves as positive or negative ultimately depends on individual preferences and cultural interpretations.
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Do you like curves?
As an AI, I don't have personal preferences or feelings, so I don't have the capacity to like or dislike anything, including curves. However, I can provide information or assistance on the topic of curves if you have a specific question or need help with something related to curves.
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Can one improve their spatial visualization skills?
Yes, it is possible to improve spatial visualization skills through practice and training. Engaging in activities such as puzzles, building models, and playing spatial reasoning games can help develop these skills. Additionally, practicing mental rotation exercises and regularly challenging oneself with spatial tasks can also contribute to improvement. With consistent effort and dedication, individuals can enhance their spatial visualization abilities over time.
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What are problems with spatial visualization skills?
Some problems with spatial visualization skills include difficulty in understanding and interpreting maps, graphs, and diagrams. Individuals with poor spatial visualization skills may struggle with tasks such as navigating through unfamiliar environments, understanding 3D objects, and mentally rotating objects. This can impact their performance in subjects such as math, science, and engineering, as well as in everyday activities such as driving and assembling furniture. Additionally, poor spatial visualization skills can lead to frustration and decreased confidence in one's abilities.
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What are the issues regarding closed curves in parametric representation and parameter curves?
One issue with closed curves in parametric representation is that it can be difficult to determine the direction of the curve, which can affect calculations such as finding the area enclosed by the curve. Additionally, closed curves can have multiple representations in parametric form, leading to ambiguity in the parameterization. For parameter curves, an issue arises when the parameterization is not injective, meaning that the same point on the curve can be reached by multiple values of the parameter. This can lead to difficulties in defining the curve and performing calculations on it. Additionally, parameter curves can have singular points where the parameterization breaks down, causing issues in analyzing the curve at those points.
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How do you get curves?
To get curves, you can focus on building muscle in specific areas such as your glutes, hips, and thighs through strength training exercises like squats, lunges, and hip thrusts. Additionally, incorporating resistance training and weightlifting into your workout routine can help sculpt and define your curves. It's also important to maintain a balanced diet that includes enough protein to support muscle growth and reduce body fat to help accentuate your curves. Remember that everyone's body is unique, so it's essential to focus on what makes you feel strong and confident.
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