J-curve Books

I thoroughly enjoyed reading Ahead of the Curve and applying the fundamentals taught in this book. Dr. Stowell provides ideas on how the application of strategic thinking can be a turn-key process. Not only does his knowledge help you fill in the gaps you knew your organization had, it assists in identifying how to avoid the gaps and speed bumps all together by following a simple method. I would recommend this book for anyone who is looking to establish a more analytical and decisive approach when focusing on strategy.

Ahead of the Curve; Applied Strategic Thinking - during performance reviews last year, I came to the realization that my team of managers was very good at executing our plans, but were spending very little time planning strategy for the future. Having read and discussed the concepts together, my team felt better prepared to make strategic thinking a part of their developmental plan. This book was an excellent tool to help us jump start our teams strategic thinking and energized the team.

Ahead of the Curve: A Guide to Applied Strategic Thinking (Hardcover)

Are you an active force in shaping your future or simply being on the receiving side of the inevitable "jolt" of change? Stowell and Mead suggest a practical approach to becoming a strategic force in an organization's future. The strategic leader lays the groundwork for future opportunities. Examples of powerful questions set the context for establishing a cultural of reflective and analytical thinking. This starts by "stepping back" from daily activity and discovering what strategic thinking means to each individual and member of any leadership, management or natural work team: how are you adding value to your organization in the long term.

A practical model is presented to help us visualize our work environment from a strategic perspective. Of the four zones described (Operator, Planner, Inventor, Strategist) on a horizontal axis of time and a vertical axis of imagination, the Strategist operates in environment of strategic opportunity, thinking both broad and long term. The Strategist has an uncanny ability to anticipate, recognize and convert changes into opportunities. Strategy is about improving your position to make a difference in the organization. The secret is recognizing how to apply this way of thinking on a daily basis to the most mundane of activities in order to uncover new ideas, proving value and moving ahead of the curve.

What can we do to make this applied approach work? We must find a way to mentally step back and have a conversation about the future with a mentor, team member, supervisor or trusted advisor. Observe how the organization and its parts fit together, gain a perspective of perspicacity. Develop habits that will strengthen the strategic mind: Seek out knowledge and information; be curious; be self-motivated; be collaborative; be playful with ideas; go on a learning journey.

A C.L.E.A.R. target provides a basic rule: Nothing about strategic thinking is all that complex. A good target that is well defined has a certain profile. Controllable, Linked, Energizing, Actionable, Result-Oriented. The importance of this goal model to me is the focus on the energizing and action focus of the entire book. The initiative must be exciting, fun and rewarding, but must at all costs lead to reasonable implementation or you gain nothing. If not result-oriented, then you have wasted finite resources and are simply marking time. Finally, the future is not as far away as you think - so get ahead of the curve and avoid the jolt of running into the wall of change you did not anticipate. This book is worth having at your desk and reviewing in a reflective intentional manner.

Dennis Rogers, Director of Strategic Learning, Division of Strategic Development, Social and Rehabilitation Services, State of Kansas.

As much as this title is about strategy, in my opinion, it is also about being innovative and acting on innovation - what the author might call "strategic thoughts". If you are thinking about how to satisfy the future needs of customers, I think you would like this. It has a plenty of good information.

I bought this book after reading one of the Amazon reviews. After reading the book, I was impressed in the value and concepts it offered towards the idea of strategy. From a Senior Management perspective, this works for both the organization as an entity and those "individuals using it daily" as was mentioned in another review. Strategic gold.

This is a superbly written introduction to elliptic curves. I like the straight-forward language. I dread the stiff elaborations, one finds in some german books with awkward idioms etc..

I found it fascinating, how the elements of general theory, explicit formulae and geometric ideas (the group law on an elliptic curve is constructed via means of geometry) are interwoven.

However, if you want to get a glimpse of such fundamental theorems like the Mordell-Weil theorem, you will need a solid understanding of the basics of algebraic number theory.

Also, if the author tells you "it is clear", it may take you two or three pages of your own thoughts and scribblings to actually see, why it is "clear". Sometimes it really is clear, but sometimes he might be referring to basic results from algebraic number theory. For example in VIII.$1 Proposition 1.6, a field is constructed, which is unramified outside a certain set of places of the number field K. The notion "It is clear .... is unramified if and only if ord_v(a) = 0 ..." had me puzzled for a while, until it dawned on me, that I needed a certain separability criterium for the polynomial to show what was needed.

All in all, still a great book.

The theory of elliptic curves has to rank as one of the most fascinating fields in all of mathematics. Being around for almost two centuries, elliptic curves are finding myriads of applications, including cryptography, superstring theory, and computer imaging. The author does a brilliant job of organizing and explaining the theory in this book. Although the book requires a thorough understanding of algebraic geometry and modern algebra, the book is packed full of insights without sacrificing mathematical rigor. This is rare in most textbooks on modern mathematics. Numerous exercises exist at the end of each chapter, which allow readers to test their understanding of the subject as well as giving extensions to the main results in the text. The author reserves the cases of elliptic curves in characteristics 2 and 3 to the appendix. This may be disappointing for those reading the book for cryptographic applications of elliptic curves, but it does prepare one for further reading on the subject. By far the best chapter in the book is Chapter 10 on computing the Mordell-Weil group as the author does a nice job of detailing the relevant constructions. This book is well worth the time and effort required to study, and could serve well in an actual class on the subject. The author does have a follow-up book called "Advanced Topics in the Theory of Elliptic Curves" for those who need further stimulation in this intriguing and important field of mathematics.

This is a standard text now, and indeed it has it merits. The book uses algebraic geometry of curves throughout, instead of using the so-called 'Lefschetz principle' as done in older texts like Serge Lang's. Using general theorems of algebraic geometry instead of explicit polynomial calculation simplifies discussion, and at the same time paved the way for the reader towards the higher dimensional version of elliptic curves --- abelian varieties, whose geometry and arithmetic predate much of modern number theory research.
After preliminary chapters on the underlying geometry of elliptic curves, the book take up its main aim -- proving the Mordell-Weil theorem, in chapter 8. The Mordell-Weil theorem states that the group of rational points over a number field is finitely generated, and finding the rank of this finitely generated abelian group effectively is subject to much current research (c.f. the Birch Swinnerton-dyer conjecture).
The proof of Mordell-Weil theorem in this book is standard: one first establishes the weak version: E(F)/m E(F) for any integer m >1 , is a finite group. To prove this one has to know basic algebraic number theory, Kummer theory, and some Galois cohomology. For those who are not familiar with Galos cohomology, the author has provided an appendix on Galois cohomology, which should contain all that 's needed.
To deduce the full Mordell-Weil from the weak one, one establishes an important device: the theory of heights on elliptic curves. The height of a point is roughly a kind of norm, which measures the arithmetic complexity of the point (i.e. set of rational points with height bounded is finite) . The height function come with a whole family, but there's a canonical one , the so-called Neron-Tate height, which actually is a quadratic form on the algebraic points of the elliptic curve. After establishing the property of this height, one nearly trivially deduce that the rational points must be finitely generated.
The heights on elliptic curves and abelian varieties contain lots of (conjectured) information about the arithmetic of the varieties. One readily realise this when one look at the BSD conjecture, the Gross-Zagier formula, and various Diophantine approximation type conjecture (e.g. Vojta's) .Therefore it's worth spending time to study the theory of height. Unfortunately the author develop just that amount of theory to prove the Mordell-Weil theorem. For those who want furhter information , one can look at the book "Introduction to Diophantine Geometry" by M. Hindry and Silverman. But to really go to the heart of the matter, one must learn the intrinsic formulation of height by Arakelov (so-called Arakelov theory), as witnessed in Faltings' work on this subject.
The Final two chapters are: Chapter 9 on integral points, Chapter 10 on computation of the weak Mordell-Weil group. Superficially, these 2 chapters are of completely different style: the theory of integral points employ classical Diophantine approximation technique, such as Roth's theorem and Baker's transcendence theory; while the theory of rational points (i.e. the structure of the Mordell-Weil group) employs the theoy of principal homogeneous space, Galois cohomology to measure failure of Hasse's principle, etc. As J. Tate had remarked in a 1974 article 'The theory of integral points on elliptic curves involves completely diffrent concepts (from rational points) and that we mention it only in passing...'. The situation now changed completely. The classical style of Diopahntine approximation, is employed by Vojta, Faltings, Bombieri to prove even stronger version of Mordell conjecture, which is about finitebess of rational points! The proof is much more elementary when compared to Falting's original proof. One can look at the book 'Diophantine approximation and abelian varieties' by Edihoxen and Everste for an introduction to this revival of the subject.
But now back to this book written in 1986, the most importanr result of chapter 9 is Siegel 's theorem: finiteness of integral points on hyperelliptic curves, with application to the establishment of the Shafarevich conjecture of elliptic curves: finiteness of isomorphism class of elliptic curves with good reduction outside finite set of primes. (Note: the general Shafarevich conjecture lies at the heart of Faltings' original proof of the Mordell conjecture!). While Chapter 10 is an introduction to the Galois cohomology methos of calculating the weak Mordell -Weil group. Both theories and numerical examples are richly presented. In particular the important Selmer groups and Tate-Shafarevich group are introduced.Finding the 'size' of these two groups is subject to much current research. For example, bounding the size of a certain Selmer group lies at the heart of Wiles' proof of the semistable case of Shimura-Taniyama conjecture( hence Fermat). This is indeed a very rich subject. For further information, one must studt further Galois chomology, arithmetic duality, Iwasawa theory, and finally Euler system.
Overall, I think this book will appeal to anyone who want to know how to apply algebriac geometry to study Diophantine problems.

I bought this book because I was designing a cryptographic protocol, and wanted to know if I could use ECC in my design. It begins with an explanation of "traditional" public key cryptography (i.e., cryptography over prime fields), introduces binary fields and elliptic curves, shows how to perform computations over elliptic curves, puts this together into ECC protocols, and then includes very useful implementaiton information. This book does a good job explaining not only how to use ECC algorithms, but why they work.

As advertised, this book doesn't go into too much mathematical depth, omitting most proofs. This doesn't mean that there is no math in this book; if you don't have a decent background in algebra (no, not the stuff you learned in seventh grade), you're likely to get confused. However, if you have a little background in theoretical math and cryptography, you'll find this a very readable and easy to understand book.

The one thing that's left out of this book are intellectual property issues. Certicom owns a lot of patents on ECC, and it's not clear which ideas in this book are covered by Certicom patents. This is a minor complaint though; overall, the book is excellent. It's rare to find a book that is so exactly on target. Highly recommeneded.

This book is a must have if you are interested in implementing elliptic curve cryptography. It does not have any of the juicy ellpitic curve mathematics, but that is okay as this book is directed towards engineers and others who want to learn about how elliptic curve cryptosystems are being deployed.

This is the only source I've found that goes into the nuts and bolts of elliptic curve (EC) cryptography. The mathematical content is rich, although proofs are generally in references rather than in the text itself. The real value is in its many and detailed algorithm examples, and in the way it builds up to them.

Before it even gets into the text, Hankerson et al have created a model of clarity. In addition to the usual, front matter includes a list of abbreviations. If you've ever choked on the alphabet soup in other books, you'll appreciate how this makes the discussion much easier to absorb. There's also a list of the algorithms presented - what the practitioner wanted in the first place.

After an introductory chapter, the authors present finite field arithmetic in a thorough but readable way. First they present prime fields over the integers, then optimal extension fields and (most importantly) binary fields. There's nothing here for the cut&paste programmer, but dozens of algorithms help the thoughtful developer work through material that is immensely complicated in other presentations. Other goodies, like Karatsuba-Ofman fast multiplication appear here as well.

The third chapter is the book's real payload: EC techniques. I've been looking for years for a book that was so explicit in the how-to, without watering down the technical content. This is practical stuff - not just the theory of EC operations, but the techniques that make EC calculations practical for high-speed implementations.

The rest of the book - about half - discusses what to do with EC codes. That includes protocols for choosing parameters, public-key and signature algorithms, and standard kinds of attacks. It also includes hardware-level description of possible implementations, down to specific instruction sets and cache structures and different kinds of chip implementations. That leads to another set of discussions on attacks, the kind that go in through the power supply or RF emissions. Appendices provide or point to pragmatic details such as parameters to use or software support available.

The only thing that could be improved in this book is the index - it's just too brief, and lacks the thoroughness the rest of the book led me to expect. I hope you realize just how small a complaint that is. In all other ways, this book meets the highest expectations.

Highly recommended for anyone who needs to understand exactly how EC cryptography works, right down to the bit level.

//wiredweird

It's a thin volume, and I usually like a little more meat to my quilting books, but Blendable Curves has everything one would want to know about easy cutting and piecing of freehand curves and numerous well illustrated examples. Another sign of the quality of this book is that a full-color page is dedicated to a professional photo of each of the finished quilts. It frustrates me to read an quilting magazine article or book that does not show a clearly visible finished product. I also love the suggestions on quilting designs and appreciate the concise instructions for easy binding with mitered corners. Too many books gloss over these important finishing steps. Peggy Barkle has written a quality book.

Have you been looking for a pattern to use up that collection of black and white prints? Check out the log-cabin based Pleasantville. Bored with the Sawtooth Star? I love how the author takes the points on the traditional Sawtooth Star and makes them curvy. It adds a delicious interest to the ubiquitous block and the resulting quilt.

Our quild members produce a prodigious amount of 9-patch blocks and I think Blended Nines would be a wonderful technique to add some interest and fun to the quilts we make for donations. There's nothing wrong with a Nine patch block or quilt, but they can get a little boring in the making.

I have a set of 64 sixteen-inch Log Cabin blocks that I have been avoiding putting together because after working on them for so long, I'm just bored silly of looking at them. The Curvaceous Cabins pattern would spark my interest in finishing the quilt and creating a more exciting finished result. Although I never intended slashing my blocks through the middle, I'm inspired now to do so.

I just got to talk to Peggy and now I know why I love her book - Blendable Curves. She takes basic blocks that are simple for any quilter - like nine-patches - and cuts them in half with a free form curve. THEN, she has you sew the curved sides back together to complete the block.

I know what you're thinking - I don't sew curves. Well I didn't either, until now - because once you've sewn the curve, the block is re-sized! Nothing has to match - shoot, it's not SUPPOSED to match - so this is the perfect beginner project. You can just have fun with color and design. And while you're at it, you can take all of those blocks that WEREN'T perfect - and transform them into works of art!

Our local guild just hosted a nine-patch exchange. As you know, not all seam allowances are created equal, so the blocks are not all exactly the same size. Peggy has the perfect solution. In "A Leap of Faith" she used the "blended nines" to create a breathtaking backdrop for an applique quilt.

Pleasantville is my favorite quilt in the book because it is very graphic - reds, whites and blacks - or if you are in Buckeye country, we swear it reads as Scarlet and Gray! But, for those of you who cheer for the wrong team, this quilt would work just as well in other school colors.

In this particular quilt, Peggy inserted red piping between the curved sides of the black and white log cabins. It gives the whole quilt an "art deco" look with a very masculine feel - and as a mother of four boys, I love finding a quilt that the men in my life appreciate!

For those of you who loved Piping Hot Curves by Susan Cleveland, this is a natural progression.

Peggy describes this as a transitional book. First, beginning students can learn to make the traditional blocks - half-square triangles, nine-patches, quarter-square triangles, etc. There is no pressure because if their points don't match, they will learn how to "curve them up" in the next class! She has totally eliminated the intimidation factor!

Once the students have learned the basics, they can bring those blocks to a "Blendable Curves" class and let their imagination soar! Now that they have learned the rules - Peggy can promptly show you how to break them - with absolutely stunning results!

And, PLEASE take the time to read her instructions!!! I know it is more fun to skip to the projects, but this woman knows what she is doing. I especially like her explanation about how to press seams. AND, she actually gives instructions - with graphics - on how to bind a quilt the right way! Keep this book by your machine so you can pull it out every time you finish a project - you'll be glad you did!

Once you have explored her techniques, you will want to play with all of those loose blocks in your stash left over from other projects. Remember, the blocks are resized after the sewing is complete so you are free to mix and match to your heart's content! The skies the limit!

My advisor in graduate school told me to read this book. My office mate followed his advice. From then on, whenever I asked a question of my office mate, he stared into space searching for an answer, and then he replied, "Read Walker." In my opinion, it is the single most important book you can read if you want to become an algebraic geometer, or if you want to understand what an algebraic geometer is talking about. I am astonished to see that it is out of print. If the book has any flaws, I haven't been able to find them. Thank God for Robert J. Walker.

This book arrived quickly, the same day as my Amazon order even though it was from a private vendor. Great condition.

This book presented information regarding plane curves in a clear, concise manner. The illustrations add to the book's quality. This is a good reference for people who work with plane curves.

The book "Curves and Singularities" is an excellent introduction to the the use of calculus in studying curves and surfaces. I enjoyed the sections on osculating cirles, degree of contace, envelopes, and jets. There are many exercies and examples to guide the reader.

I saw a copy once and read the intro which alluded to removing the mystery from elliptic curve cryptography, disdaining the popular 'myth' that it's "very complicated."

Elliptic curves are so ubiquitous in mathematics and science and such beautiful objects that no author who expounds on them would do a bad job. This book is no exception to this axiom, and even though short the author, a noted expert on the subject, gives the reader important insights into the main properties of elliptic curves.

A highly interesting topic that is included in the book concerns Neron models, which the author motivates by considering an elliptic curve E over the p-adic number field Q(p). A change of variables to its Weierstrass equation is made so that ord() takes on its minimal value and the coefficients are in Z(p). The resulting elliptic curve over Z(p) is viewed as a minimal or "good" model of E with respect to plane projective curves. The idea of a Neron model is to generalize this strategy so that the dependence on plane projective curves is dropped. This involves the theory of schemes, a topic which the author only lightly touches on in this book. His motivation of the Neron model though is excellent, for he uses the work of the mathematician K. Kodaira on elliptic surfaces, which have the property that they are as "regular" as possible. This means that the "fibers" are elliptic curves that have the "minimal" number of singularities. By "blowing up" of points and "blowing down" of curves as much of the bad behavior of the fibers is removed as possible, a process sometimes called "good reduction." The price to be paid for this strategy is that the surface cannot be embedded into projective space.

Those readers familiar with the concept of smoothness in the classical theory of minimal surfaces will see the analogy with the concept of regularity in this case. In the more general theory of algebraic curves, if V is an algebraic curve over a ground field K, where K is a number field or a function field of a smooth projective curve C then one can construct a scheme using K and C. For a number field, S is the spectrum of the ring of integers in K, whereas for a function field it is C. The object is to construct the "best" model over S with the goal of understanding the arithmetic of V. Minimality of a (projective) model of the algebraic curve is unique up to a birational morphism, i.e. a projective minimal model of C is the same as another is every birational morphism between them is also an isomorphism. One can show that every algebraic curve over K with genus greater than or equal to one has a unique projective minimal model. An algebraic curve has a "good" reduction if the special fiber of its minimal model is smooth. An algebraic curve over K has a "bad" reduction if the special fiber of the minimal model has only ordinary double points as singularities.

Computing the rank of an elliptic curve E(Q) is still a major unsolved problem and as is the case in other books it is discussed in the context of the Selmer and Tate-Shafarevich groups. The Selmer group gives an upper bound for the rank, and the Tate-Shafarevich group measures the difference between the upper bound and the actual rank. The importance of these groups is illustrated via the proof of the (weak) Mordell-Weil theorem, which gives the finiteness of E(K)/nE(K) for any elliptic curve over a number field K and integer n.

In order to prove this theorem, the author takes the reader on a journey through group cohomology, starting first with the cohomology of finite groups and then with the cohomology of the infinite Galois group. As is well known in other contexts, cohomology theories essentially measure the obstruction to maps between spaces to be injective or surjective. For the case of group cohomology this is true also, where in this case the first cohomology group, at least the way it is described by the author, where the lack of surjectivity is measured by the `principal crossed' homomorphisms. Both the Selmer and the Tate-Shafarevich groups are defined in terms of the first cohomology group of an elliptic curve E(Q), and the author proves that the Selmer group is finite. Having done this, and using height theory, he proves the finiteness of E(K)/nE(K).

Because of its great complexity, a book of this size would not be able to include a detailed proof of Fermat's Last Theorem. The author discusses modular forms as a preparation for this theorem, but leaves the details to other works on the subject.