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This digital document is an article from Science and Its Times, brought to you by Gale®, a part of Cengage Learning, a world leader in e-research and educational publishing for libraries, schools and businesses.The length of the article is 1868 words.The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase.You can view it with any web browser.The histories of science, technology, and mathematics merge with the study of humanities and social science in this interdisciplinary reference work. Essays on people, theories, discoveries, and concepts are combined with overviews, bibliographies of primary documents, and chronological elements to offer students a fascinating way to understand the impact of science on the course of human history and how science affects everyday life. Entries represent people and developments throughout the world, from about 2000 B.C. through the end of the twentieth century. ... Read more

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This digital document is an article from Macmillan Reference USA Science Library: Mathematics, brought to you by Gale®, a part of Cengage Learning, a world leader in e-research and educational publishing for libraries, schools and businesses.The length of the article is 407 words.The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase.You can view it with any web browser.Explores the functions of math in daily life, as well as its role as a tool for measurement, data analysis, and technological development. This illustrated set also explains basic concepts of math and geometry, and provides information on historical milestones, notable mathematicians, and today's career choices. ... Read more

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"Deeply informed and insightful, Zachary has thoroughly captured thespirit of Bush and his times." -- Thomas P. Hughes, New York TimesBook Review

"This fascinating biography, superbly researched, well organized andengagingly written, will probably become the standard work on Bush andremain so for years to come." -- Roger Bridgman, The NewScientist

As a young professor at MIT in the 1920s, Vannevar Bush (1890-1974) didseminal work on analog computing and was a cofounder of Raytheon, whoseinitial success was based on long-lasting radio tubes. But he is bestknown for his role in Washington during World War II: as PresidentRoosevelt's advisor, he organized the Manhattan Project and oversaw thework of 6,000 civilian scientists designing new weapons. His 1945 report"Science--The Endless Frontier" spurred the creation of a system ofpublic support for university research that endures to this day.

Although he helped to give rise to the military-industrial complex, Bushwas a skeptical observer of the interplay between science and politics.He warned against the dangers of an arms race and led a failed effort tohalt testing of the hydrogen bomb. This balanced and gracefully writtenbiography brings to life an American original and his times. ... Read more

Customer Reviews (4)

Biography of great scientific leader and public servant
Zachary deserves great credit for writing a book that offers many virtues and lessons of lasting relevance. Because the author's commitment is worthy of his subject, this book should have timeless value.The roles for science and technology and how best to harness them for prosperity and for security to enable the preservation of peace are questions which transcend any particular time.

The subtitle, Engineer of the American Century, is justified.Bush contributed to American society in many ways.He was a fecund, tireless inventor, helping launch Raytheon Corporation.He was dedicated to boosting the Massachusetts Institute of Technology (MIT) and thereby strengthening society through teaching and seeking practical knowledge.He was a pioneer and convenor of advances in computing.

Clear-mindedly appreciating the gathering evil of Nazi Germany, Bush decided to do something, as typical. He left MIT and got to Washington as head of the Carnegie Institution.Though a Republican, he persuaded President Franklin Roosevelt that those who were technically educated needed to be harnessed within a National Defense Research Committee, in service to their nation's needs.By helping harness the extraordinary abilities of civilian and academic technologists to serve their nation in meeting the challenges of World War II, Bush helped unleash a cornucopia of inventions and advances in thinking, with extraordinary economic legacies (computing, electronics, medicine, radar).

A few words from Zachary:
--Bush's "was a life not of looking back, but of charging ahead."
--He had a "commitment to excellence and integrity that reinforced his belief in the power of one person to make a difference."
--"Bush shared Eisenhower's unease about the alliance between academia, the military, and industry"
--"The proliferation of nuclear weapons, the rise of environmental hazards, and the evident political partisanship of many scientists - all combined to engender a cynicism in the public about the aims and evidence of science."

Several other books of possible interest in relation to the contributions of technologists:
Philip Taubman, Secret Empire (2003)
James Phinney Baxter, Scientists Against Time (1946)
Biographies of Edwin Land
James Killian, Sputniks, Scientists, and Eisenhower (1977). Killian was a 1950s Bush, down to earth and his book is movingly endowed with wisdom.

Vannevar Bush a key player in American military strength
More than one person has written on this page that Vannevar Bush is "little known", "forgotten", etc. I am only 54 years old, but I remember seeing Bush's name in print many, many times while growing up. He was always described as crucial to American military and technological supremacy since 1943 or so. A few of his accomplishments: He mobilized American science and engineering during WWII. His leadership was crucial to the Manhattan project. His differential analyzer led to MIT's Lincoln Labs playing an important role in the rise of information technology. He was Claude Shannon's teacher.

Vannevar like beaver
This is a very well written and entertaining book about a scientific administrator who played a major effort in organizing the technical responses required to anticipate and successfully meet the challenges ofWWII. His skillful analysis, technical comprehension and politicalastuteness not only provided outstanding leadership at the time but shapedthe intractions of goverment, industry and the academic community in such afashion as to remain intact to this time. One comes awawy with an enormousrespect for Dr. Bush. He must have been one tough character and difficultto deal with but he got the jobs done. It is a pity that his battles withAdmiral Ernest King have, to my knowledge, never been documented. Theissues they disagreed about were not trivial and their interactions musthave been awesome. I read this book shortly after completing Tycho's Islandand the similarity between the two men and the administrative issues theydealt with is both striking and illuminating.

Good men are hard to findand good books about them deserve our attention.

An excellent biography of an important but little known man.
A very interesting and thorough biography of Vannevar Bush, who more than any other individual is responsible (for good or for ill) for the shape of today's scientific establishment.Well-written and engaging, with lots of interesting historical tidbits and good insight on the personalities involved.Excellent! ... Read more

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Ideas from quantum field theory and string theory have had considerable impact on mathematics over the past 20 years. Advances in many different areas have been inspired by insights from physics.

In 1996-97 the Institute for Advanced Study (Princeton, NJ) organized a special year-long program designed to teach mathematicians the basic physical ideas which underlie the mathematical applications. The purpose is eloquently stated in a letter written by Robert MacPherson: "The goal is to create and convey an understanding, in terms congenial to mathematicians, of some fundamental notions of physics ... [and to] develop the sort of intuition common among physicists for those who are used to thought processes stemming from geometry and algebra."

These volumes are a written record of the program. They contain notes from several long and many short courses covering various aspects of quantum field theory and perturbative string theory. The courses were given by leading physicists and the notes were written either by the speakers or by mathematicians who participated in the program. The book also includes problems and solutions worked out by the editors and other leading participants. Interspersed are mathematical texts with background material and commentary on some topics covered in the lectures.These two volumes present the first truly comprehensive introduction to this field aimed at a mathematics audience. They offer a unique opportunity for mathematicians and mathematical physicists to learn about the beautiful and difficult subjects of quantum field theory and string theory. ... Read more

Customer Reviews (3)

Amazingly different!
If you are a mathematician and want to know what QFT and string theory (ST) are about, or if you are a string theorist, but want to know more about the mathematics behind the theory, then this book is what you are looking for. This book is totally different than any other standard textbook on QFT or ST. Mathematicians will love the fact that it is written in a language that is (close to) theirs, and physicists will enjoy it (provided they have a more solid background in mathematics than the average practical physicists), because it shows QFT and ST from completely "new" angles.

The book is a collection of lectures given by the various contributors, which fit together perfectly . The first volume has a very good overview of concepts and definitions at the very beginning and serves as a more mathematically oriented introductory treatment of SUSY and QFT with many advanced topics near the end. The second volume starts with an axiomatic approach of CFT and its use in string theory and then quantises strings with the BRST method (on a more mathematical level than usual), which is done superbly.

It's a great reference, a wonderful textbook and a true delicacy in modern mathematical physics. A MUST HAVE for every mathematically inclined physicst or any mathematician with interests in physics! Great value for money...

Lots to learn...
These articles are great. They do well in delineating theconceptual and rigorous frameworksof the subjects.

Included are exercises (and solutions)culminating from the problem sessions held at Quantum Field Theory program at IAS.

Physicists interested in the mathematical aspects of quantum field/string theory would do well to read these volumes as well.

Deserving, in my opinion, more than 5 stars -- many more!!

Definitely for mathematicians only
This book is an excellent compliation of articles written formathematicians who want to understand quantum field theory. It is notsurprising then that the articles are very formal and there is no attemptto give any physical intuition to the subject of quantum field theory. Thisdoes not mean however that aspiring physicists who want to specialize inquantum field theory should ont take a look at the contents. The twovolumes are worth reading, even if every article cannot be read because oftime constraints. All of the articles are written by the some of the majorplayers in the mathematics of quantum field theory.Volume 1 starts offwith a glossary of the terms used by physicists in quantum field theory andis nicely written. The next few hundred pages are devoted to supersymmetryand supermanifolds. A very abstract approach is given to these areas, withthe emphasis not on computation but on the structure of supermanifolds asthey would be studied mathematically. There is an article on classicalfield theory put in these pages, which is written by Pierre Deligne andDaniel Freed, and discussed in the framework of fiber bundles. Thediscussion of topological terms in the classical Lagrangian is especiallywell written. There is an introduction to smooth Deligne cohomology in thisarticle, and this is nice because of the difficulty in findingunderstandable literature on this subject.Part Two of Volume 1 isdevoted to the formal mathematical aspects of quantum field theory. After ashort introduction to canonical quantization, the Wightman approach isdiscussed in an article by David Kazhdan. Most refreshing is that statementof Kazhdan that the Wightman approach does not work for gauge fieldtheories. This article is packed with interesting insights, especially thesection on scattering theory, wherein Kazdan explains how the constructionsin scattering theory have no finite dimensional analogs. The article byWitten on the Dirac operator in finite dimensions is fascinating and a goodintroduction to how powerful concepts from quantum field theory can be usedto prove important results in mathematics. A fairly large collection ofproblems (with solutions) ends Volume 1.The first part of Volume 2 isdevoted entirely to the mathematics of string theory and conformal fieldtheory. The article by D'Hoker stands out as one that is especiallyreadable and informative. D. Gaitsgory has a well written article on vertexalgebras and defines in a very rigorous manner the constructions that occurin the subject. The last part of Volume 2 discusses the dynamics ofquantum field theory and uses as much mathematical rigor as possible. Onegets the impression that it this is the area where it is most difficult toproceed in an entirely rigorous way. Path integrals, not yet definedmathematically and used throughout the discussion. The best article inVolume 2, indeed of the entire two volumes is the one on N = 2 Yang-Millstheory in four dimensions. It is here that the most fascinatingconstructions in all of mathematics find their place.These two volumesare definitely worth having on one's shelf, and the price is veryreasonable considering the expertise of the authors and considering whatone will take away after reading them. ... Read more

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This book provides a comprehensive treatment of quantum mechanics from a mathematics perspective and is accessible to mathematicians starting with second-year graduate students. In addition to traditional topics, like classical mechanics, mathematical foundations of quantum mechanics, quantization, and the Schrodinger equation, this book gives a mathematical treatment of systems of identical particles with spin, and it introduces the reader to functional methods in quantum mechanics. This includes the Feynman path integral approach to quantum mechanics, integration in functional spaces, the relation between Feynman and Wiener integrals, Gaussian integration and regularized determinants of differential operators, fermion systems and integration over anticommuting (Grassmann) variables, supersymmetry and localization in loop spaces, and supersymmetric derivation of the Atiyah-Singer formula for the index of the Dirac operator. Prior to this book, mathematicians could find these topics only in physics textbooks and in specialized literature. This book is written in a concise style with careful attention to precise mathematics formulation of methods and results. Numerous problems, from routine to advanced, help the reader to master the subject. In addition to providing a fundamental knowledge of quantum mechanics, this book could also serve as a bridge for studying more advanced topics in quantum physics, among them quantum field theory. Prerequisites include standard first-year graduate courses covering linear and abstract algebra, topology and geometry, and real and complex analysis. ... Read more

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What does the 2000 U.S. presidential election have in common with selecting a textbook for a calculus course in your department? Was Ralph Nader's influence on the election of George W. Bush greater than the now-famous chads? In Chaotic Elections!, Don Saari analyzes these questions, placing them in the larger context of voting systems in general. His analysis shows that the fundamental problems with the 2000 presidential election are not with the courts, recounts, or defective ballots, but are caused by the very way Americans vote for president.

This expository book shows how mathematics can help to identify and characterize a disturbingly large number of paradoxical situations that result from the choice of a voting procedure. Moreover, rather than being able to dismiss them as anomalies, the likelihood of a dubious election result is surprisingly large. These consequences indicate that election outcomes--whether for president, the site of the next Olympics, the chair of a university department, or a prize winner--can differ from what the voters really wanted. They show that by using an inadequate voting procedure, we can, inadvertently, choose badly. To add to the difficulties, it turns out that the mathematical structures of voting admit several strategic opportunities, which are described.

Finally, mathematics also helps identify positive results: By using mathematical symmetries, we can identify what the phrase "what the voters really want" might mean and obtain a unique voting method that satisfies these conditions.

Saari's book should be required reading for anyone who wants to understand not only what happened in the presidential election of 2000, but also how we can avoid similar problems from appearing anytime any group is making a choice using a voting procedure. Reading this book requires little more than high school mathematics and an interest in how the apparently simple situation of voting can lead to surprising paradoxes. ... Read more

Customer Reviews (4)

Interesting analysis of biases in voting systems, but with a hidden bias itself
Saari's book, as he states in the title and his introduction, is very mathematical. This does not bother me; my own background in science gives me strong enough math to handle this book, though more purely social-science-oriented people may find the book too heavy on the mathematics to help them.

The book analyzes a number of voting systems, and makes a good case for his point that the procedure of casting and counting votes will often determine the result more than the actual preferences of the voters. And he comes up with some conclusions with which I agree: the weakness of approval voting (though his reasons for disliking it differ from mine) and the insufficiency of Banzhaf's method of calculating power in a weighted voting system, for example.

But he generally makes one assumption which does not adequately reflect reality. This assumption is that an ordinal sequence of preference is an adequate representation of a voter's wishes (and that, in consequence, how much a voter prefers candidate A to candidate B is measured by how many candidates are between them on a list of preferences). In fact, with enough candidates in a race, there are bound to be several that a voter likes almost equally well, others that a voter dislikes equally well, and probably others about whom the voter is indifferent (possibly because he knows nothing about them!) Thus, there may be a huge gap between a voter's opinion of, for example, his fourth and fifth preferences, while he may like the fourth one almost as much as his top preference. As a result, Saari ends up favoring a system, the Borda count, which gives absolutely equal differences between the values assigned to consecutively numbered preferences, with no recognition (at least until the next-to-last page of the book!) of the idea that voters' preferences might not work that way. And consequently he fails to see the great advantage of cumulative voting (if one has enough votes!) compared to a Borda count. This is the one serious weakness in Saari's analysis.

At a couple of points, Saari points out that (in an election with enough candidates) if you want to assure the election of a candidate, you can design the election procedure to yield that result even if the candidate actually has little true support. In a sense, Saari does the same in the question of choosing the best voting system. He obviously favors the Borda count, and thus emphasizes the criteria which will make the Borda count score high (and de-emphasizes, or even declares valueless, criteria like the Condorcet criteria that the Borda count violates); other criteria might point toward other methods. But this methodology is subject to the same objections that he raises to some voting procedures!

An Insightful Look at Voting
Saari has put together a small but useful book on the trickiness inherent in voting and the potential paradoxes that can get minor candidates elected.In races with more than two candidates, the method of vote counting is extremely important, and it is possible that by changing the counting process, you could have any candidate you want winning.Theoretically, an election could be rigged without a single dishonest vote.

The obvious solution is to choose the counting method before the election, not afterwards, but there are perils to watch out for nonetheless.Saari goes into depth about these dangers.

This depth often gets very technical, something Saari is up front about.Less than half the book is really aimed for the lay reader; the remainder is aimed more towards mathematicians.Nonetheless, I recommend this book for everyone interested in the democratic process; even if you can't get into the math, there are still enough important insights to make this book more than worthwhile.

Great on math, weak on policy
First, I'm a physicist, so the math was fine for me, but some people might find it frustrating. However, if you're willing to sink your teeth into it you'll get the important ideas.

Second, Saari's insights into the role of symmetry in three-person elections are beautiful. He shows that even if none of the three (or more) candidates can beat all of the others head-to-head there is still interesting information present. When resolving cyclic ambiguities (George beats Bill, Bill beats Ross, Ross beats George) Saari's mathematical insights may be quite useful.

However, I have to take Saari to task for his criticism of Approval Voting (where you simply indicate yes or no for each candidate). He points out that the Approval winner cannot be predicted based solely on people's preference orders (e.g. I might like Ross better than Bill or George, and Bill better than George). Saari sees this as a defect, because "anybody could win." Approval, however, makes use of different information. Which of those candidates pass your threshold? Vote yes for all that you find acceptable.

Seen in this light, Approval is a perfectly rational policy.

Also, Saari doesn't think too highly of the Condorcet criterion:If one candidate can beat all others in one-on-one contests then that candidate should win.It is true that sometimes no candidate meets that criterion, and in those cases Saari's analysis provides important insights on how to resolve the situation.However, sometimes there is in fact one person who can beat all others one-on-one.In that case, no amount of analysis can change the fact that the Condorcet candidate is preferred over all others, and should win.

Finally, Saari gives short shrift to strategic considerations. If everybody is honest his analysis gives excellent advice on running elections.However, his methods have loopholes that voters and candidates can exploit, trying to get the best outcome even if it means indicating an insincere preference order.

Ultimately, the study of elections has to balance two different approaches: Understanding what the people want based on the info they give, and understanding whether the system gives them incentives to give insincere info. Saari has great insight into the first part, but he doesn't seem as interested in the second part.

Election Math made Accessible: Cures Headaches, too!
This book makes some of Saari's most important research into the mathematics of voting accessible to a general audience for the first time. Personally, I greatly appreciate this book. With very little math background, I have tried in vain for the past year to comprehend some of Saari's research articles, with the assistance of a math professor. The result was very little comprehension, and a lot of headaches. This book has, for the first time, enabled me to understand some of the things I had struggled with in vain for months, and greatly increased my comprehension of many of those things I saw only dimly before. I thank the author for the mercy he has shown towards me, and similarly interested readers of his work.

At this time, Saari seems to be the world's leading researcher in the mathematics of voting and group decision making. While most of the general public, in the US at least, has remained almost entirely ignorant of the paradoxes of voting, mathematicians have recognized and struggled with them for centuries, since they recognized that the widespread rule that 'a plurality shall elect' can result in the election of the voters' least preferred candidate; for example, when there are 3 candidates, the plurality winner may be a candidate who is the last choice of up to two-thirds of the voters. Saari's recently published research papers, which resolve many of these profoundly difficult mind stumpers, and the recent US Presidential election, not to mention the begging and pleading of mathematical simpletons like myself, combined to motivate Saari to write this book.

If you are at all interested in having your vote properly accounted for in everything from selecting your group's next officer, to future national elections, I recommend this book to you. I guarantee that you will learn something worthwhile from it.

Let me add one last personal note for Wisconsin readers. I am briefly cited in this book in regard to the use of an alternative to the plurality voting procedure, called the 'Second Choice' procedure, in state primaries of Wisconsin's 'Progressive Era.' The use of such alternatives in the history of Wisconsin, and other states, proves that such electoral reforms are actually possible, given a sufficiently educated and motivated electorate. Saari has done the analysis, and made it accessible. Now, it is up to us to educate ourselves, and other voters, and then, in the light of our newfound knowledge, to demand more democratic election procedures.

Also recommended: Principles of Electoral Reform ... Read more

Product Description
Graduate school marks the first step toward a career in mathematics for young mathematicians. During this period, they make important decisions which will affect the rest of their careers. Here now is a detailed guide to help students navigate graduate school and the years that follow.

In his inimitable and forthright style, Steven Krantz addresses the major issues of graduate school, including choosing a program, passing the qualifying exams, finding an advisor, writing a thesis, and getting that first job. As with his earlier guide, How to Teach Mathematics, he avoids generalities, giving clear advice on how to handle real situations. The book also contains a description of the basic elements of a mathematical education, as well as a glossary and appendices on the structure of a typical department and university and the standard academic ranks.

Steven G. Krantz is an accomplished mathematician and an award-winning author. He has published 130 research articles and 45 books. He has worked in many different types of mathematics departments, supervised both masters and doctoral students, and is currently the Chair of the Mathematics Department at Washington University in St. Louis. ... Read more

Customer Reviews (9)

Clear, Helpful Grad School Insight
I graduated a couple years ago with BS in Mathematics and was trying to decide if I should return for my PhD. This book was extremely helpful. It presents a very thorough overview of the PhD process with helpful information regarding thesis advisors (both selecting and working with) and thesis preparation. Material is easy to read (conversational tone) and very specific. Definitely recommend this to anyone considering a graduate program in mathematics.

Also gives extensive information regarding the application of a PhD in academia- such as types of jobs (tenure track, post-doc fellow, etc.), types of colleges and the workload (and pay) to be expected at those colleges.

End of text is an overview of mathematics topics important to the post-bachelors, pre-grad student.

It does not spend time explaining all the different areas of mathematics, so that part you'll need to figure out for yourself. Reading this book will get you excited to talk to your professors about a doctorate program. Good luck!

THE Survival Guide for Graduate Students
I'm a graduate student in computer science, working on my PhD. If you're looking for a sort of rulebook that contains all the meta-knowledge one needs to know to survive in the scientific game, this is it.
The book includes helpful information to questions you probably wouldn't dare to ask anyone:
"How do i choose a thesis advisor?",
"What if I can't solve my thesis problem?",
"Am I in competition with the other graduate students?",
"What kind of money can I make as a professor?"
There's also lots of information about life after graduation, especially relevant for those of us who want to pursue an academic career.

The book is written in an easy to follow style, and gets straight to the point. You really feel that the author knows what he's talking about.
I highly recommend it to anyone planning a career in a science related to maths.

A good starting point for graduate school
Dr. Krantz's lucid "Survival" guide is rich in advice for the aspiring mathematician who sees a plum job in academia as the ultimate career goal. With section names such as "How do I work my thesis problem?", and "Why does everyone else appear to be succeeding?" Dr. Krantz's chronological account of Math graduate school and the first few years in the work force does an excellent job of providing step-by-step guidance for us future mathematicians. This advice, and the author himself are at their best when talking about prevalent insecurity issues with which all of us mathematicians deal and showing us how such issues are indeed very commonplace and how the solutions are also commonplace and readily available to you.
Now, that being said, it is also important to remember that this is just a rough guide and that not every section in the book should be followed to the letter. More to the point: Dr. Krantz's advice should be used in addition to, not instead of, grad advisors, faculty in your department, and even more senior grad students. Dr. Krantz's advice can be detrimental in some instances and in others, it's just plain wrong. For instance, his advice that a student should NOT study for general and subject GRE's is particularly questionable; in fact I do believe the opposite to be true. GRE tests follow a well-defined set of rules and question formatting; thus, the question themselves have a finite amount of variation to them, and therefore it is precisely in this type of standardized exam MOST students will benefit from reviewing old material and going through numerous practice tests before taking the real thing.

Overall, this is a very good book, full of wisdom and it is, alas, even entertaining at times. If you're considering a career as a mathematician, you would be doing yourself a favor by buying this book and reading it with an epsilon amount of caution.

College Math Major
I gave this to my son who is a high school junior planning to major in mathematics in college.He thought it was great because it looks beyond just getting into college and taking a bunch of math classes.What does a math major do next?Do you have to teach? What do professors and TA's really do? What does it take to get into grad school and is it worth it?I would recommend this book to anyone contemplating any type of career involving higher level mathematics.

Must have for all graduate students
This is a great book with lots of important information on what it's like to be in academia. I recommend it highly for all graduate students as well as for their advisors. ... Read more

Product Description
This entertaining book presents a collection of 180 famous mathematical puzzles and intriguing elementary problems that great mathematicians have posed, discussed, and/or solved. The selected problems do not require advanced mathematics, making this book accessible to a variety of readers. Mathematical recreations offer a rich playground for both amateur and professional mathematicians. Believing that creative stimuli and aesthetic considerations are closely related, great mathematicians from ancient times to the present have always taken an interest in puzzles and diversions. The goal of this book is to show that famous mathematicians have all communicated brilliant ideas, methodological approaches, and absolute genius in mathematical thoughts by using recreational mathematics as a framework. Concise biographies of many mathematicians mentioned in the text are also included. The majority of the mathematical problems presented in this book originated in number theory, graph theory, optimization, and probability. Others are based on combinatorial and chess problems, while still others are geometrical and arithmetical puzzles. This book is intended to be both entertaining as well as an introduction to various intriguing mathematical topics and ideas. Certainly, many stories and famous puzzles can be very useful to prepare classroom lectures, to inspire and amuse students, and to instill affection for mathematics. ... Read more

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A successful mathematical career involves doing good mathematics, to be sure, but also requires a wide range of skills that are not normally taught in graduate school. The purpose of this book is to provide guidance to the professional mathematician in how to develop and survive in the profession. There is information on how to begin a research program, how to apply for a grant, how to get tenure, how to teach, and how to get along with one's colleagues. After tenure, there is information on how to direct a Ph.D. student, how to serve on committees, and how to serve in various posts in the math department. There is extensive information on how to serve as Chairman. There is also material on trouble areas: sexual harassment, legal matters, disputes with colleagues, dealing with the dean, and so forth. One of the themes of the book is how to have a fulfilling professional life. In order to achieve this goal, Krantz discusses keeping a vigorous scholarly program going and finding new challenges, as well as dealing with the everyday tasks of research, teaching, and administration. In short, this is a survival manual for the professional mathematician--both in academics and in industry and government agencies. It is a sequel to the author's A Mathematician's Survival Guide. ... Read more

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Every map is a tool, a product of human effort and creativity, that represents some aspects of our world or universe ... [This] course was powered by the belief that by exploring the mathematical ideas involved in creating and analyzing maps, students would see how mathematics could help them to understand and explain their world."

--from the Preface

Portraits of the Earth exemplifies the AMS's mission to bring the power and vitality of mathematical thought to the nonexpert. It is designed to teach students to think logically and to analyze the technical information that they so readily encounter every day.

Maps are exciting, visual tools that we encounter on a daily basis: from street maps to maps of the world accompanying news stories to geologic maps depicting the underground structure of the earth. This book explores the mathematical ideas involved in creating and analyzing maps, a topic that is rarely discussed in undergraduate courses. It is the first modern book to present the famous problem of mapping the earth in a style that is highly readable and mathematically accessible to most students. Feeman's writing is inviting to the novice, yet also interesting to readers with more mathematical experience. Through the visual context of maps and mapmaking, students will see how contemporary mathematics can help them to understand and explain the world.

Topics explored are the shape and size of the earth, basic spherical geometry, and why one can't make a perfect flat map of the planet. The author discusses different attributes that maps can have and determines mathematically how to design maps that have the desired features. The distortions that arise in making world maps are quantitatively analyzed. There is an in-depth discussion on the design of numerous map projections--both historical and contemporary--as well as conformal and equal-area maps. Feeman looks at how basic map designs can be modified to produce maps with any center, and he indicates how to generalize methods to produce maps of arbitrary surfaces of revolution. Also included are end-of-chapter exercises and laboratory projects. Particularly interesting is a chapter that explains how to use Maple® add-on software to make maps from geographic data points.

This book would make an excellent text for a basic undergraduate mathematics or geography course and would be especially appealing to the teacher who is interested in exciting visual applications in the classroom. It would also serve nicely as supplementary reading for a course in calculus, linear algebra, or differential geometry. Prerequisites include a solid grasp of trigonometry and basic calculus. ... Read more

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A drama about the confrontation between two great men who changed history. The focus of the book centers around the epic struggle between the great Tuscan Galileo and his arch-opponent and one-time-friend, Pope Urban VIII--now prince of a church threatened by Galileo's new science. In this surprising, original, and thought-provoking work, we see the forces that doomed Galileo and vindicated the Pope's authority, but weakened it in the end. ... Read more

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Satan is a Mathematician is a huge new collection of sciencefiction, fantasy and horror poems by "one of the foremost science fictionpoets of our time." (Dreams & Nightmares) The title poem and several othersare Rhysling Award finalists. ... Read more

Customer Reviews (1)

Wide Ranging Collection of Interesting SF/Fantasy Poetry
Here is Satan is a Mathematician, a collection of poems, dating from as far back as 1980, but mostly from the 1990's, which cover a wide range of subjects, science-fictional, fantastical, horrific, and scientific. KeithAllen Daniels is an interesting poet, and at the high end of his range isvery fine.

The book is subtitled "Poems of the Weird, Surreal, andFantastic", which is pretty much what we get.In a previous draft ofthis review I dithered about trying to define "SF poetry", or"Fantastic poetry".To some extent I was interested indisproving the existence of such a beast: after all, poetry is about soundand emotion (and ideas), and at least the first two seem not to bedefinable in genre terms.But then, some poems really are about ideas, andideas, famously, are the stuff of much science fiction.And some emotionsare perhaps best evoked by images from SF or the fantastic.A trivialconclusion, I'm afraid.I will say, though, that it seems to me that Iread poetry of all sorts for the same reasons: sound and emotion, while Iread science fiction, at times, for explicitly different (neither superioror inferior) reasons than I read mainstream fiction.Enough, though.Whatof the poems at hand?

One of my favorites is "The Poetasters'Cafe", which takes a harsh look at the contemporary"coffeehouse" fashion for poetry readings and overly confessionalwriting.It's a fine poem, but it's not SF, unless the use of vocabularysuch as "coelecanth" and "phagocyte" is sufficient toso mark a poem.On the other hand, "Sciomancy Nights", anotherfine effort, uses an explicitly fantastical device, raising the spirits ofthe dead to speak to them, to consider, in a slightly humorous manner, fourhistorical figures (Bierce, Archimedes, Aldous Huxley, Lincoln).Anotherangle Daniels uses is pure science: "The Discourse of the Stones"imagines "deep time" through the history of rock.Not SF poetry,perhaps, but "geology poetry".

On the whole these areinteresting poems.Occasionally Daniels seems to believe that an exoticuse of vocabulary is sufficient to make a sequence of words poetry; onother occasions, the poems seem not much but doggerel.But that is tocomplain about the lesser works of what is, after, quite a long collectionby poetry standards.The best poems here are very good.For example,"Leap to Infinity" is a lovely double haiku: "A doe's leg,fractured/ in mid-leap and torn in half/ hangs from the barbed wire.Onthe ground beneath/ her body has fallen far/ behind her spirit."Orthe fine extended metaphor in "Lithic": "in caverns of theforebrain/ suffering forms grottos/ of fanciful dripstone ...".Or from"The Poetasters' Café": "There the poets are mired in self/like insects in pitcher plants/ of their own device."

Anyoneinterested in contemporary poetry would do well to check out this book. And if you are also interested in SF and fantasy, attuned to the vocabularyand images of science and "the weird, surreal, and fantastic",you'll be even more likely to be attracted by Keith Allen Daniels' favoredimage sets. ... Read more

Product Description
A³ & HIS ALGEBRA is the true story of a struggling young boy from Chicago’s west side who grew to become a force in American mathematics. For nearly 50 years, A. A. Albert thrived at the University of Chicago, one of the world’s top centers for algebra. His “pure research” in algebra found its way into modern computers, rocket guidance systems, cryptology, and quantum mechanics, the basic theory behind atomic energy calculations.

This first-hand account of the life of a world-renowned American mathematician is written by Albert’s daughter. Her memoir, which favors a general audience, offers a personal and revealing look at the multidimensional life of an academic who had a lasting impact on his profession.

Customer Reviews (2)

A childhood friend's view
Nancy Albert has been a dear friend since we were five years old so I knew her parents, both kind, loving people. We had no idea of her father's accomplishments.To us kids he was a quiet, soft spoken man, always smiling, always reading something. I am so proud of Nancy for her massive research and ability to put it all together in a style those of us less knowledgeable in mathematics can understand.A major plus was bringing back memories of our childhood in Chicago. Thank you, Nancy.From your sister in spirit, Mibs

What Mathematicians Do and A Father Fondly Remembered
I enjoyed this book very much.Many carefully researched details recreate the times and places mentioned.Personal observations and insights give the feel of an intimate memoir.The book is very well written and gives the feel and excitement of mathematics without going into the details so it is fully readable and enjoyable by persons without any mathematics background.It takes the reader from the depression through World War II, the Korean War, The Vietnam War, right up to the 1970s, all from the point of view of a mathematician and his family.Very interesting for those who lived through it and enlightening for those who didn't.This is the best book I've read for giving a picture of what mathematicians do.It may even inspire some young people to study mathematics seriously.To me (a retired mathematician) the mention of certain theorems awoke a nostalgia and almost made me want to start all over again and perhaps understand things deeper and better.As Nancy Albert says "mathematics is a beautiful but never fully attainable mistress". ... Read more

Product Description
In this book the author ofInnumeracy : MathematicalIlliteracy and Its Consequences reveals the hidden mathematical anglesin countless media stories.His real life perspective on the statistics werely on and how they can mislead is for anyone interested in gaining a moreaccurate view of their world.The book is written with a humorous andknowledgeable style that makes it great reading.Amazon.com Review
In this book the author ofInnumeracy : MathematicalIlliteracy and Its Consequences reveals the hidden mathematical anglesin countless media stories.His real life perspective on the statistics werely on and how they can mislead is for anyone interested in gaining a moreaccurate view of their world.The book is written with a humorous andknowledgeable style that makes it great reading. ... Read more

Customer Reviews (34)

Foxy Numbers
Have read only a few pages as assigned to date- very good, so far.

As concerns vendor action, it was very good and book was received ahead of schedule and in very good condition.

Interesting and instructive
A very well written book, both interesting and instructive. Full of common sense, the author provides a plethora of reports commonly found in almost any newspaper, and highlights errors of facts, of inferences from bad assumptions, of statements supported by little or no evidence, of our poor grasp of probabilities of events, and of much else. An excellent read that will make us more critical in our reading of newspapers.

Underwhelming
Some interesting anecdotes don't save you from feeling a little cheated by this book which promises an entire mathematical world view but only delivers a few snippets.

When did you last read the Newspaper?
"Don't believe everything you read in the papers" - more or less sums up what John Allen Paulos says in this Mathematician's eye-view of the printed news. But I would take that caveat a step further - especially in the light of today's news media: "Don't believe what you hear or see either!" Mainstream media it seems, is way to easy to manipulate, subjugate and otherwise coerce into only telling stories which the powers-that-be want the people to hear. Who decides what is written about? Who decides what ends up on television? This book was written at a time when the Internet was not quite the ubiquitous source of information it is today. Heck, in 1995 - even to someone like me, the word "Amazon" still conjured up the image of a lush, steamy rainforest somewhere in South America. In this light, the book represents a sort of snapshot of history in the days when people still had a modicum of respect for print on pulp from (possibly) rainforest trees, delivered every morning to their doorsteps. Strangely enough, this book may even serve as an epitaph to the Newspaper itself.

The book is actually structured like a regular newspaper, however with insightful (if a little mathematical) criticism by the author himself. You won't need a degree to understand what he is saying, however you will require some basic (High School level) knowledge of Statistics and Probability. John A.Paulos is a Ph.D. in Mathematical Logic - and thus he frames most of his arguments in an Aristotelian fashion, avoiding the cryptographic symbolism which pollutes (or, clarifies?) modern day mathematics. In short, you can read this book without a pencil and paper. What makes the book delightful however, is the author's ever-present sense of humor (which I suspect is a little funnier to those with some mathematical background themselves!)

The only problem I have with this book is the subject matter itself. I do believe that eventually, newspapers will go the way of the dinosaur. And maybe in another 65 million years or so, sapient beings will wonder at how strangely attached our minds were to the woody pulp of Amazonian trees.

Excellent book
I love this book. It gives concrete numbers to common sense -- and not-so-common sense. I particularly liked how Paulos uses examples from all areas of life. The political/voting section is especially interesting! ... Read more

Product Description
Does Black English stand between black students and success in math and science? Eleanor Wilson Orr, a teacher for over 35 years, discovered that many of her students' difficulties were rooted in language., and she offers here an account of the program she established to help them reach their potential. In the light of the current debate over Ebonics, she has written an introduction for the reissue of this important study. ... Read more

Customer Reviews (1)

Extremely helpful in teaching remedial critical thinking
Without this book I might never have been aware of some of the 'shortcuts' students take in their thinking.Although written about black english, I find many of the linguistic mistakes mentioned are not limited to those whospeak black english.With this knowledge, I could see my students (of allraces) making critical conceptual mistakes based on their lack ofappreciation for the importance of certain words in indicating abstractrelationships.This book is a labor of love; it is of tremendous value toany teacher who wonders who they can't seem to help some students who seembright enough and motivated enough, but just don't seem to understand. Thank you Elearnor Orr! ... Read more