I needed a firmer mathematical foundation for some work on financial models, so I went back to Introduction to Probability Theory, which I bought for I needed a firmer mathematical foundation for some work on financial models, so I went back to Introduction to Probability Theory, which I bought for a long-ago college course. I worked through the text and accompanying problems and now have a much better understanding of the topics covered than I did as a college student.
The book covers both discrete and continuous random variables. The authors describe specific distributions (binomial distributions, Poisson distributions, normal distributions, gamma distributions, etc.) and provide examples illustrating situations where these distributions can arise. Of course, the book also covers the general theory of probability spaces, independence, expectation, higher-order moments, densities, conditional probability, and characteristic functions. The main body of the book builds to proofs of the Weak Law of Large Numbers and the Central Limit Theorem. The final chapter introduces random walks and Poisson processes.
The back of the book has the answers to those problems that require calculations. The answers provided are only the final result, not complete step-by-step solutions. There are no solutions to those problems that require proof. The answers made it easy for me to check my work, or, in some cases, obtain a hint. Without the answers, I would have had much less confidence that my solutions were correct.
A prospective reader should have familiarity with both differential and integral calculus and related concepts such as Taylor series. The reader needs a grasp of basic set theory, basic trigonometry, and sums of power series. Although there are certainly newer textbooks, the theorems in the book are as true now as they were when the book was first published in 1971, and the book will serve a current student of probability as well as it did its first readers nearly 50 years ago....more
Gallwey started playing tennis as a child and competed at a high level through high school. After graduating from Harvard, he found himself working asGallwey started playing tennis as a child and competed at a high level through high school. After graduating from Harvard, he found himself working as a tennis pro. In the process of teaching club players, he had an epiphany: that students improved more when he taught less and encouraged them to explore more. After writing The Inner Game of Tennis: The Classic Guide to the Mental Side of Peak Performance, he went on to a long career as a consultant.
Gallwey views people as composed of two entities, which he calls Self 1 and Self 2. Gallwey’s Self 1 and Self 2 are analogs of Daniel Kahneman’s System 1 and System 2, as described in the fabulous Thinking, Fast and Slow, though Gallwey reverses Kahneman's numbering. Kahneman’s System 1 is the quick, automatic part of the mind that recognizes faces; System 2 is responsible for slower, complex tasks like solving math problems. As Gallwey puts it, when people talk to themselves, it is Self 1 (the conscious self) talking to Self 2 (the unconscious self).
Gallwey’s central thesis is that Self 2 is capable of great things if Self 1 gets out of the way. However, most athletes try to use Self 1 to control Self 2 instead of letting it perform its magic on its own. He encourages athletes to rely more on observation than on direct control to give hints to Self 2. For example, rather than trying to move the racket in a particular path, the student should observe the path that the racket is actually taking, visualize the desired path, and then observe the new path.
Gallwey’s book is in some sense a sports-oriented analog to Robert Wright’s Why Buddhism is True: The Science and Philosophy of Meditation and Enlightenment in that The Inner Game advocates for an Eastern approach to competitive sport. For example, Gallwey suggests that players should refrain from judgment, i.e., classifying particular actions as “good” or “bad.” They should instead view the movements as they are and patiently observe change as desired. Gallwey also opines that competition is best used as an opportunity to strive to play at one’s best rather than to seek fame, trophies, or victories over others.
The book is entirely accessible to athletes who play sports other than tennis. Though tennis is used as an example throughout, it is easy to generalize the advice given to any other sport. As someone who has attempted to develop skills in several athletic disciplines, and who has attempted to coach others, I believe that there is merit to Gallwey’s advice. Those of us who tend to over-analyze have often heard that we should “get out of our own way”; Gallwey provides some concrete advice in that regard. However, I am skeptical that Gallwey’s approach is the panacea he suggests; different athletes seem to find different methods, and many benefit from a combination of approaches. Every athlete should have Gallwey’s techniques in his or her toolbox, but most will need other tools as well....more
Carlton Fisk was baseball's preeminent catcher over his 25-year career, was honored as an All-Star 11 times, and entered the Hall of Fame on tCarlton Carlton Fisk was baseball's preeminent catcher over his 25-year career, was honored as an All-Star 11 times, and entered the Hall of Fame on tCarlton Fisk was baseball's preeminent catcher over his 25-year career, was honored as an All-Star 11 times and entered the Hall of Fame on the second ballot.
Wilson's biography is in standard chronological order, beginning with a brief history of Fisk's ancestors, proceeding through Fisk's childhood in Charlestown, New Hampshire, and then provides an almost season-by-season account of Fisk's professional career. There is a brief concluding section that covers Fisk's life after baseball. Wilson portrays Fisk as the quintessential New Englander; rugged, hard-working, self-sufficient, and stoic. However, the entire story, successful as Fisk was, is tinged with sadness. Fisk's relationships with the management and ownership of the Red Sox and White Sox (the two teams for which he played) were strained to the point of bitterness, particularly around issues of compensation. And, he resented the way in which he was summarily released, on a road trip, by the White Sox at the end of his career. Though Fisk appears to have strong family relationships, he is quoted as saying that he "will never forgive the game for what I lost with my children."
Wilson emphasizes Fisk's work ethic throughout the book. Fisk was one of the first players to commit to serious weight training at the age of 37. Wilson credits Fisk's commitment to strength training for helping Fisk to recover from a severe oblique strain and, ultimately, for allowing him to play for eight more years. Fisk was often one of the last to leave the ballpark, lifting weights after games when other players had long since departed for evening entertainment. Earlier in his career, Fisk had to recover from some gruesome injuries, including a knee injury during the 1974 All-Star game, a parallel to the injury Ray Fosse sustained when blocking the plate in the 1970 All-Star game.
Wilson also highlight's Fisk's participation in some of the pivotal moments in baseball's labor negotiations. Fisk was one of the first players to hire an agent, and one of the first to test the waters of free agency. Later, he was one of the players to take an active role in fighting against the collusion scandals of the late 1980s. Fisk, due to the time at which he played and the length of his career, was the rare player who experienced both the reserve clause and the modern system of contract negotiation.
Fisk is famously private, and Wilson wrote his biography without the benefit of direct interaction with Fisk himself. Though Wilson has done excellent research, and though he spoke with friends and relatives of Fisk, it's hard to feel that Fisk is fully human without hearing more of his voice. Wilson gives his reader a comprehensive view of the public Fisk, but the private Carlton eludes him. But, for those interested in those who have achieved greatness, or for fans with an interest in baseball of the 1960s, 1970s, and 1980s, the book will prove satisfying....more
All too often, the first book in a series is better than any of the follow-ups. The characters become tired, the plots repetitive. The author is unablAll too often, the first book in a series is better than any of the follow-ups. The characters become tired, the plots repetitive. The author is unable to recapture the magic of the first installment. But, Mark Greaney avoids that fate; in Back Blast, he has created a sequel that is better than any of the books that have preceded it.
Court Gentry returns to Washington, D.C., determined to figure out why the CIA disavowed him. The trail leads back to one of Gentry's old operations, but Gentry is unable to determine what he did that lead to the CIA issuing a "shoot on sight" order against him. As Gentry tries to work out what has gone wrong, the CIA is hunting him on its home territory. The intricate plot involves agents of multiple foreign agencies, reporters for the Washington Post, and several figures from Gentry's past.
The story the usual Gray Man fast-paced action with an intriguing mystery. The reader, like Gentry, cannot help but be drawn into the question of what happened to estrange Gentry from his former employer. Meanwhile, while Greaney has given vague hints about Gentry's backstory in previous books, Back Blast provides more complete answers. The final twist in the story is both unexpected and, in retrospect, inevitable; it is thus eminently satisfying....more
In the fourth installment of the series that began with The Gray Man, Mark Greaney's Court Gentry confronts an opponent who sees himself as Gentry's mIn the fourth installment of the series that began with The Gray Man, Mark Greaney's Court Gentry confronts an opponent who sees himself as Gentry's mirror-image. Dead Eye is, like the Gray Man, a lone-wolf assassin-for-hire -- but, unlike Gentry, has no moral code. The action ranges across Europe, from Russia to Copenhagen, and includes representatives from organized crime, the CIA, and the Israeli Mossad.
Greaney provides an enjoyable yarn written in his usual action-packed style, though the "we are not so different, you and I" trope is a little tired. Fortunately, the plot's overall complexity keeps the story interesting. Greaney reveals a little more of Gentry's history, including the "Kiev thing" that has been mentioned (but never explained) in previous books in the series. And, Greaney gives a few more hints as to what has gone so very wrong between Gentry and his former masters in the CIA....more
The story picks up right where On Target leaves off: Court Gentry is on the run from the CIA. Wandering in Central America, he discovers that Eddie GaThe story picks up right where On Target leaves off: Court Gentry is on the run from the CIA. Wandering in Central America, he discovers that Eddie Gamboa -- to whom he owes his life -- has been murdered. Court decides to pay his respects by visiting his friend's grave and is then drawn into a conflict between Mexican drug cartels, the corrupt government officials under their control, and Gamboa's family. Via a series of flashbacks, Greaney also explains how Gentry and Gamboa knew each other.
As with the books in the series, it's impossible to claim that Ballistic is anything other than decadent pulp fiction. That said, Greaney delivers a satisfying story with his usual excellent craftsmanship. The customary Gray Man tropes apply: the pace is lively, Gentry is outnumbered and outgunned, and the body count is absurd. Good fun!...more
The thesis of Ben Lindbergh and Travis Sawchik’s book is that until recently professional baseball organizations made efforts to obtain the most talenThe thesis of Ben Lindbergh and Travis Sawchik’s book is that until recently professional baseball organizations made efforts to obtain the most talented players (viewing their abilities as fixed), but that they are now making much more significant efforts (aided by technology) to improve the players in their organizations. The authors argue largely by anecdote, using Trevor Bauer, Justin Turner, and other players who were once considered “fringe”, but have used “new-school” approaches to transform themselves into superstars. Thus, they argue, we are no longer in the Moneyball: The Art of Winning an Unfair Game era in which the best organizations were able to spot undervalued players; teams now have to compete on their ability to improve the players they already have as much as on selecting the best players in the first place.
Much of the discussion revolves around applications of new technology: Edgertronic cameras that provide high-resolution slow-motion video that allows pictures to refine the spin on their pitches, Rapsodo devices that measure the flight and spin on batted balls, Blast bat sensors that measure swings. The book also dives into some of the independent facilities (like Driveline Baseball and the Texas Baseball Ranch) that had humble beginnings, but have now become influential in the development of pitchers, and, to some extent, hitters. There is also a fascinating history of the early days of what is now called “player development”, including Branch Rickey’s creation of affiliated minor-league teams.
The book is aimed more at the interested fan that at the aspiring player. It is not a technical book; there are no instructions for how a young pitcher could improve his curveball by use of an Edgertronic camera. Instead, Lindbergh and Sawchik help the curious to better understand what goes on during the modern journey from draft day to major league debut to MVP award. While intriguing, and enjoyable to read, the book is neither scientific nor particularly profound. It will be of most interest to that small fraction of the population that is fascinated by baseball, technology, and skill acquisition....more
Court Gentry returns, as lethal as ever, in the second installment of Greaney's The Gray Man series. Under duress, Gentry collaborates with both his fCourt Gentry returns, as lethal as ever, in the second installment of Greaney's The Gray Man series. Under duress, Gentry collaborates with both his former CIA colleagues and Russian mobsters in an operation in Sudan. In the process, he has to avoid Sudanese military forces, terrorists, criminals, and a representative of the International Criminal Court. Many things explode and many people die.
Greaney has a gift, reminiscent of Tom Clancy, for describing weaponry in realistic detail without being tedious. And, like Lee Child, Greaney provides a slow-motion telling of tactical situations (flying bullets, thrown punches, weapons reloading, combatants moving, etc.) that allows readers to envision the scene in detail. The Gray Man's body counts, however, are far higher than those of Clancy's Jack Ryan or Child's Jack Reacher. And nobody would suggest that Greaney is a realist. Gentry, like Houdini, routinely escapes certain death, even when grievously wounded. International organizations make decisions that one hopes they would never make in real life. And improbable coincidences occur with regularity. But, while hardly great literature, this book, like its predecessor, is an engaging page-turner....more
Epstein's book is a long-form argument that the advantage of the "early head start" (in school, sports, or career) is a myth and that one should neverEpstein's book is a long-form argument that the advantage of the "early head start" (in school, sports, or career) is a myth and that one should never "feel behind" due to a lack of specialization. Rather, Epstein claims, it is those with "range" (a base of broad knowledge and experience) who make the greatest contributions. Though thoroughly enjoyable and well worth reading, the book itself is so wide-ranging that I found it hard to reach a firm conclusion as to its central claim.
Epstein has a knack for story-telling. He provides fascinating anecdotes about foundling musicians in seventeenth-century Venice, villagers in Uzbekistan in the early days of the Soviet Union, Johannes Kepler's thoughts on what we now call gravity, and the evolution of Nintendo from a manufacturer of playing cards to a titan of video games. In every case, he shows how knowledge from a variety of disciplines, or experience in a variety of situations, provided people with insights or abilities that people with more limited backgrounds did not have. He interleaves these anecdotes with science, referencing academic work on the benefits that accrue to generalists.
Epstein highlights Robin Hogarth's ideas about "kind" and "wicked" learning environments. Those that are "kind" (like sports, music, or chess) have clear rules, oft-repeated patterns and provide rapid, accurate feedback; those that are "wicked" (like business planning, scientific research, or public policy) have unclear rules, lack repeating patterns, or provide delayed, or misleading, feedback. Epstein makes a plausible argument that deliberate practice (as described in K. Anders Ericsson's seminal Peak: Secrets from the New Science of Expertise) is better-suited to kind environments than to wicked ones.
Although the book begins in the context of sports (comparing Tiger Woods, who specialized in golf before he could walk, with Roger Federer, who did not specialize in tennis until his mid teens), and although Epstein's previous book The Sports Gene: Inside the Science of Extraordinary Athletic Performance was focused exclusively on sports, Epstein's focus in this book is elsewhere. In fact, his comments on sports in this book are ambiguous. He says "among athletes who go on to become elite, broad early experience and delayed specialization is the norm" -- but he also acknowledges that Tiger was an early specialist who achieved extraordinary success, and that "kind" learning environments (including most sports) are more amenable to early specialization.
Unfortunately, a similar ambiguity hangs over the entire book, and weakens Epstein's argument. Nobody in their right mind would argue that most people should pick a narrow area of focus at the first opportunity, but neither would any sane person suggest that people should flit from one thing to another day by day. (And, in some areas, including sports, there is a point at which one can no longer afford to delay specialization, unless, perhaps, your name is Bo Jackson.) Clearly, a balance between specialization and generalization is desirable, and Epstein acknowledges that generalists would be challenged to perform their interdisciplinary magic without the aid of specialists with deep knowledge in particular domains. The trick, of course, is to find the appropriate balance, and Epstein offers little guidance on that topic....more
Munroe's how-to advice is, as he says in the subtitle, absurd both due to the nature of the problems to be solved (powering a Martian house) and the sMunroe's how-to advice is, as he says in the subtitle, absurd both due to the nature of the problems to be solved (powering a Martian house) and the solutions (crossing a river via kite). The book, though, is thoroughly enjoyable due to Muroe's unique ability to blend humorous writing with accurate science, including the use of equations where appropriate. For example, he models riding a horse through a crowd of people as an air-resistance problem, "treating the [people] as a uniform gas with very large molecules". And, of course, the illustrations are in the style of Munroe's XKCD cartoons.
Part of the fun is that the chapter titles are generally named using mundane activities ("How to Charge Your Phone", "How to Throw Things", "How to Get Somewhere Fast", etc.), but the chapters themselves explore extreme situations. The discussions include charging phones using a paddle wheel on an escalator, NFL quarterbacks throwing blenders, and traveling at relativistic speeds to the cosmological event horizon. There are also some fascinating historical footnotes, including the U.S. government's testing of beer quality subsequent to a nuclear detonation, and the tragic accidental death of a 5,000 year-old tree.
The book is written for those of us that are unabashed nerds. If you are seeking an interested layperson's serious introduction to a scientific field, this isn't the droid you're looking for. On the other hand, if you have an interest in physics and a sense of humor, you will find yourself consistently amused....more
Courtland Gentry (known by many as “The Gray Man” due to his ability to fade away) is part James Bond, part Jack Reacher. He’s a super-spy who can useCourtland Gentry (known by many as “The Gray Man” due to his ability to fade away) is part James Bond, part Jack Reacher. He’s a super-spy who can use any weapon, drive any vehicle, and lives by his own moral code. Though he had a storied career with the CIA, he’s been disavowed, and an army of contract killers are after him. But, innocent lives are at stake, and Gentry will risk his life to save them. All that sounds rather trite, but Greaney writes well and introduces enough complexity to keep it fun. There’s nothing deep about the tale, but in the way of Ian Fleming’s books, the action is fast-paced and the forces of darkness are just unrealistic enough to be scary without becoming comical....more