Five places you didn’t expect to encounter applied math

You don’t need to step into a classroom to have a run-in with mathematics. Professionals from a range of backgrounds — engineering, economics, physics, biology, computer science — use mathematics every day. To celebrate the publication of the much-anticipated Princeton Companion to Applied Mathematics, edited by Nicholas J. Higham, we’re thinking about all of the unique places and situations where applied mathematics is at work. Here is a list of just a few, compiled with a little help from our numerically inclined friends.

On the Golf Course

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Golf involves mathematics, and not just when keeping score. The flight of your golf ball is affected by how air interacts with the surface of the ball. Did you know that the dimples in golf balls have a purpose, one with a mathematical explanation? Douglas N. Arnold, professor of Mathematics at the University of Minnesota, tells us more:

In the middle of the nineteenth century, when rubber golf balls were introduced, golfers noticed that old scuffed golf balls traveled farther than new smooth balls, although no one could explain this unintuitive behavior. This eventually gave rise to the modern dimpled golf ball. Along the way a great deal was learned about aerodynamics and its mathematical modeling. Hundreds of different dimple patterns have been devised, marketed, and patented. However, even today the optimal dimple pattern lies beyond our reach, and its discovery remains a tough challenge for applied mathematics and computational science.

Check out Dr. Arnold’s entry, “The Flight of a Golf Ball,” where he explains why golf ball dimples are an important part of your Saturday morning tee time.

On Wall Street

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Wall Street is all about the numbers. Whether modeling the risk of a single stock or mapping the complex interactions that make up the world’s financial structure, mathematics helps the financial sector to study and evaluate systemic risk.

“The complexity, unpredictability, and evolving nature of financial markets continues to provide an enormous challenge to mathematicians, engineers, and economists in identifying, analyzing, and quantifying the issues and risks they pose,” write Dr. René A. Carmona and Dr. Ronnie Sircar of Princeton University.

In their entry, “Financial Mathematics,” Dr. Carmona and Dr. Sircar discuss how the finance industry uses mathematics. They also examine the role of mathematics in understanding and regulating financial markets in light of the financial crisis of 2008.

On Your Phone’s Weather App

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Do you check the 10-day forecast during the weekend before a big outdoor event, fingers crossed for clear skies and no rain? There’s math behind that “chance of thunderstorms” prediction. NWP [numerical weather prediction] helps meteorologists to predict weather patterns for more than a week ahead. Better numerical schemes are partially responsible for moving us forward from the weather prediction methods of fifty years ago.

In his article “Numerical Weather Prediction,” Peter Lynch presents the mathematical principles of NWP and illustrates the process by considering some specific models and their application to practical forecasting. Dr. Lynch describes the many conditions that can be better predicted using NWP:

NWP models are used to generate special guidance for the marine community. Predicted winds are used to drive wave models, which predict sea and swell heights and periods. Prediction of road ice is performed by specially designed models that use forecasts of temperature, humidity, precipitation, cloudiness, and other parameters to estimate the conditions on the road surface. Trajectories are easily derived from limited-area models. These are vital for modeling pollution drift, for nuclear fallout, smoke from forest fires, and so on. Aviation benefits significantly from NWP guidance, which provides warnings of hazards such as lightning, icing, and clear-air turbulence.

In the Airport Security Line

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On your next trip through airport security, take a look at the x-ray machine. Once an object, like your suitcase, is scanned, the image can be viewed from multiple angles by a security officer. Threat detection software can also be used to locate problematic items. There is math at work here too.

W. R. B. Lionheart, professor of Applied Mathematics at the University of Manchester, explains this technology in his entry “Airport Baggage Screening with X-Ray Tomography.”

While Researching Your Next Vacation

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Getting ready for your first vacation of the fall? Buying tickets, making dinner reservations, researching tourist attractions — what did we do without the internet? Or rather, what did we do before the organized internet?

When the internet was still in its early stages, search engines were not as advanced as they are today, and webpage results were ranked by simple rules. Searching for “New York sightseeing” may have led you to the page where the search term appears the most, instead of a page with the most useful information. Today, search engines use a more advanced method for ranking web pages: grouping pages into authority pages, which have many links to them, and hub pages, which point to many authorities. The catch is that these terms depend on one another. How does this work? In the Princeton Companion to Applied Mathematics, editor Nicholas Higham explains the mathematics behind webpage ranking.

Looking for more examples of math in the world? Check out this video from SIAM, where SIAM conference attendees are asked how they use math in their work. Math really is all around us.

Birdfair 2015 at Rutland Water, UK

blue TitBirdfair 2015, the birdwatcher’s Glastonbury, took place last weekend at Rutland Water, UK.  This year’s event – three days of events and lectures with hundreds of stands for wildlife fans – was hot and thundery.  Princeton University Press and the WildGuides team were there displaying the breadth and importance of our natural history books and chatting to enthusiastic birders, authors, potential authors, booksellers, and bloggers. Andrew Brewer, PUP Europe Sales Director, called the event a huge success.

Andy Swash, Brian Clews, and Andrew Brewer at Birdfair 2015

Andy Swash, Brian Clews, and Andrew Brewer at Birdfair 2015

Seven PUP authors gave talks at the event: Adam Scott Kennedy (Birds of Kenya’s Rift Valley), David Newland (Britain’s Butterflies), James Lowen (Antarctic Wildlife), Sophie Lake (Britain’s Habitats), Dominic Couzens (The Crossley ID Guide), Dave Smallshire (Britain’s Dragonflies), Stuart Ball (Britain’s Hoverflies). All talks were well attended and followed by book sales and signings. David Newland’s talk, in which he shared tips on searching for, identifying and photographing butterflies and moths in the wild, was given to a full house. He signed copies and sold books after the event until they ran out and the queue of eager butterfly spotters moved across the large Birdfair site to continue chatting and buying at the WildSounds bookshop.

Plans are already afoot for Birdfair 2016 which will be particularly exciting as we will have our new and magnificent Britain’s Birds to share.  Perhaps we’ll see you there?

Bird Fact Friday – How do birds produce such varied songs?

From page 12 of Birds of South America: Passerines:

Have you ever stopped to notice the beauty of birdsong? It turns out birds are built for singing! Birds produce sound in the syrinx (as opposed to the larynx, where humans and other mammals produce sound) located deep in their chests where the trachea splits into two bronchi. Many birds can produce sound in both bronchi, making it possible for them to produce two notes at once. No wonder they have so much range!

Birds of South AmericaBirds of South America: Passerines
Ber van Perlo
Sample Entry

This comprehensive field guide to the birds of South America covers all 1,952 passerine species to be found south of Panama, including offshore islands such as Trinidad, the Galapagos, and the Falklands, and the islands of the Scotia Arc leading to the Antarctic mainland. It features 197 stunning color plates and detailed species accounts that describe key identification features, habitat, songs, and calls. All plumages for each species are illustrated, including males, females, and juveniles. This easy-to-use guide is the essential travel companion for experienced birdwatchers and novice birders alike.

Weekly Wanderlust: Cruises

Cruises are the perfect getaway, combining the allure of the vast open sea with a boat full of activities and nightlife, while offering the unique opportunity to experience the ocean in a way that would never be possible from the shore. Before your ocean adventure, check out some of the sea life you could encounter!

Howell Jacket Two-thirds of our planet lies out of sight of land, just offshore beyond the horizon. What wildlife might you see out there? This handy guide, designed for quick use on day trips off the East Coast, helps you put a name to what you find, from whales and dolphins to shearwaters, turtles, and even flying fish. Carefully crafted color plates show species as they typically appear at sea, and expert text highlights identification features. Essential for anyone heading out on a whale-watching or birding trip, this guidebook provides a handy gateway to the wonders of the ocean.
Howell jacket If your ocean adventure takes you off the west coast, this Offshore Sea Life ID Guide, designed for quick use on day trips off the West Coast, helps you identify whales and dolphins, albatrosses, turtles, and even flyingfish. Carefully crafted color plates show species as they typically appear at sea, and expert text highlights identification features. This user-friendly field guide is essential for anyone going out on a whale-watching or birding trip, and provides a handy gateway to the wonders of the ocean.
Howell jacket If you travel the open ocean anywhere in the tropics, you are very likely to see flyingfish. These beautifully colored “ocean butterflies” shoot out of the water and sail on majestic, winglike pectoral fins to escape from predators such as dolphins, swordfish, and tuna. Some can travel for more than six hundred feet per flight. The ideal gift for fish lovers, seasoned travelers, and armchair naturalists alike, The Amazing World of Flyingfish provides a rare and incomparable look at these spectacular marine creatures.
Ebert Jacket This is the first field guide to identify, illustrate, and describe the world’s 501 shark species. Its compact format makes it handy for many situations, including recognizing living species, fishery catches, or parts sold at markets. The book also contains useful sections on identifying shark teeth and the shark fins most commonly encountered in the fin trade. A Pocket Guide to Sharks of the World is an essential resource for fisheries management, international trade regulation, and shark conservation.
Palumbi Jacket The ocean teems with life that thrives under difficult situations in unusual environments. The Extreme Life of the Sea takes readers to the absolute limits of the ocean world—the fastest and deepest, the hottest and oldest creatures of the oceans. It dives into the icy Arctic and boiling hydrothermal vents—and exposes the eternal darkness of the deepest undersea trenches—to show how marine life thrives against the odds.

Memorable Quotes from Alice’s Adventures in Wonderland

Alice's Adventures in WonderlandHere at PUP, we’re celebrating the 150th anniversary of the publication of Alice’s Adventures in Wonderland with a new edition that combines the text of the 1897 version (thought to be the most authentic and correct by Lewis Carroll himself) with the illustrations done by Salvador Dalí for the 1969 Random House version. Readers can enjoy this familiar tale alongside Dalí’s hyper-saturated, surrealist pictures. In honor of Alice, here are some of the most memorable quotes from the book. Which is your favorite?

 

“Off with her head!”
–the Queen of Hearts

“A cat may look at a king.”
–Alice

“Curiouser and curiouser!”
–Alice

“[W]e’re all mad here. I’m mad. You’re mad.”
–the Cheshire Cat

“Everything’s got a moral, if only you can find it.”
–the Duchess

“For the Duchess. An invitation from the Queen to play croquet.”
–the Frog-Footman

“Begin at the beginning … and go on till you come to the end: then stop.”
the King

“I ca’n’t explain myself, I’m afraid, Sir … because I’m not myself, you see.”
Alice

“The Duchess! The Duchess! Oh my dear paws! Oh my fur and whiskers! She’ll get me executed, as sure as ferrets are ferrets!”
–the White Rabbit

Bird Fact Friday – Albatross

From page 26 of Offshore Sea Life ID Guide: West Coast:

The Black-footed Albatross is common offshore from spring to fall and uncommon in the winter. It often follows boats and scavenges. It is dark overall with a white noseband and a dusky bill. Older adults have white tail coverts; some birds bleach to whitish on their head and neck. It breeds in November and December, mostly in Hawaii.

Offshore Sea Life ID Guide: West Coast
Steve N.G. Howell & Brian L. Sullivan
Introduction

k10465Two-thirds of our planet lies out of sight of land, just offshore beyond the horizon. What wildlife might you find out there? And how might you identify what you see? This Offshore Sea Life ID Guide, designed for quick use on day trips off the West Coast, helps you put a name to what you see, from whales and dolphins to albatrosses, turtles, and even flyingfish. Carefully crafted color plates show species as they typically appear at sea, and expert text highlights identification features. This user-friendly field guide is essential for anyone going out on a whale-watching or birding trip, and provides a handy gateway to the wonders of the ocean.

• First state-of-the-art pocket guide to offshore sea life
• Over 300 photos used to create composite plates
• Includes whales, dolphins, sea lions, birds, sharks, turtles, flyingfish, and more
• Accessible and informative text reveals what to look for
• Great for beginners and experts alike

Washington Post highlights historic clash between Einstein and Bergson on the nature of time

2015_Einstein_bannerWith the 100th anniversary of the general theory of relativity coming up in November, Einstein is popping up everywhere. Yesterday’s Washington Post ran a terrific feature on Einstein books, including three of our own: Hanoch Gutfreund and Jürgen Renn’s The Road to Relativity, Einstein’s Relativity: The Special and the General Theory, and Jimena Canales’s The Physicist and the Philosopher.

One of the most fascinating chapters of Einstein’s public life revolves around an encounter he had with Henri Bergson, the renowned philosopher, on April 6, 1922, in Paris. It was on this day that Einstein and Bergson publicly debated the nature of time, touching off a clash of worldviews between science and the humanities that persists today. The philosopher Bergson argued that time was not merely mechanical, and should be seen in terms of lived experience; Einstein dismissed Bergson’s psychological notions as irreconcilable with the realities of physics. The Physicist and the Philosopher tells the remarkable story of how this explosive debate between two famous thinkers created intellectual rifts and revolutionized an entire generation’s understanding of time.

Nancy Szokan’s piece in Washington Post recounts the dramatic collision:

In The Physicist and the Philosopher, Canales recounts how Bergson challenged Einstein’s theories, arguing that time is not a fourth dimension definable by scientists but a ‘vital impulse,’ the source of creativity. It was an incendiary topic at the time, and it shaped a split between science and humanities that persisted for decades—though Einstein was generally seen as the winner and Bergson is all but forgotten.

Bergson and Einstein, toward the end of their lives, each reflected on his rival’s legacy and dedication to the pursuit of truth: Bergson during the Nazi occupation of Paris and Einstein in the wake of the first hydrogen bomb. Referencing Einstein’s quest for scientific truth, Hanoch Gutfreund recently had an article in the Huffington Post on how Einstein helped shape the Hebrew University of Jerusalem (home of the Albert Einstein Archives online):

On the occasion of the opening of the university, Albert Einstein published a manifesto “The Mission of our University”, which generated interest and excitement in the entire Jewish and academic worlds.

It states: “The opening of our Hebrew University on Mount Scopus, at Jerusalem, is an event which should not only fill us with just pride, but should also inspire us to serious reflection. … A University is a place where the universality of human spirit manifests itself. Science and investigation recognize as their aim the truth only.”

Read the rest here.

November’s big anniversary serves as a reminder of the enduring commitment to scientific investigation that continues at The Hebrew University and centers of learning all over the world today.

Read sample chapters of The Physicist and the Philosopher here, The Road to Relativity here, and Relativity here.

You can find information on the Digital Einstein Papers, an open access site for The Collected Papers of Albert Einstein, comprising more than 30,000 unique documents here.

A Q&A with Richard Layard and David Clark, authors of THRIVE

Thrive jacketHow can mental illness—an affliction that affects at least 20 percent of people in developed countries, reduces life expectancy, and wrecks havoc on educational potential—remain chronically under-treated? The answer is simple: mental and physical pain are not viewed equally, and even in a relatively progressive culture, the former remains profoundly stigmatized. As a result, most who suffer from mental health issues suffer in silence, or receive inadequate support. Can this change? Richard Layard and David Clark say it can.

In Thrive, Layard and Clark look at the practical politics of increasing access to mental health care, arguing that the therapies that exist—and work—are available at little to no cost. Recently, both took the time to answer some questions about the book, and the transformative power of mental health care.

What is the message of your book?

Depression and anxiety disorders are the biggest single cause of misery in Western societies. They also cause enormous damage to the economy. But they are curable, in most cases, by modern evidence-based psychological therapy. The shocking thing is that very few of those who need it get any help and fewer still get help based on evidence. In England such help is now becoming available to many of millions who need it. As we show, this help involves no net cost to society. It’s a no-brainer.

What is the scale of the problem?

Surveys of households in rich countries show that around 1 in 6 adults have depression or anxiety disorders severe enough to cause major distress and impair the person’s functioning. Only a quarter of these people are in any form of treatment, most usually medication. This is shocking. For surveys show that mental illness is the biggest single reason why people feel dissatisfied with their lives – accounting for more of the misery in our societies than either poverty or unemployment do.

What is its economic cost?

Mental illness accounts for nearly a half of all absenteeism from work and for nearly a half of all those who do not work because of disability. This imposes huge costs on employers and taxpayers. Mental illness also increases the use of physical healthcare. People with a given physical illness of a given severity use 50% more physical healthcare if they are also mentally ill. This is a huge cost to those who fund healthcare.

Does psychological therapy help?

In the last 40 years considerable progress has been made in developing effective psychological therapies. The most studied therapy is CBT – cognitive behavioural therapy, which is a broad heading for therapies which focus on directly influencing thoughts and behaviours – in order to affect the quality of human experience. In hundreds of randomised controlled trials CBT has been shown to produce recovery rates of over 50% for depression and anxiety disorders. For anxiety, recovery is generally sustained; for depression, the risk of relapse is greatly reduced.

The range of therapies which have been shown to work has been surveyed internationally by the Cochrane Collaboration and in England by the National Institute for Health and Care Excellence (NICE). Besides CBT, NICE also recommend for all depressions Interpersonal Therapy (IPT) and, for mild to moderate depression, Brief Psychodynamic Therapy, Couples Therapy and Counselling. Modern psychological therapies have also been shown to be effective in a wide range of other mental health conditions.

Do these therapies really cost nothing?

Yes. If delivered to a representative group of patients they pay for themselves twice over. First, they pay in reduced invalidity benefits and lost taxes due to invalidity. We know this from a series of controlled trials. Second, they pay for themselves in reduced costs of physical healthcare. Again we know this from controlled trials. It is so partly because the typical cost of an evidence-based course of treatment is only about $2,000.

How can these therapies become more widely available?

Two things are needed. First, there have to be enough people trained to deliver these therapies. This is the responsibility of universities and colleges, including of course supervised on-the-job training. Second, there have to be effective frameworks where trained people can be employed. The evidence is that recovery rates are higher where people are employed in teams where they can get supervision, in-service training, and clear career progression.

Those who fund healthcare have in the USA and UK the legal obligation to provide parity of esteem for mental and physical healthcare, and this requires that they are willing to fund high quality evidence-based therapies that are made easily available and provide the necessary duration of treatment, based on evidence. Insurers never fund half a hip replacement and they should not fund only half a proper course of psychological therapy.

What can be learnt from the English experience?

The English National Health Service has in recent years developed a totally new service to deliver evidence-based psychological therapies. (It’s called Improving Access to Psychological Therapies (IAPT)). This service has, over six years, trained altogether 6,000 therapists and is now treating nearly half a million people a year, with a recovery rate of 46% and rising. The prestigious journal Nature has called it “world-beating”.

How can we prevent mental illness in the first place?

First we must of course treat it as soon as it appears. This is often in childhood, where the same evidence-based treatments for depression and anxiety disorders apply as in adulthood. For children’s behaviour problems, parent training and family therapy are recommended.

But we must also reduce the overall prevalence of mental illness. This requires major changes throughout society. First, more support and education for parents. Second, schools which give more priority to the well-being of children. Third, employers who treat their workers with appreciation and encouragement and not as income-maximising machines. Fourth, more positively-oriented media. And finally, a new citizens’ culture giving more priority to compassion, both as an emotion and as a spring for action.

Richard Layard is one of the world’s leading labor economists and a member of the House of Lords.  David M. Clark is professor of psychology at the University of Oxford. Layard and Clark were the main drivers behind the UK’s Improving Access to Psychological Therapies program.

Read chapter one here.

Weekly Wanderlust: Yellowstone

Yellowstone is the world’s first national park, and home to some of the oldest and most awe inspiring sites in the United States. Commonly known for tourist attractions such as the geyser Old Faithful, Yellowstone is a complex geothermal area containing half the world’s natural geysers. It is also a highly valued protected ecosystem, home to some of the most amazing wildlife, from grizzly bears and wolves, to herds of bison and elk. The human story of Yellowstone spans more than 11,000 years, making the area an important archaeological site as well.

Grand Canyon

Grand Canyon of Yellowstone

Grand Prismatic Spring

Grand Prismatic Spring

Excelsior geyser

Excelsior geyser

 

Whether you plan to camp, hike, fly-fish, or immerse yourself in the region’s history, you may want to check out Justin Farrell’s new book, The Battle for Yellowstone for some background on the park’s moral, cultural, and spiritual roots.

Farrell jacketYellowstone is globally recognized as the crown jewel of modern environmental preservation. But the park and its surrounding regions have recently become a lightning rod for environmental conflict, plagued by intense and intractable political struggles among the federal government, National Park Service, environmentalists, industry, local residents, and elected officials. The Battle for Yellowstone asks why it is that, with the flood of expert scientific, economic, and legal efforts to resolve disagreements over Yellowstone, there is no improvement?

Justin Farrell argues that the battle for Yellowstone has deep moral, cultural, and spiritual roots that until now have been obscured by the supposedly rational and technical nature of the conflict. Tracing the moral causes and consequences of large-scale social change in the American West, he describes how a “new-west” social order has emerged that has devalued traditional American beliefs about manifest destiny and rugged individualism.

Justin Farrell is assistant professor of sociology in the School of Forestry and Environmental Studies at Yale University. You can read a Q&A with him here.

Photos of Yellowstone courtesy of Claudia Classon

Bird Fact Friday – Warblers

From page 539 of The Warbler Guide:

17D_SpeciesAccounts_422-511A Yellow-rumped Warbler can be identified in flight by a numbers of features. It’s slight is bouncy and strongly tacking with irregular wing beats that are mostly below the body. It takes short glides, both open- and closed-winged and often mixes flight with chip calls. It is large, stocky, and hunchbacked with long blunt wings. Its color is overall gray with yellow shoulders, wing bars and rump.

 

The Warbler Guide
Tom Stephenson & Scott Whittle

k9968Warblers are among the most challenging birds to identify. They exhibit an array of seasonal plumages and have distinctive yet oft-confused calls and songs. The Warbler Guide enables you to quickly identify any of the 56 species of warblers in the United States and Canada. This groundbreaking guide features more than 1,000 stunning color photos, extensive species accounts with multiple viewing angles, and an entirely new system of vocalization analysis that helps you distinguish songs and calls.

The Warbler Guide revolutionizes birdwatching, making warbler identification easier than ever before. For more information, please see the author videos on the Princeton University Press website.

Download the app here!

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PHISHING FOR PHOOLS and CLIMATE SHOCK included in the long list for FT & McKinsey Business Book of the Year Award

Climate ShockPhishing for Phools jacketThe long list for the FT & McKinsey Business Book of the Year Award has been published, and we’re thrilled to see that two Princeton University Press titles have been included. Nobel Prize winners George Akerlof and Robert Shiller’s new book on on economic trickery, Phishing for Phools, and Gernot Wagner and Martin Weitzman’s examination of the global crisis of climate change, Climate Shock have both been listed in the top 15. Other titles appearing include Ashlee Vance’s biography of Elon Musk, Martin Ford’s study of jobs and automation, The Rise of the Robots, and Anne-Marie Slaughter’s take on how to narrow the gender gap, Unfinished Business.

Read more about this year’s long listed titles and the other books recognized during the award’s 11-year history here.

The shortlist of up to six finalists will be published on September 22nd.  The £30,000 prize will be awarded on November 17th in New York.

Find sample chapters of Climate Shock and Phishing for Phools here and here respectively.

 

 

Weekly Wanderlust: The Caribbean

Southeast of the Gulf of Mexico, the Caribbean (taken from Caribs, an ethnic group native to the Lesser Antilles and parts of South America at the time of the Spanish conquest) is home to over 700 islands and reefs. With its warm water, proximity to ports, and easy accessibility from the mainland US, the islands have long been a popular vacation destination. Whether you enjoy swimming with the dolphins in the islands of Aruba or taking advantage of the Bahamas’ extensive nightlife scene, the Caribbean offers enough variety in activities, climate, and geography for everyone. Make sure to make time during your trip for plenty of snorkeling with the migratory schools of fish, and exploring the wildlife that can only be found in these islands. If you’re lucky, you’ll even catching a glimpse of some of the unusual animals inhabiting the area.

Caribbean Image

Perhaps these books will help you familiarize yourself with the Caribbean’s natural offerings.

Raffaele Jacket Wildlife of the Caribbean is the first comprehensive illustrated guide to the natural world of the Caribbean islands. It contains 600 vivid color images featuring 451 species of plants, birds, mammals, fish, seashells, and much more. While the guide primarily looks at the most conspicuous and widespread species among the islands, it also includes rarely seen creatures—such as the Rhinoceros Iguana and Cuban Solenodon—giving readers a special sense of the region’s diverse wildlife.
Kohn Jacket Conus is the largest genus of animals in the sea, occurring throughout the world’s tropical and subtropical oceans and contributing significantly to marine biodiversity. The shells of these marine mollusks are prized for their amazing variety and extraordinary beauty.  This beautifully illustrated book identifies 53 valid species of the southeastern United States and the Caribbean, a region that supports a diverse but taxonomically challenging group of Conus.
Lieske Jacket Expanded and updated to include an additional 44 species, Coral Reef Fishes is a handy guide to those fishes that are likely to be observed by anybody visiting or diving on the coral reefs of the Caribbean, the Indian Ocean, and the Pacific to a depth of sixty meters. Accessible to amateur marine life enthusiasts, this book is the first comprehensive guide of its kind. It enables the reader to quickly identify 2,118 species of fish and includes over 2,500 color illustrations depicting the major forms of each species–male, female, immature, or geographical varieties.