Theory of Groups of Finite Order by William Burnside

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Theory of Groups of Finite Order by William Burnside

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By Charlotte Girard Posted on Nov 15, 2025

In Category - Literary Mystery

Authors: Burnside, William, 1852-1927 Published By : Burnside, William, 1852-1927

Book Language: English

Okay, hear me out. I know a 1911 math textbook doesn't sound like a page-turner, but stick with me. This book is about uncovering the hidden rules of symmetry. Burnside wasn't just writing a manual; he was on a deep, almost philosophical hunt for the fundamental building blocks of symmetry itself. The real mystery? How can something as abstract as a 'group' explain the patterns in everything from crystals to card shuffles? It's a puzzle box of pure logic, and Burnside is your brilliant, slightly obsessive guide. If you've ever wondered how mathematicians think about structure, this is a fascinating, challenging look under the hood.

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devices and articles as will add to one's personal comfort and welfare. It is, therefore, the aim of this book to suggest certain diversions of this character for the boy camper which, aside from affording him plenty of physical exercise, will also develop his mental faculties, and above all stimulate that natural genius which is characteristic of every typical American boy. To this end the story contains descriptions of a large collection of articles which can be made by any boy of average intelligence, not only in the camp but at home as well. The use of a narrative to connect the various incidents marks a departure in this class of book, and it is believed that the matter will thus be made more realistic and interesting. In all cases full directions are given for making the various articles. While it is not presumed that the directions will be slavishly followed, for this would defeat the general aim of the work, yet all the principal dimensions are given so that they can be used, if desired. I beg to acknowledge the courtesy of Mr. Daniel C. Beard and Mr. Henry D. Cochrane in supplying a number of photographs. The directions for making the lee boards (page 119) were obtained from data furnished by the latter. Many of the details recorded in the chapter on Tramping Outfits are to be accredited to Mr. Edward Thorpe. In the preparation of this book I have received valuable assistance from my colleague, Mr. A. A. Hopkins. A. RUSSELL BOND. New York, October, 1905. CONTENTS CHAPTER I. PAGE "BILL" 17 The Old Trunk. Christmas Vacation. "Bill's" Skate Sail. Willow Clump Island. Organizing the Society. CHAPTER II. SKATE SAILS 26 The Double Swedish Sail. The Single Swedish Sail. The Lanteen Sail. The Danish Sail. Bat's Wings. CHAPTER III. SNOW SHOES, SKIS AND SWAMP SHOES 35 Chair Seat Snow Shoe. Barrel Stave Snow Shoe. Barrel Hoop Snow Shoe. The Sioux Snow Shoe. The Iroquois Snow Shoe. The Ainu Snow Shoe. The Norwegian Ski. The Swamp Shoe or Swiss Snow Shoe. CHAPTER IV. TENT MAKING 44 Farewell Meeting. Word from Uncle Ed. The Canvas Tent. Adjustable Ridge Pole. Tie Blocks. The Annex. CHAPTER V. PREPARING FOR THE EXPEDITION 53 Tent Fly. Provisions and Supplies. Umbrella Rib Crossbow. Megaphone. The Scow. CHAPTER VI. OFF TO THE ISLAND 63 A Unique Alarm Clock. The Trip to the Island. Preliminary Exploration. A Rustic Table. The Small Filter. The Barrel Filter. The _Klepalo_. CHAPTER VII. SURVEYING 73 The Surveying Instrument. Spirit Levels. The Tripod. Surveyor's Chain. Surveyor's Rod. A Simple Method of Surveying. Mapping the Island. CHAPTER VIII. SWIMMING 84 Swimming on a Plank. Shooting the Rapids. Restoring the Drowned. How to Work over a Patient Alone. CHAPTER IX. BRIDGE BUILDING 95 The Spar Bridge. The Rope Railway. The Suspension Bridge. The Pontoon Bridge. The King Rod Truss. Stiffening the Bridge. The King Post Bridge. CHAPTER X. CANVAS CANOES 109 Uncle Ed's Departure. A Visit from Mr. Schreiner. The Sailing Canoe. Stretching on the Canvas. The Rudder. The Deep Keel. Canoe Sails. Lee Boards. Indian Paddling Canoe. CHAPTER XI. HOUSE BUILDING 124 The Grass Hut. The Goblins' Dancing Platform. Dutchy Takes a Dare. A Path Up the Fissure. Rope Ladders. The Derrick. The Tree House. Sliding Doors. CHAPTER XII. TROUBLE WITH THE TRAMPS 138 The Scow is Stolen. A Council of War. Vengeance. A Double Surprise. Tramp-proof Boat Mooring. CHAPTER XIII. WIGWAGGING AND HELIOGRAPHING 144 Wigwag Signals. The Wigwag Alphabet. Abbreviations. Wigwagging at Night. The Heliograph. The Single Mirror Instrument. The Sight Rod. The Screen. Focusing the Instrument. Heliograph Signaling. The International...

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Let's be clear from the start: this is not a novel. "Theory of Groups of Finite Order" is a foundational mathematics text. Burnside's goal was to organize and expand everything known about a specific, powerful algebraic concept called a 'group.' Think of a group as a complete set of symmetrical actions—like all the ways you can rotate a square and have it still look like a square. Burnside systematically lays out the rules, explores different types of groups, and proves critical theorems about their structure. The 'plot' is the logical journey from basic definitions to deep, complex results about how these abstract systems are put together.

Why You Should Read It

You read this for the intellectual thrill. It's like watching a master architect at work. Burnside's writing is dense and precise, but there's a beautiful clarity to his logic. You get a direct line to the mind of a pioneer. The themes are universality and hidden order—the idea that complex patterns in nature and science can often be broken down into these elegant, finite systems. It's humbling and inspiring to see how much can be built from a few simple rules.

Final Verdict

This book is absolutely not for casual readers. It's a specialized, demanding work. However, it's perfect for serious students of mathematics, physics, or anyone with a strong background in abstract algebra who wants to engage with a classic text. It's also a fascinating historical artifact for those interested in the development of modern algebra. Approach it not as a story, but as a challenging and rewarding conversation with one of the great mathematical minds of the early 20th century.

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