He who untied the Gordian knot would rule all of Asia So goes the legend of the tricky knot of Gordius, king of Phrygia.Many had tried; many had failed, but Alexander the Great simplycut the knot with his sword. He went on to conquer most of Asia, eventually reaching as far east as Northern India. Cut the Knot is a book of probability riddles curated to challenge the mind andexpand mathematical and logical thinking skills. First housed on cut-the-knot.org, these puzzles and their solutions represent the efforts of great minds around theworld. Follow along as Alexander Bogomolny presents these selected riddles bytopical progression. Try them for yourself before reading their solutions. Just like itwas for Alexander the Great, the non-trivial, unexpected solution might be exactlythe one you need.

Knots are familiar objects. Yet the mathematical theory of knots quickly leads to deep results in topology and geometry. This work offers an introduction to this theory, starting with our understanding of knots. It presents the applications of knot theory to modern chemistry, biology and physics.

This book introduces the study of knots, providing insights into recent applications in DNA research and graph theory. It sets forth fundamental facts such as knot diagrams, braid representations, Seifert surfaces, tangles, and Alexander polynomials. It also covers more recent developments and special topics, such as chord diagrams and covering spaces. The author avoids advanced mathematical terminology and intricate techniques in algebraic topology and group theory. Numerous diagrams and exercises help readers understand and apply the theory. Each chapter includes a supplement with interesting historical and mathematical comments.

From the #1 wedding website, The Knot, comes their bestselling binder—the indispensable organizer and planner that hundreds of thousands of married-couples-to-be have relied on—now completely revised and updated for a wide variety of ceremonies. The go-to online resource that has been helping couples plan their wedding ceremonies for more than twenty-five years, The Knot has compiled all their essential planning tools into this beautiful wedding binder that features a linen-textured cover and foil stamping. In addition to dozens of ideas brand-new to this edition, you will find: Detailed timelines and worksheets for scheduling and budgeting Planning and money-saving tips on everything from the dress to the music to the reception decor 8 tabbed dividers packed with visual inspiration, including more than 100 brand-new color photos of updated centerpieces, table settings, favors, and more Extensive information on choosing your vendors, including checklists of key questions to ask Inclusive ideas for modern weddings, including inspiration for LGBTQ+, multicultural, interfaith, and nontraditional ceremonies A PVC pocket for collecting tear sheets, important contracts, and business cards Removable stickers on the front, spine, and back so you can make the binder your own Since it first published in 1999, The Knot Ultimate Wedding Planner & Organizer has become a go-to resource and guide for anyone preparing to say "I do." Now updated for today's couples, it's also a lovely keepsake after the meaningful, joyful, and customized celebration you're sure to have.

Tying the Knot by Rob Green offers soon-to-be-married couples a practical vision of Christ-centered marriage that is realistic, hopeful, and actionable. With homework to help any counselor or couple put crucial lessons into practice, Tying the Knot is a highly relevant premarital counseling book. This eight-session study guides couples through issues like conflict, expectations, communication, finances, and intimacy, showing how each can be successfully resolved with Christ at the center of the marriage. Knowing the stresses and needs of a couple in their season of engagement, Green has helpfully designed the study to require a manageable (and healthy) 60 minutes of at-home work per session, with questions and exercises to build communication and intimacy at the end of each chapter. Tying the Knot also includes an appendix for mentors, making it easy for a married couple, lay leader, or counselor to lead an engaged couple through the book. Field-tested and recommended by multiple counselors in a thriving counseling practice, Tying the Knot has already guided many couples into a stronger and more joyful union. Let this eight-week premarital study reorient your life and marriage around Christ, so you both will experience all the blessings of marriage as God designed it.

From the #1 wedding brand, the bestselling wedding book, updated with all-new budget ideas, online tools, and event planning and personalizing trends. First comes love, then comes . . . planning! Before a fabulous celebration, there are vendors to hire, budgets to calculate, decisions galore to make. Packed with The Knot’s top tips and worksheets, checklists, and contact sheets for you to fill in, this book is the one-stop resource that keeps brides focused but stress-free. The Knot Ultimate Wedding Planner paperback takes you through the process step by easy-to-follow step, with: · Budget worksheets (and all the latest digital tools for keeping track of costs) as well as hundreds of invisible ways to cut costs when selecting everything from flowers to the venue and menu · Wedding planning timelines (including a brand-new express timeline for couples getting married in 3 months or fewer) · Guest list and invitation worksheets (with guidance on what you can now do online) · Vendor contract checklists (and tons of new online resources for finding the pros you need) · Fun ideas for personalizing your reception, from photo booths to signature cocktails in any color your heart desires · Web links and other useful resources for planning on the go (including recommended apps to download and up-to-the-minute advice on building your wedding website)

Rolfsen's beautiful book on knots and links can be read by anyone, from beginner to expert, who wants to learn about knot theory. Beginners find an inviting introduction to the elements of topology, emphasizing the tools needed for understanding knots, the fundamental group and van Kampen's theorem, for example, which are then applied to concrete problems, such as computing knot groups. For experts, Rolfsen explains advanced topics, such as the connections between knot theory and surgery and how they are useful to understanding three-manifolds. Besides providing a guide to understanding knot theory, the book offers 'practical' training. After reading it, you will be able to do many things: compute presentations of knot groups, Alexander polynomials, and other invariants; perform surgery on three-manifolds; and visualize knots and their complements.It is characterized by its hands-on approach and emphasis on a visual, geometric understanding. Rolfsen offers invaluable insight and strikes a perfect balance between giving technical details and offering informal explanations. The illustrations are superb, and a wealth of examples are included. Now back in print by the AMS, the book is still a standard reference in knot theory. It is written in a remarkable style that makes it useful for both beginners and researchers. Particularly noteworthy is the table of knots and links at the end. This volume is an excellent introduction to the topic and is suitable as a textbook for a course in knot theory or 3-manifolds. Other key books of interest on this topic available from the AMS are ""The Shoelace Book: A Mathematical Guide to the Best (and Worst) Ways to Lace your Shoes"" and ""The Knot Book.""