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Lateral Solutions to Mathematical Problems by Desmond MacHale Pdf
Lateral Solutions to Mathematical Problems offers a fresh approach to mathematical problem solving via lateral thinking. Lateral thinking has long been used informally by good mathematics teachers and lecturers to spice up their material and interest their students in the more artistic aspects of mathematical problem solving. In this book, the author attempts to carry out this process formally, with reference to specific, non-technical problems that are easily understood and explained at an intermediate level. This book is appropriate for interested high school students, undergraduates and postgraduates, looking for relief from technical material and also looking for insight into the methodology of mathematics; for teachers and lecturers looking for a novel approach to course material; and anyone interested in both mathematics and lateral thinking.
Parabolic Problems by David Angell,Thomas Britz Pdf
Parabola is a mathematics magazine published by UNSW, Sydney. Among other things, each issue of Parabola has contained a collection of puzzles/problems, on various mathematical topics and at a suitable level for younger (but mathematically sophisticated) readers. Parabolic Problems: 60 Years of Mathematical Puzzles in Parabola collects the very best of almost 1800 problems and puzzles into a single volume. Many of the problems have been re-mastered, and new illustrations have been added. Topics covered range across geometry, number theory, combinatorics, logic, and algebra. Solutions are provided to all problems, and a chapter has been included detailing some frequently useful problem-solving techniques, making this a fabulous resource for education and, most importantly, fun! Features Hundreds of diverting and mathematically interesting problems and puzzles. Accessible for anyone with a high school-level mathematics education. Wonderful resource for teachers and students of mathematics from high school to undergraduate level, and beyond.
Mathematics of Tabletop Games by Aaron Montgomery Pdf
Mathematics of Tabletop Games provides a bridge between mathematics and hobby tabletop gaming. Instead of focusing on games mathematicians play, such as nim and chomp, this book starts with the tabletop games played by avid gamers and hopes to address the question: which field of mathematics concerns itself with this situation? Readers interested in either mathematics or tabletop games will find this book an engaging way to begin exploring the other topic or the connection between the topics. Features Presents an entry-level exposition of interesting mathematical concepts that are not commonly taught outside of upper-level mathematics courses Acts as a resource for mathematics instructors who wish to provide new examples of standard mathematical concepts Features material that may help game designers and developers make design decisions about game mechanisms Provides working Python code that can be used to solve common questions about games Covers a broad range of mathematical topics that could be used as survey material for undergraduates curious about mathematics.
Want to sharpen your mathematical wits? If so, then Mathematical Conundrums is for you. Daily Telegraph enigmatologist, Barry R. Clarke, presents over 120 fiendish problems that will test both your ingenuity and persistence. Between these covers are puzzles in geometry, arithmetic, and algebra (there is even a section for computer programmers). And, for the smartest readers who wish to stretch their mind to its limits, a selection of engaging logic and visual lateral puzzles is included. Although no puzzle requires a greater knowledge of mathematics than the high school curriculum, this collection will take you to the edge. But are you equal to the challenge? Features High-school level of mathematics is the only pre-requisite Variety of algebraic, route-drawing, and geometrical conundrums Hints section for the lateral puzzles Warm-up excercises to sharpen the wits Full solutions to every problem Barry R. Clarke has published over 1,500 puzzles in The Daily Telegraph and has contributed enigmas to New Scientist, The Sunday Times, Reader’s Digest, The Sunday Telegraph, and Prospect magazine. His book Challenging Logic Puzzles Mensa has sold over 100,000 copies. As well as a PhD in Shakespeare Studies, Barry has a master’s degree and academic publications in quantum physics. He is now working on a revised theory of the hydrogen atom. Other skills include mathematics tutor, filmmaker, comedy-sketch writer, cartoonist, computer programmer, and blues guitarist! For more information please visit http://barryispuzzled.com.
Puzzle and Proof by Samuel Dittmer,Hiram Golze,Grant Molnar,Caleb Stanford Pdf
Puzzle and Proof: A Decade of Problems from the Utah Math Olympiad is a compilation of the problems and solutions for the first 10 years of the Utah Math Olympiad. The problems are challenging but should be understandable at a high school level. Besides putting all problems in one place (70 in total), which have not previously appeared in print, the book provides additional inspiration for many of the problems and will contain the first published solutions for 10 problems that were originally published on the contest flyer. The book will be a fantastic resource for anyone who enjoys mathematical and/or logic puzzles or is interested in studying for mathematics competitions. Features 70 carefully designed, high-quality high-school level math proof problems, with full solutions Detailed pictures and diagrams throughout to aid understanding Suitable for anyone with high school-level mathematics skills with an interest in furthering their understanding, or just enjoying the puzzles Solutions in the back of the book, sorting the problems by difficulty and topic.
Basic Gambling Mathematics: The Numbers Behind the Neon, Second Edition explains the mathematics involved in analyzing games of chance, including casino games, horse racing and other sports, and lotteries. The book helps readers understand the mathematical reasons why some gambling games are better for the player than others. It is also suitable as a textbook for an introductory course on probability. Along with discussing the mathematics of well-known casino games, the author examines game variations that have been proposed or used in actual casinos. Numerous examples illustrate the mathematical ideas in a range of casino games while end-of-chapter exercises go beyond routine calculations to give readers hands-on experience with casino-related computations. New to the Second Edition Thorough revision of content throughout, including new sections on the birthday problem (for informal gamblers) and the Monty Hall problem, as well as an abundance of fresh material on sports gambling Brand new exercises and problems A more accessible level of mathematical complexity, to appeal to a wider audience.
The Baseball Mysteries by Jerry Butters,Jim Henle Pdf
The Baseball Mysteries: Challenging Puzzles for Logical Detectives is a book of baseball puzzles, logical baseball puzzles. To jump in, all you need is logic and a casual fan’s knowledge of the game. The puzzles are solved by reasoning from the rules of the game and a few facts. The logic in the puzzles is like legal reasoning. A solution must argue from evidence (the facts) and law (the rules). Unlike legal arguments, however, a solution must reach an unassailable conclusion. There are many puzzle books. But there’s nothing remotely like this book. The puzzles here, while rigorously deductive, are firmly attached to actual events, to struggles that are reported in the papers every day. The puzzles offer a unique and scintillating connection between abstract logic and gritty reality. Actually, this book offers the reader an unlimited number of puzzles. Once you’ve solved a few of the challenges here, every boxscore you see in the papers or online is a new puzzle! It can be anywhere from simple, to complex, to impossible. For anyone who enjoys logical puzzles For anyone interested in legal reasoning For anyone who loves the game of baseball. Jerry Butters has a BA in mathematics from Oberlin College, and an MS in mathematics and a PhD in economics from the University of Chicago. He taught mathematics for two years at Mindanao State University in the Philippines as a Peace Corps volunteer. He taught economics for five years at Princeton University. For most of his career, he worked on consumer protection cases and policy issues at the Federal Trade Commission. In his retirement, he has become a piano teacher and performer. He enjoys hobbies ranging from reading Chinese to practicing Taiji. This book is an outgrowth of another of his hobbies - his love of designing and solving puzzles of all sorts. Jim Henle has a BA in mathematics from Dartmouth College and a PhD from M.I.T. He taught for two years at U. P. Baguio in the Philippines as a Peace Corps volunteer, two years at a middle school as alternative service, and 42 years at Smith College. His research is primarily in logic and set theory, with additional papers in geometry, graph theory, number theory, games, economics, and music. He edited columns for The Mathematical Intelligencer. He authored or co-authored five books. His most recent book, The Proof and the Pudding, compares mathematics and gastronomy. He has collaborated with Jerry on puzzle papers and chamber music concerts.
Problems and Solutions in Mathematics by Ji-Xiu Chen Pdf
This book contains a selection of more than 500 mathematical problems and their solutions from the PhD qualifying examination papers of more than ten famous American universities. The mathematical problems cover six aspects of graduate school mathematics: Algebra, Topology, Differential Geometry, Real Analysis, Complex Analysis and Partial Differential Equations. While the depth of knowledge involved is not beyond the contents of the textbooks for graduate students, discovering the solution of the problems requires a deep understanding of the mathematical principles plus skilled techniques. For students, this book is a valuable complement to textbooks. Whereas for lecturers teaching graduate school mathematics, it is a helpful reference.
Design Techniques for Origami Tessellations by Yohei Yamamoto,Jun Mitani Pdf
Design Techniques for Origami Tessellations is both a collection of origami tessellations and a manual to design them. This book begins by explaining general design methods, the history and definitions of origami tessellations, and the geometric features of flat origami, before moving on to introduce a brand-new design method: the "twist-based design method." This method generates base parts that connect "twist patterns” (that can be folded with a twist) without using a lattice. Therefore, it can generate base parts such as regular pentagons, which cannot be generated with more conventional methods, and can generate new origami tessellations connected to them. Features: No proofs or formulas in the text and minimal jargon. Suitable for readers with a roughly middle school to high school level of mathematical background. Web application implementing the method described in this book is available, allowing the readers to design their own patterns.
String art is a well-known and popular activity that uses string, a board, and nails to produce artistic images (although there are variations that use different modalities). This activity is beloved because simple counting rules are used to create beautiful images that can both adorn walls and excite young minds. The downside of this highly tactile activity is that it is quite time-consuming and rigid. By contrast, electronic string art offers much more flexibility to set up or change nail locations and counting rules, and the images created from those changes change instantaneously. Electronic String Art: Rhythmic Mathematics invites readers to use the author’s digital resources available on the ESA website to play with the parameters inherent in string art models while offering concise, accessible explanations of the underlying mathematical principles regarding how the images were created and how they change. Readers will have the opportunity to create visually beautiful works of art while learning concepts from geometry, number theory, and modular arithmetic from approximately 200 short-interdependent sections. Features Readers are able to drill-down on images in order to understand why they work using short (1 to 2 page) stand-alone sections Sections are lessons that were created so that they could be digested in a single sitting These sections are stand-alone in the sense that they need not be read sequentially but can be referred to based on images that the reader finds interesting An open-ended, inherently flexible teaching resource for elementary, middle, and high school-level mathematics The most mathematically challenging sections (or portions of a section) are designated MA and may not be accessible to elementary and middle school readers Will be appreciated by anyone interested in recreational mathematics or mathematical artworks even if the users are not interested in the underlying mathematics Includes exercises, solutions, and many online digital resources These QR codes take you to these digital resources. One takes you directly to the web version of the string art model (used as a starting point for teaching the parameters of the model in Section 25.5). The other takes you to the ESA web page with additional links to a variety of resources.
Features Suitable for anyone with an interest in games and mathematics. Could be especially useful to middle and high school students and their teachers Partial solutions to the various exercises included in the book.
This is a book about infinity — specifically the infinity of numbers, and how one kind of infinity is greater than all the rest. Along the way the author will demonstrate how infinity can be made to create beautiful ‘art’, and how this process can help us to understand the fundamental nature of numbers. This book will provide a fascinating read for anyone interested in number theory, infinity, math art, and/or generative art, and could be used a valuable supplement to any course on these topics. Features Beautiful examples of generative art. Accessible to anyone with a reasonable high school level of mathematics. Full of challenges and puzzles to engage readers.
Mathematical Lateral Thinking Puzzles by Paul Sloane,Des MacHale Pdf
A collection of mathematical conundrums with a twist. It presents you with mathematical conundrums, but instead of requiring brute calculating power, each puzzle relies upon a clever insight or unexpected shortcut.
This concise, self-contained textbook gives an in-depth look at problem-solving from a mathematician’s point-of-view. Each chapter builds off the previous one, while introducing a variety of methods that could be used when approaching any given problem. Creative thinking is the key to solving mathematical problems, and this book outlines the tools necessary to improve the reader’s technique. The text is divided into twelve chapters, each providing corresponding hints, explanations, and finalization of solutions for the problems in the given chapter. For the reader’s convenience, each exercise is marked with the required background level. This book implements a variety of strategies that can be used to solve mathematical problems in fields such as analysis, calculus, linear and multilinear algebra and combinatorics. It includes applications to mathematical physics, geometry, and other branches of mathematics. Also provided within the text are real-life problems in engineering and technology. Thinking in Problems is intended for advanced undergraduate and graduate students in the classroom or as a self-study guide. Prerequisites include linear algebra and analysis.
Teaching With Author Web Sites, K8 by Rose Reissman,Mark Gura Pdf
Drawing on extensive classroom experience, the authors demonstrate how shy students, reluctant readers, English language learners, and students who may be less active during class discussion become energized when they explore rich Web sites available from popular, respected children's authors. This book illustrates how this easy, no-risk technology--available at a keystroke--offers wide-ranging benefits, including: - Inviting students into a literacy community of readers and writers - Fostering the development of discrete, test-mandated skills - Capitalizing on and deepening students' familiarity with the digital world in ways that enhance their literacy growth
