Street-Fighting Mathematics PDF Download

Author: Sanjoy Mahajan
Publisher: MIT Press
ISBN: 0262265591
Category : Education
Languages : en
Pages : 152

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Book Description
An antidote to mathematical rigor mortis, teaching how to guess answers without needing a proof or an exact calculation. In problem solving, as in street fighting, rules are for fools: do whatever works—don't just stand there! Yet we often fear an unjustified leap even though it may land us on a correct result. Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions. This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation. In Street-Fighting Mathematics, Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and down-and-dirty, opportunistic problem solving across diverse fields of knowledge—from mathematics to management. Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool—the general principle—from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest. Street-Fighting Mathematics grew out of a short course taught by the author at MIT for students ranging from first-year undergraduates to graduate students ready for careers in physics, mathematics, management, electrical engineering, computer science, and biology. They benefited from an approach that avoided rigor and taught them how to use mathematics to solve real problems. Street-Fighting Mathematics will appear in print and online under a Creative Commons Noncommercial Share Alike license.

Author: Michael F. Ashby
Publisher: Elsevier
ISBN: 1483297217
Category : Technology & Engineering
Languages : en
Pages : 380

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Book Description
Provides a thorough explanation of the basic properties of materials; of how these can be controlled by processing; of how materials are formed, joined and finished; and of the chain of reasoning that leads to a successful choice of material for a particular application. The materials covered are grouped into four classes: metals, ceramics, polymers and composites. Each class is studied in turn, identifying the families of materials in the class, the microstructural features, the processes or treatments used to obtain a particular structure and their design applications. The text is supplemented by practical case studies and example problems with answers, and a valuable programmed learning course on phase diagrams.

Author: Milo McRays
Publisher:
ISBN: 9781091112452
Category :
Languages : en
Pages : 120

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Book Description
Half and half paper (dual designs) / Half Wide Ruled-Half Graph 5x5 Notebook: 8 x 10 inch (20.32 x 25.4 cm.) Half and half paper (dual designs) allow you to get creative. * There are lots of reasons someone may want mixed paper styles on one sheet. * Adults may like to plot designs, craft projects or solve engineering problems and write accompanying notes or draw sketches. * Kids may like to solve a math problem and describe how they solved it (or even write a story about the problem!) * The blank and lined papers can also be used as a story paper for writing practice. * Use your imagination to find functions for this paper in different niches. * This is the standard for composition or writing books for elementary school kids. * It can also be a good choice for the elderly, for people who have large handwriting and people with visual impairment. * It is also a good choice for 'casual' writing notebooks for teens. * 120 pages - 60 sheets Wide Rule: The horizontal spacing is 9/32" or 7.1 mm. Trim sizes with a width over 6"" include a margin ruled 1 1⁄4 inches (32 mm) from the left hand of the page. Smaller trim sizes do not include a margin. Quad Rule graph paper: also known as 'engineering' paper has five squares per inch, so each square measures .20" x .20" Have fun & enjoy this Notebook.

Author: Ellen Lupton
Publisher: Princeton Architectural Press
ISBN: 9781568989792
Category : Design
Languages : en
Pages : 0

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Book Description
Creativity is more than an inborn talent; it is a hard-earned skill, and like any other skill, it improves with practice. Graphic Design Thinking: How to Define Problems, Get Ideas, and Create Form explores a variety of informal techniques ranging from quick, seat-of-the-pants approaches to more formal research methods for stimulating fresh thinking, and ultimately arriving at compelling and viable solutions. In the style with which author Ellen has come to been known hands-on, up-close approach to instructional design writing brainstorming techniques are grouped around the three basic phases of the design process: defining the problem, inventing ideas, and creating form. Creative research methods include focus groups, interviewing, brand mapping, and co-design. Each method is explained with a brief narrative text followed by a variety of visual demonstrations and case studies. Also included are discussions with leading professionals, including Art Chantry, Ivan Chermayeff, Jessica Helfand, Steven Heller, Abott Miller, Christoph Niemann, Paula Scher, and Martin Venezky, about how they get ideas and what they do when the well runs dry. The book is directed at working designers, design students, and anyone who wants to apply inventive thought patterns to everyday creative challenges.

Author: National Research Council
Publisher: National Academies Press
ISBN: 0309131979
Category : Education
Languages : en
Pages : 386

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Book Description
First released in the Spring of 1999, How People Learn has been expanded to show how the theories and insights from the original book can translate into actions and practice, now making a real connection between classroom activities and learning behavior. This edition includes far-reaching suggestions for research that could increase the impact that classroom teaching has on actual learning. Like the original edition, this book offers exciting new research about the mind and the brain that provides answers to a number of compelling questions. When do infants begin to learn? How do experts learn and how is this different from non-experts? What can teachers and schools do-with curricula, classroom settings, and teaching methodsâ€"to help children learn most effectively? New evidence from many branches of science has significantly added to our understanding of what it means to know, from the neural processes that occur during learning to the influence of culture on what people see and absorb. How People Learn examines these findings and their implications for what we teach, how we teach it, and how we assess what our children learn. The book uses exemplary teaching to illustrate how approaches based on what we now know result in in-depth learning. This new knowledge calls into question concepts and practices firmly entrenched in our current education system. Topics include: How learning actually changes the physical structure of the brain. How existing knowledge affects what people notice and how they learn. What the thought processes of experts tell us about how to teach. The amazing learning potential of infants. The relationship of classroom learning and everyday settings of community and workplace. Learning needs and opportunities for teachers. A realistic look at the role of technology in education.

Author: Anne Watson
Publisher: Springer
ISBN: 331909629X
Category : Education
Languages : en
Pages : 339

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Book Description
*THIS BOOK IS AVAILABLE AS OPEN ACCESS BOOK ON SPRINGERLINK* This open access book is the product of ICMI Study 22 Task Design in Mathematics Education. The study offers a state-of-the-art summary of relevant research and goes beyond that to develop new insights and new areas of knowledge and study about task design. The authors represent a wide range of countries and cultures and are leading researchers, teachers and designers. In particular, the authors develop explicit understandings of the opportunities and difficulties involved in designing and implementing tasks and of the interfaces between the teaching, researching and designing roles – recognising that these might be undertaken by the same person or by completely separate teams. Tasks generate the activity through which learners meet mathematical concepts, ideas, strategies and learn to use and develop mathematical thinking and modes of enquiry. Teaching includes the selection, modification, design, sequencing, installation, observation and evaluation of tasks. The book illustrates how task design is core to effective teaching, whether the task is a complex, extended, investigation or a small part of a lesson; whether it is part of a curriculum system, such as a textbook, or promotes free standing activity; whether the task comes from published source or is devised by the teacher or the student.

Author: Jay Devore
Publisher: Cengage Learning
ISBN: 9780495382171
Category : Mathematics
Languages : en
Pages : 768

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Book Description
This market-leading text provides a comprehensive introduction to probability and statistics for engineering students in all specialties. This proven, accurate book and its excellent examples evidence Jay Devore’s reputation as an outstanding author and leader in the academic community. Devore emphasizes concepts, models, methodology, and applications as opposed to rigorous mathematical development and derivations. Through the use of lively and realistic examples, students go beyond simply learning about statistics-they actually put the methods to use. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Author: Robert Kaplinsky
Publisher: Taylor & Francis
ISBN: 1003839886
Category : Education
Languages : en
Pages : 193

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Book Description
This book is an amazing resource for teachers who are struggling to help students develop both procedural fluency and conceptual understanding.. --Dr. Margaret (Peg) Smith, co-author of5 Practices for Orchestrating Productive Mathematical Discussions Robert Kaplinsky, the co-creator of Open Middle math problems, brings hisnew class of tasks designed to stimulate deeper thinking and lively discussion among middle and high school students in Open Middle Math: Problems That Unlock Student Thinking, Grades 6-12. The problems are characterized by a closed beginning,- meaning all students start with the same initial problem, and a closed end,- meaning there is only one correct or optimal answer. The key is that the middle is open- in the sense that there are multiple ways to approach and ultimately solve the problem. These tasks have proven enormously popular with teachers looking to assess and deepen student understanding, build student stamina, and energize their classrooms. Professional Learning Resource for Teachers: Open Middle Math is an indispensable resource for educators interested in teaching student-centered mathematics in middle and high schools consistent with the national and state standards. Sample Problems at Each Grade: The book demonstrates the Open Middle concept with sample problems ranging from dividing fractions at 6th grade to algebra, trigonometry, and calculus. Teaching Tips for Student-Centered Math Classrooms: Kaplinsky shares guidance on choosing problems, designing your own math problems, and teaching for multiple purposes, including formative assessment, identifying misconceptions, procedural fluency, and conceptual understanding. Adaptable and Accessible Math: The tasks can be solved using various strategies at different levels of sophistication, which means all students can access the problems and participate in the conversation. Open Middle Math will help math teachers transform the 6th -12th grade classroom into an environment focused on problem solving, student dialogue, and critical thinking.

Author: Mario Livio
Publisher: Simon and Schuster
ISBN: 0743274628
Category : Mathematics
Languages : en
Pages : 367

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Book Description
What do Bach's compositions, Rubik's Cube, the way we choose our mates, and the physics of subatomic particles have in common? All are governed by the laws of symmetry, which elegantly unify scientific and artistic principles. Yet the mathematical language of symmetry-known as group theory-did not emerge from the study of symmetry at all, but from an equation that couldn't be solved. For thousands of years mathematicians solved progressively more difficult algebraic equations, until they encountered the quintic equation, which resisted solution for three centuries. Working independently, two great prodigies ultimately proved that the quintic cannot be solved by a simple formula. These geniuses, a Norwegian named Niels Henrik Abel and a romantic Frenchman named Évariste Galois, both died tragically young. Their incredible labor, however, produced the origins of group theory. The first extensive, popular account of the mathematics of symmetry and order, The Equation That Couldn't Be Solved is told not through abstract formulas but in a beautifully written and dramatic account of the lives and work of some of the greatest and most intriguing mathematicians in history.

Author: Alice Zheng
Publisher: "O'Reilly Media, Inc."
ISBN: 1491953195
Category : Computers
Languages : en
Pages : 218

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Book Description
Feature engineering is a crucial step in the machine-learning pipeline, yet this topic is rarely examined on its own. With this practical book, you’ll learn techniques for extracting and transforming features—the numeric representations of raw data—into formats for machine-learning models. Each chapter guides you through a single data problem, such as how to represent text or image data. Together, these examples illustrate the main principles of feature engineering. Rather than simply teach these principles, authors Alice Zheng and Amanda Casari focus on practical application with exercises throughout the book. The closing chapter brings everything together by tackling a real-world, structured dataset with several feature-engineering techniques. Python packages including numpy, Pandas, Scikit-learn, and Matplotlib are used in code examples. You’ll examine: Feature engineering for numeric data: filtering, binning, scaling, log transforms, and power transforms Natural text techniques: bag-of-words, n-grams, and phrase detection Frequency-based filtering and feature scaling for eliminating uninformative features Encoding techniques of categorical variables, including feature hashing and bin-counting Model-based feature engineering with principal component analysis The concept of model stacking, using k-means as a featurization technique Image feature extraction with manual and deep-learning techniques