A lecture class taught by Wittgenstein, however, hardly resembled a lecture. He sat on a chair in the middle of the room, with some of the class sitting in chairs, some on the floor. He never used notes. He paused frequently, sometimes for several minutes, while he puzzled out a problem. He often asked his listeners questions and reacted to their replies. Many meetings were largely conversation. These lectures were attended by, among others, D. A. T. Gasking, J. N. Findlay, Stephen Toulmin, Alan Turing, G. H. von Wright, R. G. Bosanquet, Norman Malcolm, Rush Rhees, and Yorick Smythies. Notes taken by these last four are the basis for the thirty-one lectures in this book. The lectures covered such topics as the nature of mathematics, the distinctions between mathematical and everyday languages, the truth of mathematical propositions, consistency and contradiction in formal systems, the logicism of Frege and Russell, Platonism, identity, negation, and necessary truth. The mathematical examples used are nearly always elementary.

    

    It can urge the reader to explore new methodologies to have maximum fun with numbers, and opt for a higher course in mathematics. The book was specifically designed to help the student community, and develop a strong affinity towards problem solving.the book offers many complicated, and interesting challenges for the user, keeping them engaged throughout. A large number of solved problems are also included in challenge and thrill of pre-college mathematics, to give readers an insight into the subject. The book can be an eye-opener for school students of class 7 and above. The materials given in the book are powerful enough to help them develop a strong interest for the subject. The concepts are explained in a simple and comprehensive manner, providing them with a good understanding of mathematical fundamentals.what makes the book distinct is its detailed sections on geometry, that can improve the reasoning skills of students. There are also detailed accounts on algebra and trigonometry, enhancing the competitive ability of the users. The topics such as combinatorics, number theory, and probability are also explained in detail, in the book. Each chapter was designed with the intention of motivating students to appreciate the excitement that mathematical problems can provide. Published in 2003 by new age international publishers, the book is available in paperback. Key features: the book includes a collection of more than 300 solved numerical problems, compiled from various national, as well as international mathematical olympiads.it is widely recommended by students and teachers, alike as an essential preparatory book for those writing competitive examinations.

    You will also learn the 3 elements of practical psychology, what someone's music taste says about them, and will be provided practical exercises at the end of each chapter to follow through on.Furthermore, How to Analyze & Read People with Human Psychology, Body Language, and the 6 Human Needs will teach you about: Transactional Analysis and How it Can Benefit You The 5 Rules That WILL Make Your Life Miserable The Stroke Economy Bottom Lines and How They Dictate Your Life Even Though You Had No Say in Them - Until Now! What The Four Primal and Two Spiritual Needs are in Your Life Gaining a Deeper Understanding of Yourself to Analyze Others Accurately Macro versus Micro Facial Expressions Cold Reading People at First Glance The Winner's Triangle and The Drama Triangle And more... What are you waiting for? Stop overthinking and start ANALYZING! Scroll up and 'Buy with 1-Click' NOW!

    But this book will help you to do something that humans have only recently understood how to do: to count to regions that no animal has ever reached. By the end of this book you'll be able to count to infinity... and beyond. On our way to infinity we'll discover how the ancient Babylonians used their bodies to count to 60 (which gave us 60 minutes in the hour), how the number zero was only discovered in the 7th century by Indian mathematicians contemplating the void, why in China going into the red meant your numbers had gone negative and why numbers might be our best language for communicating with alien life.But for millennia, contemplating infinity has sent even the greatest minds into a spin. Then at the end of the nineteenth century mathematicians discovered a way to think about infinity that revealed that it is a number that we can count. Not only that. They found that there are an infinite number of infinities, some bigger than others. Just using the finite neurons in your brain and the finite pages in this book, you'll have your mind blown discovering the secret of how to count to infinity.Do something amazing and learn a new skill thanks to the Little Ways to Live a Big Life books!

    It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity. Topics include sets, logic, counting, methods of conditional and non-conditional proof, disproof, induction, relations, functions and infinite cardinality.

    Master Python Programming with a unique Hands-On Project Have you always wanted to learn computer programming but are afraid it'll be too difficult for you? Or perhaps you know other programming languages but are interested in learning the Python language fast? This book is for you. You no longer have to waste your time and money learning Python from lengthy books, expensive online courses or complicated Python tutorials. What this book offers... Python for Beginners Complex concepts are broken down into simple steps to ensure that you can easily master the Python language even if you have never coded before. Carefully Chosen Python Examples Examples are carefully chosen to illustrate all concepts. In addition, the output for all examples are provided immediately so you do not have to wait till you have access to your computer to test the examples. Careful selection of topics Topics are carefully selected to give you a broad exposure to Python, while not overwhelming you with information overload. These topics include object-oriented programming concepts, error handling techniques, file handling techniques and more. Learn The Python Programming Language Fast Concepts are presented in a "to-the-point" style to cater to the busy individual. With this book, you can learn Python in just one day and start coding immediately. How is this book different... The best way to learn Python is by doing. This book includes a complete project at the end of the book that requires the application of all the concepts taught previously. Working through the project will not only give you an immense sense of achievement, it"ll also help you retain the knowledge and master the language. Are you ready to dip your toes into the exciting world of Python coding? This book is for you. With the first edition of this book being a #1 best-selling programming ebook on Amazon for more than a year, you can rest assured that this new and improved edition is the perfect book for you to learn the Python programming language fast. Click the BUY button and download it now. What you'll learn: - What is Python? - What software you need to code and run Python programs? - What are variables? - What are the common data types in Python? - What are Lists and Tuples? - How to format strings - How to accept user inputs and display outputs - How to control the flow of program with loops - How to handle errors and exceptions - What are functions and modules? - How to define your own functions and modules - How to work with external files - What are objects and classes - How to write your own class - What is inheritance - What are properties - What is name mangling .. and more... Finally, you'll be guided through a hands-on project that requires the application of all the topics covered. Click the BUY button and download the book now to start learning Python. Learn it fast and learn it well. Tags: ------------ Python, Object-oriented Python, Python course, Python book, learning Python, Python language, Python examples, Python tutorials, Python programming language, Python coding, Pyth

    The fear of mispronouncing or misusing complex words is real and leaves many of us consigned to the lower levels* of the English Language. The secret to eloquence, however, lies in simplicity—the ability to use ordinary words in extraordinary ways.The Well-Spoken Thesaurus is your guide to eloquence, replacing the ordinary with the extraordinary. While a common thesaurus provides only synonyms as mere word-for-word equivalents, The Well-Spoken Thesaurus is filled with* dynamic reinventions of standard words and phrases.*lofty word, pretentious word *know what it is to *lower reaches, lower echelons *awash in, instilled with, dense with, rich in

    The truth is, we no longer live in a world of six degrees of separation. In fact, we're now down to only six pixels of separation, which changes everything we know about doing business. This is the first book to integrate digital marketing, social media, personal branding, and entrepreneurship in a clear, entertaining, and instructive manner that everyone can understand and apply. Through the use of timely case studies and fascinating stories, SIX PIXELS OF SEPARATION offers a complete set of the latest tactics, insights, and tools that will empower you to reach a global audience and consumer base-and, best yet, you can do this pretty much for free. Digital marketing expert Mitch Joel unravels this fascinating world of new media-but does so with a brand-new perspective that is driven by compelling results. The smarter entrepreneurs and top executives are leveraging these digital channels to get their voice "out there"-connecting with others, becoming better community citizens, and, ultimately, making strategic business moves that are increasing revenue, awareness, and overall success in the marketplace-without the support of traditional mass media. Everyone is connected. Isn't it time for you and your company to connect to everyone? SIX PIXELS OF SEPARATION will show you how.

    

    Without a doubt, the development of the computer was a massive leap forward in humankind's progress and will stand as one of the twentieth century's greatest achievements. But how many of us know how it really works? "Turing And The Computer" offers a brilliant encapsulation of the groundwork that led to the invention of the computer as we know it, and an absorbing account of the man who helped develop it, only to be largely forgotten after his death. Eccentric and principled, Turing would lay aside a brilliant career in mathematics to serve his country by breaking German codes during the Second World War. Openly homosexual, he would later be put on trial on indecency charges and forced to undergo hormone treatments that wrecked his body and his spirit. But the modern machine he helped create lives on.Concise and thoroughly compelling, "Turing And The Computer" is for all those curious about the philosophy and mechanics behind the now indispensable computer, and for anyone awed by the spark of invention that inspires its birth.

    You can think of Python as your tool to solve problems that are far beyond the capability of a spreadsheet. It is an easy-to-use and easy-to learn programming language that is freely available on Windows, Macintosh, and Linux computers. There are free downloadable copies of this book in various electronic formats and a self-paced free online course where you can explore the course materials. All the supporting materials for the book are available under open and remixable licenses. This book is designed to teach people to program even if they have no prior experience.

    Equal parts personal, practical, and profound, Applied Minds charts a path to a future where we borrow strategies from engineering to find inspired solutions to our most pressing challenges.

    Quality assurance was conducted on each of these books in an attempt to remove books with imperfections introduced by the digitization process. Though we have made best efforts - the books may have occasional errors that do not impede the reading experience. We believe this work is culturally important and have elected to bring the book back into print as part of our continuing commitment to the preservation of printed works worldwide.

    Old School Entrepreneur Meets New School.