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Video
Hidden truths permeate our world; they're inaccessible to our senses, but math allows us to go beyond our intuition to uncover their mysteries. In this survey of mathematical breakthroughs, Fields Medal winner Cédric Villani speaks to the thrill of discovery and details the sometimes perplexing life of a mathematician. "Beautiful mathematical explanations are not only for our pleasure," he says. "They change our vision of the world."
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematics
- Resource Type:
- Video
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e-book
"In 2013, Lyryx forked the now-popular Calculus open textbook written by David Guichard. Michael Cavers of the University of Calgary, together with the Lyryx editorial team, further redeveloped the content, examples, diagrams, and overall look-and-feel of the book, making it more accessible to first year college and university students. Additional contributors have helped improve the content, including Mark Blenkinsop of Carleton University. In particular, there was the addition of an introductory chapter reviewing the fundamental topics required in a first semester Calculus course, and the paring down of topics that are typically beyond the scope of math and engineering service courses. Currently, the book covers the standard Calculus I and II courses, with Calculus III under development."--Open Textbook Library.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Textbooks Calculus
- Resource Type:
- e-book
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e-book
"A Brief Introduction to Engineering Computation with MATLAB is specifically designed for students with no programming experience. However, students are expected to be proficient in First Year Mathematics and Sciences and access to good reference books are highly recommended. Students are assumed to have a working knowledge of the Mac OS X or Microsoft Windows operating systems. The strategic goal of the course and book is to provide learners with an appreciation for the role computation plays in solving engineering problems. MATLAB specific skills that students are expected to be proficient at are: write scripts to solve engineering problems including interpolation, numerical integration and regression analysis, plot graphs to visualize, analyze and present numerical data, and publish reports."--BC Campus website.
- Subjects:
- Computing, Data Science and Artificial Intelligence and Mechanical Engineering
- Keywords:
- Systems engineering Textbooks
- Resource Type:
- e-book
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e-book
Este libro está dirigido, principalmente, a Estudiantes y Docentes que quieren aprender a programarcomo forma de fortalecer sus capacidades cognoscitivas y así obtener un beneficio adicional de su computador para lograr un mejor provecho de sus estudios. Dada la orientación del libro respecto a programar para resolver problemas asociados a las Ciencias e Ingenierías, el requisito mínimo de matemáticas que hemos elegido para presentar el contenido del mismo se cubre, normalmente, en el tercer año del bachillerato. No obstante, el requisito no es obligatorio para leer el libro en su totalidad y adquirir los conocimientos de programación obviando el contenido matemático.
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e-book
Prior to 1990, the performance of a student in precalculus at the University of Washington was not a predictor of success in calculus. For this reason, the mathematics department set out to create a new course with a specific set of goals in mind: A review of the essential mathematics needed to succeed in calculus. An emphasis on problem solving, the idea being to gain both experience and confidence in working with a particular set of mathematical tools. This text was created to achieve these goals and the 2004-05 academic year marks the eleventh year in which it has been used. Several thousand students have successfully passed through the course. This book is full of worked out examples. We use the the notation “Soluion.” to indicate where the reasoning for a problem begins; the symbol ?? is used to indicate the end of the solution to a problem. There is a Table of Contents that is useful in helping you find a topic treated earlier in the course. It is also a good rough outline when it comes time to study for the final examination. The book also includes an index at the end. Finally, there is an appendix at the end of the text with ”answers” to most of the problems in the text. It should be emphasized these are ”answers” as opposed to ”solutions”. Any homework problems you may be asked to turn in will require you include all your work; in other words, a detailed solution. Simply writing down the answer from the back of the text would never be sufficient; the answers are intended to be a guide to help insure you are on the right track.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Precalculus Textbooks
- Resource Type:
- e-book
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e-book
This text covers the standard material for a US undergraduate first course: linear systems and Gauss's Method, vector spaces, linear maps and matrices, determinants, and eigenvectors and eigenvalues, as well as additional topics such as introductions to various applications. It has extensive exercise sets with worked answers to all exercises, including proofs, beamer slides for classroom use, and a lab manual for computer work. The approach is developmental. Although everything is proved, it introduces the material with a great deal of motivation, many computational examples, and exercises that range from routine verifications to a few challenges. Ancillary materials are available at the publisher link.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Textbooks Algebras Linear
- Resource Type:
- e-book
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e-book
Teaching Mathematics is nothing less than a mathematical manifesto. Arising in response to a limited National Curriculum, and engaged with secondary schooling for those aged 11 ̶ 14 (Key Stage 3) in particular, this handbook for teachers will help them broaden and enrich their students’ mathematical education. It avoids specifying how to teach, and focuses instead on the central principles and concepts that need to be borne in mind by all teachers and textbook authors—but which are little appreciated in the UK at present. This study is aimed at anyone who would like to think more deeply about the discipline of ‘elementary mathematics’, in England and Wales and anywhere else. By analysing and supplementing the current curriculum, Teaching Mathematics provides food for thought for all those involved in school mathematics, whether as aspiring teachers or as experienced professionals. It challenges us all to reflect upon what it is that makes secondary school mathematics educationally, culturally, and socially important.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematics -- Study teaching (Secondary)
- Resource Type:
- e-book
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e-book
This textbook was born of a desire to contribute a viable, free, introductory Numerical Analysis textbook for instructors and students of mathematics. The ultimate goal of Tea Time Numerical Analysis is to be a complete, one-semester, single-pdf, downloadable textbook designed for mathematics classes. Now includes differential equations. Over 350 pages Over 1000 lines of code Over 200 figures Open source
- Subjects:
- Mathematics and Statistics
- Keywords:
- Textbooks Numerical analysis -- Data processing
- Resource Type:
- e-book
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e-book
Data structures and algorithms are among the most important inventions of the last 50 years, and they are fundamental tools software engineers need to know. But in my opinion, most of the books on these topics are too theoretical, too big, and too bottom-up: Too theoretical: Mathematical analysis of algorithms is based on simplifying assumptions that limit its usefulness in practice. Many presentations of this topic gloss over the simplifications and focus on the math. In this book I present the most practical subset of this material and eliminate the rest. Too big: Most books on these topics are at least 500 pages, and some are more than 1000. By focusing on the topics I think are most useful for software engineers, I kept this book under 250 pages. Too bottom-up: Many data structures books focus on how data structures work (the implementations), with less about how to use them (the interfaces). In this book, I go “top down”, starting with the interfaces. Readers learn to use the structures in the Java Collections Framework before getting into the details of how they work. Finally, many present this material out of context and without motivation: it’s just one damn data structure after another! I try to alleviate the boredom by organizing the topics around an application—web search—that uses data structures extensively, and is an interesting and important topic in its own right. This application also motivates some topics that are not usually covered in an introductory data structures class, including persistent data structures, with Redis, and streaming algorithms. This book also presents basic aspects of software engineering practice, including version control and unit testing. Each chapter ends with an exercise that allows readers to apply what they have learned. Each exercise includes automated tests that check the solution. And for most exercises, I present my solution at the beginning of the next chapter. This book is intended for college students in computer science and related fields, as well as professional software engineers, people training in software engineering, and people preparing for technical interviews. I assume that the reader knows Java at an intermediate level, but I explain some Java features along the way, and provide pointers to supplementary material. People who have read Think Java or Head First Java are prepared for this book.
- Subjects:
- Computing, Data Science and Artificial Intelligence
- Keywords:
- Java (Computer program language) Textbooks Data structures (Computer science)
- Resource Type:
- e-book
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e-book
Most computer users have an incorrect, but useful, cognitive metaphor for computers in which the user says (or types or clicks) something and a mystical, almost intelligent or magical, behavior happens. It is not a stretch to describe computer users as believing computers follow the laws of magic, where some magic incantation is entered, and the computer responds with an expected, but magical, behavior. This magic computer does not actually exist. In reality computer are machines, and every action a computer performs reduces to a set of mechanical operations. In fact the first complete definition of a working computer was a mechanical machine designed by Charles Babbage in 1834, and would have run on steam power. Probably the biggest success of Computer Science (CS) in the 20th century was the development of abstractions that hide the mechanical nature of computers. The fact that average people use computers without ever considering that they are mechanistic is a triumph of CS designers. This purpose of this monograph is to break the abstract understanding of a computer, and to explain a computer's behavior in completely in mechanistic terms. It will deal specifically with the Central Processing Unit (CPU) of the computer, as this is where the magic happens. All other parts of a computer can be seen as just providing information for the CPU to operate on. This monograph will deal with a specific type of CPU, a one-address CPU, and will explain this CPU using only standard gates, specifically AND, OR, NOT, NAND and XOR gates, and 4 basic Integrated Circuits (ICs), the Decoder, Multiplexer, Adder, and Flip Flop. All of these gates and components can be described as mechanical transformations of input data to output data, and the overall CPU can then be seen as a mechanical device.
- Subjects:
- Computing, Data Science and Artificial Intelligence
- Keywords:
- Textbooks Computer science
- Resource Type:
- e-book