Real Math
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| Author | : Daniel Rosenthal |
| Publisher | : Springer |
| Total Pages | : 171 |
| Release | : 2014-07-03 |
| Genre | : Mathematics |
| ISBN | : 3319056549 |
Designed for an undergraduate course or for independent study, this text presents sophisticated mathematical ideas in an elementary and friendly fashion. The fundamental purpose of this book is to engage the reader and to teach a real understanding of mathematical thinking while conveying the beauty and elegance of mathematics. The text focuses on teaching the understanding of mathematical proofs. The material covered has applications both to mathematics and to other subjects. The book contains a large number of exercises of varying difficulty, designed to help reinforce basic concepts and to motivate and challenge the reader. The sole prerequisite for understanding the text is basic high school algebra; some trigonometry is needed for Chapters 9 and 12. Topics covered include: mathematical induction - modular arithmetic - the fundamental theorem of arithmetic - Fermat's little theorem - RSA encryption - the Euclidean algorithm -rational and irrational numbers - complex numbers - cardinality - Euclidean plane geometry - constructability (including a proof that an angle of 60 degrees cannot be trisected with a straightedge and compass). This textbook is suitable for a wide variety of courses and for a broad range of students in the fields of education, liberal arts, physical sciences and mathematics. Students at the senior high school level who like mathematics will also be able to further their understanding of mathematical thinking by reading this book.
| Author | : Charles Chapman Pugh |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 445 |
| Release | : 2013-03-19 |
| Genre | : Mathematics |
| ISBN | : 0387216847 |
Was plane geometry your favourite math course in high school? Did you like proving theorems? Are you sick of memorising integrals? If so, real analysis could be your cup of tea. In contrast to calculus and elementary algebra, it involves neither formula manipulation nor applications to other fields of science. None. It is Pure Mathematics, and it is sure to appeal to the budding pure mathematician. In this new introduction to undergraduate real analysis the author takes a different approach from past studies of the subject, by stressing the importance of pictures in mathematics and hard problems. The exposition is informal and relaxed, with many helpful asides, examples and occasional comments from mathematicians like Dieudonne, Littlewood and Osserman. The author has taught the subject many times over the last 35 years at Berkeley and this book is based on the honours version of this course. The book contains an excellent selection of more than 500 exercises.
| Author | : Zvi Artstein |
| Publisher | : Prometheus Books |
| Total Pages | : 428 |
| Release | : 2014-09-02 |
| Genre | : Mathematics |
| ISBN | : 1616145463 |
In this accessible and illuminating study of how the science of mathematics developed, a veteran math researcher and educator looks at the ways in which our evolutionary makeup is both a help and a hindrance to the study of math. Artstein chronicles the discovery of important mathematical connections between mathematics and the real world from ancient times to the present. The author then describes some of the contemporary applications of mathematics—in probability theory, in the study of human behavior, and in combination with computers, which give mathematics unprecedented power. The author concludes with an insightful discussion of why mathematics, for most people, is so frustrating. He argues that the rigorous logical structure of math goes against the grain of our predisposed ways of thinking as shaped by evolution, presumably because the talent needed to cope with logical mathematics gave the human race as a whole no evolutionary advantage. With this in mind, he offers ways to overcome these innate impediments in the teaching of math.
| Author | : Francis Su |
| Publisher | : Yale University Press |
| Total Pages | : 287 |
| Release | : 2020-01-07 |
| Genre | : Mathematics |
| ISBN | : 0300237138 |
"The ancient Greeks argued that the best life was filled with beauty, truth, justice, play and love. The mathematician Francis Su knows just where to find them."--Kevin Hartnett, Quanta Magazine" This is perhaps the most important mathematics book of our time. Francis Su shows mathematics is an experience of the mind and, most important, of the heart."--James Tanton, Global Math Project For mathematician Francis Su, a society without mathematical affection is like a city without concerts, parks, or museums. To miss out on mathematics is to live without experiencing some of humanity's most beautiful ideas. In this profound book, written for a wide audience but especially for those disenchanted by their past experiences, an award-winning mathematician and educator weaves parables, puzzles, and personal reflections to show how mathematics meets basic human desires--such as for play, beauty, freedom, justice, and love--and cultivates virtues essential for human flourishing. These desires and virtues, and the stories told here, reveal how mathematics is intimately tied to being human. Some lessons emerge from those who have struggled, including philosopher Simone Weil, whose own mathematical contributions were overshadowed by her brother's, and Christopher Jackson, who discovered mathematics as an inmate in a federal prison. Christopher's letters to the author appear throughout the book and show how this intellectual pursuit can--and must--be open to all.
| Author | : Genene Rhodes |
| Publisher | : Teacher Created Resources |
| Total Pages | : 114 |
| Release | : 2002-09 |
| Genre | : Education |
| ISBN | : 0743932676 |
Guided practice and activity pages help students formulate complete answers to real-life problems involving logical reasoning, pre-algebra, decimals, percentages, basic geometry, graphs, and statistics.
| Author | : Christopher Monahan |
| Publisher | : Simon and Schuster |
| Total Pages | : 364 |
| Release | : 2013-11-08 |
| Genre | : Mathematics |
| ISBN | : 1440566445 |
All the math basics you'll ever need! It's not too late to learn practical math skills! You may not need to use quadratic equations very often, but math does play a large part in everyday life. On any given day, you'll need to know how long a drive will take, what to tip a waiter, how large a rug to buy, and how to calculate a discount. With The Everything Everyday Math Book, you'll get a refresher course in all the basics you need, including: Adding and subtracting fractions Understanding percentages Using ratios Finding area and perimeter You'll the learn formulas and shortcuts to help in hundreds of everyday situations, from budgeting and paying bills to shopping, redecorating, preparing taxes, and evaluating loans and other financial instruments. With this easy-to-follow guide, you'll never get stuck on a math problem again!
| Author | : Matt Parker |
| Publisher | : Penguin |
| Total Pages | : 337 |
| Release | : 2021-01-19 |
| Genre | : Mathematics |
| ISBN | : 0593084691 |
#1 INTERNATIONAL BESTSELLER AN ADAM SAVAGE BOOK CLUB PICK The book-length answer to anyone who ever put their hand up in math class and asked, “When am I ever going to use this in the real world?” “Fun, informative, and relentlessly entertaining, Humble Pi is a charming and very readable guide to some of humanity's all-time greatest miscalculations—that also gives you permission to feel a little better about some of your own mistakes.” —Ryan North, author of How to Invent Everything Our whole world is built on math, from the code running a website to the equations enabling the design of skyscrapers and bridges. Most of the time this math works quietly behind the scenes . . . until it doesn’t. All sorts of seemingly innocuous mathematical mistakes can have significant consequences. Math is easy to ignore until a misplaced decimal point upends the stock market, a unit conversion error causes a plane to crash, or someone divides by zero and stalls a battleship in the middle of the ocean. Exploring and explaining a litany of glitches, near misses, and mathematical mishaps involving the internet, big data, elections, street signs, lotteries, the Roman Empire, and an Olympic team, Matt Parker uncovers the bizarre ways math trips us up, and what this reveals about its essential place in our world. Getting it wrong has never been more fun.
| Author | : Jim Libby |
| Publisher | : McFarland |
| Total Pages | : 213 |
| Release | : 2017-01-19 |
| Genre | : Education |
| ISBN | : 1476667497 |
"Where are we ever going to use this?" Every high school math student has asked this question. Often teachers themselves aren't sure how to respond. One answer is that higher mathematics learned in high school will be essential to learning yet more at the college level. A more satisfactory answer calls for an awareness of how math is applied in many specific areas. Written primarily for teachers, this book presents hundreds of practical applications for mathematics--from baseball statistics to the theory of relativity--that can be understood by anyone with a knowledge of high school algebra, geometry and trigonometry.
| Author | : David Corfield |
| Publisher | : Cambridge University Press |
| Total Pages | : 300 |
| Release | : 2003-04-24 |
| Genre | : Philosophy |
| ISBN | : 1139436392 |
In this ambitious study, David Corfield attacks the widely held view that it is the nature of mathematical knowledge which has shaped the way in which mathematics is treated philosophically and claims that contingent factors have brought us to the present thematically limited discipline. Illustrating his discussion with a wealth of examples, he sets out a variety of approaches to new thinking about the philosophy of mathematics, ranging from an exploration of whether computers producing mathematical proofs or conjectures are doing real mathematics, to the use of analogy, the prospects for a Bayesian confirmation theory, the notion of a mathematical research programme and the ways in which new concepts are justified. His inspiring book challenges both philosophers and mathematicians to develop the broadest and richest philosophical resources for work in their disciplines and points clearly to the ways in which this can be done.
| Author | : Apoorva Khare |
| Publisher | : Yale University Press |
| Total Pages | : 480 |
| Release | : 2015-08-25 |
| Genre | : Mathematics |
| ISBN | : 0300190891 |
In this vibrant work, which is ideal for both teaching and learning, Apoorva Khare and Anna Lachowska explain the mathematics essential for understanding and appreciating our quantitative world. They show with examples that mathematics is a key tool in the creation and appreciation of art, music, and literature, not just science and technology. The book covers basic mathematical topics from logarithms to statistics, but the authors eschew mundane finance and probability problems. Instead, they explain how modular arithmetic helps keep our online transactions safe, how logarithms justify the twelve-tone scale commonly used in music, and how transmissions by deep space probes are similar to knights serving as messengers for their traveling prince. Ideal for coursework in introductory mathematics and requiring no knowledge of calculus, Khare and Lachowska's enlightening mathematics tour will appeal to a wide audience.
