Discovering Higher Mathematics PDF Download
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| Author | : Alan Levine |
| Publisher | : Academic Press |
| Total Pages | : 196 |
| Release | : 1999-10-29 |
| Genre | : Mathematics |
| ISBN | : 9780124454606 |
Download Discovering Higher Mathematics Book in PDF, ePub and Kindle
Funded by a National Science Foundation grant, Discovering Higher Mathematics emphasizes four main themes that are essential components of higher mathematics: experimentation, conjecture, proof, and generalization. The text is intended for use in bridge or transition courses designed to prepare students for the abstraction of higher mathematics. Students in these courses have normally completed the calculus sequence and are planning to take advanced mathematics courses such as algebra, analysis and topology. The transition course is taken to prepare students for these courses by introducing them to the processes of conjecture and proof concepts which are typically not emphasized in calculus, but are critical components of advanced courses. * Constructed around four key themes: Experimentation, Conjecture, Proof, and Generalization * Guidelines for effective mathematical thinking, covering a variety of interrelated topics * Numerous problems and exercises designed to reinforce the key themes
| Author | : Oscar Fernandez |
| Publisher | : Princeton University Press |
| Total Pages | : 164 |
| Release | : 2014-04-14 |
| Genre | : Mathematics |
| ISBN | : 0691157553 |
Download Everyday Calculus Book in PDF, ePub and Kindle
A fun look at calculus in our everyday lives Calculus. For some of us, the word conjures up memories of ten-pound textbooks and visions of tedious abstract equations. And yet, in reality, calculus is fun, accessible, and surrounds us everywhere we go. In Everyday Calculus, Oscar Fernandez shows us how to see the math in our coffee, on the highway, and even in the night sky. Fernandez uses our everyday experiences to skillfully reveal the hidden calculus behind a typical day's events. He guides us through how math naturally emerges from simple observations—how hot coffee cools down, for example—and in discussions of over fifty familiar events and activities. Fernandez demonstrates that calculus can be used to explore practically any aspect of our lives, including the most effective number of hours to sleep and the fastest route to get to work. He also shows that calculus can be both useful—determining which seat at the theater leads to the best viewing experience, for instance—and fascinating—exploring topics such as time travel and the age of the universe. Throughout, Fernandez presents straightforward concepts, and no prior mathematical knowledge is required. For advanced math fans, the mathematical derivations are included in the appendixes. Whether you’re new to mathematics or already a curious math enthusiast, Everyday Calculus invites you to spend a day discovering the calculus all around you. The book will convince even die-hard skeptics to view this area of math in a whole new way.
| Author | : Tony Barnard |
| Publisher | : CRC Press |
| Total Pages | : 286 |
| Release | : 2016-12-19 |
| Genre | : Mathematics |
| ISBN | : 1315405768 |
Download Discovering Group Theory Book in PDF, ePub and Kindle
Discovering Group Theory: A Transition to Advanced Mathematics presents the usual material that is found in a first course on groups and then does a bit more. The book is intended for students who find the kind of reasoning in abstract mathematics courses unfamiliar and need extra support in this transition to advanced mathematics. The book gives a number of examples of groups and subgroups, including permutation groups, dihedral groups, and groups of integer residue classes. The book goes on to study cosets and finishes with the first isomorphism theorem. Very little is assumed as background knowledge on the part of the reader. Some facility in algebraic manipulation is required, and a working knowledge of some of the properties of integers, such as knowing how to factorize integers into prime factors. The book aims to help students with the transition from concrete to abstract mathematical thinking.
| Author | : Levine Alan |
| Publisher | : |
| Total Pages | : |
| Release | : |
| Genre | : |
| ISBN | : 9780124454613 |
Download Discovering Higher Mathematics: Four Habits Highly Effective Mathematics Book in PDF, ePub and Kindle
| Author | : Stephen Fletcher Hewson |
| Publisher | : World Scientific |
| Total Pages | : 562 |
| Release | : 2003 |
| Genre | : Mathematics |
| ISBN | : 9789812385550 |
Download A Mathematical Bridge Book in PDF, ePub and Kindle
This book is an alternative and highly engaging introduction to the highlights of a typical undergraduate mathematics course. Building on very simple principles, it develops these mathematical highlights, known to every well-rounded mathematician, in an intuitive and entertaining way. The aim of the book is to motivate and inspire the reader to discover and understand some of these truly amazing mathematical structures and ideas which are frequently not fully grasped, pass unnoticed or simply swamped in an undergraduate mathematics course. For the experienced mathematician the book offers refreshing, often enlightening, hindsight. For the novice it is an exciting intellectual journey.
| Author | : Brian Thomson |
| Publisher | : ClassicalRealAnalysis.com |
| Total Pages | : 267 |
| Release | : 2011-04-28 |
| Genre | : Mathematics |
| ISBN | : 1453892923 |
Download Mathematical Discovery Book in PDF, ePub and Kindle
This book is an outgrowth of classes given at the University of California, Santa Barbara, mainly for students who had little mathematical background. Many of the students indicated they never understood what mathematics was all about (beyond what they learned in algebra and geometry). Was there any more math-ematics to be discovered or created? How could one actually discover or create new mathematics? In order to give these students some sort of answers to such questions, we designed a course in which the students could actually participate in the discovery of mathematics.
| Author | : Sherman K. Stein |
| Publisher | : John Wiley & Sons |
| Total Pages | : 296 |
| Release | : 1996-09-06 |
| Genre | : Juvenile Nonfiction |
| ISBN | : |
Download Strength In Numbers Book in PDF, ePub and Kindle
Joy and power in math? Of course! As well as practicality, versatility, simplicity . . . and fun. Strength in Numbers offers a highly entertaining exploration of the math we use in our daily lives—from calculating mortgage payments, to choosing credit card rates, to deciphering statistics. As award-winning teacher and author Sherman Stein reveals, math is much more than "a collection of procedures to calculate numbers." It is an essential tool with which to understand the world around us. And while the relevance of math to everyday life is emphasized, the author's lively survey of such intriguing concepts as "hot" and "cool" numbers, as well as brainteasers like the puzzle of the Egyptian rope, make Strength in Numbers rich reading. Along the way, Stein exposes many myths—from the idea that there is nothing new in math to the notion that there may be a gene for mathematical talent. He praises the beauty of such mathematical wonders as the Golden Triangle, and reveals the fascinating ways in which math is used to solve problems in science, such as biologists' use of the slope of a curve to calculate species growth. With his engaging style, Stein offers a new appreciation for the amazing properties of mathematics, from the beauty of its logic ("as inevitable and memorable as a Mozart symphony") to its power and pervasiveness in our lives. Requiring no math knowledge beyond basic arithmetic and high school geometry, Strength in Numbers is an enlightening introduction to all the math we need. What is the spell of cool numbers? Was the golden ratio used to build the Great Pyramid of Khufu? What do two goats and a car have to do with making good decisions? In Strength in Numbers, award-winning teacher and author Sherman K. Stein offers an entertaining exploration of the surprising ways in which the language of mathematics can enhance our understanding of the world around us. "After finishing this book, you should have a clearer idea of the importance of mathematics in the 'real' world and the ability to read the language of mathematics. I hope, in addition, you will have gained an appreciation of the beauty of mathematics and the elegance of its reasoning."—from Chapter 1
| Author | : George R. Exner |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 212 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461239982 |
Download An Accompaniment to Higher Mathematics Book in PDF, ePub and Kindle
Designed for students preparing to engage in their first struggles to understand and write proofs and to read mathematics independently, this is well suited as a supplementary text in courses on introductory real analysis, advanced calculus, abstract algebra, or topology. The book teaches in detail how to construct examples and non-examples to help understand a new theorem or definition; it shows how to discover the outline of a proof in the form of the theorem and how logical structures determine the forms that proofs may take. Throughout, the text asks the reader to pause and work on an example or a problem before continuing, and encourages the student to engage the topic at hand and to learn from failed attempts at solving problems. The book may also be used as the main text for a "transitions" course bridging the gap between calculus and higher mathematics. The whole concludes with a set of "Laboratories" in which students can practice the skills learned in the earlier chapters on set theory and function theory.
| Author | : Tony Barnard |
| Publisher | : CRC Press |
| Total Pages | : 232 |
| Release | : 2016-12-19 |
| Genre | : Mathematics |
| ISBN | : 1315405776 |
Download Discovering Group Theory Book in PDF, ePub and Kindle
Discovering Group Theory: A Transition to Advanced Mathematics presents the usual material that is found in a first course on groups and then does a bit more. The book is intended for students who find the kind of reasoning in abstract mathematics courses unfamiliar and need extra support in this transition to advanced mathematics. The book gives a number of examples of groups and subgroups, including permutation groups, dihedral groups, and groups of integer residue classes. The book goes on to study cosets and finishes with the first isomorphism theorem. Very little is assumed as background knowledge on the part of the reader. Some facility in algebraic manipulation is required, and a working knowledge of some of the properties of integers, such as knowing how to factorize integers into prime factors. The book aims to help students with the transition from concrete to abstract mathematical thinking.
| Author | : A. D. Gardiner |
| Publisher | : Oxford University Press on Demand |
| Total Pages | : 226 |
| Release | : 1987 |
| Genre | : Education |
| ISBN | : 0198532652 |
Download Discovering Mathematics Book in PDF, ePub and Kindle
An examination of how one can begin to explore unfamiliar ideas and chance observations, how one can pursue them through various stages until the light begins to dawn, and how this process throws up other questions one might never have thought of.
