Complex Numbers and Geometry

DOWNLOAD NOW »

Author: Liang-shin Hahn

Publisher: Cambridge University Press

ISBN: 9780883855102

Category: Mathematics

Page: 192

View: 4129

The purpose of this book is to demonstrate that complex numbers and geometry can be blended together beautifully. This results in easy proofs and natural generalizations of many theorems in plane geometry, such as the Napoleon theorem, the Ptolemy-Euler theorem, the Simson theorem, and the Morley theorem. The book is self-contained - no background in complex numbers is assumed - and can be covered at a leisurely pace in a one-semester course. Many of the chapters can be read independently. Over 100 exercises are included. The book would be suitable as a text for a geometry course, or for a problem solving seminar, or as enrichment for the student who wants to know more.

Geometry of Complex Numbers

DOWNLOAD NOW »

Author: Hans Schwerdtfeger

Publisher: Courier Corporation

ISBN: 0486135861

Category: Mathematics

Page: 224

View: 2838

Illuminating, widely praised book on analytic geometry of circles, the Moebius transformation, and 2-dimensional non-Euclidean geometries.

Complex Numbers from A to ... Z

DOWNLOAD NOW »

Author: Titu Andreescu,Dorin Andrica

Publisher: Springer Science & Business Media

ISBN: 0817684158

Category: Mathematics

Page: 391

View: 9623

* Learn how complex numbers may be used to solve algebraic equations, as well as their geometric interpretation * Theoretical aspects are augmented with rich exercises and problems at various levels of difficulty * A special feature is a selection of outstanding Olympiad problems solved by employing the methods presented * May serve as an engaging supplemental text for an introductory undergrad course on complex numbers or number theory

Differential Geometry and Its Applications

DOWNLOAD NOW »

Author: John Oprea

Publisher: MAA

ISBN: 9780883857489

Category: Mathematics

Page: 469

View: 2158

Differential geometry has a long, wonderful history it has found relevance in areas ranging from machinery design of the classification of four-manifolds to the creation of theories of nature's fundamental forces to the study of DNA. This book studies the differential geometry of surfaces with the goal of helping students make the transition from the compartmentalized courses in a standard university curriculum to a type of mathematics that is a unified whole, it mixes geometry, calculus, linear algebra, differential equations, complex variables, the calculus of variations, and notions from the sciences. Differential geometry is not just for mathematics majors, it is also for students in engineering and the sciences. Into the mix of these ideas comes the opportunity to visualize concepts through the use of computer algebra systems such as Maple. The book emphasizes that this visualization goes hand-in-hand with the understanding of the mathematics behind the computer construction. Students will not only “see” geodesics on surfaces, but they will also see the effect that an abstract result such as the Clairaut relation can have on geodesics. Furthermore, the book shows how the equations of motion of particles constrained to surfaces are actually types of geodesics. Students will also see how particles move under constraints. The book is rich in results and exercises that form a continuous spectrum, from those that depend on calculation to proofs that are quite abstract.

Euclidean Geometry in Mathematical Olympiads

DOWNLOAD NOW »

Author: Evan Chen

Publisher: The Mathematical Association of America

ISBN: 0883858398

Category: Mathematics

Page: 311

View: 4494

This is a challenging problem-solving book in Euclidean geometry, assuming nothing of the reader other than a good deal of courage. Topics covered included cyclic quadrilaterals, power of a point, homothety, triangle centers; along the way the reader will meet such classical gems as the nine-point circle, the Simson line, the symmedian and the mixtilinear incircle, as well as the theorems of Euler, Ceva, Menelaus, and Pascal. Another part is dedicated to the use of complex numbers and barycentric coordinates, granting the reader both a traditional and computational viewpoint of the material. The final part consists of some more advanced topics, such as inversion in the plane, the cross ratio and projective transformations, and the theory of the complete quadrilateral. The exposition is friendly and relaxed, and accompanied by over 300 beautifully drawn figures. The emphasis of this book is placed squarely on the problems. Each chapter contains carefully chosen worked examples, which explain not only the solutions to the problems but also describe in close detail how one would invent the solution to begin with. The text contains as selection of 300 practice problems of varying difficulty from contests around the world, with extensive hints and selected solutions. This book is especially suitable for students preparing for national or international mathematical olympiads, or for teachers looking for a text for an honor class.

Introduction to the Geometry of Complex Numbers

DOWNLOAD NOW »

Author: Roland Deaux

Publisher: Courier Corporation

ISBN: 0486158047

Category: Mathematics

Page: 208

View: 2456

Geared toward readers unfamiliar with complex numbers, this text explains how to solve problems that frequently arise in the applied sciences and emphasizes constructions related to algebraic operations. 1956 edition.

Number Theory Through Inquiry

DOWNLOAD NOW »

Author: David C. Marshall,Edward Odell,Michael Starbird

Publisher: MAA

ISBN: 0883857510

Category: Mathematics

Page: 140

View: 1191

This innovative textbook leads students on a carefully guided discovery of introductory number theory. The book has two equally significant goals. The first is to help students develop mathematical thinking skills, particularly theorem-proving skills. The other goal is to help students understand some of the wonderfully rich ideas in the mathematical study of numbers. This book is appropriate for a proof transitions course, for independent study, or for a course designed as an introduction to abstract mathematics. It is designed to be used with an instructional technique variously called guided discovery or Modified Moore Method or Inquiry Based Learning (IBL). Instructors' materials explain the instructional method, which gives students a totally different experience compared to a standard lecture course. Students develop an attitude of personal reliance and a sense that they can think effectively about difficult problems; goals that are fundamental to the educational enterprise within and beyond mathematics.

An Episodic History of Mathematics

Mathematical Culture Through Problem Solving

DOWNLOAD NOW »

Author: Steven G. Krantz

Publisher: MAA

ISBN: 0883857669

Category: Mathematics

Page: 381

View: 3129

An Episodic History of Mathematics will acquaint students and readers with mathematical language, thought, and mathematical life by means of historically important mathematical vignettes. It will also serve to help prospective teachers become more familiar with important ideas of in the history of mathematicsboth classical and modern.Contained within are wonderful and engaging stories and anecdotes about Pythagoras and Galois and Cantor and Poincar, which let readers indulge themselves in whimsy, gossip, and learning. The mathematicians treated here were complex individuals who led colorful and fascinating lives, and did fascinating mathematics. They remain interesting to us as people and as scientists.This history of mathematics is also an opportunity to have some fun because the focus in this text is also on the practicalgetting involved with the mathematics and solving problems. This book is unabashedly mathematical. In the course of reading this book, the neophyte will become involved with mathematics by working on the same problems that, for instance, Zeno and Pythagoras and Descartes and Fermat and Riemann worked on.This is a book to be read, therefore, with pencil and paper in hand, and a calculator or computer close by. All will want to experiment; to try things; and become a part of the mathematical process.

Knots and Surfaces

A Guide to Discovering Mathematics

DOWNLOAD NOW »

Author: David W. Farmer,Theodore B. Stanford

Publisher: American Mathematical Soc.

ISBN: 0821804510

Category: Mathematics

Page: 101

View: 2001

In most mathematics textbooks, the most exciting part of mathematics - the process of invention and discovery - is completely hidden from the reader. The aim of ""Knots and Surfaces"" is to change all that. By means of a series of carefully selected tasks, this book leads readers to discover some real mathematics. There are no formulas to memorize; no procedures to follow. The book is a guide: its job is to start you in the right direction and to bring you back if you stray too far. Discovery is left to you. Suitable for a one-semester course at the beginning undergraduate level, there are no prerequisites for understanding the text. Any college student interested in discovering the beauty of mathematics will enjoy a course taught from this book. The book has also been used successfully with non science students who want to fulfill a science requirement. Also available from the AMS by David W. Farmer is ""Groups and Symmetry: A Guide to Discovering Mathematics"".

Algebraic Geometry over the Complex Numbers

DOWNLOAD NOW »

Author: Donu Arapura

Publisher: Springer Science & Business Media

ISBN: 1461418097

Category: Mathematics

Page: 329

View: 8880

This is a relatively fast paced graduate level introduction to complex algebraic geometry, from the basics to the frontier of the subject. It covers sheaf theory, cohomology, some Hodge theory, as well as some of the more algebraic aspects of algebraic geometry. The author frequently refers the reader if the treatment of a certain topic is readily available elsewhere but goes into considerable detail on topics for which his treatment puts a twist or a more transparent viewpoint. His cases of exploration and are chosen very carefully and deliberately. The textbook achieves its purpose of taking new students of complex algebraic geometry through this a deep yet broad introduction to a vast subject, eventually bringing them to the forefront of the topic via a non-intimidating style.

Visual Complex Analysis

DOWNLOAD NOW »

Author: Tristan Needham

Publisher: Oxford University Press

ISBN: 9780198534464

Category: Mathematics

Page: 592

View: 9115

Now available in paperback, this successful radical approach to complex analysis replaces the standard calculational arguments with new geometric ones. With several hundred diagrams, and far fewer prerequisites than usual, this is the first visual intuitive introduction to complex analysis. Although designed for use by undergraduates in mathematics and science, the novelty of the approach will also interest professional mathematicians.

Applications of Algebra and Geometry to the Work of Teaching

DOWNLOAD NOW »

Author: Bowen Kerins,Benjamin Sinwell, Darryl Yong,Al Cuoco,Glenn Stevens

Publisher: American Mathematical Soc.

ISBN: 1470419246

Category: Algebra

Page: 187

View: 345

Designed for precollege teachers by a collaborative of teachers, educators, and mathematicians, Applications of Algebra and Geometry to the Work of Teaching is based on a course offered in the Summer School Teacher Program at the Park City Mathematics Institute. But this book isn't a "course" in the traditional sense. It consists of a carefully sequenced collection of problem sets designed to develop several interconnected mathematical themes, and one of the goals of the problem sets is for readers to uncover these themes for themselves. The specific theme developed in Applications of Algebra and Geometry to the Work of Teaching is the use of complex numbers--especially the arithmetic of Gaussian and Eisenstein integers--to investigate some questions that are at the intersection of algebra and geometry, like the classification of Pythagorean triples and the number of representations of an integer as the sum of two squares. Applications of Algebra and Geometry to the Work of Teaching is a volume of the book series "IAS/PCMI-The Teacher Program Series" published by the American Mathematical Society. Each volume in that series covers the content of one Summer School Teacher Program year and is independent of the rest. Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.

Methods for Euclidean Geometry

DOWNLOAD NOW »

Author: Owen Byer,Felix Lazebnik,Deirdre L. Smeltzer

Publisher: MAA

ISBN: 0883857634

Category: Mathematics

Page: 461

View: 7986

Methods for Euclidean Geometry explores one of the oldest and most beautiful of mathematical subjects. The book begins with a thorough presentation of classical solution methods for plane geometry problems, but its distinguishing feature is the subsequent collection of methods which have appeared since 1600. For example, the coordinate method, which is a central part of the book, has been part of mathematics for four centuries. However, it has rarely served as a tool that students consider using when faced with geometry problems. The same holds true regarding the use of trigonometry, vectors, complex numbers, and transformations. The book presents each of these as self-contained topics, providing examples of their applications to geometry problems. Both strengths and weaknesses of various methods, as well as the ranges of their effective applications, are discussed. Importance is placed on the problems and their solutions. The book contains numerous problems of varying difficulty; over a third of its contents are devoted to problem statements, hints, and complete solutions. The book can be used as a textbook for geometry courses; as a source book for geometry and other mathematics courses; for capstone, problem-solving, and enrichment courses; and for independent study courses.

A Course in Mathematical Modeling

DOWNLOAD NOW »

Author: Douglas D. Mooney,Randall J. Swift

Publisher: Cambridge University Press

ISBN: 9780883857120

Category: Mathematics

Page: 431

View: 2345

This book teaches elementary mathematical modeling.

Euler

The Master of Us All

DOWNLOAD NOW »

Author: William Dunham

Publisher: MAA

ISBN: 9780883853283

Category: Mathematics

Page: 185

View: 5166

Leonhard Euler was one of the most prolific mathematicians that have ever lived. This book examines the huge scope of mathematical areas explored and developed by Euler, which includes number theory, combinatorics, geometry, complex variables and many more. The information known to Euler over 300 years ago is discussed, and many of his advances are reconstructed. Readers will be left in no doubt about the brilliance and pervasive influence of Euler's work.

Which Numbers Are Real?

DOWNLOAD NOW »

Author: Michael Henle

Publisher: MAA

ISBN: 0883857774

Category: Mathematics

Page: 219

View: 5058

Everyone knows the real numbers, those fundamental quantities that make possible all of mathematics from high school algebra and Euclidean geometry through the Calculus and beyond; and also serve as the basis for measurement in science, industry, and ordinary life. This book surveys alternative real number systems: systems that generalize and extend the real numbers yet stay close to these properties that make the reals central to mathematics.Alternative real numbers include many different kinds of numbers, for example multidimensional numbers (the complex numbers, the quaternions and others), infinitely small and infinitely large numbers (the hyperreal numbers and the surreal numbers), and numbers that represent positions in games (the surreal numbers). Each system has a well-developed theory, including applications to other areas of mathematics and science, such as physics, the theory of games, multi-dimensional geometry, and formal logic. They are all active areas of current mathematical research and each has unique features, in particular, characteristic methods of proof and implications for the philosophy of mathematics, both highlighted in this book.Alternative real number systems illuminate the central, unifying role of the real numbers and include some exciting and eccentric parts of mathematics. Which Numbers Are Real? Will be of interest to anyone with an interest in numbers, but specifically to upper-level undergraduates, graduate students, and professional mathematicians, particularly college mathematics teachers.

An Introduction to Complex Analysis and Geometry

DOWNLOAD NOW »

Author: John P. D'Angelo

Publisher: American Mathematical Soc.

ISBN: 0821852744

Category: Mathematics

Page: 163

View: 4881

An Introduction to Complex Analysis and Geometry provides the reader with a deep appreciation of complex analysis and how this subject fits into mathematics. The book developed from courses given in the Campus Honors Program at the University of Illinois Urbana-Champaign. These courses aimed to share with students the way many mathematics and physics problems magically simplify when viewed from the perspective of complex analysis. The book begins at an elementary level but also contains advanced material. The first four chapters provide an introduction to complex analysis with many elementary and unusual applications. Chapters 5 through 7 develop the Cauchy theory and include some striking applications to calculus. Chapter 8 glimpses several appealing topics, simultaneously unifying the book and opening the door to further study. The 280 exercises range from simple computations to difficult problems. Their variety makes the book especially attractive. A reader of the first four chapters will be able to apply complex numbers in many elementary contexts. A reader of the full book will know basic one complex variable theory and will have seen it integrated into mathematics as a whole. Research mathematicians will discover several novel perspectives.

Who Gave You the Epsilon?

And Other Tales of Mathematical History

DOWNLOAD NOW »

Author: Marlow Anderson,Victor Katz,Robin Wilson

Publisher: MAA

ISBN: 9780883855690

Category: Mathematics

Page: 431

View: 1072

Follows on from Sherlock Holmes in Babylon to take the history of mathematics through the nineteenth and twentieth centuries.

Mathematics and Its History

DOWNLOAD NOW »

Author: John Stillwell

Publisher: Springer Science & Business Media

ISBN: 144196052X

Category: Mathematics

Page: 662

View: 1611

From a review of the second edition: "This book covers many interesting topics not usually covered in a present day undergraduate course, as well as certain basic topics such as the development of the calculus and the solution of polynomial equations. The fact that the topics are introduced in their historical contexts will enable students to better appreciate and understand the mathematical ideas involved...If one constructs a list of topics central to a history course, then they would closely resemble those chosen here." (David Parrott, Australian Mathematical Society) This book offers a collection of historical essays detailing a large variety of mathematical disciplines and issues; it’s accessible to a broad audience. This third edition includes new chapters on simple groups and new sections on alternating groups and the Poincare conjecture. Many more exercises have been added as well as commentary that helps place the exercises in context.