Number and Its Algebra
Author: Arthur Lefevre
Publisher:
Published: 1903
Total Pages: 244
ISBN-13:
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College Algebra
Author: Jay Abramson
Publisher:
Published: 2018-01-07
Total Pages: 892
ISBN-13: 9789888407439
DOWNLOAD EBOOKCollege Algebra provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra course. The modular approach and richness of content ensure that the book meets the needs of a variety of courses. College Algebra offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they've learned. Coverage and Scope In determining the concepts, skills, and topics to cover, we engaged dozens of highly experienced instructors with a range of student audiences. The resulting scope and sequence proceeds logically while allowing for a significant amount of flexibility in instruction. Chapters 1 and 2 provide both a review and foundation for study of Functions that begins in Chapter 3. The authors recognize that while some institutions may find this material a prerequisite, other institutions have told us that they have a cohort that need the prerequisite skills built into the course. Chapter 1: Prerequisites Chapter 2: Equations and Inequalities Chapters 3-6: The Algebraic Functions Chapter 3: Functions Chapter 4: Linear Functions Chapter 5: Polynomial and Rational Functions Chapter 6: Exponential and Logarithm Functions Chapters 7-9: Further Study in College Algebra Chapter 7: Systems of Equations and Inequalities Chapter 8: Analytic Geometry Chapter 9: Sequences, Probability and Counting Theory
Visual Complex Analysis
Author: Tristan Needham
Publisher: Oxford University Press
Published: 1997
Total Pages: 620
ISBN-13: 9780198534464
DOWNLOAD EBOOKThis radical first course on complex analysis brings a beautiful and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. Aimed at undergraduate students in mathematics, physics, and engineering, the book's intuitive explanations, lack of advanced prerequisites, and consciously user-friendly prose style will help students to master the subject more readily than was previously possible. The key to this is the book's use of new geometric arguments in place of the standard calculational ones. These geometric arguments are communicated with the aid of hundreds of diagrams of a standard seldom encountered in mathematical works. A new approach to a classical topic, this work will be of interest to students in mathematics, physics, and engineering, as well as to professionals in these fields.
Number Systems
Author: Sergei Ovchinnikov
Publisher: American Mathematical Soc.
Published: 2015-02-26
Total Pages: 154
ISBN-13: 147042018X
DOWNLOAD EBOOKThis book offers a rigorous and coherent introduction to the five basic number systems of mathematics, namely natural numbers, integers, rational numbers, real numbers, and complex numbers. It is a subject that many mathematicians believe should be learned by any student of mathematics including future teachers. The book starts with the development of Peano arithmetic in the first chapter which includes mathematical induction and elements of recursion theory. It proceeds to an examination of integers that also covers rings and ordered integral domains. The presentation of rational numbers includes material on ordered fields and convergence of sequences in these fields. Cauchy and Dedekind completeness properties of the field of real numbers are established, together with some properties of real continuous functions. An elementary proof of the Fundamental Theorem of Algebra is the highest point of the chapter on complex numbers. The great merit of the book lies in its extensive list of exercises following each chapter. These exercises are designed to assist the instructor and to enhance the learning experience of the students.
Lectures on the Theory of Algebraic Numbers
Author: E. T. Hecke
Publisher: Springer Science & Business Media
Published: 2013-03-09
Total Pages: 251
ISBN-13: 1475740921
DOWNLOAD EBOOK. . . if one wants to make progress in mathematics one should study the masters not the pupils. N. H. Abel Heeke was certainly one of the masters, and in fact, the study of Heeke L series and Heeke operators has permanently embedded his name in the fabric of number theory. It is a rare occurrence when a master writes a basic book, and Heeke's Lectures on the Theory of Algebraic Numbers has become a classic. To quote another master, Andre Weil: "To improve upon Heeke, in a treatment along classical lines of the theory of algebraic numbers, would be a futile and impossible task. " We have tried to remain as close as possible to the original text in pre serving Heeke's rich, informal style of exposition. In a very few instances we have substituted modern terminology for Heeke's, e. g. , "torsion free group" for "pure group. " One problem for a student is the lack of exercises in the book. However, given the large number of texts available in algebraic number theory, this is not a serious drawback. In particular we recommend Number Fields by D. A. Marcus (Springer-Verlag) as a particularly rich source. We would like to thank James M. Vaughn Jr. and the Vaughn Foundation Fund for their encouragement and generous support of Jay R. Goldman without which this translation would never have appeared. Minneapolis George U. Brauer July 1981 Jay R.
The Theory of Algebraic Number Fields
Author: David Hilbert
Publisher: Springer Science & Business Media
Published: 2013-03-14
Total Pages: 360
ISBN-13: 3662035456
DOWNLOAD EBOOKA translation of Hilberts "Theorie der algebraischen Zahlkörper" best known as the "Zahlbericht", first published in 1897, in which he provides an elegantly integrated overview of the development of algebraic number theory up to the end of the nineteenth century. The Zahlbericht also provided a firm foundation for further research in the theory, and can be seen as the starting point for all twentieth century investigations into the subject, as well as reciprocity laws and class field theory. This English edition further contains an introduction by F. Lemmermeyer and N. Schappacher.
Algebraic Number Theory
Author: Edwin Weiss
Publisher: Courier Corporation
Published: 2012-01-27
Total Pages: 308
ISBN-13: 048615436X
DOWNLOAD EBOOKIdeal either for classroom use or as exercises for mathematically minded individuals, this text introduces elementary valuation theory, extension of valuations, local and ordinary arithmetic fields, and global, quadratic, and cyclotomic fields.
Intermediate Algebra 2e
Author: Lynn Marecek
Publisher:
Published: 2020-05-06
Total Pages:
ISBN-13: 9781951693848
DOWNLOAD EBOOKAn Imaginary Tale
Author: Paul Nahin
Publisher: Princeton University Press
Published: 2010-02-22
Total Pages: 297
ISBN-13: 1400833892
DOWNLOAD EBOOKToday complex numbers have such widespread practical use--from electrical engineering to aeronautics--that few people would expect the story behind their derivation to be filled with adventure and enigma. In An Imaginary Tale, Paul Nahin tells the 2000-year-old history of one of mathematics' most elusive numbers, the square root of minus one, also known as i. He recreates the baffling mathematical problems that conjured it up, and the colorful characters who tried to solve them. In 1878, when two brothers stole a mathematical papyrus from the ancient Egyptian burial site in the Valley of Kings, they led scholars to the earliest known occurrence of the square root of a negative number. The papyrus offered a specific numerical example of how to calculate the volume of a truncated square pyramid, which implied the need for i. In the first century, the mathematician-engineer Heron of Alexandria encountered I in a separate project, but fudged the arithmetic; medieval mathematicians stumbled upon the concept while grappling with the meaning of negative numbers, but dismissed their square roots as nonsense. By the time of Descartes, a theoretical use for these elusive square roots--now called "imaginary numbers"--was suspected, but efforts to solve them led to intense, bitter debates. The notorious i finally won acceptance and was put to use in complex analysis and theoretical physics in Napoleonic times. Addressing readers with both a general and scholarly interest in mathematics, Nahin weaves into this narrative entertaining historical facts and mathematical discussions, including the application of complex numbers and functions to important problems, such as Kepler's laws of planetary motion and ac electrical circuits. This book can be read as an engaging history, almost a biography, of one of the most evasive and pervasive "numbers" in all of mathematics. Some images inside the book are unavailable due to digital copyright restrictions.
Quaternions and Cayley Numbers
Author: J.P. Ward
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 252
ISBN-13: 9401157685
DOWNLOAD EBOOKIn essence, this text is written as a challenge to others, to discover significant uses for Cayley number algebra in physics. I freely admit that though the reading of some sections would benefit from previous experience of certain topics in physics - particularly relativity and electromagnetism - generally the mathematics is not sophisticated. In fact, the mathematically sophisticated reader, may well find that in many places, the rather deliberate progress too slow for their liking. This text had its origin in a 90-minute lecture on complex numbers given by the author to prospective university students in 1994. In my attempt to develop a novel approach to the subject matter I looked at complex numbers from an entirely geometric perspective and, no doubt in line with innumerable other mathematicians, re-traced steps first taken by Hamilton and others in the early years of the nineteenth century. I even enquired into the possibility of using an alternative multiplication rule for complex numbers (in which argzlz2 = argzl- argz2) other than the one which is normally accepted (argzlz2 = argzl + argz2). Of course, my alternative was rejected because it didn't lead to a 'product' which had properties that we now accept as fundamental (i. e.
