First Steps in Number Theory
Author: S. Shirali
Publisher: Universities Press
Published: 2001-07
Total Pages: 176
ISBN-13: 9788173713682
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First Steps for Math Olympians
Author: J. Douglas Faires
Publisher: MAA
Published: 2006-12-21
Total Pages: 344
ISBN-13: 9780883858240
DOWNLOAD EBOOKA major aspect of mathematical training and its benefit to society is the ability to use logic to solve problems. The American Mathematics Competitions have been given for more than fifty years to millions of students. This book considers the basic ideas behind the solutions to the majority of these problems, and presents examples and exercises from past exams to illustrate the concepts. Anyone preparing for the Mathematical Olympiads will find many useful ideas here, but people generally interested in logical problem solving should also find the problems and their solutions stimulating. The book can be used either for self-study or as topic-oriented material and samples of problems for practice exams. Useful reading for anyone who enjoys solving mathematical problems, and equally valuable for educators or parents who have children with mathematical interest and ability.
First Steps in Mathematics
Author: Western Australia. Department of Education and Training
Publisher: Don Mills, Ont. : Pearson Professional Learning
Published: 2005
Total Pages: 322
ISBN-13: 9780132018869
DOWNLOAD EBOOKFirst Steps in Differential Geometry
Author: Andrew McInerney
Publisher: Springer Science & Business Media
Published: 2013-07-09
Total Pages: 420
ISBN-13: 1461477328
DOWNLOAD EBOOKDifferential geometry arguably offers the smoothest transition from the standard university mathematics sequence of the first four semesters in calculus, linear algebra, and differential equations to the higher levels of abstraction and proof encountered at the upper division by mathematics majors. Today it is possible to describe differential geometry as "the study of structures on the tangent space," and this text develops this point of view. This book, unlike other introductory texts in differential geometry, develops the architecture necessary to introduce symplectic and contact geometry alongside its Riemannian cousin. The main goal of this book is to bring the undergraduate student who already has a solid foundation in the standard mathematics curriculum into contact with the beauty of higher mathematics. In particular, the presentation here emphasizes the consequences of a definition and the careful use of examples and constructions in order to explore those consequences.
Steps into Analytic Number Theory
Author: Paul Pollack
Publisher: Springer Nature
Published: 2021-02-08
Total Pages: 191
ISBN-13: 3030650774
DOWNLOAD EBOOKThis problem book gathers together 15 problem sets on analytic number theory that can be profitably approached by anyone from advanced high school students to those pursuing graduate studies. It emerged from a 5-week course taught by the first author as part of the 2019 Ross/Asia Mathematics Program held from July 7 to August 9 in Zhenjiang, China. While it is recommended that the reader has a solid background in mathematical problem solving (as from training for mathematical contests), no possession of advanced subject-matter knowledge is assumed. Most of the solutions require nothing more than elementary number theory and a good grasp of calculus. Problems touch at key topics like the value-distribution of arithmetic functions, the distribution of prime numbers, the distribution of squares and nonsquares modulo a prime number, Dirichlet's theorem on primes in arithmetic progressions, and more. This book is suitable for any student with a special interest in developing problem-solving skills in analytic number theory. It will be an invaluable aid to lecturers and students as a supplementary text for introductory Analytic Number Theory courses at both the undergraduate and graduate level.
First Steps in Mathematics
Author: Sue Willis
Publisher: First Steps
Published: 2005-01-01
Total Pages:
ISBN-13: 9780975998687
DOWNLOAD EBOOKProvides teachers with a range of practical tools to improve the mathematical learning for all students
A Conversational Introduction to Algebraic Number Theory
Author: Paul Pollack
Publisher: American Mathematical Soc.
Published: 2017-08-01
Total Pages: 329
ISBN-13: 1470436531
DOWNLOAD EBOOKGauss famously referred to mathematics as the “queen of the sciences” and to number theory as the “queen of mathematics”. This book is an introduction to algebraic number theory, meaning the study of arithmetic in finite extensions of the rational number field Q . Originating in the work of Gauss, the foundations of modern algebraic number theory are due to Dirichlet, Dedekind, Kronecker, Kummer, and others. This book lays out basic results, including the three “fundamental theorems”: unique factorization of ideals, finiteness of the class number, and Dirichlet's unit theorem. While these theorems are by now quite classical, both the text and the exercises allude frequently to more recent developments. In addition to traversing the main highways, the book reveals some remarkable vistas by exploring scenic side roads. Several topics appear that are not present in the usual introductory texts. One example is the inclusion of an extensive discussion of the theory of elasticity, which provides a precise way of measuring the failure of unique factorization. The book is based on the author's notes from a course delivered at the University of Georgia; pains have been taken to preserve the conversational style of the original lectures.
Number Theory
Author: George E. Andrews
Publisher: Courier Corporation
Published: 2012-04-30
Total Pages: 292
ISBN-13: 0486135101
DOWNLOAD EBOOKUndergraduate text uses combinatorial approach to accommodate both math majors and liberal arts students. Covers the basics of number theory, offers an outstanding introduction to partitions, plus chapters on multiplicativity-divisibility, quadratic congruences, additivity, and more.
FIRST STEPS to Mathematics
Author: C. Greenidge
Publisher:
Published: 2017-04-27
Total Pages: 134
ISBN-13: 9781545501269
DOWNLOAD EBOOKFirst Steps to Mathematics for Infants is a three-part book which introduces the young learner to Mathematics. The concepts are presented in an easy and interesting manner with a variety of activities for reinforcement. The first part introduces concepts like left right and middle, same and different, bigger and smaller, patterns, light and heavy, tall, short and long, and holds more and holds less. The second part focuses on numbers zero to ten. The activities include tracing and writing the numbers, drawing objects for the numbers, circling and completing sets, and counting and matching to the number.The third part presents concepts like shapes, one to one correspondence, equals, more than and less than, bigger and smaller number, missing numbers in series 0-10, number names zero to ten, ordinals, whole and fractions, pictographs, classifying, and adding and taking away. Although designed for the 4-6 age group, it may be helpful to older children who have not mastered the concepts.
First Steps for Math Olympians: Using the American Mathematics Competitions
Author: J. Douglas Faires
Publisher: American Mathematical Soc.
Published: 2020-10-26
Total Pages: 307
ISBN-13: 1470451263
DOWNLOAD EBOOKAny high school student preparing for the American Mathematics Competitions should get their hands on a copy of this book! A major aspect of mathematical training and its benefit to society is the ability to use logic to solve problems. The American Mathematics Competitions (AMC) have been given for more than fifty years to millions of high school students. This book considers the basic ideas behind the solutions to the majority of these problems, and presents examples and exercises from past exams to illustrate the concepts. Anyone taking the AMC exams or helping students prepare for them will find many useful ideas here. But people generally interested in logical problem solving should also find the problems and their solutions interesting. This book will promote interest in mathematics by providing students with the tools to attack problems that occur on mathematical problem-solving exams, and specifically to level the playing field for those who do not have access to the enrichment programs that are common at the top academic high schools. The book can be used either for self-study or to give people who want to help students prepare for mathematics exams easy access to topic-oriented material and samples of problems based on that material. This is useful for teachers who want to hold special sessions for students, but it is equally valuable for parents who have children with mathematical interest and ability. As students' problem solving abilities improve, they will be able to comprehend more difficult concepts requiring greater mathematical ingenuity. They will be taking their first steps towards becoming math Olympians!
