For example, here are some problems in number theory that remain unsolved. I ask only that you acknowledge the source and make no commercial use of it. Loaded with pedagogical features including fully worked examples, graded exercises, chapter summaries, and computer exercises. Every natural number is built, in a unique way, out of prime numbers. A friendly introduction to number theory is an introductory undergraduate text designed to entice nonmath majors into learning some mathematics, while at the same time teaching them how to think mathematically. In the complex plane the points representing a complex number and its conjugate are mirror images with respect to the real axis. The basic concepts of elementary number theory are included in the first six chapters. An undergraduatelevel introduction to number theory, with the emphasis on fully explained proofs and examples. An introduction to elementary set theory guram bezhanishvili and eachan landreth 1 introduction in this project we will learn elementary set theory from the original historical sources by two key gures in the development of set theory, georg cantor 18451918 and richard dedekind 18311916.
Number theory or arithmetic or higher arithmetic in older usage is a branch of pure mathematics devoted primarily to the study of the integers and integervalued functions. The basic concepts illustrated in the text can be readily grasped if the reader has a good background in high school mathematics and an inquiring mind. American river software elementary number theory, by david. High school math without using a calculator, which of the following is the best estimate for. This chapter lays the foundations for our study of the theory of numbers by weaving together the themes of prime numbers, integer factorization, and the distribution of primes.
I will assume that you dont know anything at the beggining and want to learn just for fun. The first part discusses elementary topics such as primes, factorization, continued fractions, and quadratic forms, in the context of cryptography, computation, and deep open research problems. Elements of number theory undergraduate texts in mathematics. Elementary number theory springer undergraduate mathematics. Divisibility is an extremely fundamental concept in number theory, and has applications including puzzles, encrypting messages, computer security, and many algorithms. Chapter approximate number of days 7 15 14 15 12 17. Note that if n is divisible by a power of a prime higher than one then n0. Elementary number theory usf department of mathematics. Pdf some remarks on number theory in high school education. The course is ideal for a student who has completed the usual high school curriculum of algebra, geometry, trigonometry, precalculus and calculus and is looking for new. A primary focus of number theory is the study of prime numbers, which can be. A good undergradlevel textbook is steins elementary number theory, but there are many options with the same title that are excellent as well by rosen, dudley, kraft and others. Introduction to number theory with applications to middle. Elementary number theory in nine chapters is primarily intended for a onesemester course for upperlevel students of mathematics, in particular, for prospective secondary school teachers.
The downloadable files below, in pdf format, contain answers to the exercises from chapters 1 9 of the 5th edition. Elementary number theory a revision by jim hefferon, st michaels college, 2003dec of notes by w. The following theorem states somewhat an elementary but very useful result. This game is similar to 20 questions and can be adjusted to students level of understanding of numbers and number theory. Every natural number can be written as a product of primes uniquely up to order. An example is checking whether universal product codes upc or international standard book number isbn codes are legitimate. Elementary mathematics consists of mathematics topics frequently taught at the primary or secondary school levels there are five basic strands in elementary mathematics. Edwin clarks home page university of south florida. In the figure below, shown are the prime numbers less than 100.
Note that primes are the products with only one factor and 1. Help yourself to the postscript file or pdf file of my book elementary number theory. Introduction to number theory with applications to middle school mathematics and cryptography. The exposition is informal, with a wealth of numerical examples that are analyzed for patterns and used to make conjectures. The course is ideal for a student who has completed the usual high school curriculum of algebra, geometry, trigonometry, precalculus and calculus and is looking for new challenges. The absolute value of any real number, a, written as a, is defined as. German mathematician carl friedrich gauss 17771855 said, mathematics is the queen of the sciencesand number theory is the queen of mathematics.
Find materials for this course in the pages linked along the left. The theory of numbers has always occupied a unique. Number theory, known to gauss as arithmetic, studies the properties of the. I would strongly recommend underwood dudleys elementary number theory and harold starks an introduction to number theory. A bit expensive, but if you want to own one book on elementary number theory, this ones a pretty good candidate. Waclaw sierpinski 250 problems in elementary number theory presents problems and their solutions in five specific areas of this branch of mathe matics. The text would be suitable for the standard elementary number theory course.
Number theorists study prime numbers as well as the. This is a first draft version of workbooktext for mtht 467. Edwin clark department of mathematics university of south florida revised june 2, 2003 copyleft 2002 by w. Elementary school number theory math and multimedia. Arnold ross says of number theory, his choice for teaching the most brilliant high school students in the country as well as his own graduate students at ohio state, that the purpose is to think deeply of. Undergraduatehighschoololympiad level introductory number. This book, elementary methods in number theory, is divided into three parts. Elementary number theory 1st edition textbook solutions. Also you may have the latex file in case you want to revise it to suit your own taste.
To download any exercise to your computer, click on the appropriate file. The notes contain a useful introduction to important topics that need to be addressed in a course in number theory. Olympiad number theory through challenging problems. Pdf elementary number theory sixth edition b higher. It provides students an opportunity to think about the many ways numbers can be described oddeven, whole number, fraction less than or greater than one, prime number, multiple of n, etc.
Number theory vocabulary 1 number theory vocabulary for middle school teachers a absolute value the absolute value of a real number is its distance from zero on the number line. Number theory is all about adding and multiplying integers. Here and there some of the problems might use certain properties of the complex numbers. Nov 24, 2018 its hard to know what is meant by elementary. Since the material is geared to high school students talented ones, though i assume very little mathematical knowledge beyond algebra and trigonometry. This version is onesided, but may be converted to twosided by the appropriate printer or by a photocopy machine. I tried to cover most number theory that is useful in contests. Most if not all universities worldwide offer introductory courses in number theory for math majors and in many cases as an elective course. The number 5 is a prime number, while 8 is not prime because 8 is divisible by 2 and 4.
Our intention in writing this book is to give an elementary introduction to number theory which does not demand a great deal of mathematical back ground or maturity from the reader, and which can be read and understood with no extra assistance. Understanding elementary number theory 7th edition homework has never been easier than with chegg study. B higher education elementary number theory, sixth. Elementary school children know how to tell if a number is even, or divisible by. Recall that a prime number is an integer greater than 1 whose only positive. On the website you can also help me collecting solutions for the problems in the book all available solutions will be on the website only. This is quite comprehensive and has a nice collection of topics and exercises. There are several elementary number theory books which you could use and which do not assume a level of knowledge beyond high school math.
I assume a knowledge of the basic rules of high school algebra which applyto and therefore to, and. This is the version used in spring 2012 and is currently being updated. Edwin clark copyleft means that unrestricted redistribution and modi. It very much depends on your starting position and your goal. If we examine the 10 positive integers, it is easy to see that only four are prime numbers. Elementary number theory with applications 2e is ideally suited for undergraduate students and is especially appropriate for prospective and inservice math teachers at the high school and middle school levels. Number theory vocabulary for middle school teachers. September 6, 2014 guillermo bautista elementary school number theory, high school mathematics a factor is an integer that divides another integer.
What is the best book for elementary number theory. These notes were prepared by joseph lee, a student in the class, in collaboration with prof. Syllabus theory of numbers mathematics mit opencourseware. In that case, i think that it is good to start with basic divisibility. Prime numbers number theory is the mathematical study of the natural numbers, the positive whole numbers such as 2, 17, and 123. Note to tfachers i based on the teaching experience of nearly 200 junior thigh.
Understanding elementary number theory 1st edition homework has never been easier than with chegg study. A prime number is a positive integer that is divisible only by 1 and itself. These notes serve as course notes for an undergraduate course in number the ory. There are many books on elementary number theory, most of. This is a textbook about classical elementary number theory and elliptic curves. Despite their ubiquity and apparent simplicity, the natural integers are chockfull of beautiful ideas and open problems. Solutions manuals are available for thousands of the most popular college and high school textbooks in subjects such as math, science physics, chemistry, biology, engineering mechanical, electrical, civil, business and more.
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