An Introduction to Number Theory (Guidebook, parts 1,2) by Edward Burger

Number Theory

By Edward Burger

2 DVD set with 24 lectures half-hour each one for a complete of 720 minutes...Performers: Taught through: Professor Edward B. Burger, Williams College.Annotation Lectures 1-12 of 24."Course No. 1495"Lecture 1. quantity conception and mathematical study -- lecture 2. normal numbers and their personalities -- lecture three. Triangular numbers and their progressions -- lecture four. Geometric progressions, exponential progress -- lecture five. Recurrence sequences -- lecture 6. The Binet formulation and towers of Hanoi -- lecture 7. The classical thought of major numbers -- lecture eight. Euler's product formulation and divisibility -- lecture nine. The best quantity theorem and Riemann -- lecture 10. department set of rules and modular mathematics -- lecture eleven. Cryptography and Fermat's little theorem -- lecture 12. The RSA encryption scheme.Summary Professor Burger starts off with an summary of the high-level innovations. subsequent, he presents a step by step clarification of the formulation and calculations that lay on the center of every conundrum. via transparent motives, interesting anecdotes, and enlightening demonstrations, Professor Burger makes this exciting box of analysis available for someone who appreciates the attention-grabbing nature of numbers. -- writer.

Show description

Read Online or Download An Introduction to Number Theory (Guidebook, parts 1,2) PDF

Best number theory books

Multiplicative Number Theory I. Classical Theory

A textual content in keeping with classes taught effectively over a long time at Michigan, Imperial collage and Pennsylvania nation.

Mathematical Problems in Elasticity

This quantity good points the result of the authors' investigations at the improvement and alertness of numerical-analytic equipment for traditional nonlinear boundary price difficulties (BVPs). The tools into consideration provide a chance to resolve the 2 very important difficulties of the BVP idea, specifically, to set up life theorems and to construct approximation recommendations

Iwasawa Theory Elliptic Curves with Complex Multiplication: P-Adic L Functions

Within the final fifteen years the Iwasawa conception has been utilized with extraordinary good fortune to elliptic curves with advanced multiplication. a transparent but common exposition of this thought is gifted during this book.

Following a bankruptcy on formal teams and native devices, the p-adic L services of Manin-Vishik and Katz are built and studied. within the 3rd bankruptcy their relation to category box idea is mentioned, and the purposes to the conjecture of Birch and Swinnerton-Dyer are handled in bankruptcy four. complete proofs of 2 theorems of Coates-Wiles and of Greenberg also are provided during this bankruptcy that could, moreover, be used as an creation to the more moderen paintings of Rubin.

The booklet is essentially self-contained and assumes familiarity in basic terms with basic fabric from algebraic quantity idea and the idea of elliptic curves. a few effects are new and others are awarded with new proofs.

Extra info for An Introduction to Number Theory (Guidebook, parts 1,2)

Sample text

This can easily be seen by considering the exponent a of any prime p which occurs in the prime-power factorization of (m*, (mi, m2)). Let the exponent of p in the factorization of my be Pj, for j = 1, 2 , , i. Then p occurs in (mi, m2) with exponent max (Pi, P2) r so tbat a = min (ft, max (ft, f t ) ) = max (min (Pi, Pi), min (ft, f t )). But our assumption is that pmSn<* ’*)| (ci - Ci) and Jf**<**)\ (C2 _ Ci)j and since p&l\(cx - f) and p^2\(c2 - f ) we see, by writing Cl Ci = (ci f) (f Ci), C2 Ci = (c2 f) (f Ci), that pBdnWb*>| f e - / ) and - /), so that also pa\(ci — / ) .

Problem s 1. In the notation of Problem 2, Section 2-3, show that ) = <(a, b), (a, c)>. CHAPTER 3 CONGRUENCES 3-1 Introduction. The problem of solving the Diophantine equa­ tion ax + by = c is just that of finding an x such that ax and c leave the same remainder when divided by b, since then &|(c — ax) and we can take y = (c — a x )/b . As we shall see, there are many other instances also in which a comparison must be made of the remainders after dividing each of two numbers a and b by a third, say m.

As a consequence of Theorem 3-12, we have the following im­ portant result. 3-13 (Chinese Remainder Theorem). Every system of linear congruences in which the moduli are relatively prime in pairs is solvable, the solution being unique modulo the product of the moduli. T heorem 36 CONGRUENCES [CHAP. 3 PROBLEM S 1. Solve the congruence 6s + Iby = 9 (mod 18). 2. Solve simultaneously: x = 1 (mod 2), 2 = 1 (mod 3), x = S (mod 4), x = 4 (mod 5). 3. Suppose that the system of congruences x = di (mod m*), i = 1, 2, .

Download PDF sample

Rated 4.69 of 5 – based on 12 votes