Download e-book for kindle: An Introduction to Number Theory (Guidebook, parts 1,2) by Edward Burger

By Edward Burger

ISBN-10: 1598034200

ISBN-13: 9781598034202

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 examine -- lecture 2. average numbers and their personalities -- lecture three. Triangular numbers and their progressions -- lecture four. Geometric progressions, exponential development -- lecture five. Recurrence sequences -- lecture 6. The Binet formulation and towers of Hanoi -- lecture 7. The classical thought of top numbers -- lecture eight. Euler's product formulation and divisibility -- lecture nine. The major 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 with an outline of the high-level thoughts. subsequent, he presents a step by step rationalization of the formulation and calculations that lay on the center of every conundrum. via transparent factors, interesting anecdotes, and enlightening demonstrations, Professor Burger makes this fascinating box of research obtainable for someone who appreciates the interesting nature of numbers. -- writer.

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

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Our system could not precisely express 1234! Let’s say our system only allowed the exponent to be 0 to 9. 12 or very big ones. JavaScript is better than what I just described, but if and when a number exceeds its capacity in one of these ways, JavaScript says the number is infinity! Try it. As it turns out, though iterative factorial does not produce the too much recursion error, the fact that the number is outside the capacity of double precision occurs the same time for both methods. If you have an application in which double precision is not good enough, then you can try and find a library for arbitrary or unlimited precision.

In other words, the program should calculate f(n) for each n = 1, 2, …, N and add the results to a running sum. Then find 100 4k3 + 6k2 + 2k + 3 . Does it matter that the dummy variable is k instead of n? 2). How will you handle cn + d? Which program is faster for large values of N? 9 13 is the smallest prime such that reversing its digits yields a different prime, namely, 31. Find five more primes with this property. ∗ 10 Show that none of the first 100 triangular numbers are the sum of two consecutive squares.

Note: 2 is sometimes not considered a prime and sometimes is…. ) Whenever we determine that something is a prime, we add it to the list. This is done using a built-in JavaScript method called push. push(n); The header for the inner loop will be slightly more complex. The loop variable, shown here with the variable name fi, serves as the index into the primes array. The stopping condition has two parts: checking the length of the array (remember: the index values for arrays go from 0 to 1 less than the length of the array) and then checking if the factor, the particular prime in the array, is less than or equal to the square root of n.

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

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