Formal Number Theory 1
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Formal Number Theory 1
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Author : Open University Course Team
language : en
Publisher:
Release Date : 2009-05-16
Formal Number Theory 1 written by Open University Course Team and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-16 with Logic, Symbolic and mathematical categories.
In this unit we complete the description of the formal system started in units ML04 and ML05, and use the system to produce more complex formal proofs. We then discuss how to use it as a framework for proving theorems of number theory.To order all 8 units in the Mathematical Logic series please see product M381/PP01
Formal Number Theory And Computability
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Author : Alec Fisher
language : en
Publisher: Oxford University Press, USA
Release Date : 1982
Formal Number Theory And Computability written by Alec Fisher and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with History categories.
Formal Number Theory Ii
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Author : Open University Course Team
language : en
Publisher:
Release Date : 2009-05-16
Formal Number Theory Ii written by Open University Course Team and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-16 with Logic, Symbolic and mathematical categories.
In this unit we look at some theorems of a small but deeply significant fragment of number theory, called Q. We introduce the notion of a function being representable in a formal system. We shall discover that, although Q is quite a weak theory, it is sufficiently powerful to allow all total recursive functions (as discussed in unit ML03) to be representable in Q. This unit concludes with a discussion of diagonalization and Godel's Diagonal Lemma.To order all 8 units in the Mathematical Logic series please see product M381/PP01
Integers And Theory Of Numbers
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Author : Abraham Adolf Fraenkel
language : en
Publisher: Courier Corporation
Release Date : 2004-01-01
Integers And Theory Of Numbers written by Abraham Adolf Fraenkel and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-01 with Mathematics categories.
A concise work on important topics in number theory, this classic text was devised by a prominent mathematician to explain the essentials of mathematics in a manner accessible to high school and college students as well as to other readers. Clear-cut explanations cover natural numbers as cardinals, with discussions of positional notation and the ordering of numbers according to magnitude; natural numbers as ordinals, including Peano's axioms and the relation of ordinals to cardinals; the theory of numbers, encompassing prime numbers and their distribution, partitions of the circle, Fermat's simple and last theorems, perfect numbers, amicable numbers, and algebraic and ideal numbers; and rational numbers, with considerations of positive fractions, negative integers, and the field of rationals. 1955 ed.
Elementary Theory Of Numbers
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Author : William J. LeVeque
language : en
Publisher: Courier Corporation
Release Date : 2014-01-15
Elementary Theory Of Numbers written by William J. LeVeque and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with Mathematics categories.
This superb text introduces number theory to readers with limited formal mathematical training. Intended for use in freshman- and sophomore-level courses in arts and science curricula, in teacher-training programs, and in enrichment programs for high-school students, it is filled with simple problems to stimulate readers' interest, challenge their abilities and increase mathematical strength. Contents: I. Introduction II. The Euclidean Algorithm and Its Consequences III. Congruences IV. The Powers of an Integer Modulo m V. Continued Fractions VI. The Gaussian Integers VII. Diophantine Equations Requiring only a sound background in high-school mathematics, this work offers the student an excellent introduction to a branch of mathematics that has been a strong influence in the development of higher pure mathematics, both in stimulating the creation of powerful general methods in the course of solving special problems (such as Fermat conjecture and the prime number theorem) and as a source of ideas and inspiration comparable to geometry and the mathematics of physical phenomena.
Number Theory And Mathematical Logic
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Author : Open University Course Team
language : en
Publisher:
Release Date : 2004-01
Number Theory And Mathematical Logic written by Open University Course Team and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01 with Logic, Symbolic and mathematical categories.
In this unit we complete the description of the formal system started in units ML04 and ML05, and use the system to produce more complex formal proofs. We then discuss how to use it as a framework for proving theorems of number theory.
Number Theory
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Author : George E. Andrews
language : en
Publisher: Courier Corporation
Release Date : 2012-04-30
Number Theory written by George E. Andrews and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-30 with Mathematics categories.
Undergraduate 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.
Invitation To Number Theory Second Edition
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Author : Oystein Ore
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-12-29
Invitation To Number Theory Second Edition written by Oystein Ore and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-29 with Number theory categories.
Number theory is the branch of mathematics concerned with the counting numbers, 1, 2, 3, … and their multiples and factors. Of particular importance are odd and even numbers, squares and cubes, and prime numbers. But in spite of their simplicity, you will meet a multitude of topics in this book: magic squares, cryptarithms, finding the day of the week for a given date, constructing regular polygons, pythagorean triples, and many more. In this revised edition, John Watkins and Robin Wilson have updated the text to bring it in line with contemporary developments. They have added new material on Fermat's Last Theorem, the role of computers in number theory, and the use of number theory in cryptography, and have made numerous minor changes in the presentation and layout of the text and the exercises.
Number Theory And Mathematical Logic
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Author : Open University Course Team
language : en
Publisher:
Release Date : 2004-01
Number Theory And Mathematical Logic written by Open University Course Team and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01 with Logic, Symbolic and mathematical categories.
In this unit we look at some theorems of a small but deeply significant fragment of number theory, called Q. We introduce the notion of a function being representable in a formal system. We shall discover that, although Q is quite a weak theory, it is sufficiently powerful to allow all total recursive functions (as discussed in unit ML03) to be representable in Q. This unit concludes with a discussion of diagonalization and Gödel's Diagonal Lemma.
Famous Functions In Number Theory
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Author : Bowen Kerins
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-10-15
Famous Functions In Number Theory written by Bowen Kerins and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-15 with Education categories.
Designed for precollege teachers by a collaborative of teachers, educators, and mathematicians, Famous Functions in Number Theory is based on a course offered in the Summer School Teacher Program at the Park City Mathematics Institute. But this book isn't a "course" in the traditional sense. It consists of a carefully sequenced collection of problem sets designed to develop several interconnected mathematical themes, and one of the goals of the problem sets is for readers to uncover these themes for themselves. Famous Functions in Number Theory introduces readers to the use of formal algebra in number theory. Through numerical experiments, participants learn how to use polynomial algebra as a bookkeeping mechanism that allows them to count divisors, build multiplicative functions, and compile multiplicative functions in a certain way that produces new ones. One capstone of the investigations is a beautiful result attributed to Fermat that determines the number of ways a positive integer can be written as a sum of two perfect squares. Famous Functions in Number Theory is a volume of the book series "IAS/PCMI-The Teacher Program Series" published by the American Mathematical Society. Each volume in that series covers the content of one Summer School Teacher Program year and is independent of the rest. Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.