A01=Ramin Takloo-Bighash
A01=Steven J. Miller
arithmetic mean
Author_Ramin Takloo-Bighash
Author_Steven J. Miller
axiom of choice
Benford's Law
Benford’s Law
Cantor set
Category=PBH
Chebyshev's Theorem
Chebyshev’s Theorem
Cramer model
Dirac delta functional
divide and conquer
eigenvalues
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Euclid's Theorem
Euclid’s Theorem
Fejer's Theorem
Fejér’s Theorem
golden mean
Horner's algorithm
Horner’s algorithm
Isoperimetric Inequality
Liouville's Theorem
Liouville’s Theorem
Newton's Method
Newton’s Method
order of approximation
Pigeon-Hole Principle
Poisson Summation
Quadratic Reciprocity
Riemann zeta function
supremum
symmetric property
Tauberian theorems
Taylor series
uncertainty principle
unit point mass
Product details
- ISBN 9780691120607
- Weight: 879g
- Dimensions: 152 x 235mm
- Publication Date: 26 Mar 2006
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Hardback
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In a manner accessible to beginning undergraduates, An Invitation to Modern Number Theory introduces many of the central problems, conjectures, results, and techniques of the field, such as the Riemann Hypothesis, Roth's Theorem, the Circle Method, and Random Matrix Theory. Showing how experiments are used to test conjectures and prove theorems, the book allows students to do original work on such problems, often using little more than calculus (though there are numerous remarks for those with deeper backgrounds). It shows students what number theory theorems are used for and what led to them and suggests problems for further research. Steven Miller and Ramin Takloo-Bighash introduce the problems and the computational skills required to numerically investigate them, providing background material (from probability to statistics to Fourier analysis) whenever necessary. They guide students through a variety of problems, ranging from basic number theory, cryptography, and Goldbach's Problem, to the algebraic structures of numbers and continued fractions, showing connections between these subjects and encouraging students to study them further.
In addition, this is the first undergraduate book to explore Random Matrix Theory, which has recently become a powerful tool for predicting answers in number theory. Providing exercises, references to the background literature, and Web links to previous student research projects, An Invitation to Modern Number Theory can be used to teach a research seminar or a lecture class.
Steven J. Miller is an Assistant Professor of Mathematics at Brown University. Ramin Takloo-Bighash is an Assistant Professor of Mathematics at Princeton University.
