A First Course In Theory Of Numbers
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A First Course In Theory Of Numbers
Contents: Number System; Congruencies And Its Basic Properties; Algebraic Congruences And Primitive Roots; Arithmetic Functions; Farey Sequence, Continued Fraction, Pell S Equations; Quadratic Residues, Levender S Symbols, Jacobi S Symbols; Homogeneous Quadratic Diophantine Equation; Some Number Theoretic Problems Related To Mathematics Olympiads; Answers; Etc.
Topics from the Theory of Numbers
Author: Emil Grosswald
language: en
Publisher: Springer Science & Business Media
Release Date: 2010-02-23
Many of the important and creative developments in modern mathematics resulted from attempts to solve questions that originate in number theory. The publication of Emil Grosswald’s classic text presents an illuminating introduction to number theory. Combining the historical developments with the analytical approach, Topics from the Theory of Numbers offers the reader a diverse range of subjects to investigate, including: (1) divisibility, (2) congruences, (3) the Riemann zeta function, (4) Diophantine equations and Fermat’s conjecture, (5) the theory of partitions. Comprehensive in nature, Topics from the Theory of Numbers is an ideal text for advanced undergraduates and graduate students alike.
An Illustrated Theory of Numbers
Author: Martin H. Weissman
language: en
Publisher: American Mathematical Soc.
Release Date: 2020-09-15
News about this title: — Author Marty Weissman has been awarded a Guggenheim Fellowship for 2020. (Learn more here.) — Selected as a 2018 CHOICE Outstanding Academic Title — 2018 PROSE Awards Honorable Mention An Illustrated Theory of Numbers gives a comprehensive introduction to number theory, with complete proofs, worked examples, and exercises. Its exposition reflects the most recent scholarship in mathematics and its history. Almost 500 sharp illustrations accompany elegant proofs, from prime decomposition through quadratic reciprocity. Geometric and dynamical arguments provide new insights, and allow for a rigorous approach with less algebraic manipulation. The final chapters contain an extended treatment of binary quadratic forms, using Conway's topograph to solve quadratic Diophantine equations (e.g., Pell's equation) and to study reduction and the finiteness of class numbers. Data visualizations introduce the reader to open questions and cutting-edge results in analytic number theory such as the Riemann hypothesis, boundedness of prime gaps, and the class number 1 problem. Accompanying each chapter, historical notes curate primary sources and secondary scholarship to trace the development of number theory within and outside the Western tradition. Requiring only high school algebra and geometry, this text is recommended for a first course in elementary number theory. It is also suitable for mathematicians seeking a fresh perspective on an ancient subject.