The 1998-1999 Master Class Program in Mathematical Logic These Lecture Notes con tain the material of a series of lectures I ga v e in the Spring of 1999, in the Master Class Program Mathematical Logic. << /S /GoTo /D (section.6.1) >> << /S /GoTo /D (chapter.5) >> endobj (VII Rational, Real, and Complex Numbers) %���� << /S /GoTo /D (section.1.7) >> It is observed that many students have difficulty in producing correct proofs by the method of mathematical induction. endobj 275 0 obj << 160 0 obj endobj << /S /GoTo /D (chapter.18) >> 92 0 obj 89 0 obj (Contents) endobj endobj endobj (Very Good Approximation) << /S /GoTo /D (subsection.2.3.2) >> 265 0 obj 129 0 obj 104 0 obj >> endobj 40 0 obj (Introduction to Analytic Number Theory) endobj (Jacobi Symbol) /D [266 0 R /XYZ 88.936 668.32 null] (Introduction to congruences) 221 0 obj 149 0 obj 96 0 obj (Integer Divisibility) (Principle of Mathematical Induction, Variation 2) Let ( )Sn denote a statement involving a variable n.Suppose (1) S(1) and S(2) are true; (2) if Sk() and Sk(1)+ are true for some positive integer k, then Sk(2)+ is also true. << /S /GoTo /D (section.3.2) >> (Multiplicative Number Theoretic Functions) endobj (X Limits and Continuity) endobj (Theorems and Conjectures involving prime numbers) xڍTMo� ���T�Қ6_�5U�j�*Q�=%=xm�Eu`������lv[K��7o��@ج���v���2@*��`�p)��0� �l[�}69�Fg���،ښ� �F�ouγq���U7u���~�0�P����8v��}NH�|= 0�1ix� endobj 24 0 obj 161 0 obj endobj endobj endobj endobj endobj << /S /GoTo /D (chapter.8) >> %���� 260 0 obj 59 0 obj 141 0 obj << /S /GoTo /D (section.4.1) >> 77 0 obj endobj Handbook of Mathematical Induction: Theory and Applications shows how to find and write proofs via mathematical induction. << /S /GoTo /D (chapter.13) >> << /S /GoTo /D (section.2.4) >> 164 0 obj endobj endobj << /S /GoTo /D (chapter.9) >> endobj endobj Introduction to Mathematical Structures and Proofs is a textbook intended for such a course, or for self-study. The notion of a correct proof by this method is analysed mathematically. (Linear Diophantine Equations) endobj 75 0 obj 84 0 obj 168 0 obj >> 51 0 obj �Bj�SȢ�l�(̊�s*�? (Congruences) (The Greatest Common Divisor) << /S /GoTo /D (chapter.3) >> x�-�=�@@w~EG����F5���`.q0(g��0����4�o��N��&� �F�T���XwiF*_�!�z�!~x� c�=�͟*߾��PM��� 181 0 obj endobj endobj 4 0 obj 233 0 obj (The Chinese Remainder Theorem) (The Riemann Zeta Function) 45 0 obj endobj endobj (Representations of Integers in Different Bases) << /S /GoTo /D (chapter.17) >> 20 0 obj endobj 201 0 obj 29 0 obj (Introduction to Continued Fractions) 216 0 obj (The Law of Quadratic Reciprocity) << /S /GoTo /D (subsection.1.2.1) >> endobj endobj 241 0 obj 105 0 obj endobj (Getting Closer to the Proof of the Prime Number Theorem) 63 0 obj << /S /GoTo /D (chapter.6) >> Mathematical Database Page 5 of 21 Theorem 3.2. 117 0 obj (Divisibility and the Division Algorithm) 19 0 obj 61 0 obj endobj 256 0 obj /Type /Page Online Corrected Edition version 1:0 (February 5, 2010), based on the “second edition” (second printing) of April 1920, incorporating additional corrections,marked in green. 57 0 obj 88 0 obj endobj (A Formula of Gauss, a Theorem of Kuzmin and L\351vi and a Problem of Arnold) (II Definition of Number) endobj << /S /GoTo /D (TOC.0) >> 116 0 obj 125 0 obj endobj << /S /GoTo /D (section.4.2) >> endobj 95 0 obj (XII Selections and the Multiplicative Axiom) << /S /GoTo /D (chapter.3) >> endobj (The function [x] , the symbols "O", "o" and "") endobj 81 0 obj << /S /GoTo /D (Index.0) >> (The Pigeonhole Principle) << /S /GoTo /D (subsection.3.2.2) >> 165 0 obj 228 0 obj << /S /GoTo /D (section.5.4) >> endobj endobj (XVIII Mathematics and Logic) endobj >> endobj << /S /GoTo /D (chapter.4) >> 8 0 obj 109 0 obj 91 0 obj 73 0 obj 212 0 obj }_�잪W3�I�/5 << /S /GoTo /D (chapter.11) >> endobj endobj /D [266 0 R /XYZ 88.936 688.12 null] endobj endobj << /S /GoTo /D (section*.55) >> endobj (Editor's Note) endobj endobj endobj endobj endobj 68 0 obj endobj (Theorems of Fermat, Euler, and Wilson) endobj (Main Technical Tool) endobj 37 0 obj << /S /GoTo /D (section.2.3) >> 87 0 obj << /S /GoTo /D (section.6.4) >> endobj endobj 48 0 obj << /S /GoTo /D (chapter.7) >> 184 0 obj (III Finitude and Mathematical Induction) (The Mobius Function and the Mobius Inversion Formula) << /S /GoTo /D [97 0 R /Fit ] >> 85 0 obj 24 0 obj endobj endobj endobj /ProcSet [ /PDF /Text ] 101 0 obj (Euler's -Function) << /S /GoTo /D (section.5.1) >> endobj << /S /GoTo /D (section.5.6) >> endobj 11 0 obj (The Fundamental Theorem of Arithmetic) << /S /GoTo /D (subsection.4.2.2) >> (XIV Incompatibility and the Theory of Deduction) 33 0 obj 12 0 obj endobj << /S /GoTo /D (subsection.2.6.1) >> << /S /GoTo /D (chapter.8) >> endobj << /S /GoTo /D (subsection.3.2.1) >> 35 0 obj endobj endobj (Preface) 180 0 obj (Algebraic Operations With Integers) << /S /GoTo /D (section.3.3) >> 76 0 obj 32 0 obj >> 48 0 obj << /S /GoTo /D (subsection.2.3.1) >> endobj (An Application) 99 0 obj << endobj 40 0 obj endobj endobj << /S /GoTo /D (section.2.2) >> %PDF-1.4 endobj 36 0 obj endobj endobj << /S /GoTo /D (section*.1) >> (IV The Definition of Order) (The Sieve of Eratosthenes) endobj $e!��X>xۛ������R 209 0 obj 93 0 obj 205 0 obj 204 0 obj %PDF-1.4 << /S /GoTo /D (section.4.4) >> endobj 5 0 obj << /S /GoTo /D (section.5.3) >> endobj endobj endobj endobj 136 0 obj (Linear Congruences) 200 0 obj endobj 79 0 obj 197 0 obj 96 0 obj 193 0 obj endobj endobj /Filter /FlateDecode (The infinitude of Primes) 236 0 obj endobj << /S /GoTo /D (subsection.1.2.2) >> /Length 1149 endobj 80 0 obj << /S /GoTo /D (section.6.3) >> 225 0 obj << /S /GoTo /D (section.5.7) >> endobj endobj

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