Mathematical foundations Books
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Springer New York A Course in Mathematical Logic for Mathematicians 53 Graduate Texts in Mathematics
Book SynopsisIn the intervening three decades, a lot of interesting things have happened to mathematical logic: (i) Model theory has shown that insights acquired in the study of formal languages could be used fruitfully in solving old problems of conventional mathematics.Trade ReviewFrom the reviews of the second edition:"As one might expect from a graduate text on logic by a very distinguished algebraic geometer, this book assumes no previous acquaintance with logic, but proceeds at a high level of mathematical sophistication. Chapters I and II form a short course. Chapter I is a very informal introduction to formal languages, e.g., those of first order Peano arithmetic and of ZFC set theory. Chapter II contains Tarski's definition of truth, Gödel's completeness theorem, and the Löwenheim-Skolem theorem. The emphasis is on semantics rather than syntax. Some rarely-covered side topics are included (unique readability for languages with parentheses, Mostowski's transitive collapse lemma, formalities of introducing definable constants and function symbols). Some standard topics are neglected. (The compactness theorem is not mentioned!) The latter part of Chapter II contains Smullyan's quick proof of Tarski's theorem on the undefinability of truth in formal arithmetic, and an account of the Kochen-Specker "no hidden variables" theorem in quantum logic. There are digressions on philosophical issues (formal logic vs. ordinary language, computer proofs). A wealth of material is introduced in these first 100 pages of the book..."--MATHEMATICAL REVIEWS“Manin’s book on mathematical logic is addressed to a working-mathematician with some knowledge of naive set theory … . incorporate some of the exciting developments in mathematical logic of the last four decades into this edition. … The exquisite taste and the elegant style of the author have produced an outstanding treatment of mathematical logic that allows one to understand some of the pillars of this area of mathematical research … and Manin’s original treatment of the subject provides an extraordinary introduction to mathematical logic.” (F. Luef, Internationale Mathematische Nachrichten, Issue 217, August, 2011)“The new extended title of this book corresponds more to its concept, contents, spirit and style. The book is really addressed to mathematicians and introduces the reader to the glorious discoveries in logic during the last century through the difficult and subtle results, problems, proofs and comments. … due to the author’s brilliant style, each part of the book provokes new opinions and pleasure of a different understanding of basic results and ideas of contemporary mathematical logic.” (Branislav Boričić, Zentralblatt MATH, Vol. 1180, 2010)Table of ContentsPROVABILITY.- to Formal Languages.- Truth and Deducibility.- The Continuum Problem and Forcing.- The Continuum Problem and Constructible Sets.- COMPUTABILITY.- Recursive Functions and Church#x2019;s Thesis.- Diophantine Sets and Algorithmic Undecidability.- PROVABILITY AND COMPUTABILITY.- G#x00F6;del#x2019;s Incompleteness Theorem.- Recursive Groups.- Constructive Universe and Computation.- MODEL THEORY.- Model Theory.
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Springer New York Reflexive Structures An Introduction to Computability Theory
Book Synopsis1 Functions and Predicates.- 1. Definitions.- 2. Numerical Functions.- 3. Finitary Rules.- 4. Closure Properties.- 5. Minimal Closure.- 6. More Elementary Functions and Predicates.- 2 Recursive Functions.- 1. Primitive Recursion.- 2. Functional Transformations.- 3. Recursive Specifications.- 4. Recursive Evaluation.- 5. Church's Thesis.- 3 Enumeration.- 1. Predicate Classes.- 2. Enumeration Properties.- 3. Induction.- 4. Nondeterministic Computability.- 4 Reflexive Structures.- 1. Interpreters.- 2. A Universal Interpreter.- 3. Two Constructions.- 4. The Recursion Theorem.- 5. Relational Structures.- 6. Uniform Structures.- 5 Hyperenumeration.- 1. Function Quantification.- 2. Nonfinitary Induction.- 3. Functional Induction.- 4. Ordinal Notations.- 5. Reflexive Systems.- 6. Hyperhyperenumeration.- References.Table of Contents1 Functions and Predicates.- §1. Definitions.- §2. Numerical Functions.- §3. Finitary Rules.- §4. Closure Properties.- §5. Minimal Closure.- §6. More Elementary Functions and Predicates.- 2 Recursive Functions.- §1. Primitive Recursion.- §2. Functional Transformations.- §3. Recursive Specifications.- §4. Recursive Evaluation.- §5. Church’s Thesis.- 3 Enumeration.- §1. Predicate Classes.- §2. Enumeration Properties.- §3. Induction.- §4. Nondeterministic Computability.- 4 Reflexive Structures.- §1. Interpreters.- §2. A Universal Interpreter.- §3. Two Constructions.- §4. The Recursion Theorem.- §5. Relational Structures.- §6. Uniform Structures.- 5 Hyperenumeration.- §1. Function Quantification.- §2. Nonfinitary Induction.- §3. Functional Induction.- §4. Ordinal Notations.- §5. Reflexive Systems.- §6. Hyperhyperenumeration.- References.
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Springer Introduction to Mathematical Structures and Proofs
Book SynopsisPreface to the Second Edition.- Preface to the First Edition.- 1. Logic.- 2. Sets.- 3. Functions.- 4. Finite and Infinite Sets.- 5. Combinatorics.- 6. Number Theory.- 7. Complex Numbers.- Hints and Partial Solutions to Selected Odd-Numbered Exercises.- Index.Table of Contents-Preface.- 1. Logic.- 2. Sets.- 3. Functions.- 4. Finite and Infinite Sets. - 5. Permutations and Combinations.- 6. Number Theory.- 7. Complex Numbers.- Hints and Partial Solutions to Selected Odd-Numbered Exercises.- Index
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Birkhauser Boston Theory of Finite and Infinite Graphs
Book SynopsisCommentary.- Theory of Finite and Infinite Graphs.- Dénes König: A Biographical Sketch.Table of ContentsCommentary.- Theory of Finite and Infinite Graphs.- Dénes König: A Biographical Sketch.
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Createspace Independent Publishing Platform Fractions Decimals Percents Math Workbook Includes Repeating Decimals Improve Your Math Fluency Series Volume 17
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Createspace Independent Publishing Platform Multiplication Facts Math Worksheet Practice Arithmetic Workbook With Answers: Daily Practice guide for elementary students
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Mark Twain Media Common Core Math Workouts, Grade 7
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