A Problem Course in Mathematical Logic

This is a text for a problem-oriented course on mathematical logic and computability.

**Tag(s):**
Mathematics

**Publication date**: 01 Sep 2003

**ISBN-10**:
1616100060

**ISBN-13**:
9781616100063

**Paperback**:
166 pages

**Views**: 22,257

**Type**: Book

**Publisher**:
n/a

**License**:
GNU Free Documentation License Version 1.2

**Post time**: 03 Sep 2006 11:25:43

A Problem Course in Mathematical Logic

This is a text for a problem-oriented course on mathematical logic and computability.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation License".

Click**here** to read the full license.

Click

Terms and Conditions:

Book Excerpts:

This book is a free text intended to be the basis for a problem-oriented course(s) in mathematical logic and computability for students with some degree of mathematical sophistication. Parts I and II cover the basics of propositional and first-order logic respectively, Part III covers the basics of computability using Turing machines and recursive functions, and Part IV covers Godel's Incompleteness Theorems. They can be used in various ways for courses of various lengths and mixes of material. The author typically uses Parts I and II for a one-term course on mathematical logic, Part III for a one-term course on computability, and/or much of Part III together with Part IV for a one-term course on computability and incompleteness.

In keeping with the modified Moore-method, this book supplies definitions, problems, and statements of results, along with some explanations, examples, and hints. The intent is for the students, individually or in groups, to learn the material by solving the problems and proving the results for themselves. Besides constructive criticism, it will probably be necessary for the instructor to supply further hints or direct the students to other sources from time to time. Just how this text is used will, of course, depend on the instructor and students in question. However, it is probably not appropriate for a conventional lecture-based course nor for a really large class.

The material presented in this text is somewhat stripped-down. Various concepts and topics that are often covered in introductory mathematical logic and computability courses are given very short shrift or omitted entirely. Instructors might consider having students do projects on additional material if they wish to to cover it.

Prerequisites:

The material in this text is largely self-contained, though some knowledge of (very basic) set theory and elementary number theory is assumed at several points. A few problems and examples draw on concepts from other parts of mathematics; students who are not already familiar with these should consult texts in the appropriate subjects for the necessary definitions. What is really needed to get anywhere with all of the material developed here is competence in handling abstraction and proofs, including proofs by induction. The experience provided by a rigorous introductory course in abstract algebra, analysis, or discrete mathematics ought to be sufficient.

More Resources:

Stefan Bilaniuk wrote:See the GNU Free Documentation License in Appendix D for what you can do with this text. The gist is that you are free to copy, distribute, and use it unchanged, but there are some restrictions on what you can do if you wish to make changes. If you wish to use this text in a manner not covered by the GNU Free Documentation License, please contact the author.

Book Excerpts:

This book is a free text intended to be the basis for a problem-oriented course(s) in mathematical logic and computability for students with some degree of mathematical sophistication. Parts I and II cover the basics of propositional and first-order logic respectively, Part III covers the basics of computability using Turing machines and recursive functions, and Part IV covers Godel's Incompleteness Theorems. They can be used in various ways for courses of various lengths and mixes of material. The author typically uses Parts I and II for a one-term course on mathematical logic, Part III for a one-term course on computability, and/or much of Part III together with Part IV for a one-term course on computability and incompleteness.

In keeping with the modified Moore-method, this book supplies definitions, problems, and statements of results, along with some explanations, examples, and hints. The intent is for the students, individually or in groups, to learn the material by solving the problems and proving the results for themselves. Besides constructive criticism, it will probably be necessary for the instructor to supply further hints or direct the students to other sources from time to time. Just how this text is used will, of course, depend on the instructor and students in question. However, it is probably not appropriate for a conventional lecture-based course nor for a really large class.

The material presented in this text is somewhat stripped-down. Various concepts and topics that are often covered in introductory mathematical logic and computability courses are given very short shrift or omitted entirely. Instructors might consider having students do projects on additional material if they wish to to cover it.

Prerequisites:

The material in this text is largely self-contained, though some knowledge of (very basic) set theory and elementary number theory is assumed at several points. A few problems and examples draw on concepts from other parts of mathematics; students who are not already familiar with these should consult texts in the appropriate subjects for the necessary definitions. What is really needed to get anywhere with all of the material developed here is competence in handling abstraction and proofs, including proofs by induction. The experience provided by a rigorous introductory course in abstract algebra, analysis, or discrete mathematics ought to be sufficient.

More Resources:

- The book's webpage at the Department of Mathematics at Trent University

Tweet

About The Author(s)

Stefan Bilaniuk is Associate Professor in the Department of Mathematics at Trent University. His interests are in combinatorial set theory, particularly problems about Souslin trees, and in geometry, on non-Desarguesian projective planes. He has also worked a bit on binary codes.

Book Categories

Computer Science
Introduction to Computer Science
Introduction to Computer Programming
Algorithms and Data Structures
Artificial Intelligence
Computer Vision
Machine Learning
Neural Networks
Game Development and Multimedia
Data Communication and Networks
Coding Theory
Computer Security
Information Security
Cryptography
Information Theory
Computer Organization and Architecture
Operating Systems
Image Processing
Parallel Computing
Concurrent Programming
Relational Database
Document-oriented Database
Data Mining
Big Data
Data Science
Digital Libraries
Compiler Design and Construction
Functional Programming
Logic Programming
Object Oriented Programming
Formal Methods
Software Engineering
Agile Software Development
Information Systems
Geographic Information System (GIS)

Mathematics
Mathematics
Algebra
Abstract Algebra
Linear Algebra
Number Theory
Numerical Methods
Precalculus
Calculus
Differential Equations
Category Theory
Proofs
Discrete Mathematics
Theory of Computation
Graph Theory
Real Analysis
Complex Analysis
Probability
Statistics
Game Theory
Queueing Theory
Operations Research
Computer Aided Mathematics

Supporting Fields
Web Design and Development
Mobile App Design and Development
System Administration
Cloud Computing
Electric Circuits
Embedded System
Signal Processing
Integration and Automation
Network Science
Project Management

Operating System
Programming/Scripting
Ada
Assembly
C / C++
Common Lisp
Forth
Java
JavaScript
Lua
Microsoft .NET
Rexx
Perl
PHP
Python
R
Rebol
Ruby
Scheme
Tcl/Tk

Miscellaneous
Sponsors