- published: 23 Dec 2011
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Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics. It bears close connections to metamathematics, the foundations of mathematics, and theoretical computer science. The unifying themes in mathematical logic include the study of the expressive power of formal systems and the deductive power of formal proof systems.
Mathematical logic is often divided into the fields of set theory, model theory, recursion theory, and proof theory. These areas share basic results on logic, particularly first-order logic, and definability. In computer science (particularly in the ACM Classification) mathematical logic encompasses additional topics not detailed in this article; see Logic in computer science for those.
Since its inception, mathematical logic has both contributed to, and has been motivated by, the study of foundations of mathematics. This study began in the late 19th century with the development of axiomatic frameworks for geometry, arithmetic, and analysis. In the early 20th century it was shaped by David Hilbert's program to prove the consistency of foundational theories. Results of Kurt Gödel, Gerhard Gentzen, and others provided partial resolution to the program, and clarified the issues involved in proving consistency. Work in set theory showed that almost all ordinary mathematics can be formalized in terms of sets, although there are some theorems that cannot be proven in common axiom systems for set theory. Contemporary work in the foundations of mathematics often focuses on establishing which parts of mathematics can be formalized in particular formal systems (as in reverse mathematics) rather than trying to find theories in which all of mathematics can be developed.
Definitions and examples. Truth tables. Equivalent statements. For more free math videos, visit: http://www.professorserna.com
Mathematical Logic | CET (17th November 2015) Centre : Andheri, Borivali, Thane, Nerul, Dadar, Chembur & Kharghar Date : 17th November 2015 Faculty : Manoj Gupta Subscribe Now - https://www.youtube.com/channel/UCFvb... Watch this Lecturer and more in my 'Daily VC Lecture' playlist: https://www.youtube.com/playlist?list... Visit my channel for more videos: https://www.youtube.com/paceiit&m...; Social Media links: FaceBook https://www.facebook.com/PaceEducare/... Twitter https://twitter.com/paceeducare PACE IIT & MEDICAL http://www.iitianspace.com/index.php
A Scene from (The Oxford Murders 2008) Film where a doctorate student in the field of mathematical philosophy attends a Lecture given by prof. Arthur Seldom which he wants to work with and seeks for his recognition.
Here is a quick tutorial on two different truth tables. If you have any questions or would like me to do a tutorial on a specific example, then please comment down below and I will get back to you as soon as possible!
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Visit my website: http://bit.ly/1zBPlvm Subscribe on YouTube: http://bit.ly/1vWiRxW Hello, welcome to TheTrevTutor. I'm here to help you learn your college courses in an easy, efficient manner. If you like what you see, feel free to subscribe and follow me for updates. If you have any questions, leave them below. I try to answer as many questions as possible. If something isn't quite clear or needs more explanation, I can easily make additional videos to satisfy your need for knowledge and understanding. Today we introduce propositional logic. We talk about what statements are and how we can determine truth values.
John Allen Paulos (born July 4, 1945) is an American professor of mathematics at Temple University in Philadelphia, Pennsylvania. He has gained fame as a writer and speaker on mathematics and the importance of mathematical literacy. Paulos writes about many subjects, especially of the dangers of mathematical innumeracy; that is, the layperson's misconceptions about numbers, probability, logic. Paulos was born in Denver Colorado and grew up in Chicago, Illinois and Milwaukee, Wisconsin. In an interview he described himself as lifelong skeptic.[1] He went to high school in Milwaukee, Wisconsin. After his Bachelor of Mathematics at University of Wisconsin (1967) and his Master of Science at University of Washington (1968) he received his Ph.D. in mathematics from the University of Wisconsin–...
"Cognitive Logic vs. Mathematical Logic", presented by Pei Wang Recorded in August 2011, Reykjavik, Iceland
Introductory video of Discrete Mathematics: Foundation for Computer Science Course by Dimik Computing School. The course will be conducted online and in Bangla. This course will teach about mathematical proof and basic probability and some mathematical theories required for a computer science student. This course require prior knowledge of basics arithmetic and some preliminary knowledge of Probability . Anyone can en-roll in this course free of cost. The course is designed in a complete MOOC pattern. The course started on 15th, March, 2014 The course is conducted by - Hammad Ali, Senior Lecturer, Department of CSE, Brac University Follow us on Facebook:https://www.facebook.com/turbotechbd94/ website:http://turbotechbd.jimdo.com/ কোর্সটি পরিচালনা করবেন - হাম্মাদ আলী, শিক্ষক, কম্পিউটার সা...
Need Answer Sheet of this Question paper Contact us at answersheethelp@gmail.com M: 7019944355 Business Communication 1. Explain how watching a movie from another country might help you prepare to interpret nonverbal behavior from that culture correctly. 2. One of your co-workers is originally from Saudi Arabia. You like him, and the two of you work well together. However, he stands so close when you speak with him that it makes you very uncomfortable. Do you tell him of your discomfort, or do you try to cover it up ? 1. What are the communication challenges and barriers Barry faces? 2. What are some ways Barry might use effective communication as a motivator for employees to follow safe food handling practices? 3. What Standard Operating Procedures (SOPs) would be helpful for B...
Listen to the full audiobook: http://easyget.us/mabk/30/en/B00HWVQR7U/book By North-american standards, philosophy is not new in Quebec: the first men tion of philosophy lectures given by a Jesuit in the College de Quebec (founded 1635) dates from 1665, and the oldest logic manuscript dates from 1679. In English-speaking universities such as Mcgill (founded 1829), philosophy began to be taught later, during the second half of the 19th century. The major influence on English-speaking philosophers was, at least initially, that of Scottish Empiricism. On the other hand, the strong influence of the Catholic Church on French-canadian society meant that the staff of the facultes of the French-speaking universities consisted, until recently, almost entirely of Thomist philosophers. There was acco...
Listen to the full audiobook: http://appgame.space/mabk/30/en/B00AA8JVC0/book If there is a movement or school that epitomizes analytic philosophy in the middle of the twentieth century, it is logical empiricism. Logical empiricists created a scientifically and technically informed philosophy of science, established mathematical logic as a topic in and tool for philosophy, and initiated the project of formal semantics. Accounts of analytic philosophy written in the middle of the twentieth century gave logical empiricism a central place in the project. The second wave of interpretative accounts was constructed to show how philosophy should progress, or had progressed, beyond logical empiricism. The essays survey the formative stages of logical empiricism in central Europe and its acculturat...
here we do 6 examples, 5 with standard arguments and 1 with a truth table. This should help you understand the types of logical arguments you are likely to encounter in your math class...and that makes us happy!! :)
Now we're going to "upgrade" our logic to predicate logic, which lets us have a good bit more flexibility in how we describe various situations, including the use of quantifiers. http://www.polymathlectures.org/
In this video we give a very quick overview of a highly controversial period in the development of modern mathematics: the rise of set theory, logic and computability in the late 19th and early 20th centuries. Starting with the pioneering but contentious work of Georg Cantor in creating Set Theory arising from questions in harmonic analysis, we discuss Dedekind's construction of real numbers, ordinals and cardinals, and some of the paradoxes that this new way of thinking led to. We also explain how the Schools of Logicism, Intuitionism and Formalism all tried to steer a path around these paradoxes. I should qualify this lecture by stating clearly that in fact I don't really ascribe to any of the theories presented here. My objections will be laid out at length in my MathFoundations serie...
Lecture 1: Introduction and Proofs Instructor: Tom Leighton View the complete course: http://ocw.mit.edu/6-042JF10 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
This is an introduction to logic for Contemporary College Mathematics (MAT 146) at Maysville Community and Technical College. The course is based on "Mathematics All Around" by Thomas Pirnot.
In this video we will build upon our intuition developed from the previous discussion of colors and see how we arrive at the formalized mathematical notion of languages and structures.