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4434The Math Forum - Internet Mathematics Library
https://www.merlot.org/merlot/viewMaterial.htm?id=89910
A huge list of resources in various topics of mathematics and math education.Tue, 8 Aug 2000 00:00:00 -0700Khan Academy
https://www.merlot.org/merlot/viewMaterial.htm?id=371570
Thousands of FREE, short, online videos that are focused on explaining and modeling the learning of specific topics in math (basic arithmetic and math to calculus), statistics, biology, physics, chemistry, finance, and other topics. The topics cover K-12 levels and higher education. The simple and clear presented information enables learners to see and review the topics and how to solve the problems at their pace with as much practice as they wish. In particular there are over a thousand videos just for mathematics. The site also contains a handful of interactive mathematics learning objects that are of the drill and practice type.Fri, 6 Mar 2009 17:48:47 -0800We use mathematics
https://www.merlot.org/merlot/viewMaterial.htm?id=579310
WeUseMath.org is a non-profit website that helps to answer this question. This website describes the importance of mathematics and many rewarding career opportunities available to students who study mathematics. Includes a video and teacher resources. Fri, 2 Sep 2011 09:54:04 -0700Proof Designer
https://www.merlot.org/merlot/viewMaterial.htm?id=78631
Proof designer is a tool intended to help students who are beginning to learn how to write proofs. While proving theorems certainly is a creative task, there are many steps that actually are schematic and mathematicians have internalized them. For example, to prove a universally quantified statement we need to pick an arbitrary element and prove the statement for it. These types of nestings are not automatically done by novices and they take time to internalize. In proof designer such steps are created upon selection with the characteristic start (״Let a be ") and the characteristic ending (״Since a was arbitrary "). The user still has to fill in the steps in between. In the above fashion proof designer can be used to keep track of and demonstrate the macroscopic structure of the proof as well as the nesting of sub-proofs within a proof.Mon, 10 Feb 2003 00:00:00 -0800Eric Weisstein's World of Mathematics
https://www.merlot.org/merlot/viewMaterial.htm?id=76247
This site provides an extremely large encyclopedia-style collection of material related to mathematics at the college level and beyond. Much of the material deals with advanced topics. A large number of animated GIFs and java applets are presented as visual aids and the site has won numerous web awards. The World of Mathematics is hosted by Wolfram Research, Inc., and is offered as a free service to the mathematics community.Wed, 23 Jan 2002 00:00:00 -0800forall X: An Introduction to Formal Logic
https://www.merlot.org/merlot/viewMaterial.htm?id=302325
'forall x is an introduction to sentential logic and first-order predicate logic with identity, logical systems that significantly influenced twentieth-century analytic philosophy. After working through the material in this book, a student should be able to understand most quantified expressions that arise in their philosophical reading. This books treats symbolization, formal semantics, and proof theory for each language. The discussion of formal semantics is more direct than in many introductory texts. Although forall x does not contain proofs of soundness and completeness, it lays the groundwork for understanding why these are things that need to be proven.In formal logic, sentences and arguments are translated into mathematical languages with well-defined properties. If all goes well, properties of the argument that were hard to discern become clearer. This text describes two formal languages which have been of special importance to philosophers: truth-functional sentential logic and quantified predicate logic. The book covers translation, formal semantics, and proof theory for both languages. This can be used as the textbook for a semester long course in logic, for a unit on logic, or for self-directed study. Each chapter contains practice exercises; solutions to selected exercises appear in an appendix.'Sun, 13 Apr 2008 00:44:52 -0700Formal Logic
https://www.merlot.org/merlot/viewMaterial.htm?id=351071
This is an 'undergraduate college level textbook covering first order predicate logic with identity but omitting metalogical proofs.'Brief ContentsPreliminariesSentential LogicPredicate LogicIdentity Theory Mon, 17 Nov 2008 13:55:10 -0800A Modern Formal Logic Primer
https://www.merlot.org/merlot/viewMaterial.htm?id=352745
This is a 'two-volume introduction to formal logic. Volume I presents sentence logic and Volume II covers predicate logic and metatheory.' It 'features easy-to-understand explanations and graded exercises.''Each volume is broken into individual chapters. And each volume has an associated solutions manual (the last item under each volume). There is a file with corrections to both the text and the answer manual. Also note a file with the diagrammatic summary of the rules that appeared on the inside cover of the published version of the primmer. All files are in Adobe Acrobat PDF 6 format. they require version 6, or newer, of Adobe, which can be down loaded here. All files are fully searchable.'Tue, 25 Nov 2008 16:29:48 -0800A Problem Course in Mathematical Logic
https://www.merlot.org/merlot/viewMaterial.htm?id=302304
A Problem Course in Mathematical Logic is intended to serve as the text for an introduction to mathematical logic for undergraduates with some mathematical sophistication. It supplies definitions, statements of results, and problems, along with some explanations, examples, and hints. The idea is for the students, individually or in groups, to learn the material by solving the problems and proving the results for themselves. The book should do as the text for a course taught using the modified Moore-method.The material and its presentation are pretty stripped-down and it will probably be desirable for the instructor to supply further hints from time to time or to let the students consult other sources. Various concepts and and topics that are often covered in introductory mathematical logic or computability courses are given very short shrift or omitted entirely, among them normal forms, definability, and model theory.Sat, 12 Apr 2008 23:51:27 -0700blogic: a web logic textbook
https://www.merlot.org/merlot/viewMaterial.htm?id=79868
Interactive textbook for introductory logic courses. Topics include: (i) Boolean searching (ii) propositional logic with truth-tables (iii) the logic of frequencies and probabilities (iv) modal logic and counterfactuals (v) quantification. Textbook includes interactive exercises.Wed, 13 Aug 2003 00:00:00 -0700