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4434The Math Forum - Internet Mathematics Library
http://www.merlot.org/merlot/viewMaterial.htm?id=89910
A huge list of resources in various topics of mathematics and math education.Khan Academy (Math Portion)
http://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.We use mathematics
http://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. Proof Designer
http://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.Eric Weisstein's World of Mathematics
http://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.Formal Logic
http://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 A Modern Formal Logic Primer
http://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.'forall X: An Introduction to Formal Logic
http://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.'Intro to Logic
http://www.merlot.org/merlot/viewMaterial.htm?id=352728
This is 'an introduction to reasoning with propositional and first-order logic, with applications to computer science. It is Part of the TeachLogic Project (www.teachlogic.org).'Contents include:IntroductionPropositional LogicRelations and ModelsFirst-Order LogicConclusion, AcknowledgementsAppendices and Reference SheetsFigure This! Math Challenges for Families
http://www.merlot.org/merlot/viewMaterial.htm?id=85249
'The rigors and demands of our increasingly complex, technologically dependent society have made high student achievement in mathematics a top priority among educators, policymakers, and employers. Todays citizens need more than basic computation and rote mathematical skills. They must master the higher-level concepts and approaches to problem solving that are key to success in work and everyday life.To meet this need, the National Council of Teachers of Mathematics, in cooperation with the National Action Council for Minorities in Engineering, Widmeyer Communications, and the Learning First Alliance, launched Figure This!Figure This! demonstrates challenging middle school mathematics and emphasizes the importance of high-quality math education for all students. Funding for the project was provided by the National Science Foundation (NSF) and the U.S. Department of Education.Figure This! Mathematical challenges for families provide interesting math challenges that middle-school students can do at home with their families.Each challenge features:a description of the important math involveda note on where the math is used in the real worlda hint to get startedcomplete solutionsa "Try This" sectionadditional related problems with answersquestions to think aboutfun facts related to the mathresources for further exploration.'