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4434Eric 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.The 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.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.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.A Problem Course in Mathematical Logic
http://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.blogic: a web logic textbook
http://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.Carnegie Mellon's Open Learning Initiative (OLI)
http://www.merlot.org/merlot/viewMaterial.htm?id=239585
This site contains the learning materials for eleven online courses that are currently taught at Carnegie Mellon University. Students anywhere may use these materials as learning resouces. Instructors at other learning institutions may use and even base their own courses on these materials free of charge. An instructor can create an account on OLI, select and sequence course materials, and take advantage of OLI’s tracking of student progress. While all courses come in the "open and free" version, at least one course (Logic and Proofs) also comes in a version that requires payment of a fee to OLI. The available couses at this time are: Biology, Calculus, Causal Reasoning, Chemistry, Economics, Emperical Research Methods, French, Logic and Proofs, Physics, Statistics, and Statics.Figure This! Math Challenges for Families
http://www.merlot.org/merlot/viewMaterial.htm?id=85249
General Math-in-life intrigue. Fun applications in daily like, Which shape holds the most popcorn?, or Why aren't manhole covers square?Good lighthearted fun.Foral 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. The author is an assistant professor of philosophy at the University at Albany, SUNY.Foundations of Computer Science
http://www.merlot.org/merlot/viewMaterial.htm?id=89637
NuMachine, as powerful as Turing machine, but more intuitive in its working is described. Adding three more derivation rules to Elementary Arithmetic of Godel and calling it Sentient Arithmetic (SA), the incompleteness theorems are proved within SA, without using any metalanguage. Intuitive Set Theory (IST), a theory in which we do not have to deal with cardinals higher than aleph-null, is described. In IST, there is no Skolem Paradox and there are no nonLebesgue measurable sets.