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4434Logic and Proofs
http://www.merlot.org/merlot/viewMaterial.htm?id=907321
Logic is a remarkable discipline. It is deeply tied to mathematics and philosophy, as correctness of argumentation is particularly crucial for these abstract disciplines. Logic systematizes and analyzes steps in reasoning: correct steps guarantee the truth of their conclusion given the truth of their premise(s); incorrect steps allow the formulation of counterexamples, i.e., of situations in which the premises are true, but the conclusion is false.Recognizing (and having conceptual tools for recognizing) the correctness or incorrectness of steps is crucial in order to critically evaluate arguments, not just in philosophy and mathematics, but also in ordinary life. This skill is honed by working in two virtual labs. In the ProofLab you learn to construct complex arguments in a strategically guided way, whereas in the TruthLab the emphasis is on finding counterexamples systematically.Who should take this course?This is an introductory course designed for students from a broad range of disciplines, from mathematics and computer science to drama and creative writing. The highly interactive presentation makes it possible for any student to master the material. Concise multimedia lectures introduce each chapter; they discuss, in detail, the central notions and techniques presented in the text, but also articulate and motivate the learning objectives for each chapter.Open & Free VersionThe Open & Free, Logic & Proofs course includes the first five chapters of Logic & Proofs, providing a basic introduction to sentential logic. A full version of Logic & Proofs, including both sentential and predicate logic, is also available without technical or instructor support to independent users, for a small fee. No credit is awarded for completing either the Open & Free, Logic & Proofs course or the full, unsupported Logic & Proofs course.Fermat's Proof to his "Last Theorem" [A Restoration]
http://www.merlot.org/merlot/viewMaterial.htm?id=830512
This is a free textbook that is offered by Amazon for reading on a Kindle. Anybody can read Kindle books—even without a Kindle device—with the free Kindle app for smartphones and tablets. Download the app for your device and start reading for free.'The Holy Grail of mathematics revealed as a truly 17th-century numerical and geometrical proof as a letter by Fermat to a colleague. This will withstand all challenges.'Symbolic Logic
http://www.merlot.org/merlot/viewMaterial.htm?id=815523
This is a free textbook that is offered by Amazon for reading on a Kindle. Anybody can read Kindle books—even without a Kindle device—with the free Kindle app for smartphones and tablets. Download the app for your device and start reading for free.‘This book was converted from its physical edition to the digital format by a community of volunteers.’'Yes, this is the Lewis Carroll who wrote Alice in Wonderland, and these two works show the same quirky humor. Here you see Carroll the mathematician at his playful best. Don't let the title of the first work mislead you--this isn't about modern symbolic logic but about ways of expressing classical logic with symbols. It's loaded with amusing problems to delight any mathematical puzzler. In the second work he turns logic into a game played with diagrams and colored counters, giving you hundreds of challenging and witty syllogisms to solve. Great mind-stretching fun.'A System Of Logic, Ratiocinative And Inductive
http://www.merlot.org/merlot/viewMaterial.htm?id=815588
This is a free textbook that is offered by Amazon for reading on a Kindle. Anybody can read Kindle books—even without a Kindle device—with the free Kindle app for smartphones and tablets. Download the app for your device and start reading for free.‘This book was converted from its physical edition to the digital format by a community of volunteers.’'A System of Logic was first published in 1843 and immediately enjoyed a wide circulation, going through numerous editions. Mill himself made substantial changes in the third edition, published in 1850, and the eighth edition, published in 1872, a year before his death. This book is Mill’s most comprehensive and systematic philosophical work, elaborating his inductive method, which helped to free the empirical sciences from the rigidity of analysis by way of syllogisms. Syllogisms are arguments grounded in general principles, in which two premises are used to deduce a third premise, or conclusion. In A System of Logic, Mill breaks away from this age-old practice and instead proposes the use of a form of logic derived from the principles of the natural sciences. He uses his method to address questions of language and logic, induction, the relativity of knowledge, the structure of the scientific method, the structure of arithmetic and geometry, and the principles of the moral sciences. In effect, Mill provides a solid, scientific methodology for reasoning and for philosophy, derived from science and mathematics.The introduction discusses the role and purpose of logic in human understanding. Logic is the art and science of reasoning, a means for the pursuit of truth. However, logic is only concerned with making inferences from observed phenomena, not with intuitive truths. Logic does not produce new evidence, but it can determine whether something offered as evidence is valid. Logic judges but does not observe, invent, or discover. Logic serves a purpose in some larger project of inquiry that gives it meaning. Fundamentally, logic is a method of evaluating evidence.'Mathematical Reasoning: Writing and Proof
http://www.merlot.org/merlot/viewMaterial.htm?id=802450
This textbook is designed for the first course in the college mathematics curriculum that introduces students to the process of constructing and writing proofs.A Gentle Introduction to the Art of Mathematics
http://www.merlot.org/merlot/viewMaterial.htm?id=800958
'This book is designed for the transition course between calculus and differential equations and the upper division mathematics courses with an emphasis on proof and abstraction. The book has been used by the author and several other faculty at Southern Connecticut State University. There are nine chapters and more than enough material for a semester course. Student reviews are favorable.It is written in an informal, conversational style with a large number of interesting examples and exercises, so that a student learns to write proofs while working on engaging problems.'Mathematical Reasoning: Writing and Proof
http://www.merlot.org/merlot/viewMaterial.htm?id=800960
'Mathematical Reasoning: Writing and Proof is designed to be a text for the ﬁrst course in the college mathematics curriculum that introduces students to the pro-cesses of constructing and writing proofs and focuses on the formal development of mathematics. The primary goals of the text are as follows:To help students learn how to read and understand mathematical deﬁnitions and proofs;To help students learn how to construct mathematical proofs;To help students learn how to write mathematical proofs according to ac-cepted guidelines so that their work and reasoning can be understood by others; andTo provide students with material that will be needed for their further study of mathematics.'Combinatorics Through Guided Discovery
http://www.merlot.org/merlot/viewMaterial.htm?id=800962
'This book is an introduction to combinatorial mathematics, also known as combinatorics. The book focuses especially but not exclusively on the part of combinatorics that mathematicians refer to as “counting.” The book consists almost entirely of problems. Some of the problems are designed to lead you to think about a concept, others are designed to help you ﬁgure out a concept and state a theorem about it, while still others ask you to prove the theorem. Other problems give you a chance to use a theorem you have proved. From time to time there is a discussion that pulls together some of the things you have learned or introduces a new idea for you to work with. Many of the problems are designed to build up your intuition for how combinatorial mathematics works. There are problems that some people will solve quickly, and there are problems that will take days of thought for everyone. Probably the best way to use this book is to work on a problem until you feel you are not making progress and then go on to the next one. Think about the problem you couldn’t get as you do other things. The next chance you get, discuss the problem you are stymied on with other members of the class. Often you will all feel you’ve hit dead ends, but when you begin comparing notes and listening carefully to each other, you will see more than one approach to the problem and be able to make some progress.In fact, after comparing notes you may realize that there is more than one way to interpret the problem. In this case your ﬁrst step should be to think together about what the problem is actually asking you to do. You may have learned in school that for every problem you are given, there is a method that has already been taught to you, and you are supposed to ﬁgure out which method applies and apply it. That is not the case here. Based on some simpliﬁed examples, you will discover the method for yourself. Later on, you may recognize a pattern that suggests you should try to use this method again.'Fermat's Proof to his "Last Theorem" [A Restoration]
http://www.merlot.org/merlot/viewMaterial.htm?id=801037
This is a free version of the Boundless textbook that is offered by Amazon for reading on a Kindle. If one creates a Kindle account, it can be downloaded to a laptop or iPad with a Kindle app.'The Holy Grail of mathematics revealed as a truly 17th-century numerical and geometrical proof as a letter by Fermat to a colleague. This will withstand all challenges.'Introductory Maths for Chemists - Chemistry Maths 1
http://www.merlot.org/merlot/viewMaterial.htm?id=736044
'Chemistry Maths 1 teaches Maths from a “chemical” perspective and is the first of a three part series of texts taken during a first-year university course. It is the Maths required by a Chemist, or Chemical Engineer, Chemical Physicist, Molecular Biologist, Biochemist or Biologist. Tutorial questions with fully worked solutions are used and structured on a weekly basis to help the students to self-pace themselves. Coloured molecular structures, graphs and diagrams bring the text alive. Navigation between questions and their solutions is by page numbers for use with your PDF reader.'