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-1-1The Math Forum - Internet Mathematics Library
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<p>A huge list of resources in various topics of mathematics and math education.</p>Tue, 08 Aug 2000 07:00:00 GMTThe Math Forum Swarthmore CollegeKhan Academy
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<p>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.</p>Sat, 07 Mar 2009 01:48:47 GMTSalman Khan; Salman Khan The Khan AcademyMathematical Reasoning: Writing and Proof
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<p>'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:</p><p>To help students learn how to read and understand mathematical deﬁnitions and proofs;</p><p>To help students learn how to construct mathematical proofs;</p><p>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; and</p><p>To provide students with material that will be needed for their further study of mathematics.'</p>Mon, 14 Oct 2013 22:21:09 GMTTed Sundstrom Grand Valley State UniversityMenu Math
https://www.merlot.org/merlot/viewMaterial.htm?id=594769
<p>This is a lesson created for fifth grade, but can be modified to fit other grade levels. The assignment is based on a real world task of ordering food and following a budget. The objective is for students to compute the total of the dinner without using a calculator. The lesson outlines all of the steps necessary for this assignment.</p>Wed, 02 Nov 2011 02:37:40 GMTKelly MahoneySolve a 4x4 Sudoku Puzzle
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<p>This lesson plan was developed to help early grade school teachers demonstrate to students how to use simple deductive logic to solve a simple 4x4 matrix Sudoku puzzle. </p><p>There is a description of instructional objectives as they apply to the NET-S and to the Michigan Grade level Content Expectations. There is a description of important content for the learner to grasp in order to complete the objectives. There is a PDF of an example puzzle to use as practice or assessment. There is a link to developmentally appropriate puzzle web sites to be used as practice or assessment. Finally, there is a brief description of an instructional plan.</p>Mon, 31 Jan 2011 02:56:50 GMTJeffrey PowersThe Teacher's Guide
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<p>Provides free worksheets, printouts, lesson plans, SMARTBoard templates, and more. Also provides f<a name="Free_Math_Interactive_Sites_"></a>ree Math Interactive Sites.</p>Tue, 17 Jul 2012 20:02:42 GMTWe use mathematics
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<p>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.</p><p> </p>Fri, 02 Sep 2011 16:54:04 GMTBrigham Young University, Department of MathematicsProof Designer
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<p>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. <br /><br />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. <br /><br />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.</p>Mon, 10 Feb 2003 08:00:00 GMTDaniel J. Velleman Amherst College18.100A Introduction to Analysis (MIT)
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Analysis I (18.100) in its various versions covers fundamentals of mathematical analysis: continuity, differentiability, some form of the Riemann integral, sequences and series of numbers and functions, uniform convergence with applications to interchange of limit operations, some point-set topology, including some work in Euclidean n-space. MIT students may choose to take one of three versions of 18.100: Option A (18.100A) chooses less abstract definitions and proofs, and gives applications where possible. Option B (18.100B) is more demanding and for students with more mathematical maturity; it places more emphasis from the beginning on point-set topology and n-space, whereas Option A is concerned primarily with analysis on the real line, saving for the last weeks work in 2-space (the plane) and its point-set topology. Option C (18.100C) is a 15-unit variant of Option B, with further instruction and practice in written and oral communication.Thu, 07 Aug 2014 00:18:00 GMTProf. Arthur Mattuck18.S996 Category Theory for Scientists (MIT)
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The goal of this class is to prove that category theory is a powerful language for understanding and formalizing common scientific models. The power of the language will be tested by its ability to penetrate into taken-for-granted ideas, either by exposing existing weaknesses or flaws in our understanding, or by highlighting hidden commonalities across scientific fields.Wed, 06 Aug 2014 23:58:14 GMTDavid I. SpivakA Gentle Introduction to the Art of Mathematics
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<p>'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.</p><p>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.'</p>Mon, 14 Oct 2013 22:13:53 GMTJoseph E. FieldsA+Click Math Skill Self-Study Tests for Grade 1 to 12
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<p>A+Click Math Self-study Tests and Skill Assessment for Grade 1 to Grade 12. It includes more than 1000 challenging problems and answers and tons of illustrations. The practice tests adapt to student ability. This website has a graduated set of problems, starting from very simple, to quite difficult. To progress to a new level, you have to answer five consecutive questions correctly. The questions are appropriate to elementary students; almost any second grader could answer the easiest. This is a good assessment test without being insulting or frustrating.</p>Sat, 20 Nov 2010 16:52:40 GMTIgor Kokcharov AplusclickCombinatorics Through Guided Discovery
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<p>'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.</p><p>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.'</p>Mon, 14 Oct 2013 22:29:33 GMTKenneth P. Bogart Dartmouth UniversityD. Brice - MATH 300: Sets and Logic - Faculty Showcase at California State University, Bakersfield
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<p>This open textbook is being utilized in a mathematics course for undergraduate mathematics and computer science majors by Daniel Brice, Ph.D., at CSU Bakersfield. The open textbook is a printable PDF document. The main motivation to adopt an open textbook was cost savings for students. Students can access the open textbook in bound-copy form or on their smartphones, tablets, or computers.</p>Tue, 09 Jan 2018 01:46:27 GMTCalifornia Open Online Library (COOLforEd) COOLforEdDefinition of Intuitive Set Theory
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The two axioms which define intuitive set theory, Axiom of Combinatorial Sets and Axiom of Infinitesimals, are stated. Generalized Continuum Hypothesis is derived from the first axiom, and the infinitesimal is visualized using the latter.Sat, 03 Nov 2001 08:00:00 GMTKannan NambiarFermat's Proof to his "Last Theorem" [A Restoration]
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<p>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.</p><p>'<span>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.'</span></p>Tue, 15 Oct 2013 00:05:39 GMTJack GerberFigure This! Math Challenges for Families
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<p>'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.</p>
<p>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!</p>
<p>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.</p>
<p>Figure This! Mathematical challenges for families provide interesting math challenges that middle-school students can do at home with their families.</p>
<p>Each challenge features:</p>
<ul>
<li><span style="font-size: 11px;">a description of the important math involved</span></li>
<li><span style="font-size: 11px;">a note on where the math is used in the real world</span></li>
<li><span style="font-size: 11px;">a hint to get started</span></li>
<li><span style="font-size: 11px;">complete solutions</span></li>
<li><span style="font-size: 11px;">a "Try This" section</span></li>
<li><span style="font-size: 11px;">additional related problems with answers</span></li>
<li><span style="font-size: 11px;">questions to think about</span></li>
<li><span style="font-size: 11px;">fun facts related to the math</span></li>
<li><span style="font-size: 11px;">resources for further exploration.'</span></li>
</ul>Sat, 26 Nov 2005 08:00:00 GMTNational Council of Teachers of MathematicsGeneralized Continuum Hypothesis and the Axiom of Combinatorial Sets
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Axiom of Combinatorial Sets is defined and used to derive Generalized Continuum Hypothesis.Sun, 07 Apr 2002 08:00:00 GMTKannan NambiarInteraktive Logik (Gateway to Logic) (CG1-1)
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interactive propositional logic; show syntax tree, alpha graph, Fregean notation of propositions; display truth tables, normal forms; optimize expressions; check proofs in predicate logicTue, 27 Jan 1998 08:00:00 GMTChristian GottschallLearn how to write mathematical proofs
https://www.merlot.org/merlot/viewMaterial.htm?id=424855
<p>PC-based software and interactive tutorial to learn how to write mathematical proofs. Makes use of innovative proof-checking technology to provide instant feedback to students/users. Free, full-version download available at website.</p>Wed, 30 Dec 2009 05:20:43 GMTDan ChristensenLogsets and ZF Theory
https://www.merlot.org/merlot/viewMaterial.htm?id=77049
Logset, the inverse of the powerset operation, is introduced into set theory.Thu, 20 Jun 2002 07:00:00 GMTKannan NambiarMathematical Logic
https://www.merlot.org/merlot/viewMaterial.htm?id=80999
Conteudo de Logica Matematica em PortuguesSun, 23 May 2004 07:00:00 GMTCelina AbarMathematical Reasoning: Writing and Proof
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<p><span>This textbook is designed for the first course in the college mathematics curriculum that introduces students to the process of constructing and writing proofs.</span></p>Fri, 18 Oct 2013 16:22:30 GMTTed Sundstrom Grand Valley State UniversityMathematics 2: Number Theory
https://www.merlot.org/merlot/viewMaterial.htm?id=384183
<p>Assists teachers in understanding and interpreting the properties of numbers and provides a background to the numerous proofs and solutions to various mathematical equations. Material is crucial for the teaching of secondary school mathamatics.</p><p><a href="http://teachingcommons.cdl.edu/avu/math/documents/Number%20Theory_readings.pdf">Compulsory Readings for Mathematics II: Number Theory (PDF)</a></p>Thu, 21 May 2009 21:57:04 GMTPaul Cheqe Amoud University