Various lecture notes. Think for yourself | Lecture-accompanying blog by Julia Goedecke | Page 5. I’m trying to find out what other people are thinking and have found some blogs by Tim Gowers which I find extremely interesting. This one is about A-level teaching. But also about why understanding is far better than remembering! This is about what well-defined really means. Since I’ve had a few questions about that, others may be interested. If you have some thoughts about teaching (in particular Maths, perhaps), and none of my other teaching posts fit your answer, do feel free to comment here. Thanks for your feedback, it has been very useful. Just to let you know that I do really read it and take your thoughts and comments into account: Continue reading in which we find out about fixed points and permutation properties of Möbius maps. Continue reading in which we view Möbius maps via matrices, and compose geometrically meaningful maps. Continue reading The most important thing you learn at University is how to learn.
Continue reading Continue reading Continue reading. Packing problems. This article is about geometric packing problems. For numerical packing problems, see Knapsack problem. Packing problems are a class of optimization problems in mathematics that involve attempting to pack objects together into containers. The goal is to either pack a single container as densely as possible or pack all objects using as few containers as possible. Many of these problems can be related to real life packaging, storage and transportation issues. Each packing problem has a dual covering problem, which asks how many of the same objects are required to completely cover every region of the container, where objects are allowed to overlap.
In a packing problem, you are given: 'containers' (usually a single two- or three-dimensional convex region, or an infinite space)A set of 'objects' some or all of which must be packed into one or more containers. Usually the packing must be without overlaps between goods and other goods or the container walls. Packing infinite space[edit] . . Into. Erich's Packing Center. Packing Equal Copies Covering Packing Copies to Maximize Total Perimeter Tiling Other Packing Problems Animations and Rigid Packings Heilbronn Problems Related Problems Packing Links | Torsten Sillke | James Buddenhagen | Anton Sherwood | Eduard Baumann | | Mike Reid | Andrew Clarke | Livio Zucca | Packomania | Isohedral Tilings | Packomania. Outlet de estadística y probabilidad | AQ. Commutator subgroup.
2010 Mathematics Subject Classification: Primary: 20-XX [MSN][ZBL] The commutator subgroup of a group G, also called the derived group, second term of the lower central series, of G, is the subgroup of G generated by all commutators of the elements of G (cf. Commutator). The commutator subgroup of G is usually denoted by [G,G], G' or \Gamma_2(G). The commutator subgroup is a fully-characteristic subgroup, and any subgroup containing the commutator subgroup is a normal subgroup. The quotient group with respect to some normal subgroup is Abelian if and only if this normal subgroup contains the commutator subgroup of the group. The commutator ideal of a ring R is the ideal generated by all products ab, a,b \in R; it is also called the square of R and is denoted by [R,R] or R^2. Both the above concepts are special cases of the notion of the commutator subgroup of a multi-operator \def\O{\Omega}\O-group G, which is defined as the ideal generated by all commutators and all elements of the form.
Abstract algebra - Prove that any group $G$ of order $p^2$ is abelian, where $p$ is a prime number. Groupprops. ProofWiki. FUEJUM Title Page. Www-math.mit.edu/phase2/UJM/vol1/index.html. Undergraduate Mathematics Journal ::: Article Archives. Links. Here's our collection of useful web sites! Disclaimer: MathNerds is not responsible for the content of sites other than our own.
We believe the sites mentioned here contain reliable information, but you should use your own judgment. Don't believe everything you read, especially on the Internet! Photo Gallery Our Photo Gallery includes pictures from recent MathNerds activities! MathNerds Mentoring Network The MathNerds Mentoring Network is an exciting new project for linking school district classes to university classes to support local school districts and better prepare future teachers. Mathematics Mentoring Network info Explains how to join the project and establish a mentoring network at your school or college. Top 5 Web Sites These are the web sites that we refer people to most often; one of them probably already had the explanation you are looking for. Purplemath Covers all aspects of high-school algebra in detail. Already-answered questions Maybe your question has already been answered! Guilford Journal of Undergraduate Mathematics - Items Index. Summer 2007 REU - Discrete Mathematics.
! DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"> Instructor: László Babai What's New? | Course Info | Puzzle sheets and Handouts | DM Class Notes | Apprentice Class Notes What's New? "Transfinite Combinatorics" (TC) (second module of Discrete Mathematics) started on Monday, July 23 TC: Class 9 notes posted (proofread by instructor) TC: Class 8 notes posted (proofread by instructor) TC: Class 7 notes posted (NOT proofread by instructor) TC: Class 6 notes posted (proofread by instructor) TC: Class 5 notes posted (proofread by instructor) TC: Class 4 notes posted (proofread by instructor) TC: Class 3 notes posted (proofread by instructor) TC: Class 2 notes posted (NOT proofread by instructor) TC: UPDATED Class 1 notes posted (partially proofread by instructor) Old News Puzzle solutions to be discussed both in the remaining apprentice classes (Thu and Fri, July 12 and 13) and in the DM class (Thu, July 12).
DM: Class 10 notes posted (class Tue 7-10, notes posted 7-12, 12:45am) Back to top. Mathematical Background. This web page is a revised and extended version of Appendix A from the book Conceptual Structures by John F. Sowa. It presents a brief summary of the following topics for students and general readers of that book and related books such as Knowledge Representation and books on logic, linguistics, and computer science. Note: Special symbols in this file that are outside the Latin-1 character set (ISO 8859-1) are represented by a .gif image for each character. The alt tag for each image gives the name of the character. Students who are just learning the symbols can move the mouse to any symbol to get a brief reminder of its name. 1.
Sets, Bags, and Sequences Elementary or "naive" set theory is used to define basic mathematical structures. Curly braces are used to enclose a set specification. This specifies a set consisting of the four integers 1, 97, 63, and 12. If the set is very large, like the set of all mammals, a complete listing is impossible. 6} {x | x=1 or x=2 or x=3} . Idempotency. A. News. You've probably heard of "types" and maybe even "type systems" in your learning so far as a #c0d3r.
For example, you've possibly heard that Ruby is strongly typed, while C is weakly typed (though these definitions are actively debated). Type systems are quite helpful - to varying degrees, they ensure the integrity and expected behavior of our programs. But more generally, types provide us a formal system for posing questions of logic & determining whether said question is, in fact, answerable. But where did these super-powered "types" come from? Special thanks to Tom Ellis and Adam Chlipala for their review and corrections of an early draft of this post.
Leibniz Sets The Stage Leibniz - who demonstrated the superiority of the binary over the decimal representation for mechanical computers back in, oh, 1680 (!) "Calculemus! " Leibniz therefore had as an ideal the following: Henceforth I will refer to Leibniz's "ideal" as the challenge to define "effective calculability. " Grammar Rules. The Easiest Impossible Problem. Péter Frankl is a “Hungarian mathematician and street performer”—quoting our friends at Wikipedia.
He is also a globetrotter, noting on his personal blog that he has visited over 100 countries. He resides in Japan, where he regularly appears on television to blend mathematics and entertainment for children. He visited Atlanta last July but I did not meet him—he worked with his friend Vojtěch Rödl over at Emory University which is across town. His specialty is extremal combinatorics, which is the study of how large or small a mathematical structure can be and still satisfy certain constraints. Today I wish to talk about an approach to his famous conjecture. The amazing thing about the conjecture is that it is so easy to state, yet progress on it seems very difficult.
Frankl first stated the conjecture in 1979, and it was publicized quickly by Ron Graham. The Problem I will state it as a theory problem. Be the Boolean cube, i.e. the set . And in the cube is where Suppose that and also . Let so that. View forum - Mathematics. List of talks organised by event - Categories, Logic and Physics. We currently have videos of 59 talks over 9 events. Click here to view talks organised by speaker. Bellairs Research Centre, March 2008 (No title)Howard Barnum, Los Alamos National LaboratoryWatch video in browser | Download video Measurement-based quantum computationDan Browne, University College LondonWatch video in browser | Download video A survey of categorical quantum mechanicsBob Coecke, University of OxfordWatch video in browser | Download video The causaloid approach to quantum theory and quantum gravityLucien Hardy, Perimeter InstituteWatch video in browser | Download video Quantum theory is probabilistic but has fixed causal structure.
The mechanics of informationKeye Martin, Naval Research LaboratoryWatch video in browser | Download video The physics of anyons for computer scientistsPrakash Panangaden, McGill UniversityWatch video in browser | Download video I give a simple account of the Hall effect and the quantum Hall effect. Imperial College London, January 2008. Andrew Stacey :: Teaching. Teaching Duties In this category you can find information regarding courses that I am teaching. For information about my teaching qualifications and philosophy, see the Professional category.
Since Autumn 2009, I have used a wiki for course notes which can be found at I also maintain a forum which is intended for students of the courses that I teach, this can be found at Both produce MathML by server-side conversion. Animations and Simulations The following are small programs that may (or may) not be useful. Some are Java applets (or standalone Java programs) developed using processing. The Java applets were originally released under the GPL. TMA4115. Summary The most basic object of study in mathematics is of a process. What I put in X, what did I get out? We model processes in mathematics by functions. One of the simplest such cases is the family of continuous functions on the interval. The topics that we shall cover include: Spivak on Category Theory | The n-Category Café. The n-Category Café. Topoi, the categorial analysis of logic. Peter Selinger: Papers. Monoidal category in nLab. Marc Masdeu. Curricum Vitae Work As of January 2014 I work as a Research Associate at the University of Warwick, under the supervision of Lassina Dembele.
From September 2010 to December 2013 I worked at Columbia University as a Ritt Assistant Professor. Graduate Education I started the doctoral program in University of Illinois at Urbana Champaign (UIUC) in August 2005. I took a decent number of good courses, and met really interesting people. Believe it or not, there is certain areas in Mathematics that are not quite represented in that department, and this is why I transferred to McGill University, where I would eventually write my thesis. In May 2010 I passed my oral defense, and in July 8, 2010 my first kid was born. Undergraduate Education The year I had to start my college studies, the UPC came with a new studies program. After the success of this first idea, a new centre was created, under the name of CFIS. Topology Without Tears; Sidney A. Morris; Sid Morris; Sidney Morris; Shmuel Morris.
Tracker Video Analysis and Modeling Tool for Physics Education. GeoGebraTube. Why Most Published Research Findings Are False. Summary There is increasing concern that most current published research findings are false. The probability that a research claim is true may depend on study power and bias, the number of other studies on the same question, and, importantly, the ratio of true to no relationships among the relationships probed in each scientific field. In this framework, a research finding is less likely to be true when the studies conducted in a field are smaller; when effect sizes are smaller; when there is a greater number and lesser preselection of tested relationships; where there is greater flexibility in designs, definitions, outcomes, and analytical modes; when there is greater financial and other interest and prejudice; and when more teams are involved in a scientific field in chase of statistical significance.
Simulations show that for most study designs and settings, it is more likely for a research claim to be false than true. Figures Published: August 30, 2005 Copyright: © 2005 John P. Bias. Topology: More on Algebra and Topology | Mathematics and Such. We’ve arrived at the domain where topology meets algebra. Thus we have to proceed carefully to ensure that the topology of our algebraic constructions are well-behaved. Let’s look at topological groups again.
Our first task is to show that the topologies of subgroups and quotient groups commute. Proposition 1. Suppose N is a normal subgroup of G. If H is a subgroup of G containing N then there’re two ways to obtain the topology on H/N:apply quotient topology to G/N, then subspace topology to H/N;apply subspace topology to H, then quotient to H/N.The two topologies are identical. This follows from the more general fact that if p : X → Y is an open quotient map, then for any subspace the restriction to is also a quotient map. Once again, the fact that p is open is critical. [ To see why, suppose V is a subset of Z such that is open. For some open subset U of X. And then so p(x) is in V. Then since q is surjective, pick such that q(x)=y. Isomorphism Theorems Proposition 2. Proof. Next, we have: by: or. What do normal subgroups look like? | Fermat's Last Spreadsheet. I am in the process of writing a longer post on Galois Theory (see here ), and one of the central concepts is that of a normal subgroup .
We all know the definition (and their equivalents) from classes/books, but anyone who likes to ‘see their mathematics’ is left with the question: … but what do they look like? In this post I give a few different interpretations of the standard definitions, and go some way to explaining why it is difficult to answer this question in concrete terms. Spoiling the punchline a bit, it seems to me that problem is actually the other way round: most of the groups that you have an intuition about are normal , so the question is really when is a group not normal ?
The standard definitions Nothing new yet: A subgroup of a group is normal if any of the following conditions hold (so if one is true they will all be): , (‘left cosets equal right cosets’), is the kernal of a homomorphism . Some examples to bear in mind If is abelian then all its subgroups are normal. ‘modulo. Casual Introduction to Group Theory (5) | Mathematics and Such. Topology Atlas: Questions in Topology. Ralph L. Wojtowicz. The Regression Fallacy. Examples. Statistics in a Nutshell: A Desktop Quick Reference - Sarah Boslaugh, Dr. Paul Andrew Watters. Asymptotic Statistics - A. W. van der Vaart. 7.3.5. Do two arbitrary processes have the same central tendency? How to Analysis Data with Low Quality or Small Samples, Nonparametric Statistics. Statistics Glossary - nonparametric methods. Vedic Math ~ VedantaTree - The Tree of Knowledge. INVESTIGACION. Course Catalog. 0xDE.
KNK103: The Crystals of Mt. Zeta - Kali & the Kaleidoscope. Lecture Notes Algebraic Geometry. Jacob Fox. MathOverflow.
Mondrian - Interactive Statistical Graphics in JAVA. Rsession - Java wrapper to R. ROCR: Classifier Visualization in R. Addi - Matlab / Octave clone for Android. Free Math Help and Free Math Videos Online at MathVids.com. J Home. Constructing our lives: the mathematics of engineering. Sage: Open Source Mathematics Software. 4 sitios web para encontrar cursos universitarios gratis. 20 sitios para ver vídeos educativos gratis. Canal de MIT. Video lectures of mathematics courses available online for free. Mathematics Illuminated | Unit 10. Philosophy of Real Mathematics: Information Geometry and Machine Learning. Tags. GAP System for Computational Discrete Algebra.
Theory and Applications of Categories. John Baez's Stuff. Wolfram|Alpha—Computational Knowledge Engine. VideoLectures - exchange ideas & share knowledge. Terry Tao's Blog. The n. The polymath blog. The Unapologetic Mathematician.