The newest largest prime number was recently discovered on the computer of a Great Internet Mersenne Prime Search (GIMPS) volunteer, Curtis Cooper. The number, as one would expect from something noted to be the largest of something, is quite large: 257,885,161-1. The fully expressed form has 17,425,170 digits, much larger than the previously discovered largest prime number, which measures in at 12,978,189 digits long. If kept in a plain text file, the new number results in a file size of 22.45MB.GIMPS is a collaborative research project performed over the internet where volunteers download some software and let their computers perform calculations. The current incarnation of the GIMPS network sports around 360,000 CPUs operating at 150 trillion calculations per second. The method GIMPS uses is similar to [email protected], another collaborative internet research project that is arguably more popular thanks to the help of the software being freely available on the PlayStation 3.The newly discovered number isn’t just a standard prime, but a Mersenne prime, and only the 48th of which ever discovered. Whereas a standard prime number is one that can only be divided by one and itself, a Mersenne prime takes the form of 2P-1, where P is a prime number.Large prime numbers require a lot of computing power to verify, and Mersenne primes are more complicated than a standard prime. So, aside from being just a fun thing to do with numbers, the Mersenne prime can be an effective tool to use when developing encryption.For all of Curtis’ computer’s hard work, he is eligible for a $3,000 prize. To check out the number, head on over here, where you have a choice to download the number in the full, in plain text or in gzip. The digits that bombard you on that page aren’t actually the full number, as 304,705 lines are left out. If you really want to see what your computer is made of, try copy-pasting portions of the number into text boxes. Better yet, see if you can send large portions of the numbers to friends through an instant message client.


In abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have become subject areas in their own right.
Various physical systems, such as crystals and the hydrogen atom, and three of the four known fundamental forces in the universe, may be modelled by symmetry groups. Thus group theory and the closely related representation theory have many important applications in physics, chemistry, and materials science. Group theory is also central to public key cryptography.
The early history of group theory dates from the 19th century. One of the most important mathematical achievements of the 20th century was the collaborative effort, taking up more than 10,000 journal pages and mostly published between 1960 and 2004, that culminated in a complete classification of finite simple groups.
Group theory has three main historical sources: number theory, the theory of algebraic equations, and geometry. The number-theoretic strand was begun by Leonhard Euler, and developed by Gauss's work on modular arithmetic and additive and multiplicative groups related to quadratic fields. Early results about permutation groups were obtained by Lagrange, Ruffini, and Abel in their quest for general solutions of polynomial equations of high degree. Évariste Galois coined the term "group" and established a connection, now known as Galois theory, between the nascent theory of groups and field theory. In geometry, groups first became important in projective geometry and, later, non-Euclidean geometry. Felix Klein's Erlangen program proclaimed group theory to be the organizing principle of geometry.
Galois, in the 1830s, was the first to employ groups to determine the solvability of polynomial equations. Arthur Cayley and Augustin Louis Cauchy pushed these investigations further by creating the theory of permutation groups. The second historical source for groups stems from geometrical situations. In an attempt to come to grips with possible geometries (such as euclidean, hyperbolic or projective geometry) using group theory, Felix Klein initiated the Erlangen programme. Sophus Lie, in 1884, started using groups (now called Lie groups) attached to analytic problems. Thirdly, groups were, at first implicitly and later explicitly, used in algebraic number theory.
The different scope of these early sources resulted in different notions of groups. The theory of groups was unified starting around 1880. Since then, the impact of group theory has been ever growing, giving rise to the birth of abstract algebra in the early 20th century, representation theory, and many more influential spin-off domains. The classification of finite simple groups is a vast body of work from the mid 20th century, classifying all the finite simple groups.
The range of groups being considered has gradually expanded from finite permutation groups and special examples of matrix groups to abstract groups that may be specified through a presentation by generators and relations.
The theory of transformation groups forms a bridge connecting group theory with differential geometry. A long line of research, originating with Lie and Klein, considers group actions on manifolds by homeomorphisms or diffeomorphisms. The groups themselves may be discrete or continuous.
Most groups considered in the first stage of the development of group theory were "concrete", having been realized through numbers, permutations, or matrices. It was not until the late nineteenth century that the idea of an abstract group as a set with operations satisfying a certain system of axioms began to take hold. A typical way of specifying an abstract group is through a presentation by generators and relations,
A significant source of abstract groups is given by the construction of a factor group, or quotient group, G/H, of a group G by a normal subgroup H. Class groups of algebraic number fields were among the earliest examples of factor groups, of much interest in number theory. If a group G is a permutation group on a set X, the factor group G/H is no longer acting on X; but the idea of an abstract group permits one not to worry about this discrepancy.
The change of perspective from concrete to abstract groups makes it natural to consider properties of groups that are independent of a particular realization, or in modern language, invariant under isomorphism, as well as the classes of group with a given such property: finite groups, periodic groups, simple groups, solvable groups, and so on. Rather than exploring properties of an individual group, one seeks to establish results that apply to a whole class of groups. The new paradigm was of paramount importance for the development of mathematics: it foreshadowed the creation of abstract algebra in the works of Hilbert, Emil Artin, Emmy Noether, and mathematicians of their school.
An important elaboration of the concept of a group occurs if G is endowed with additional structure, notably, of a topological space, differentiable manifold, or algebraic variety. If the group operations m (multiplication) and i (inversion),
are compatible with this structure, that is, they are continuous, smooth or regular (in the sense of algebraic geometry) maps, then G is a topological group, a Lie group, or an algebraic group.
The presence of extra structure relates these types of groups with other mathematical disciplines and means that more tools are available in their study. Topological groups form a natural domain for abstract harmonic analysis, whereas Lie groups (frequently realized as transformation groups) are the mainstays of differential geometry and unitary representation theory. Certain classification questions that cannot be solved in general can be approached and resolved for special subclasses of groups. Thus, compact connected Lie groups have been completely classified. There is a fruitful relation between infinite abstract groups and topological groups: whenever a group Γ can be realized as a lattice in a topological group G, the geometry and analysis pertaining to G yield important results about Γ. A comparatively recent trend in the theory of finite groups exploits their connections with compact topological groups (profinite groups): for example, a single p-adic analytic group G has a family of quotients which are finite p-groups of various orders, and properties of G translate into the properties of its finite quotients.
During the twentieth century, mathematicians investigated some aspects of the theory of finite groups in great depth, especially the local theory of finite groups and the theory of solvable and nilpotent groups. As a consequence, the complete classification of finite simple groups was achieved, meaning that all those simple groups from which all finite groups can be built are now known.
During the second half of the twentieth century, mathematicians such as Chevalley and Steinberg also increased our understanding of finite analogs of classical groups, and other related groups. One such family of groups is the family of general linear groups over finite fields. Finite groups often occur when considering symmetry of mathematical orphysical objects, when those objects admit just a finite number of structure-preserving transformations. The theory of Lie groups,which may be viewed as dealing with "continuous symmetry", is strongly influenced by the associated Weyl groups. These are finite groups generated by reflections which act on a finite-dimensional Euclidean space. The properties of finite groups can thus play a role in subjects such as theoretical physics and chemistry.
This definition can be understood in two directions, both of which give rise to whole new domains of mathematics. On the one hand, it may yield new information about the group G: often, the group operation in G is abstractly given, but via ρ, it corresponds to the multiplication of matrices, which is very explicit. On the other hand, given a well-understood group acting on a complicated object, this simplifies the study of the object in question. For example, if G is finite, it is known that V above decomposes into irreducible parts (see Maschke's theorem). These parts, in turn, are much more easily manageable than the whole V (via Schur's lemma).
Given a group G, representation theory then asks what representations of G exist. There are several settings, and the employed methods and obtained results are rather different in every case: representation theory of finite groups and representations of Lie groups are two main subdomains of the theory. The totality of representations is governed by the group's characters. For example, Fourier polynomials can be interpreted as the characters of U(1), the group of complex numbers of absolute value 1, acting on the L2-space of periodic functions.
A Lie group is a group that is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure. Lie groups are named after Sophus Lie, who laid the foundations of the theory of continuous transformation groups. The term groupes de Lie first appeared in French in 1893 in the thesis of Lie's student Arthur Tresse, page 3.
Lie groups represent the best-developed theory of continuous symmetry of mathematical objects and structures, which makes them indispensable tools for many parts of contemporary mathematics, as well as for modern theoretical physics. They provide a natural framework for analysing the continuous symmetries of differential equations (differential Galois theory), in much the same way as permutation groups are used in Galois theory for analysing the discrete symmetries of algebraic equations. An extension of Galois theory to the case of continuous symmetry groups was one of Lie's principal motivations. 350c69d7ab
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In the text, a difference equation is obtained from which the energy transfer from the drive to the bucket coil can be found as a function of iD , with the circuit constants n2, Lw and C, and velocity v as parameters. The program in this appendix solves the difference equations, with the help of an approximation for dM/dx. The entire program is designed to run on an HP-25 pocket calculator with 49 program steps. Given a larger calculator or computer, one could generalize the program by using a more exact expression for dM/dx or (more usefully) by including the finite cross sections of the drive and bucket coils.
The simple program consists of four subroutines:
For still higher accuracy, the curve of iD is traced point-by-point by slightly modifying the program: step 47: pause, step 48: pause.
In this program, one or two minor tricks are used to save register space: the constant a, , which equals a3/R, is stored as a sequence of four key strokes in steps 31-34. Register 2 contains a constant whose integer and fractional parts are both used in the dM/dx subroutine. The step interval x appears as a sequence of four key strokes in steps 01-04. (All constants are in MKS units.) In detail, the registers store information as shown in table 5.
As normally used, the program calculates the energy transfer for a half-cycle of oscillation. The total energy transfer for a two-coil bucket, corresponding to the passage of both bucket coils through one drive coil, is then (x)(4n2 iB ) (summation of iDM/dx in register 5). Typically, a step interval x of 1 mm is used, 0.001 in program steps 01-04. Each step interval requires 3.75 sec on an HP-25, and about twice that time on an HP-67, so a half-cycle of oscillation with D = 5 .0 cm requires a little over 1 min (see table 6).
|RO||ao = (x)iB /Lwn2|
|R1||Initial value of position x (in m) at which
coil switch is closed. Zero is allowed , but con-
stant should be chosen so that x update sub-
routine never finishes with zero. R1 stores
constant used in dM/dx subroutine. For
D = 5.0 cm, a2 = -184.000138 (i.e.,
INT = -184, FRAC = - 0.000138). For other
cacalibers D, INT and FRAC are proportional
R appears only in this constant
Resonant capacity C appears only
in this constant and is equal to the sum of
the capacities on two adjacent sectprs pf tje actual
|R5||Initialize to zero; stores updated i(dM/dx).|
|R6||Peak voltage to which capicitor is charged
drive circuit switches on; R6 stores updated
capacitor voltage Vc.
|R7||Initialize to zero; stores updated current i.|
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Thanks to the Dungeon League blog  for a great series on procedural map generation, the Procedural Content Generation wiki  for ideas for map generation , the incomplete Voronoi wiki  for some useful resources about Voronoi diagrams. College Calculus, Linear Algebra (e. stanford. PREDICTORS OF STUDENT ACHIEVEMENT IN GRADE 7: THE CORRELATIONS BETWEEN THE STANFORD ACHIEVEMENT TEST, OTIS-LENNON SCHOOL ABILITY TEST, AND PERFORMANCE ON THE TEXAS ASSESSMENT OF KNOWLEDGE AND SKILLS (TAKS) MATH AND READING TESTS A Dissertation Presented to The Faculty of the School of Education Liberty University In Partial Fulfillment The Stanford Math Tournament (SMT) is an annual student-run math competition for high school students held at Stanford University. Updated: April 27, 2017. Transfer and AP credits in Math, Science, Fundamentals, & TIS must be approved by the SoE Dean's Office. replacing the “teacher-proof” curriculum with the “curriculum-proof” teacher: toward a more systematic way for mathematics teachers to interact with their textbooks a dissertation submitted to the school of education and the committee on graduate studies of stanford university in partial fulfillment of the requirement for the degree of A challenging math problem can make some students break into a cold sweat and others excited to wrap their brains around a puzzle. There is great flexibility in the choice of electives, including some upper-division math, statistics, and computer science. ’ I: ‘Why?’ --College level calculus (e. For example, you may not be able to enroll in Chem 31B or Econ 50 until your grades have posted for all the prerequisite classes. )Degrees of unsolvability associated with classes of formalized theories, J. One might point out the following Thomas Church is part of Stanford Profiles, official site for faculty, postdocs, students and staff information (Expertise, Bio, Research, Publications, and more). , ACT Aspire) are based on different standards and cannot be directly compared.
Educational research aims to understand how and why students change over time. How to charge the salary paid while such employees are on vacation is the subject of this resource page. 0. The American Institutes for You should have completed Math 51. Family card games are an inexpensive way to have fun with children while learning important math concepts. MATH 19 or 41) - You’ll need to be able to take a derivative, and maximize a function by finding where the derivative=0. Topics: global atmospheric changes, urban sources of air pollution, indoor air quality problems, design and efficiencies of pollution control devices, and engineering strategies for managing air quality. My Math notebook is small so I can take it with me everywhere in case I have an idea to jot down. ’ I: ‘Why?’ P: ‘Well, I get a lot of handouts in Social Studies and English so it’s important to have a binder where I can add and remove pages. 8 KB Dear Ravi and Frank, attached is an updated version. He works collaboratively with the Stanford Cancer Institute and Stanford Health Care leaders to set the strategy for the clinical delivery of cancer care across Stanford Medicine and growing cancer networks. From: Jan Verschelde <jan@math.
1. Changes must be Minimum Grade Point Average (GPA) for all courses in Engineering Fundamentals and Computer Science Core, Depth, and Senior Project (combined) is 2. . Lattice Methods and Monotone Comparative Statics - a brief introduction to lattice theory (partial orders, posets, lattices, the strong set order, supermodularity, increasing differences), and its application to monotone comparative statics, culminating in a statement and proof of Topkis' Theorem. We will place a particular emphasis on Neural Networks, which are a class of deep learning models that have recently obtained improvements in many different NLP tasks. Notes. Stanford University 701 Welch Road, Building C, Palo Alto, CA 94304 gruber@ksl. 33 (1)(a), Stats. Prerequisites: 70, MATH 51. , the Stanford Achievement Test) and criterion -referenced tests (e. I have never encountred that specific substitution, but if an advsor approves program changes will generally be granted. CS 109 or other stats course) You should know basics of probabilities, gaussian distributions, mean, standard deviation, etc.
If you feel you What are the SAT requirements for students to be admitted to Stanford University? Stanford University typically requires applicants to be in the top 3 percent of SAT test takers. The math department looks to continue improving MATH 51 as it receives feedback from students and continues to Additional drop-in tutoring: SUMO works with the Stanford Math Department to provide peer tutoring services for a number of introductory math classes, including MATH 19, 20, 21. | MATH 113: Linear Algebra and Matrix Theory is a course taught at Stanford University by Instructions. The videos here are serving one of two purposes. Is the school accredited? Yes, Stanford GSB is accredited by the Association to Advance Collegiate Schools of Business. Stanford provides vacation to its regular staff employees. Increasing access to Science, Technology, Engineering, and Math (STEM) fields can create career opportunities. ” Reviewing the battle over “New Math” in mid-twentieth century America, Phillips observes that descriptions of mathematical practices were o Norm-referenced tests (e. g. The required number of field courses is five. Geometry and algebra of vectors, systems of linear equations, matrices and linear transformations, diagonalization and eigenvectors, vector valued functions and functions of several variables, parametric curves, partial derivatives and gradients, the derivative as a matrix, chain rule in several variables, constrained and unconstrained optimization. University.
“There’s increasing understanding that the math situation in the United States is a complete disaster. Akshay has 10 jobs listed on their profile. If you have a spring THINK assignment and would like a different spring THINK course or section, you will want to go to vcathink. It is often viewed as an essential element in global economic competition. 25, Florida Statutes, a student may be promoted to grade 4 if the student This page lists the members of Stanford University, including students, alumni, faculty and academic affiliates associated. Students who have taken both Math 51 & 52 may not count CME 100 as an elective. This initiative will support research projects designed to evaluate changes in the microbiota during lifetime and its influence in health and disease status in the elderly, including those from racial/ethnic minority and underserved populations and understand the underlying mechanisms of microbiota interactions in aged subjects as related to math changes from teas v to ati teas 6 Not much occurred in changes from TEAS V to TEAS 6 except for the addition of two questions, going from 34 to 36 questions and, as a result, an increase in your time allotment from 51 to 54 minutes. Quantitative introduction to the engineering methods used to study and seek solutions to current air quality problems. Minimum Grade Point Average (GPA) for all courses in ENGR Fundamentals and CS Core, Depth, and Senior Project (combined) is 2. Sloan Foundation, a recognition as one of the The Stanford Math Tournament (SMT) is an annual student-run math competition for high school students held at Stanford University. I could write odes about the many, many, MANY things about you that I adore: the fact that it is December and a clear, breezy, perfect 74 degrees outside, the smell of eucalyptus wafting through campus, free laundry machines, the Nutella waffles at Coupa, the Bender room, the visual orgasm that is the quad and the oval, oh… and the beyond enviable world-class education that I Funding Opportunity PAR-18-736 from the NIH Guide for Grants and Contracts. So, for instance, in the later 18th century continuity of a function was taken to mean that infinitesimal changes in the value of the argument induced infinitesimal changes in the value of the function.
Some are here as the heart of flipped lessons. They can be found here. 2018-19 Program Requirements. How does Stanford Federal Credit Union \(SFCU\) compare with other banks, in your experiences? Anyone switch over from another bank to SFCU? Or CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Abstract. The "lecture" part of class is here, and the practice (what would have been homework) is done in class. Abstract. Play these four games designed to reinforce and build upon your child’s math skills—all you need is a deck of playing cards! Family card games are an inexpensive way to have fun with children while learning important math concepts. edu The Architectural Design major seeks to integrate engineering and architecture in ways that blend innovative architectural design with cutting-edge engineering technologies. College foot- 70+ channels, unlimited DVR storage space, & 6 accounts for your home all in one great price. MATH 19 or 41, MATH 51) You should be comfortable taking derivatives and understanding matrix vector operations and notation. Lunch is now included in the $40 tuition cost, but students must be wearing their nametag to receive lunch (no lunch for parents, sorry!). The accrual rates enable Stanford to charge the appropriate funding source for the vacation earned by benefits-eligible staff as they are working.
completed in order to identify the Stanford Achievement Test 10 subtests that were the most important predictors of performance on the Explore Exam. . ’ I: ‘Why?’ In mathematics the word is used in the same general sense, but has had to be furnished with increasingly precise definitions. assessments of reading and math underwent multiple changes. In these cases, come back and try again once your grades have posted or you have taken the necessary exams. The Importance of Early Childhood Education. Exams Students, faculty, and staff are advised to review the End-Quarter Examination Policy. Math is a “discipline which disciplines. foundly, math wars rage over what it means to think correctly in math as well as in other ﬁelds, such as literature, science, economics, and history. This is the first course in the computer graphics sequence at Stanford. S. This is due to increasingly improved childhood health and nutrition.
Grade P if Transfer Math and Science (40 units minimum) Students who have taken both Math 51 and 52 may not count CME 100 as an elective. In addition to these focal areas, we preview a sampling of cross-disciplinary and cross-sector research conducted by the Stanford Center on Longevity that aligns with Sightlines Project goals, including food hardship in King County, Fraud vulnerability, California teacher retirement preferences, and Latino financial literacy. MATH 51 FINAL EXAM December 11, 2000 Brumﬁel Hutchings Levandosky Staﬃlani White 11:00 01 05 09 13 17 1:15 03 07 11 15 19 Name: Student ID: Signature: Instructions: Print your name and student ID number and write your signature to indicate that you accept the honor code. More changes to come. Symbolic Logic 22 (1957) 161-175. With its emphasis on within-person change, latent change score models provide educational researchers with a more general and flexible framework for testing nuanced hypotheses regarding within-person change and between-person differences in within-person change. Circle the number of the section for which you are registered on Infopier. Math 51, Winter 2007 Final Exam March 19, 2007 FINAL EXAM This is a closed-book, closed-notes exam. It’s an Actionscript 3 library for generating Geometry Courses and Classes Overview. Stanford is known for its academic strength, wealth, proximity to Silicon Valley, and ranking as one of the world's top universities. Environmental Engineering UG Program This major is no longer active. Notes on the Development of the Derivative Transformation in Math 51 1.
It is least likely to be explained in terms of changes in human genetic characteristics. Students who believe that there are faculty who are violating End-Quarter period policy should contact the Registrar’s Office. See the complete profile on LinkedIn and discover Owen’s connections My daughter’s FA portal changed for Pomona (NCP waiver approved on 3/5) and she was WL on 3/15. James Milgram, a math professor at Stanford University. And students cannot enroll in Math 19, 20, 21, or 51 unless they have taken the Math placement diagnostic first. Dr Jo Boaler is a Professor of Mathematics Education at Stanford University, and the faculty director of youcubed. For example, if a student’s score is in the 75th The changes impact graduation requirements under s. IME, these portal change rumors are without merit. Such tasks involve recognition, diag-nosis, planning, robot control, prediction, etc. Math. Let X be a compact manifold with boundary, and g a scattering metric on X, which may be either of short range or ‘gravitational ’ long range type. Instead of using pennies, nickels, dimes, and quarters, let’s say we agree on using only 4-cent and 7-cent coins.
The site facilitates research and collaboration in academic endeavors. MATH 51 is a core requirement for many majors at Stanford. Tutoring will focus on Math 51, 52, 53, and 104 on Mondays and Wednesdays. ( 3 ) Any course of 3 or more units from the SoE Science List (Fig. Math 51: Linear Algebra and Differential Calculus of Several Variables; CME 100: Vector Calculus for Engineers Tutoring will continue through Dead Week but exclude university holidays. Hey fellow incoming frosh! I've been wondering the same thing. -- Maryam Mirzakhani, a professor at Stanford University who was the first and only woman to win the prestigious Fields Medal in mathematics, has died. Notes will be posted periodically on the course web site. Applications of probability in computer science including machine learning and the use of probability in the analysis of algorithms. Therefore grading is weighted towards in person "demos" of the code in action - creativity and the production of impressive visual imagery are highly encouraged. This fellowship provides support for graduate study at any U. National Charter School Study .
At Stanford, the hospital boards include a mixture of Stanford University trustees and non-university trustee members. Stanford University s School of Engineering Any subsequent changes must go Students who have taken both Math 51 and 52 may not count CME 100 as an elective. Changes must be petitioned (see UGHB pg 27-29) and initialed in ink Course Title Unit Math 19, 20 and 21 may be taken instead of Math 41 and 42 as long as at least 26 math units are taken. Single Variable Derivatives We are accustomed to saying that a single variable function f is “diﬀerentiable at the point a” if the limit: lim h!0 f(a+h)¡f(a) h exists. --Linear algebra (e. the Center for Research on Education Outcomes at Stanford University, was established to Charter Impact Changes with Black and, if required, by the departmental representative. Latest news from and about Stanford University. edu. Current Environmental Engineering majors should refer to the 2013-2014 (see below) degree requirements for the Environmental Engineering major. My e-mail address is andras "at" math dot stanford dot edu. Significance. There are also a few corrections to the newer Sample Plans for Completing Core Courses - Generation 3 Core with 5-course Concentrations.
Basic Probability and Statistics (e. Her Amherst FA portal never changed, still showed NCP info as not received as of 12/19 and she was accepted. Math/Sci combined) This printed form must be signed by the departmental representative. View Akshay Agrawal’s profile on LinkedIn, the world's largest professional community. My thanks to nodename for as3delaunay . The peer tutors are available to answer any questions you have about the material and homework in these classes. Solomon Feferman--Papers and Slides in PDF Format (Caveat lector: published versions of the following may contain some changes. 4-2 in the UGHB), PSYCH 30, or AP Chemistry may be used. ˜ Familiarity with the basic linear algebra (any one of Math 51, Math 103, Math 113, or CS 205 would be much more than necessary. Early childhood is a crucial time period for the development of children's mental functions. Senator Leland Stanford and his wife, Jane Stanford, the university was opened on October 1, 1891 as a coeducational and non-denominational institution. Prerequisites: 103, 106B or X, multivariate calculus at the level of MATH 51 or CME 100 or equivalent.
Topics: weathering, erosion and transportation, deposition, origins of sedimentary structures and textures, sediment composition, diagenesis, sedimentary facies, tectonics and sedimentation, and the characteristics of the major siliciclastic and carbonate depositional environments. She is the author of the first MOOC on mathematics teaching and learning. Minor course requirement Linear Algebra (5 units) select one course. Is a 700 on Math in 2016 the same as a 700 in Math in 2018? How much do percentile scores change from year to year? In this article, I'll explain what new SAT percentile scores are and how they've changed over time. The Economic Value of Education and Cognitive Skills ERIC A. Established in 1916, AACSB is a global, nonprofit membership Math. Title Unit All courses taken for the major must be taken for a letter grade if that option is offered by the instructor. Basic Concepts in Mathematical Logic. We accept credit/debit card payment through Eventbrite online (after your spot has been confirmed), cash, or checks made out to "Stanford Educational Studies Program" or "Stanford ESP". Sloan Foundation, a recognition as one of the View Notes - 07win-f from MATH 51 at Stanford University. If you took the new SAT in 2016, 2017, or 2018, you might be wondering what percentile your score is in. 51.
Both CS 229 and CS 230 specifically recommend Math 51 (or courses that rest on Math 51) for their math background; Math 51 is the only course at Stanford whose syllabus covers nearly all of the linear algebra and “matrix calculus” material used in CS 229 and CS 230. filice@stanford. assignments are available in vcathink. o Some achievement tests were used by only one school or included only a small number of students, making analyses unreliable. A student’s percentile rank represents the percentage of students whose score is equal to or lower than their score. A base class for a HeadFinder similar to the one described in Michael Collins' 1999 thesis. The former head sailing coach at Stanford, John Vandemoer, is among 50 people charged today (March 12) in a scheme in which wealthy parents and even some Hollywood stars bribed college coaches and other insiders to get their children into some of the most elite schools in the country, federal prosecutors said. July 16th, 2018 Posted by Stanford (Credit: Getty Images) “How to Learn Math,” through Stanford’s OpenEdX platform. A no-credit refresher course in mathematics and economics is offered in the two weeks preceding the start of Autumn quarter. ” Schools in New York City use a reform math curriculum, Everyday Mathematics, but some parents there, “For so long, people have held up this idea that AP Calculus is the gold standard (for college admission),” Lizzy Hull Barnes said, a district math supervisor, adding Stanford and UC Berkeley The widespread improvement in intelligence test performance during the past century. Bartels Rotation Number -- The serial number assigned to 27-day recurrence periods of solar and geophysical parameters. The After declaring the minor in Axess, students must submit the Data Science minor form to Mason Perez, Sequoia Hall, Room 124, before they can be approved.
32 to . It is the basis for all advanced courses in Economics. No changes to Swarthmore, nor to Williams where she was also accepted. Learning Objectives: Design strategies for using multi-source and multi-scale observations of land surface processes that integrate field, geospatial, and human survey data to describe biophysical and socio-economic impacts of land systems changes. Apart from minor changes, a new section was added to this first version Stanford’s iconic amphitheater reopens after extensive renovations and upgrades that make it one of the premiere music venues in the Bay Area and a place for university pomp and circumstance. In mathematics the word is used in the same general sense, but has had to be furnished with increasingly precise definitions. 51:1299-1346 (2001). When math teachers change mindset, student grades go up. SMT aims to encourage interest in math by providing students from around the world an opportunity to work on fun and challenging problems and to meet other students interested in math. The ontology includes conceptual foundations for scalar, vector, and tensor quantities, physical dimensions, units of measure, functions of quantities, and dimensionless quantities. Of the 80 units required for the major, at least 55 must be taken at Stanford in California. This is a fast paced and quite difficult course.
I guess I also think English and Social Studies sort of fit together. o Norm-referenced tests (e. iii abstract kristen karrh. edu Student Services: Jill Filice -- 316 Y2E2, jill. This best illustrates that the process of intelligence testing requires up-to-date standardization samples. Voters also said student performance on standardized tests should play a sizable role in evaluating a teacher’s effectiveness. Yet many students, especially those from lower-income backgrounds, find the high-stakes exams in courses necessary for STEM success to be stressful and anxiety provoking. Department of Justice has charged a number of people around the country in an alleged How to Get Into Stanford (by an Accepted Student) (SAT Math) or 30 (ACT Math), Stanford will realize that you don’t have a full command of standard concepts MATH 51 FINAL EXAM December 11, 2000 Brumﬁel Hutchings Levandosky Staﬃlani White 11:00 01 05 09 13 17 1:15 03 07 11 15 19 Name: Student ID: Signature: Instructions: Print your name and student ID number and write your signature to indicate that you accept the honor code. His work had a vast range, encompassing analysis, algebra, number theory, topology, differential geometry, spacetime theory, quantum mechanics, and the foundations of mathematics. My changes are all minor. The CS2013 guidelines include a redefined body of knowledge, a result of rethinking the essentials necessary for a Computer Science curriculum. edu and use the drop-down menu to request a change.
intel® math kernel library 2 disclaimer and legal information information in this document is provided in connection with intel® products. In a class-action lawsuit filed Thursday, a group of Stanford University students allege that the university has repeatedly violated state and federal anti-discrimination laws in their response to Quotes are not sourced from all markets and may be delayed up to 20 minutes. See the complete profile on LinkedIn and discover Akshay’s This volume, Computer Science Curricula 2013 (CS2013), represents a comprehensive revision. Kirst's testimony was based on a new policy paper, "The Common Core Meets State Policy: This Changes Almost Everything," published this month by Policy Analysis for California Education, a nonpartisan research center run jointly by researchers at Stanford, UC-Berkeley and the University of Southern California. X F X Claim:IfF is taken from a lognormal t t 1 t 1 Claim: If t is taken from a lognormal distribution, each X t is lognormal. The schedules below are meant to help Symbolic Systems majors, and potential majors, plan out their academic schedule for the core curriculum courses (applicable to the Generation 3 Core Curriculum). 480 530. Math education majors learn to teach the subject of geometry to students at the 7-12 levels. No background in linear algebra or proofs is assumed, and there are no formal prerequisites for the course; Math 113 is appropriate for students who have already seen some linear algebra in Math 51. If you have an old (2000) copy of the course reader, you should consult the following errata page , and make sure to make all of the changes listed there before you use your version. not be used in combination to satisfy the Math electives requirement. Transfer/AP Approval by SoE Unit Grade! if Transfer (37 units min.
Jersey is starting to make noise,” said R. Changes in activation in frontal regions positively correlated with age-standardized receptive vocabulary scores and negatively correlated with reaction time on a receptive grammar test outside the scanner. My research investigates the causes, patterns, trends, and consequences of social and educational inequality. Information is provided 'as is' and solely for informational purposes, not for trading purposes or advice. Courses may not be taken before the prerequisites are completed. The How to Use Stanford 10 Online – When versions change, no unused stock • Stanford 10 Reading & Math Only “Partial Battery” STANFORD, Calif. Most people have told me to stick with CME just because it's better for engineering (what I want to major in) and it's usually much more well-taught and clear on average than some of the Math 51 classes. View Owen Wang’s profile on LinkedIn, the world's largest professional community. uic. Leland Stanford Junior University (Stanford University or Stanford) is a private research university in Stanford, California. Please refer to the Enrollment Calendar to view enrollment dates. This opportunity supports research opportunities that will advance our understanding of, and the implementation of, the use of genomic information about an individual to inform clinical care, and the health outcomes of that clinical use.
can cause small changes which can have large effects Writing and a benchmark for Math. To apply for financial aid for Summer Quarter, students with a complete financial aid application on file for the current academic year need only to submit this completed form to the Financial Aid Office by June 1. Stanford University ! Math Language Arts Science Social Studies Not subject specific; Grades K-2: Link for Math K-2 : Link for LA K-2 : Link for Science K-2: Link for Social Studies K-2 The printed form must be signed by the departmental representative. Chapter 3, pp. no license, express or implied, by estoppel or otherwise, to any intellectual property rights is granted by this document. Thus, individual differences in language skills were associated with changes in the network in response to changing task demands. HANUSHEK Hoover Institution of Stanford University Education is one of the top priority policy areas of govern-ments around the world. The following books are recommended as optional reading: Your homework and exams will be judged accordingly. Former roles have included being the Marie Curie Professor of Mathematics Education in England, a mathematics teacher in London comprehensive schools and a That's right, because Stanford's Math 50 series spreads out linear algebra across multivariable calculus (51, 52) and differential equations (53), making it very difficult to match up with math courses elsewhere. MATH 51) - We will use matrix transpose, inverse, and other operations to do algebra with matrix expressions. tamu. October 2008 For the past several years the Carnegie Foundation has been working with a group of California community colleges to improve student success in pre-collegiate math and English.
We describe an ontology for mathematical modeling in engineering. That's right, because Stanford's Math 50 series spreads out linear algebra across multivariable calculus (51, 52) and differential equations (53), making it very difficult to match up with math courses elsewhere. Stanford Math Circle Making Change Like Frobenius Matthias Beck September 24, 2006 Let’s imagine that we introduce a new coin system. A wealth of research suggests that a student's academic "mindset Duration: Watch Now Download 51 min Topics: C/C++ Data Types - Interpretations, Sizes, Bits- How Bytes are Broken Up into Bits, Breaking Up a Character's Decimal Value into its Underlying Bit Structure, Shorts - Interpreting Data that Consists of More Than One Byte, Representations of Negative Numbers, The Sign Bit, Two's Complement Addition, Converting Between Chars and Shorts, How the Bit Third Grade Promotion • As required by the statewide public school student progression law eliminating social promotion, Section 1008. Axess is a consolidated online platform used by the Stanford community to access information and record transactions related to: Academic Advising, Teaching and Grading He is currently serving as the John and Ann Doerr Medical Director of the Stanford Cancer Center, a position he has held since July 2015. Changes must be petitioned (see UGHB pg 27-29) and initialed in ink. Restrictions: Math 51 and Math 103, or Math 51 and CME 100, or Math 103 and Math 113, or CS 157 and Phil 151, may Among parents with school children, 51 percent agreed with testing high schoolers in all subjects and 42 percent said testing should be limited to English and math. edu> 1 Attachment, 49. Talk to your advisor. The Partnership for Assessment of Readiness for College and Careers (PARCC) was selected to produce statewide tests for administration in the school year 2014-2015, but Ohio then dropped PARCC in June 2015. She was 40. Specifically, the changes require an increase in the number of science and math credits required to graduate and provide additional options for students to earn math and science credit through career and technical education (CTE) courses and computer science courses.
Nina Zubrilina, a Stanford senior majoring in Mathematics, and Indira Puri, a 2017 Stanford graduate with a bachelor’s degree in math, have been awarded the 2019 Soros Fellowship for New Americans. I'll also provide Lemann Dialogue 2014 Lemann Center, Stanford University, November 2014 •The 1990s marked a decade of structural changes in Brazil 51% of the Black do so. UG Director: John Barton -- 267 Y2E2, jhbarton@stanford. Stanford GSB was established in 1925 at the request of future U. Prerequisites: CS 107, MATH 51. The school consistently takes SAT composite scores down to 1440 on a 1600 scale, below which admission should be considered a reach. The class is designed to introduce students to deep learning for natural language processing. This is the second offering of this course. Owen has 5 jobs listed on their profile. It is further taken as a force for improving the economic standing of disad- David Bergman is part of Stanford Profiles, official site for faculty, postdocs, students and staff information (Expertise, Bio, Research, Publications, and more). It’s best to consider your future coursework and concentration plans. President and Stanford alumnus Herbert Hoover.
Founded in 1885 by former California Governor and U. Check the Environmental Systems Engineering page for the current major. With the start of classes I could not do much. I found Stanford to be very flexible in the past. Stanford’s department of mathematics launched an online placement diagnostic that is now required for students who plan on taking introductory math courses, such as Math 19 or Math 51. Percentiles . Hermann Weyl was a great and versatile mathematician of the 20 th century. In particular, I study issues of residential and school segregation and of racial/ethnic and socioeconomic disparities in academic achievement and educational success. The U. Mirzakhani, who College Calculus, Linear Algebra (e. This development, including the emergence of language, motor skills, psychosocial, cognitive, and learning abilities, is now known to be greatly influenced by exogenous factors, including the educational environment to which a child is exposed during the Machine learning usually refers to the changes in systems that perform tasks associated with arti cial intelligence (AI). Tutoring will focus on Math 19, 20, and 21 on Tuesdays and Thursdays.
edu> Subject: updated version Date: January 15, 2010 1:51:15 AM GMT+01:00 To: Ravi Vakil <vakil@math. except as provided in intel's terms and conditions of sale for such Two Stanford students have brought about a class action lawsuit against the groups involved in an admissions scheme that allowed children of rich parents to attend elite schools by means of bribery Quotes are not sourced from all markets and may be delayed up to 20 minutes. 10/15/2009 Jure Leskovec, Stanford CS322: Network Analysis Stanford Economics' Melaine Morten is awarded a $70,000 research fellowship from Alfred P. The second course is CS248 and requires this course, CS 148, as a prerequisite. Stanford University, one of the world's leading teaching and research institutions, is dedicated to finding solutions to big challenges and to preparing students for leadership in a complex world. Stanford information on college admissions case. The \changes" might be either enhancements to already performing systems or ab initio synthesis of new sys-tems. The motivation behind this is that the existence of this limit is what ensures that there The result was a report tracking students from pre-collegiate courses in English and math into the first level of transfer English and math courses. Play these four games designed to reinforce and build upon your child’s math skills—all you need is a deck of playing cards! Quantitative introduction to the engineering methods used to study and seek solutions to current air quality problems. This was not the kind of information Institutional Research staff members were in the habit of preparing; nor was it a perspective that faculty were accustomed to seeing. No calculators or other electronic aids Stanford University would have to build more than 2,000 housing units for staff and faculty, and to offer nearly half of them at below market rate, to secure permission for its ambitious campus-expansion plan under conditions that Santa Clara County released Wednesday afternoon and that Stanford is Stanford University to analyze educational outcomes for the dependent youth in the County. SAT College and Career Readiness Benchmarks.
Stanford must be a community college in California. In partnership with the SPHERE Institute, the JGC operates the Youth Data Archive (YDA), an initiative that links data across youth-serving agencies to answer questions that those agencies could not answer working independently. ) Course Materials There is no required text for this course. Math 41, 42 may be taken instead of Math 19, 20, 21 as long as at least 26 math units are taken. Changes must be initialed in ink. It remains to be seen whether or not the changes will greatly affect students’ scores. One of our tutors, Joseph Victor, wrote a supplement to the Math 51 textbook and lectures. But please get the history straight. predictors of student achievement in grade 7: the correlations between the stanford achievement test, otis-lennon school ability test, and performance on the texas To counteract the criticism, the College Boards, which administers the SAT, made sweeping changes to the test in 2016, no longer requiring students to memorize archaic vocabulary and getting rid of the point penalty for guessing. Beating the NCAA Football Point Spread Brian Liu Mathematical & Computational Sciences Stanford University Patrick Lai Computer Science Department Stanford University December 10, 2010 1 Introduction Over recent years, professional sports betting has grown to be a multi-billion dollar industry. CS Graphics program sheet continues on page 2 Stanford University s School of Engineering Tau Beta Pi will be providing tutoring for Math 51 in Terman 151 on Mondays from 7-9pm, and Tuesdays from 8-10pm. Take it only when you have completed the math requirements.
Stanford Hospital & Clinics and the Lucile Packard Children's Hospital are owned by the University, but they operate independently under the leadership of a President and CEO, who reports to a Board of Directors. Evidence-Based Reading and Writing Math. edu>, Frank Sottile <sottile@math. 118. From Special Occasion to Regular Work. (I’m a high school math teacher for goodness sake!), but I am so in Oh, Stanford. microeconomics at a level equivalent to MATH 51 (Linear Algebra and Differential Calculus of Several Variables) and ECON 50 (Calculus-based intermediate Microeconomics) before beginning the core curriculum. Stanford University Changes must be petitioned (see UGHB pg 27-29) and At each time step, size changes by a random multiplicative factor. The results suggest a predictive relationship between the two instruments in the areas of math, science, English, and reading. will (together) count as one Math elective. The Stanford Economics' Melaine Morten is awarded a $70,000 research fellowship from Alfred P. 51-57 15 The course schedule is tentative and the professors reserve the right to make changes in the within the Department of Electrical Engineering of Stanford University in association with the Stanford Solar Center and NSF’s Center for Integrated Space Weather Modeling (CISM).
This printed form must be signed by the departmental representative. The R-square values ranged from . stanford math 51 changes
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Simplest Form Algebra Calculator Ten Features Of Simplest Form Algebra Calculator That Make Everyone Love It
The protractor and the Bunsen burner. Playing the recorder in music class. Drawing arcs and circles with a ambit in geometry. These accoutrement of the apprenticeship barter become allotment of our lives for a analysis or two and afresh we move on.
Today, NPR Ed begins a new alternation analytical these icons of the classroom. We alpha off with a accessory that already was capital to higher-level math, in academy and in the workplace, but now has all but disappeared:
The accelerate rule.
“Take your batteries out,” Jim Hus says, watching his pre-calculus acceptance abolish the AA batteries that adeptness their calculators. “Let’s do those multiplication problems again.”
For the abutting calculations, Hus’s juniors and seniors at Highland Aerial Academy in Highland, Ind., will use a altered tool: A apparatus that dates aback 400 years.
Before the smartphone, the laptop and the graphing calculator, there was the accelerate rule. It’s a able automated accretion device, generally no beyond than a 12-inch ruler, apparent with numbers — but allotment of it slides in an out to to appearance relationships amid altered sets of numbers.
That acutely simple apparatus has a austere resume. NASA engineers acclimated accelerate rules to body the rockets and plan the mission that landed Apollo 11 on the moon. It’s said that Buzz Aldrin bare his abridged accelerate aphorism for last-minute calculations afore landing.
“The accelerate aphorism is an apparatus that was acclimated to architecture around everything,” says Deborah Douglas, the administrator of collections and babysitter of science and technology at the MIT Building in Cambridge, Mass. The building aloof concluded a three-year display on accelerate rules. “The admeasurement of a avenue pipe, the weight-bearing adeptness of a agenda box, alike rocket ships and cars.”
So, What Is A Accelerate Rule?
Slide rules are about ellipsoidal and about the admeasurement of a ruler. They are disconnected into thirds, the top and basal are anchored in place, but the average area slides aback and forth. Each area has scales — numbers and band marks for calculations.
The aboriginal one was congenital by William Oughtred, a apostolic teaching algebraic in England in the 1600s. It was based on John Napier’s analysis of logarithms.
In its simplest form, the accelerate aphorism adds and subtracts lengths in adjustment to account a absolute distance. But accelerate rules can additionally handle multiplication and division, acquisition aboveboard roots, and do added adult calculations.
For ancestors of engineers, technicians and scientists, the accelerate aphorism was an capital allotment of their circadian lives. Until, all of a sudden, it wasn’t.
In 1972 Hewlett-Packard came out with the aboriginal handheld cyberbanking calculator. Practically overnight, the accelerate aphorism had become obsolete.
“The afterlife of the accelerate aphorism was appealing instantaneous,” says Bob De Cesaris, who oversees dent accomplishment at Intel and has one of the better collections of accelerate rules in the country. De Cesaris estimates his accumulating has about 4,000 accelerate rules.
He is additionally the admiral of the Oughtred Society — a accumulation of 400 accelerate aphorism collectors and enthusiasts gluttonous to bottle the device’s history (and area you can acquisition out all sorts of advice about them).
And yet, admitting the artful adeptness these canicule in alike your handheld phone, the accelerate aphorism isn’t absolutely dead.
Here and there, agents like Jim Hus still use them in the classroom. Sister Paula Irving, a nun at the Community of Jesus in Orleans, Mass., teaches a computer programming advance to homeschooled aerial academy students. And aback she covers the history of the computer, she teaches acceptance how to use a apparatus she remembers watching her ancestor use as he affected their family’s finances.
More than a thousand afar west, Laurie Emery, a algebraic abecedary at South Winneshiek Aerial Academy in Calmar, Iowa, will advise her inferior pre-calculus chic how to do intricate calculations after a calculator.
There’s alike a apprentice academy about the accelerate aphorism at the University of California, San Diego, that Professor Joe Pasquale has been teaching aback 2003.
“We alive in this age aback accretion is accepting exponentially added able but we generally don’t alike anticipate about the calculations actuality made,” says Pasquale. “We aloof let our computer do all the work.”
In the seminar, Pasquale says his acceptance are generally afraid that the accelerate rule’s answers accomplish sense.
Thinking About The Math
“The nice affair about a calculator is you don’t accept to anticipate – but it’s additionally a bad thing,” he adds. “When you’re application a accelerate aphorism you accept to be engaged. You accept to be cerebration about math.”
And that’s one of the capital affidavit some agents still adhere on to the old “slipsticks.”
MIT’s Debbie Douglas says that alike admitting the accelerate aphorism isn’t as absolute as a calculator, acceptance can accept the abstraction of what it’s doing. “It absolutely makes one affianced with the process.”
Jim Hus still remembers chief to advance $400 in a calculator and abandoning his accelerate aphorism during his apprentice year at Purdue, aback in 1974.
But it’s a accessory he’ll never balloon and he hopes his acceptance at Highland Aerial Academy in Indiana won’t either. He’s planning to accept his acceptance body a classroom accelerate rule.
“I antic it will be the better accelerate aphorism in the world,” he says, laughing. “But this way, I’m not aloof handing the acceptance a tool, we’re acquirements how it operates so we can admission college algebraic concepts.”
Copyright NPR 2019.
Simplest Form Algebra Calculator Ten Features Of Simplest Form Algebra Calculator That Make Everyone Love It – simplest form algebra calculator
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This week we are joined by Tammy Coron and Greg Heo. We follow up on Learning to Learn, a MacBook Pro saving a life, where Apple products are made and the math behind a 5-star rating. This week marked the 10 year anniversary of the iPhone announcement by Apple. So we asked listeners and friends to tell us what the iPhone has meant to them. We hear from Kim Ahlberg, Justin Stanley, Aaron Douglas, Peter Cook, George Stroumboulopoulos, Jaime Lopez Jr and Rich Turton. We talk about Phil Schiller’s press tour on the iPhone early history as well as some recent turnaround in iPhone sales and market growth. We speculate Chris Lattner’s move to Tesla. Cloud storage is mentioned. Picks: Kaleidoscope, Hyperdrive USB Hub
// For x 5 stars, and 1 1 star, the average is:
Ave = (5x + 1) / (x + 1)
// Solve for x to get the number of 5 stars needed to achieve this Ave with 1 star:
5x + 1 = (Ave)x + Ave
(5 - Ave)x = Ave - 1
x = (Ave - 1) / (5 - Ave)
// So to get Ave = 4.75, with 1 1-star, you need:
x = 15 5 stars
// And to get Ave = 4.5, you need:
x = 7 5 stars
// Say you have one 5-star and one 1-star. What’s the average?
(1 + 5) ÷ 2 = 3 stars! // How horrible!
// Then you get another 5-star review. Your new average:
(1 + 5 + 5) ÷ 3 = 3.7 stars. // Getting better.
/* So you could just keep adding another 5 and increasing the number after the ÷ until you hit 4.5.
As Mark says, 7 5-star reviews is the magic number to get back up to four and a half: */
(1 + 5 + 5 + 5 + 5 + 5 + 5 + 5) ÷ 8 = 4.5
This week we answer #askMTJC about how we use the pragma mark in our apps. We also follow up as we test drive Setapp’s beta program. We discuss the @available attribute in Swift that allows you to use new iOS features while maintaining backward compatibility. We the new Bluetooth 5 announcement and discuss some contradictory articles on the wearables market. Aaron gives a status report on CarPlay in his new car. Picks: Pre-Apple return Steve Jobs TV interview, Wang 1980’s TV commercial and Inside the secret meeting where Apple revealed the state of its AI research.
This week start the FU with Jean Louis Gassée’s Monday Note on the Mac Endgame. Following that we discuss the scam apps present on the Mac App Store. We discuss Matthew Yglesias’ post on Apple having outgrown it’s own corporate structure. We also discuss Chris Eidoff’s post on the over-reliance on Protocol-Oriented Programming. We discuss Amazon’s image recognition services. We touch on the Mac Calendar spam bug. Picks: AIToolbox, mucicForProgramming and Spark For Mac.


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I am a Managing Editor of Homology, Homotopy and Applications.
My papers, preprints and talks.
Contact information is below.
|My research interests include algebraic topology (especially stable homotopy theory and model categories), homotopy type theory and univalent foundations, category theory (especially higher categories), derived categories, modular representation theory, mathematical physics (quantum gravity), and computation.|
Research groupDan Christensen (faculty)
Jarl Taxerås Flaten (Ph.D. student, Sept 2019 until present)
Karthik Boyareddygari (M.Sc. student, September 2021 until present)
Group photo, July 2021
Chris Kapulkin and I are running the Homotopy Type Theory Electronic Seminar Talks.
Graduate students: I am looking for new graduate students in the areas of homotopy theory, homotopy type theory and topology, broadly construed. If you are interested, please contact me and send an application to our department mentioning my name. To be sure your application can be evaluated fully, please have at least three people submit detailed letters of reference.
Postdocs: I encourage eligible people to apply for an NSERC Postdoctoral Fellowship, an NSERC Banting Postdoctoral Fellowship (domestic and international applicants eligible), any other NSERC postdoc, an NSF PDF, or similar to be held at Western. The standard NSF postdocs can be held in Canada, and there are other eligible NSF postdocs, e.g. an International Research Fellowship Program postdoc or a Mathematical Sciences Postdoctoral Research Fellowships.
Students and postdocs: The Canadian Government has many scholarships and fellowships that are available for people from many different countries.
|Winter 2022||Algebraic Topology, Math 4152b/9052b.|
|Fall 2021||Mathematical Structures, Math 2155F.|
|Summer 2021||Mathematical Computation, Math 9171a.|
|Fall 2020||Mathematical Structures, Math 2155F.|
SAGE is a wonderful program which interfaces to Magma, Maple, Mathematica and MATLAB, and the free programs Axiom, GAP, GP/PARI, Macaulay2, Maxima, Octave, and Singular. It is freely available and open source.
If you find math fun, consider becoming a math major. Talk to me or anyone else in the department if you're curious.
Here are some photos from trips I have been on.
I've produced plots of roots of polynomials, some of which appeared in a Scientific American article.
Department of Mathematics
The University of Western Ontario
London, Ontario N6A 5B7
Office phone: (519) 661-2111 x86530
Fax: (519) 661-3610 (include my full name)


Welcome to the Center for Machine Learning and Intelligent Systems at UC Irvine. Research in the fields of machine learning and intelligent systems addresses the fundamental problem of developing computer algorithms that can harness the vast amounts of digital data available in the 21st century and then use this data in an intelligent way to solve a variety of real-world problems. Examples of research activities in the Center range across areas as different as web search engines, statistical text mining, spam email filtering, information retrieval, automated reasoning, image and video data analysis, sensor networks, astronomy and planetary sciences, ocean and atmospheric sciences, systems biology, medical diagnosis, chemical informatics, and microarray genomics.
Research projects in the Center use theories and techniques from the intersection of computer science, statistics, and mathematics, including foundational ideas from algorithms, data structures, artificial intelligence, and databases (computer science), multivariate data analysis, Bayesian estimation, and computational statistics (from statistics), and optimization and probability theory (from mathematics). Research in the Center also has a very strong interdisciplinary component, including collaborations in areas ranging from sensors and ubiquitous computing, to databases and computer vision, to software engineering and Web applications. Projects involving collaborations with scientists are also numerous, including automated analysis of brain images, analysis of microarray gene expression data with microarrays, tracking storms in satellite data of the Earth’s oceans, and many more.
We hope you find the Center’s web site useful and encourage you to explore its contents.


Created: Feb 16, 2009
Updated: Jul 26, 2011
SVN Updated: Mar 10, 2009
Other project properties
Development status: Stable
Additional info: FPGA proven
WishBone Compliant: No
Quadratic_func is a fully pipelined quadratic polynomial that computes the relation y = ax^2 + bx + c. On each rising-edge of the clock (when en is high), the coefficients and input x term are sampled at the function inputs. The result has a latency of 3 clock cycles. All inputs to the function are 8-bit signed fractions, with the generic parameter 'fw' specifying the number of fraction bits. The output result is a 24-bit signed fraction. If integer arithmetic is preferred, then the parameter fw should be set to 0. For larger bit-widths, the design can easily be scaled up to suit the application.
The quadratic core is ideal for curve-fitting applications such as estimating SIN/COS or ATAN. It provides a useful alternative to LUT-based estimation or it may be used in conjunction with a small LUT to generate more precise results. As an example, the following plot shows the output result of the function: y = 0.86x^2 - 0.22x + 0.3 in the range [-2, 2]. For a full description of the core, please review the following Quadratic function pdf datasheet.
- Computes the relation y = ax^2 + bx + c
- Signed 8-bit fixed-point input
- Signed 8-bit fixed-point coefficients
- Signed 24-bit fixed-point output
- Configurable number of fraction bits
- Dynamic coefficients updated every clock cycle
- No internal loss of precision (no rounding or truncation)
- Fully pipelined architecture
- Result has a 3 clock-cycle latency
- Fully tested and complete
- Future versions to support generic input data and coefficient widths as well as fraction width
Help and Support
Simon Doherty is a Senior Design Consultant at ZIPcores If you require further assistance regarding the implementation of this core, you may contact me directly via my Opencores email alias at email@example.com. Alternatively you may contact me through customer support at ZIPcores.


This is just such fun. Art Benjamin’s calculating show is just remarkable. Of course a great question is how he manages to do what he does. There is obviously a lot of skill, brain power and practice but also some very sophisticated techniques that we start to see at the end of the video. Could this be a good Math Exploration? It might be although we would need to know that the topics are “requisite with the programme”
It has been a couple of weeks since I last posted about our Balancing Matters problem. During that time I have been reflecting on the problem. I did nothing new in terms of actual writing but shortly after the last time I posted I had a break through.
The problem of keeping the “liquid area” constant was getting messy but then it became obvious that with some fairly basic trigonometry and the formula for the area of the trapezium I had a fairly elegant solution on my hands. Here it is.
It also became obvious that when writing up the exploration I would need to begin with the conservation of area. You can see the write up of the “conservation of area” problem on this page.
Three important points to take from this stage on the process.
The working that I did at the beginning gave me the fertile soil to think and reflect on the problem mentally. This meant that when I returned to the task I had a clear strategy to follow and a breakthrough to explore. This takes time and having some thinking time with no writing is a good thing. Remember that the unconscious mathematical brain is often smarter than the conscious one.
If you look carefully at the working done on the conservation of area you will notice that there are two key physical restraints that allow us to make progress. The first one is that area is conserved. This is of course the 2 D equivalent of the fact a liquid, like coke, cannot be compressed under normal circumstances and so the volume of liquid in a container is conserved as we change its orientation and shape. The second one is that the “surface” of the liquid is horizontal. In our 2 D problem this means the line that is the equivalent of a 3 D surface is horizontal. Look carefully at the working and see how these two restraints are key to getting the formula for the coordinates of the trapezium.
Finally, note that I am breaking my big problem of finding when the can will tip over into sub problems of finding the centre of gravity of a trapezium and then the conservation of area problem. The “write up” phase of the exploration will be a matter of putting these notes together in a coherent way that will allow me to explain clearly and concisely my solution.
One other point I would like to make is about technology. The Geogebra file that goes with the notes on the conservation of area page is in effect the check that I am making to see whether I am correct. It took me a while to get the formula into the syntax of Geogenra properly, but once I did and I used the sliders to change the parameters in my coke can the model worked as it should “physically” and I was certain that my working was correct.
I hope you enjoy the solution to the problem. It feels nice and the formula come out elegantly. I am going to revisit the Centre of Gravity problem next and try and use vectors to get my C o G for the trapezium. The coordinates that I found in this post will then be turned into column vectors and it will be easy (I hope!!) to combine that with a Geogebra file to get my solution.
We have not posted for some time but I am pleased to announce that the next few weeks should lead to some interesting posts.
We are going to take the ideas we had about balancing the coke can introduced earlier in the year and conduct a “model exploration”. The outcome of this exercise should be an exploration that could be graded against IB criteria for Internal Assessment.
The object of this exercise is NOT to produce a perfect IA exploration, though we hope it will be quite good. However, more important is to observe the approaches and ways of thinking involved.
Finding a Focused Topic
The second post called more balancing matters actually began to look quite deeply into the problem in hand. In this post we managed to create a Geogebra file modeling the situation and start to propose what the problem of finding a balance point for a cylinder filled with liquid might be. The first thing to note is that creating this Geogebra file was no easy matter and by creating the file it became clear that one of teh primary issues was how to find out how the liquid behaved as the can was tipped in order to conserve the volume of the liquid in the can. This seems like a really tough problem.
Perhaps this is too difficult a problem for the exploration. Is there an easier problem we could solve that might be a good exploration in itself or if quite doable lead to a solution method for the actual problem of finding the tipping point of the actual can. The real challenge of the coke can is that it is 3 – dimensional. Perhaps we can solve a 2 – dimensional problem first.
Consider the following image in 2 – dimensions of a rectangle on a slope with a 2 – dimensional “liquid” inside it.
Note that the “liquid” inside the rectangle is in the shape of a trapezium since the “liquid”must keep a horizontal surface. This trapezium needs to preserve its area (the 2 d equivalent of volume) as the slope is changed. We also need to know how to find the “centre of gravity” of the trapezium.
Already we have two quite nice problems to solve. These are
Finding the centre of gravity of a trapezium.
Preserving the area of a trapezium as its base is “tipped”.
Perhaps these questions will make a good exploration on their own. If they do we will then need to construct a topic around this that is of interest as a whole. Of course, if we can make rapid progress with the 2 – d problem we may be able to tackle 3 – dimensions and then our topic would simply be “finding the balance point of a partially filled coke can”.
We will shortly post about finding the centre of gravity of a trapezium.
It does not take long to find some pretty cool ideas for math explorations. Two particularly good websites are Nrich and Plus.Math. Nrich is great because it is easily searchable and has problems that you can try and solve but there are also articles and videos. Plus.Math is also wonderful, has longer articles and really goes into the type of mathematics that Math HL students can get there teeth into. Bit like Goldilocks, the math is hard but not too hard!!
The first one poses quite a nice problem on Complex Number and if there are examples that square to real numbers (and also imaginary numbers). Great little stimulus to be able to explore an aspect of topics that Hl students will know about and enjoy.
The second article I picked on was one on adding series to interesting results. It is a long article with a lot of ideas in it but certainly some wonderful stuff for a Math HL student to get their teeth into to start to explore. This is particularly good for students who will eventually study Calculus as their option topic (e.g. Pamoja Math HL).
Please post some questions about these articles or anything else in Nrich or Plus.Math that takes your fancy. Even better, if you have examples of websites to share please send in a comment.
I was home in bed not feeling very well when my attention was drawn to a five pointed star in a picture above the bed. I started wondering how to construct the star, what were its symmetries and reminding myself that there are pentagons all over the star.
This got me to thinking that there might be a good IA Exploration here somewhere. So I decided to to a quick research of pentagons on the Internet. Nothing fancy, I just googled and used Wikipedia. Not the basis of a good research but a great place to start. During this research my attention was brought to the “Cyclic Pentagon” and thought this might be where I could do an IA Exploration.
Below are two videos (both only 5 minutes in length) that describe how I got the the point of finding Cyclic Pentagons. Hopefully this will encourage you to take one of the stimuli and do some research so that you can come up with some ideas to post in your Week 20 IA Blog post.
Trigonometry seems to be full of these annoying things called identities. Why is it that we can write a trig expression is so many different ways? I would suggest it is a matter of symmetry. Since trigonometry can all be found in a Unit Circle and a circle has lots of symmetry then the consequence is that there are lots of symmetries when we write trig expressions. In this case symmetry means that the expression looks different but actually it is identically the same.
Look at the triangle above. Check using Pythagoras and basic geometry that the triangle is correct (the key is the fact that there is an isosceles triangle in there). The cool thing about this triangle is also that we can get the double angle formula for Tanget out of it just by inspection. Can you see this?
Now here is a problem for you. This comes out of an IB exam paper one (i.e. no calculator allowed). Although the original question used complex numbers it can actually still be done without (it just requires a bit more crunching of the algebra). OK….there are three things to do.
1. Can you prove that ?
2. How about ?
3. Now use these results to prove that ?
Then comes the really cool part. Can you show from the third identity that
Now that is a pretty amazing result. We can then use other exact values for trig ratios to work out other ratios for other angles and so on.
Maybe trig identities are not so boring after all? Is there an exploration here?
I was thinking about the balance problem for a can of coke and it provoked some really interesting questions of their own that might model the kind of process IB Math HL and SL will go through when doing an exploration.
So I started by looking to do an experiment. Since we do not drink sodas in our house I instead went to make a dynamic Geogebra file to model the situation. My first attempt had an issue. Can you spot it?
OK…so if the coke was frozen in the can then this model works fine. It is easy to find a centre of gravity (the intersection of the diagonals) and so we can do our experiment without spilling coca cola all over the kitchen.
I managed to rectify the error and have a liquid in my can. At first my only problem appeared to be working out the centre of gravity but then another issued arose as I played with the angle. Can you see what it is? Play with the angle and see what happens to the liquid that is shaded blue.
So already with a stimuli of the student balancing the coke can, a few pretty dumb errors whilst making a Geogebra model and we come up with two really interesting questions.
How do you find the centre of gravity of a trapezium?
How do we fix the trapezium so that the area is conserved as we tilt it?


This guide provides sources of national, local, and international education statistics, as well as data sources on specific aspects of education. It also includes general statistical sources that may be useful for education research.
This Center ". . . serves as the International Study Center for IEA's studies in mathematics, science, and reading -- the Trends in Mathematics and Science Study (TIMSS) and the Progress in International Reading Literacy Study (PIRLS)."
This publication contains statistical trends of elementary, secondary, and higher education institutions. Text and charts describe historical shifts in educational attainment, enrollment, staff, degrees and finance. Years covered: 1870-1990.


Multivariate Data Analysis refers to any statistical technique used to analyze data that arises from more than one variable. This essentially models reality where . The Multivariate platform examines multiple variables to see how they relate to each other.
Multivariate analysis is essentially the statistical process of simultaneously analyzing. See Chapter “Correlations and Multivariate Techniques”. Statistically speaking, multivariate analysis refers to statistical models that have or more dependent or outcome variables,and multivariable analysis refers to . Learn about more advanced methods of statistical analysis, involving interactions between several variables.
A summary of multivariate analysis techniques, includes the types of research questions that can be formulated and the capabilities and limitations of each . Founded in 197 the Journal of Multivariate Analysis (JMVA) is the central venue for the publication of new, relevant methodology and particularly innovative . Multivariate statistical analysis refers to multiple advanced techniques for examining relationships among multiple variables at the same time. De très nombreux exemples de phrases traduites contenant multivariate analysis – Dictionnaire français-anglais et moteur de recherche de traductions . Definition of multivariate analysis: Statistical procedure for analysis of data involving more than one type of measurement or observation. As the name indicates, multivariate analysis comprises a set of techniques dedicated to the analysis of data sets . A GUide to STatistical Analysis for Microbial Ecology. The multivariate analysis procedures are used to investigate relationships among variables without designating some as independent and others as dependent.
Stata Data Analysis Examples Multivariate Regression Analysis. Version info: Code for this page was tested in Stata 12. The online version of Journal of Multivariate Analysis at ScienceDirect. Although the term Multivariate Analysis can be used to refer to any analysis that involves more than one variable (e.g. in Multiple Regression or GLM ANOVA), . The concepts that are more thoroughly treated are: Matrix algebra and multivariate normal distribution.
Lessons designed to teach the intermediate student how to use SPSS for multivariate statistical analysis. Welcome to STAT 5- Applied Multivariate Statistical Analysis. This is the STAT 5online course . Get information, facts, and pictures about Multivariate Analysis at Encyclopedia. Make research projects and school reports about Multivariate Analysis easy . In this course, we shall first look at basic concepts of multivariate distributions and study . TRobustEstimator is a robust method for Minimum Covariance Determinant Estimator (MCD).
That is to say, ANOVA tests for the difference in means. This course is about a large variety of methods for multivariate analysis and multidimensional data analysis. The first part (seven course-days) deals with the . Retrouvez Methods of Multivariate Analysis et des millions de livres en stock sur Amazon.


Eight Online Math Activity Sites
The following post is from contributing writer Demetria Zinga of Christian Homeschool Moms.
If you have struggling math learners who need a little jolt of fun included in the school day, you might want to locate low-cost or free resources that will assist your child in learning to love math. After doing a search in Pinterest, I was astounded by the amount of free online math games available that I haven’t been taking advantage of! This school year, I now know that I’ll be sprucing up our math programs- making it a much more fun learning experience for my kids.
ABCYa.com is a leading educational game stop for kids in grades K-5. Among the games and apps available are math games, designed to help kids understand number concepts.
Cool Math for Kids is a nice balance of colorful online lessons and practice, puzzles, and math games. Divided into two sections (kids over 13, and kids under 13), you’ll be able to match up the lessons and games with your students. Many of the games are divided into categories such as logic, skill, memory, or board games.
Math Game Time includes math videos, games, and worksheets for grades K-7.Lots of math topics are included- like addition/subtraction, multiplication/division, algebra, geometry, fractions, and probability
Fun Brain is based on the concept of arcades: complete the current level to unlock the next. Students get to choose a gender avatar and level (grade), which adds to the element of choice and fun! In addition to math, reading games as well as fun games are included on this site. Divided by both topic and grade, you can select from a variety of math games- like “Pig Toss,” “Mummy Hunt,” and “Soccer Shootout.”
Math Play consists of online games and printable worksheets for grades 1-8. From place value word search to math millionaire and math jeopardy, your kids are bound to find something they’ll enjoy playing (all while admitting to loving math)!
Toy Theater is a nice site for early learning and primary age students (and it’s in 6 different languages)! There are several other topical games included besides math – like art, music, and reading. In the math section, you can browse the teacher section to target the subject area you want to cover: patterns, directions, time, or counting. The games are displayed with attractive icons, making it easy for the child to pick an interesting one. There are also interactive flashcards, quizzes, and tests available (in game format).
Every Day Mathematics has a complete online portal of one and two-player math skills games for grades 1-6 and early childhood.
Crickweb offers a listing of a variety of math worksheets and online games for a variety of ages.
I hope you enjoy these resources, and that your kids will appreciate all the fun they can find in math!
Demetria is a blogging, homeschooling mom of two. She loves motivating homeschool moms to keep on the journey of home education. You can find her blogging, designing, and podcasting at Christian Homeschool Moms and MomZest.com.


All classes are taught by professional engineers, scientists, and other math and science based careers, such as medical and business professionals. Teachers received training in teaching techniques by our staff. Classes for the two yearly ten week programs are held from 9 a.m. to 12 noon, on Saturday mornings at CSUDH. This is a non-profit venture and there is a nominal fee for students per session, with discounts for multi enrolled family members. We also provide tuition assistance on an as-need basis. The fee is used to buy equipment, workbooks, and to defray possible field trip expenses. All classes are filled on a first-come basis.
We have classes from 2nd through the 12th grade. However, we must must continue to recruit students, especially middle and high school student; we must get out youth involved in a positive educational environment as soon as possible. Class size is generally held to approximately 15 students each. The course of study includes:
MATHEMATICS - The mathematics curriculum is designed to increase the number of under-represented students interested the field of mathematics. Students are introduced to scientific methods and other basic research techniques for problem solving. We feel it necessary to DRILL students in fundamentals, for this is the key to math excellence.
The integrated curriculum will teach the students to use effective oral and written techniques to demonstrate the depth of their newly acquired knowledge and to work cooperatively to solve problems. Students will be taught four essential problem-solving applications skills; formulating problems, analyzing problems, finding and interpreting the solution. Workbooks and Schaums type material will be provided to each student, especially in mathematics courses.
SCIENCE - The goal of the Science program is to develop a scientifically literate group of Black and other minority students. The program emphasizes hands on experiments as a way to develop scientific and conceptual problem-solving skills. Hopefully, this will make students less fearful of science, since repetition is important.
Elementary students are given exposure to biology, physics, chemistry, and environmental studies, also. They will also be exposed to non-traditional facets of science such as engineering science, and other exciting areas as volunteers become available. High school classes include biology, chemistry, pre-physics and physics.
COMPUTER SCIENCE - The computer training program is designed to enhance mathematics and science learning experiences. Professional computer scientists and engineers develop creative tools for use by students to increase computer literacy, programming skills and broaden knowledge of computer languages.
PSAT/SAT PREPARATION - This program is designed to teach the student how to take a test , as well as, what to expect from the test.
ENRICHMENT PROGRAM - Field trips will be scheduled, if possible. However, the main emphasis of this program is on learning.
Classes are estimated to start in the Fall and Spring.
For additional program information contact the LACBPE President, Michael Batie Ph.D.


Personal website of Alvin Šipraga.
I am an embedded firmware engineer at Airtame since 2017.
I was a mathematics student at the University of Copenhagen until August
2015. Before that, I was at the University of Bath. After doing
some stuff at the University of
Vienna, I then worked at
I wrote my Master's thesis—entitled The Nash problem—between February and July 2015, in which I studied the theory of arc spaces and the so-called Nash problem on singular varieties. I successfully defended on the 28th of August 2015, which involved some brief presentation slides.
In 2013 I did a project on convex analysis as part of my final year at Bath, the results of which can be found below:
In November 2013 I gave more or less the same presentation to the KU mathematics student colloquium.
During the summer of 2012 I worked on a research project at the University of Bath Department of Computer Science in the area of proof theory. It was under the supervision of Anupam Das and Alessio Guglielmi. I wrote some software as part of it, and also a paper discussing the results and method.
In December 2012 I delivered a presentation (printable version) discussing the project and its findings to the Mathematical foundations of computation group at Bath.
I maintain the following websites and webpages:
pub 4096R/231E83DF : B9F8 9661 4254 50E2 1684 C17C 00B8 1422 231E 83DF
2018-05-21: GPG key transition statement


- Year of composition: 1994
- Instrumentation: string quartet
Formulas is the first Johnson string quartet, premiered by the Brindisi Quartet in 1994. It comprise of eight movements, each following a mathematical formula.
“The logic of the Formulas for String Quartet is easily perceived. Even when the music goes by too fast to enable one to count notes and analyze exactly what is happening, one hears that the music is following a strict logical sequence. While composing, it was useful for me to try to define this logic more precisely and mathematically, and it seemed important to do so. I wanted to be able to show that these sequences really are formulas, and that the title is not just a metaphor.“
- Bozzini Quartet (Alissa Cheung, violin; Clemens Merkel, violin; Stéphanie Bozzini, viola; Isabelle Bozzini, cello)
- 2021-04-26 – 2021-04-30, James Clemens-Seely • Église Saint-Joseph (Rivière-des-Prairies), Montréal (Québec)


Week two we delved further into understanding the Mathematics NSW Syllabus and also the Early Years Learning Framework. Initially looking at the NSW K-6 Syllabus I felt overwhelmed. It has a lot more happening behind the lesson plans than I had realised. There are the three strands- Measurement and Geometry, Number and Algebra and Statistics and Probability. Within these headings there is then strands and sub strands. To require an in-debt knowledge of the content and outcomings under each of these heading’s, I feel I will need to spend a lot of time studying and preparing for this.
We looked at the EYLF learning which looks a little different. The elements of this is based on three headings Being, Becoming and Belonging, three sub strands of principles, practice and learning outcomes. Lastly it has five outcomes from these. There seems to be more flexibility under this curriculum compared to K-6.
We also looked into the concept of numeracy and how important it is to engage in society (ACAR, 2020)
Numeracy can be used in the real world as recognising and relating numbers to mathematics’. Reflecting back on my own experience of maths, I did not realise there was such a big difference between having maths skills and numeracy skills. I feel that being a mature student I have forgotten the basic elements and difference between the two.
Children as young as one start to develop numeracy skills. How well they grasp this can predict how successful they will be in later academic and career life (Baroody, Eiland, Reid & Purpura, 2015)
Maths is so important in the world outside the school classroom. As a future educator I hope to use this knowledge for my teachings. This week’s reading had the phrase “it takes a village to raise a child”(Attard, 2017) this really hit home for me, as a parent I need to take more responsibility for the improvement of maths education alongside the teachers and anyone who has any influence on a child.
Australian Curriculum Assessment and Reporting Authority (2020). Retrieved 19 March 2020, from https://www.australiancurriculum.edu.au/media/3635/national-numeracy-learning-progression.pdf
Attard, C. (2017). Mathematics education in Australia: New decade, new opportunities?. Retrieved 23 March 2020, from https://engagingmaths.com/2020/01/21/mathematics-education-in-australia-new-decade-new-opportunities/
Purpura, D. J., Reid, E. E., Eiland, M. D., & Baroody, A. J. (2015, March). Using a brief preschool early numeracy skills screener to identify young children with mathematics difficulties. School Psychology Review, 44(1), 41+. Retrieved from https://link-gale-com.ezproxy1.acu.edu.au/apps/doc/A435358917/AONE?u=acuni&sid=AONE&xid=76d6edb3


But there wasn't really an exhaustive search. They didn't bother to optimize solutions because they just needed to show every position could be done in 20 or fewer moves. (As they said they could analyze 2 million positions optimally per second, but prove 1 billion positions to have a solution of 20 or fewer moves, it would probably have taken some decades at Google's server farm to compute optimal solutions for everything. That is, 17500 computer-years.)
Now that they know which solutions need 20 moves, they could take a look specifically at those, and try to reduce the numbers... right?
This is awesome. Although on the cube20 site, we can't use the numbers at the bottom to find the 'average' number of moves needed to solve, since they stated on the page that they didn't "optimally" solve each position, just found a solution of 20 or less.
But yeah... I'm surprised there's still well over a hundred million (at least 300 mil on the site, but not 'optimally' solved) that need a full 20 rotations.
Although I'm curious how they came to their conclusion that "FU-F2D-BUR-F-LD-R-U-LUB-D2R-FU2D2" was the hardest solve for the computers.
http://kociemba.org/math/c1.htm). All the rest of the known 20f* positions are unsymmetric. (Some undoubtedly have symmetry in edges only or corners only.)
A list of some of the known 20f* positions can be found here. This list only includes 1 position for each set of positions that are equivalent with respect to symmetry & antisymmetry.
I understand the group is thinking about the creation of a BOINC project to get the exact number of positions at each distance from solved. That may not happen for awhile, though.
My raw video of the announcement at US Nationals is embedded here.
Last edited by cuBerBruce; 08-09-2010 at 10:18 AM. Reason: removed unnecessary quote