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Composite functions

Find the composite of two functions

$f(x)=x+\sqrt{x+1},g(x)=\sqrt{x+1},x\geq -1$ $f(g(x))=\sqrt{x+1}+\sqrt{x+1}=2\sqrt{x+1},x\geq -1$

$h(x)= e^{x},x\in R, g(x)=\sqrt{x},x\geq 0, h(g(x))=e^{\sqrt{x}},x\geq 0$

$x=0, h(g(0)))=e^{\sqrt{0}}=e^{0}=1$

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O ΑΡΡΗΤΟΣ ΑΡΙΘΜΟΣ Π

“Αεί ο Θεός ο Μέγας γεωμετρεί, το κύκλου μήκος ίνα ορίση διαμέτρω, παρήγαγεν αριθμόν απέραντον, καί όν, φεύ, ουδέποτε όλον θνητοί θα εύρωσι” το οποίο αντιστοιχεί στην παρακάτω δεκαδική προσέγγιση του π=3,1415926535897932384626

BBC RADIO - A Brief History of the Mathematics

BBC RADIO - A Brief History of Mathematics

Maryam Mirzakhani

Maryam Mirzakhani was an Iranian mathematician and a professor of mathematics at Stanford University. Her research topics included Teichmüller theory, hyperbolic geometry, ergodic theory, and symplectic geometry. Wikipedia

Born: 12 May 1977, Tehran, Iran

Died: 14 July 2017, Stanford Hospital at 300 Pasteur Drive, Palo Alto, California, United States

Spouse: Jan Vondrák (m. 2008–2017)

Place of burial: Los Gatos Memorial Park, San Jose, California, United States

Awards: Fields Medal, Blumenthal Award, Ruth Lyttle Satter Prize in Mathematics, Clay Research Award

Education: Harvard University (2004), Sharif University of Technology (1999), Tehran Farzanegan School

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Further Mathematics Conference 2019

Advanced Mathematics Support Programme The Advanced Mathematics Support Programme is a government-funded initiative, managed by MEI. It aims to increase participation in Core Maths, AS/A level Mathematics and Further Mathematics, and improve the teaching of these level 3 maths qualifications. The programme provides national support for teachers and students in state-funded schools and colleges in England. Additional support is offered in areas of low social mobility so that, whatever their gender, background or location, students can choose their best post-16 maths pathway and have access to high quality teaching
During Spring term 2019, the AMSP held four one-day professional development and networking conferences, dedicated to the teaching of AS and A level Further Mathematics. It was designed to provide teachers with the opportunities to: experience interesting and stimulating ways of introducing Further Mathematics topics in the classroom. gain support in meeting the challenges of establishing and sustaining AS and A level Further Mathematics. network and share ideas with fellow teachers

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Functions and Representations

Τhe relationship to each value of the variable x corresponds to two values of the y variable is not a function
The intersection points between the parabole and t...

Secondary Accountability Measures

Information for schools about secondary school accountability measures, including Progress 8 and Attainment 8

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Ο Μικρός Ευκλείδης

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Τα θέματα της μαθηματικής Ολυμπιάδας 2017

ΑΝΑΡΤΗΣΕΙΣ ΤΟΥ ΙΣΤΟΛΟΓΙΟΥ

Το πεδίο έρευνας των μαθηματικών
Απόσπασμα από τα Στοιχεία του Ευκλείδη
To θεώρημα του Πυθαγόρα
Εις άτοπον απαγωγή
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Η κβαντική μηχανική
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Στη μαθηματική λογική, μια θεωρία είναι σύνολο από...
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7 Steps to Prepare an Exciting and Effective lesson plan

7 Steps to Prepare an Exciting and Effective lesson plan. A well planned lesson can be described with two words: exciting and effective. In fact these two adjectives are interlinked as any lesson that is exciting for students will have some educational value and will be effective. This is because learning should essentially be associated with positive motivation, excitement and passion. So whatever is taught with these qualities in mind will stay with students for longer and will help them develop lifelong skills and attain knowledge.

Mathematics > Number Theory

Cracking the problem with 33

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ΙΣΤΟΛΟΓΙΑ

Ιστολόγιο με μαθηματικό περιεχόμενο και εκπαιδευτικό υλικό
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Μαθηματικά γενικής παιδείας
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Γεωμετρία Riemann και ομάδες Lie

American Mathematical Society Resources (available in PDF format)

Principles of Analysis A one-semester introduction-to-proofs course. Topics include elementary logic and set theory, axioms for the real numbers, sequences, functions of one variable, continuity, integration, differentiation, the fundamental theorems of calculus, and elementary transcendental functions
Linear Algebra My son's "text"/notes he used to teach a class.
A Crèche Course in Model Theory An introduction to pure model theory and first-order definability
Dynamical Systems I ODEs & Introduction to Nonlinear Dynamics A two-part course Ia and Ib (currently only part Ib available) on ordinary differential equations and nonlinear dynamics
A brief introduction to group representations and character theory These are notes for a brief unit on representation theory at the end of a standard graduate abstract algebra course. The notes assume no special preparation for representation theory, but take advantage of efficiencies of exposition made possible by an assumed basic graduate-level background in module theory, canonical forms, etc.
Homotopy coherent structures These lecture notes were prepared to accompany a three-hour mini course entitled “Homotopy coherent structures” delivered at the summer school accompanying the “Floer homology and homotopy theory” conference at UCLA from July 10 - 14, 2017: https://sites.google.com/site/floerhomotopy2017/home
Contact Topology Lecture notes from Prof. Robert Gompf's Contact Topology course at UT Austin, Fall 2017. (posted with permission from Robert Gompf)
Combinatorics The Art of Counting This is a preliminary version of a book which I intend to publish with the AMS. My editor is Ina Mette
Free Probability Theory This in an introduction to free probability theory, covering the basic combinatorial and analytic theory, as well as the relations to random matrices and operator algebras. The material here was presented in the winter term 2018/19 at Saarland University in 26 lectures of 90 minutes each. The lectures were recorded and can be found online at https://www.math.uni-sb.de/ag/speicher/web_video/index.html
The spectral geometry of arithmetic hyperbolic 3-manifolds These notes introduce the reader to the spectral geometry of arithmetic hyperbolic 3-manifolds and the number theoretic techniques which arise in their study.
Lecture notes on stability theory Combinatorial stability theory grew out of Shelah's work on Morley's conjecture concerned with the number of uncountable models of first-order theories. The subject gained a stronger geometric aspect and found applications to algebra and number theory through the work of Zilber, Hrushovski, Pillay and many others. In recent year, many of its methods were generalized to larger classes of theories. These lecture notes provide an introduction to this area.
Graph Theory Basics, trees, Caley's formula, matrix tree theorem, connectivity, theorems of Mader and Menger, Eulerian graphs, Hamilton cycles, theorems of Dirac, Ore, Erdös-Chvatal, matchings, theorems of Hall, König, Tutte, planar graphs, Euler's formula, Kuratowski's theorem, graph colorings, Brooks' theorem, 5-colorings of planar graphs, list colorings, Vizing's theorem, Ramsey theory, Turán's theorem

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Euclid's Elements

Bill Casselman
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450+ maths lessons and worksheets linked with an i..

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Nested Intervals Theorem and Applications

In mathematics, a sequence of nested intervals is understood as a collection of sets of real numbers In such that each set In is an interval of the real line, for n = 1, 2, 3, ..., and that further In + 1 is a subset of In for all n. In other words, the intervals diminish, with the left-hand end moving only towards the right, and the right-hand end only to the left.

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computational strategies, connecting, representing, and communicating. The Seven Math Processes

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Grade point average famously known as GPA is the calculated average of grades you earn during a stated period of time, it could be a term, semester or session. GPAs are usually determined by the accumulation of course credits, individual grades and semester hours spent in the class. It follows a 0 to 4.0 or 5.0 scale. Some colleges and universities prefer using percentage grades e.g.: 50% instead of letter grades e.g.: B. It is therefore necessary to ask about their grading system before reporting.

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Pythagoras is said to have noticed that thedifferent musical notes emitted from a blacksmiths workshop depended onthe lengths of the metal objects being struck

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The Fields Institute's Annual Report is published electronically each fall.

Annual Report 2019
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The Institute's Newsletter, renamed Fields Notes in 2004, presents more timely information and is published throughout the year.

Fields Notes, Summer/Fall 2019: PDF | E-Magazine
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The elements of Euclid

The elements of Euclid for the use of schools and ...
The first six books of the elements of Euclid, in ...
The First Six Books of The Elements of Euclid With...

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On the Duffin-Schaeffer conjecture

On the Duffin-Schaeffer conjecture

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International Mathematical Olympiad 2018
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The first 10 digits of pi (π) are 3.1415926535

The first 10 digits of pi (π) are 3.1415926535

Guide to AS and A level results for England, 2019

Guide to AS and A level results for England, 2019

Archive of Annual Reports and Newsletters published by the Fields Institute

Archive of Annual Reports and Newsletters published by the Fields Institute

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Stored Energy

Introduction. We all rely on energy being stored in various ways. Thismay be medium term storage in batteries, short term storage in capacitorsand springs or a whole variety of other storage techniques. It is interestingthat the formulas for different types of stored energy have the same form

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International Project on Mathematical Attainment (IPMA)

This is a longitudinal, international project in mathematical attainment, monitoring the mathematical progress of pupils in primary schools and relating that progress to several factors including style of teaching and organisation of curriculum. The aim is to provide recommendations for good practice in primary mathematics education

Free online math e-books pdf

Free online mathematics e-Books

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The National curriculum UK

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The Centre for Innovation in Mathematics Teaching (CIMT)

The Centre for Innovation in Mathematics Teaching (CIMT) was established in 1986. The centre is a focus for research and curriculum development in Mathematics teaching and learning, with the aim of unifying and enhancing mathematical progress in schools and colleges. This CIMT Web-site was started in May 1995, and moved to University of Plymouth servers at the end of July 2005. To enter the site, click on one of the links below

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Distortion and Distribution of Sets under Inner Functions

Distortion and Distribution of Sets under Inner Fu...

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Find the Gradient of the Curve at Specific points
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STEM Learning primary magazine 2015-2016-2017
STEM Learning primary magazine - summer 2017
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STEM Learning primary magazine - summer 2018

STEM Learning Magazine: Secondary

STEM Learning Magazine: Secondary 2015-2016-2017
STEM Learning magazine: secondary and post-16 - summer 2017
STEM learning secondary and FE magazine: autumn 2017
STEM learning secondary and FE magazine: spring 2018
STEM learning secondary and FE magazine: summer 2018

Timeline of child rights

1924

The League of Nations adopts the Geneva Declaration on the Rights of the Child, drafted by Eglantyne Jebb, founder of the Save the Children Fund. The Declaration articulates that all people owe children the right to: means for their development; special help in times of need; priority for relief; economic freedom and protection from exploitation; and an upbringing that instils social consciousness and duty.

1946

The United Nations General Assembly establishes the International Children’s Emergency Fund, UNICEF, with an emphasis on children throughout the world.

1948

The United Nations General Assembly passes the Universal Declaration of Human Rights, in which Article 25 entitles mothers and children to ‘special care and assistance’ and ‘social protection’.

1959

The United Nations General Assembly adopts the Declaration of the Rights of the Child, which recognizes, among other rights, children’s rights to education, play, a supportive environment and health care.

1966

With the International Covenants on Civil and Political Rights and on Economic, Social and Cultural Rights, United Nations Member States promise to uphold equal rights – including education and protection – for all children.

1968

The International Conference on Human Rights is convened to evaluate the progress made by countries in the 20 years since the adoption of the Universal Declaration of Human Rights. An agenda for future work is drafted and national commitments to upholding human rights are bolstered.

1973

The International Labour Organization adopts Convention 138, which sets 18 as the minimum age for undertaking work that might be hazardous to a person’s health, safety or morals.

1974

Concerned about the vulnerability of women and children in emergency and conflict situations, the General Assembly calls on Member States to observe the Declaration on the Protection of Women and Children in Emergency and Armed Conflict. The Declaration prohibits attacks against or imprisonment of civilian women and children, and upholds the sanctity of the rights of women and children during armed conflict.

1978

The Commission on Human Rights puts forth a draft of a Convention on the Rights of the Child for consideration by a working group of Member States, agencies and intergovernmental and non-governmental organizations.

1979

To mark the twentieth anniversary of the 1959 Declaration of the Rights of the Child, the United Nations General Assembly declares 1979 as the International Year of the Child, in which UNICEF plays a leading role.

1985

The United Nations Standard Minimum Rules for the Administration of Juvenile Justice detail the principles of a justice system that promotes the best interests of the child, including education and social services and proportional treatment for child detainees.

1989

The Convention on the Rights of the Child is adopted by the United Nations General Assembly and widely acclaimed as a landmark achievement for human rights, recognizing the roles of children as social, economic, political, civil and cultural actors. The Convention guarantees and sets minimum standards for protecting the rights of children in all capacities. UNICEF, which helped draft the Convention, is named in the document as a source of expertise.

1990

The World Summit for Children is held in New York. The Guidelines for the Prevention of Juvenile Delinquency outline strategies for preventing criminality and protecting young people at high social risk.

1991

Experts from UNICEF, Save the Children, Defence for Children International and other organizations meet to discuss data gathered from the reporting process of the Convention on the Rights of the Child. The meeting leads to the formal establishment of the Child Rights International Network (CRIN) in 1995.

1999

The International Labour Organization (ILO) adopts the Worst Forms of Child Labour Convention, calling for the immediate prohibition and elimination of any form of work that is likely to harm the health, safety or morals of children. UNICEF has been working with the ILO since 1996 to promote the ratification of international labour standards and policies concerning child labour.

2000

The United Nations General Assembly adopts two Optional Protocols to the 1989 Convention on the Rights of the Child, obligating State Parties to take key actions to prevent children from partaking in hostilities during armed conflict and to end the sale, sexual exploitation and abuse of children.

2002

At the United Nations Special Session on Children, child delegates address the General Assembly for the first time. The World Fit for Children agenda was adopted outlining specific goals for improving the prospects of children over the next decade.

2006

UNICEF co-publishes the Manual for the Measurement of Juvenile Justice Indicators with the United Nations Office on Drugs and Crime. The Manual enables governments to assess the condition of their juvenile justice systems and make reforms as necessary.

2010

The United Nations Secretary-General issues the Status of the Convention on the Rights of the Child.

2011

A new Optional Protocol to the 1989 Convention on the Rights of the Child is adopted. Under this Optional Protocol on a communications procedure, the Committee on the Rights of the Child can field complaints of child rights violations and undertake investigations.

2015

Somalia and South Sudan ratify the Convention. The Convention is the most widely ratified international instrument with 196 States. Only the United States has not ratified to date.

Convention on the Rights of the Child text

Resources on the Convention on the Rights of the Child
The Convention on the Rights of the Child: The children’s version
Read and download the Convention on the Rights of the Child
For students and teachers

CRM-Fields-PIMS Prize

The CRM-Fields-PIMS prize is the premier Canadian award for research achievements in the mathematical sciences. It is awarded jointly by the three Canadian mathematics institutes. The winner receives a monetary award and an invitation to present a lecture at each institute within one year after the award is announced.

The prize recognizes exceptional achievement in the mathematical sciences. It was established by the Centre de recherches mathématiques (CRM) and The Fields Institute as the CRM-Fields prize in 1994.

In 2005, the Pacific Institute for the Mathematical Sciences (PIMS) became an equal partner in awarding the prize. The name changed to the CRM-Fields-PIMS prize, the award level increased, and the terms of reference were revised. The winner is selected by a committee appointed by the three institutes.

Previous CRM-Fields-PIMS Prize Winners

2020 - Catherine Sulem, University of Toronto

2019 - Nassif Ghoussoub, University of British Columbia

2018 - Jeremy Quastel, University of Toronto

2017 - Henri Darmon, McGill University

2016 - Daniel Wise, McGill University

2015 - Kai Behrend, University of British Columbia

2014 - Niky Kamran, Université McGill 

2013 - Bruce Reed, Université McGill 

2012 - Stevo Todorcevic, University of Toronto

 2011 - Mark Lewis, University of Alberta 

2010 - Gordon Slade, University of British Columbia 

2009 - Martin Barlow, University of British Columbia 

2008 - Allan Borodin, University of Toronto

 2007 - Joel S. Feldman, University of British Columbia

 2006 - Nicole Tomczak-Jaegermann, University of Alberta

Previous CRM-Fields Prize Winners

2005 - David Boyd, University of British Columbia

2004 - Donald Dawson, Carleton University

2003 - John McKay, Concordia, and Edwin Perkins, University of British Columbie (joint winners)

2002 - John B. Friedlander, University of Toronto

2001 - William T. Tutte, University of Waterloo

2000 - Israel Michael Sigal, University of Toronto

1999 - Stephen A. Cook, University of Toronto

1998 - Robert Moody, University of Alberta

1997 - James Arthur, University of Toronto

1996 - George A. Elliott, University of Toronto

1995 - H.S.M. "Donald" Coxeter, University of Toronto

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