Möbius bagel TheMathsters 2014-04-04 | Cutting a bagel along a Möbius strip, and carving a Möbius strip out of a bagel...
Eugenia Cheng, Pure Mathematics TheMathsters 2013-03-24 | http://www.youtube.com/bbcexpertwomenDr Eugenia Cheng is a Senior Lecturer of Pure Mathematics at the University of Sheffield. She grew up in Sussex, and holds three degrees from the University of Cambridge. After completing post-doctoral work at the Universities of Cambridge, Chicago and Nice, she took up her current post at the University of Sheffield. She has published articles in eight different journals and given talks in 14 different countries. Dr Cheng is known for her communication skils both in the research community and in teaching. She was an early pioneer of YouTube lectures, beginning in 2007, and her videos have been viewed around 700,000 times to date (May 2013). http://cheng.staff.shef.ac.uktwitter.com/DrEugeniaChengThis video was a shortlisted application to one of the BBC's Expert Women's Day events, which offer free training to female specialists who would like to appear in the media as contributors and presenters. Find out more about the initiative and see other expert's videos at the Expert Women's Day YouTube channel or the BBC Academy website www.bbc.co.uk/academy.
Infinity 3 TheMathsters 2012-06-05 | Introducing the idea of infinity as "the number of natural numbers" and a first look at Hilbert's hotel.
Infinity 2 TheMathsters 2012-06-05 | More problems that arise if we try and use infinity as a "number", with addition. Introducing the idea of going back doing arithmetic by "thinking" about it.
Infinity 1 TheMathsters 2012-06-04 | What is infinity? A first look at how we can think about infinity, and some problems that arise if we try and use infinity as a "number".
Induction 13 TheMathsters 2011-11-02 | Proof by induction that if alpha + 1/alpha is an integer, then alpha^n + 1/alpha^n is an integer, for all natural numbers n.
Functions 5 TheMathsters 2011-02-09 | More examples with more formal proofs of injectivity and surjectivity, and proofs that functions are not injective and surjective
Functions 4 TheMathsters 2011-02-09 | Looking at some examples of functions to see if they are injective and surjective, introducing bijective functions at the end
Functions 3 TheMathsters 2011-01-31 | Introduction of injective and surjective functions, with definition at the end
Functions 2 TheMathsters 2010-11-16 | Some more examples of functions, definition of composition, proof that composition is associative.
Numbers 16 TheMathsters 2010-10-26 | Using Euclid's algorithm backwards to show that if hcf(x,y)=h, not necessarily 1, we can get an expression rx+sy=h
Numbers 14 TheMathsters 2010-10-26 | Using Euclid's algorithm backwards to show that if hcf(x,y)=1 we can get an expression rx+sy=1
Numbers 15 TheMathsters 2010-10-26 | Another example of Euclid's algorithm backwards to show that if hcf(x,y)=1 we can get an expression rx+sy=1
Numbers 13 TheMathsters 2010-10-18 | Proof of the converse to the result in Numbers 13: that if "p|ab implies p|a or p|b" then p must be prime.
Numbers 12 TheMathsters 2010-10-18 | Introducing prime numbers as "p|ab implies p|a or p|b" and the beginnings of a proof that prime numbers have this property
Numbers 11 TheMathsters 2010-10-11 | Proof that any natural number greater than 1 can be written as a product of primes (we don't do uniqueness here). Two proofs -- one by strong induction and one using well-ordering.
Numbers 10 TheMathsters 2010-10-11 | Proof that there is an infinite number of primes, assuming that every number has at least one prime factor. Small mind block in the middle...
Numbers 9 TheMathsters 2010-10-04 | Finishing off the Sieve of Eratosthenes to find all the prime numbers up to 100, brief discussion of Mersenne primes and largest prime number currently known to man
Numbers 8 TheMathsters 2010-10-04 | Testing a few numbers to see if they're prime, and a first look at the Sieve of Eratosthenes to find all the prime numbers up to 100
Numbers 7 TheMathsters 2010-10-04 | Introduction to prime numbers, some examples of factorising numbers into primes uniquely, basic definition of prime numbers
Sets 13 TheMathsters 2010-09-28 | Introducing the inclusion-exclusion principle for counting the elements in a union of two sets and a union of three sets
Equivalence relations 3 TheMathsters 2010-09-20 | Proof that an equivalence relation on a set S partitions S into equivalence classes
Equivalence relations 4 TheMathsters 2010-09-20 | Example of equivalence classes for congruence mod 5, and a mention of representatives
Equivalence relations 2 TheMathsters 2010-04-30 | Formal definition, and example of congruence mod 5. Introduction of the idea of equivalence classes
Equivalence relations 1 TheMathsters 2010-04-30 | Introducing equivalence relations with some examples using relationships between people
Modular arithmetic 6 TheMathsters 2010-03-30 | Comparing highest common factor and lowest common multiple.
Modular arithmetic 5 TheMathsters 2010-03-19 | For musicians: using lowest common multiples to work out how cross-rhythms go
Modular arithmetic 4 TheMathsters 2010-03-19 | Another example of the Chinese Remainder Theorem, and an explanation of how its different if the two numbers arent coprime
Modular arithmetic 3 TheMathsters 2010-03-12 | Some basic simultaneous equations in modular arithmetic, and introduction to the Chinese Remainder Theorem
Modular arithmetic 2 TheMathsters 2010-03-12 | A first look at equations mod n, adding a number to both sides, multiplying both sides by a number
Induction 12 TheMathsters 2010-03-05 | Principle of strong induction implies Well-Ordering of the natural numbers
Modular arithmetic 1 TheMathsters 2010-03-05 | Introduction to modular arithmetic using clocks and telling the time
Induction 10 TheMathsters 2010-03-05 | The principle of induction, the principle of strong induction and the well-ordering principle
Induction 9 TheMathsters 2010-03-05 | Proof by induction that all cows are the same colour. What's gone wrong?
Induction 8 TheMathsters 2009-12-04 | Proof by induction that if S is a set with n elements, then the power set of S has 2^n elements.
Induction 7 TheMathsters 2009-12-04 | Proof byinduction that 3.4^n + 4.11^n is divisible by 7 for all natural numbers n.
Induction 5 TheMathsters 2009-12-01 | Proof by induction that n^3 n is always divisible by 3. Also direct proof of this and the previous example, for comparison.
Induction 2 TheMathsters 2009-11-27 | Finishing the the proof by induction that there are n! ways of ordering the numbers 1,2,3,...n. Introducing the next example: 1+2+...+n
Induction 1 TheMathsters 2009-11-27 | Introduction to proof by induction, example of ordering the numbers 1,2,3,...,n
Numbers 5 TheMathsters 2009-11-20 | Introducing Euclids algorithm for finding highest common factors, with a couple of examples
Numbers 3 TheMathsters 2009-11-10 | Divisibility formally, and proof that if m and n are divisible by d then so is m+n
