The fourth workshop in Dr Joel Feinstein's G11FPM Foundations of Pure Mathematics module covers a proof of Bézout’s Lemma.

These videos are also available on YouTube at: https://www.youtube.com/playlist?list=PLpRE0Zu_k-BzsKBqQ-HEqD6WVLIHSNuXa

Dr Feinstein's blog may be viewed at: http://explainingmaths.wordpress.com.

Dr Joel Feinstein is an Associate Professor in Pure Mathematics at the University of Nottingham.

The eighth lecture in Dr Joel Feinstein's G11FPM Foundations of Pure Mathematics module covers definitions and examples of Cartesian products and (binary) relations, including order relations and congruence modulo k.

These videos are also available on YouTube at: https://www.youtube.com/playlist?list=PLpRE0Zu_k-BzsKBqQ-HEqD6WVLIHSNuXa

Dr Feinstein's blog may be viewed at: http://explainingmaths.wordpress.com

Dr Joel Feinstein is an Associate Professor in Pure Mathematics at the University of Nottingham.

The third workshop in Dr Joel Feinstein's G11FPM Foundations of Pure Mathematics module covers a worksheet with questions about divisibility, prime numbers, and the square root of 3.

These videos are also available on YouTube at: https://www.youtube.com/playlist?list=PLpRE0Zu_k-BzsKBqQ-HEqD6WVLIHSNuXa

Dr Feinstein's blog may be viewed at: http://explainingmaths.wordpress.com.

Dr Joel Feinstein is an Associate Professor in Pure Mathematics at the University of Nottingham.

The sixth lecture in Dr Joel Feinstein's G11FPM Foundations of Pure Mathematics module covers The statement of Bézout’s Lemma (see Workshop 4 for a proof). Application of Bézout’s Lemma to divisibility by primes. The statement of the Fundamental Theorem of Arithmetic (for integers n ≥ 2).

These videos are also available on YouTube at: https://www.youtube.com/playlist?list=PLpRE0Zu_k-BzsKBqQ-HEqD6WVLIHSNuXa

Dr Feinstein's blog may be viewed at: http://explainingmaths.wordpress.com Dr Joel Feinstein is an Associate Professor in Pure Mathematics at the University of Nottingham.

The fifth lecture in Dr Joel Feinstein's G11FPM Foundations of Pure Mathematics module covers:

• The algebra of rational numbers: sums and products of rational numbers are rational (etc.)

• Comparison with irrational numbers: investigation of combinations of rational numbers and irrational numbers.

• Density of the rationals and the irrationals in the real line.

Note the factor 2 error in the last sketch proof, as noted in the call-out.

These videos are also available on YouTube at: https://www.youtube.com/playlist?list=PLpRE0Zu_k-BzsKBqQ-HEqD6WVLIHSNuXa

Dr Feinstein's blog may be viewed at: http://explainingmaths.wordpress.com

Dr Joel Feinstein is an Associate Professor in Pure Mathematics at the University of Nottingham.

The second workshop in Dr Joel Feinstein's G11FPM Foundations of Pure Mathematics module covers a worksheet based on working with definitions. Questions involving sums of subsets of the real line, set inclusions and set equalities. These videos are also available on YouTube at: https://www.youtube.com/playlist?list=PLpRE0Zu_k-BzsKBqQ-HEqD6WVLIHSNuXa

Dr Feinstein's blog may be viewed at: http://explainingmaths.wordpress.com Dr Joel Feinstein is an Associate Professor in Pure Mathematics at the University of Nottingham.

The fourth lecture in Dr Joel Feinstein's G11FPM Foundations of Pure Mathematics module covers Highest Common Factor (HCF, also known as Greatest Common Divisor, GCD) for integers, and lowest terms for rational numbers.

How and why indirect proof (proof by contradiction) works. Examples of indirect proofs, including the proof that the square root of two is irrational.

These videos are also available on YouTube at: https://www.youtube.com/playlist?list=PLpRE0Zu_k-BzsKBqQ-HEqD6WVLIHSNuXa

Dr Feinstein's blog may be viewed at: http://explainingmaths.wordpress.com

Dr Joel Feinstein is an Associate Professor in Pure Mathematics at the University of Nottingham.

The third lecture in Dr Joel Feinstein's G11FPM Foundations of Pure Mathematics module covers an introduction to formal definitions and direct proofs, with discussion, motivation and examples. The dangers of backwards logic.

These videos are also available on YouTube at: https://www.youtube.com/playlist?list=PLpRE0Zu_k-BzsKBqQ-HEqD6WVLIHSNuXa

Dr Feinstein's blog may be viewed at: http://explainingmaths.wordpress.com

Dr Joel Feinstein is an Associate Professor in Pure Mathematics at the University of Nottingham.

The first workshop in Dr Joel Feinstein's G11FPM Foundations of Pure Mathematics module is a detailed look at some extracts from the Module Information Document including:

Module aims and learning outcomes.

The importance of understanding and being able to demonstrate. understanding of the material.

Likely style of exam questions.

The importance of looking at the feedback on student performances in the last two years' exams.

What you need to do if you want to do well in this module, rather than just passing it.

These videos are also available on YouTube at: https://www.youtube.com/playlist?list=PLpRE0Zu_k-BzsKBqQ-HEqD6WVLIHSNuXa

Dr Feinstein's blog may be viewed at: http://explainingmaths.wordpress.com

Dr Joel Feinstein is an Associate Professor in Pure Mathematics at the University of Nottingham.

The second class in Dr Joel Feinstein's G11FPM Foundations of Pure Mathematics module covers Sets and their elements. Number systems. Elementary reasoning using examples and counterexamples.Various ways to specify sets, and simplifying their descriptions. Intervals and number line sketches.

These videos are also available on YouTube at: https://www.youtube.com/playlist?list=PLpRE0Zu_k-BzsKBqQ-HEqD6WVLIHSNuXa

Dr Feinstein's blog may be viewed at: http://explainingmaths.wordpress.com

Dr Joel Feinstein is an Associate Professor in Pure Mathematics at the University of Nottingham.