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Lesson 8.4: Modelling with parametric equations

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Lesson 8.3: Solve coordinate geometry problems with parametric equations

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Lesson 8.2: Converting parametric equations into Cartesian form using trigonometric identities

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Print off accompanying notes in 'Something to Do' before watching.

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Lesson 8.1: Converting parametric equations into Cartesian equations

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pdf format
The image is based on Christian Huygens' work on the cycloid; a famous problem in mathematics that utilises parametric equations.

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By far and away the finest publication for budding mathematicians out there. Every issue has accesible articles written by a plethora of different people. The cross number is killer!

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A magazine for the mathematically curious. Issue 17 now available: Penguins, prison and PDE patterns feature in our new issue. Plus all your favourite puzzles & columns.

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MUST WATCH: Mr. Brockway's 60-second career journey! 

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MUST WATCH: Mr. Brockway's 60-second career journey! 

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It's actually 1 m 27 s. My first attempt was almost 5 minutes!

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Explore the channels and learn more about mathematics, science and other areas of fascination.

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Please read the attached document to discover what will be coming your way over the coming weeks!

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This is the final lesson from Chapter 9: Differentiation. Highly recommended for those of you studying STEM courses at university! (A pdf copy of the completed notes for this chapter is attached to this column thread).

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Lesson 9.8: Rates of change and differential equations

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Notes are posted in this column. (links closely with finding maxima, minima and points of inflection).

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Lesson 9.7: Determine whether a function is concave or convex on a given domain.

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Lesson 9.5: Differentiating parametric equations

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Lesson 9.5: Differentiating parametric equations

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The full 'Parametric Equations' chapter will be available soon! A really important topic - not to be missed!

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Some interesting research for those pursuing maths beyond A-level

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Students who drop mathematics at the age of 16 have lower amounts of a brain chemical that is critical for brain and cognitive development, compared with those who continue maths, a study has found.

Researchers at the University of Oxford found that those who stopped maths after their GCSEs had less gamma-aminobutyric acid, a chemical which is crucial for brain plasticity, than counterparts who pursued maths post-16.

The reduction in the chemical, which works as a neurotransmitter, was found in a key area of the brain that supports maths, memory, learning, reasoning and problem solving - and researchers warned it could put affected students at a disadvantage.

More than 130 students aged 14-18 took part in the study by researchers from the university's department of experimental psychology. Students over 16 were asked if they had already stopped studying maths, while younger students were asked whether they were planning to give up maths.

Each of them underwent a brain scan and cognitive assessment, and were followed up 19 months later. According to the paper, published in the Proceedings of the National Academy of Sciences, researchers were able to spot those who did or did not study maths post-16 based on concentrations of the brain chemical in each student.

They also found the amount of brain chemical present predicted changes in mathematical attainment about 19 months later, yet there were no differences in the levels of the chemical present before the adolescents stopped studying maths.

The findings are significant because pupils in the UK are allowed to drop maths at 16, unlike those in much of the rest of the world. They are likely to be seized upon by those in favour of extending compulsory maths to the age of 18. They also raise questions about the possible impact on children's cognitive development of disrupted learning due to Covid.

Prof Roi Cohen Kadosh, the cognitive neuroscientist at Oxford who led the study, said: "Adolescence is an important period in life that is associated with important brain and cognitive changes. Sadly, the opportunity to stop studying maths at this age seems to lead to a gap between adolescents who stop their maths education compared to those who continue it.

"Our study provides a new level of biological understanding of the impact of education on the developing brain and the mutual effect between biology and education. It is not yet known how this disparity, or its long-term implications, can be prevented."

Acknowledging that not every adolescent enjoys maths, he said alternatives which produce the same effect should be investigated, including training in logic and reasoning that engage the same brain area as maths.

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Studying maths beyond GCSEs helps brain development, say scientists

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Students who drop mathematics at the age of 16 have lower amounts of a brain chemical that is critical for brain and cognitive development, compared with those who continue maths, a study has found.

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This document contains the full chapter including the lessons that were omitted due to time constraints. You will find 'rates of change' (lesson 9.8) particularly useful if you have opted to study a STEM course at university.

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Choose from a wide range of online courses aimed at beginners up to advanced.

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Learn online and earn valuable credentials from top universities like Yale, Michigan, Stanford, and leading companies like Google and IBM. Join Coursera for free and transform your career with degrees, certificates, Specializations, & MOOCs in data science, computer science, business, and dozens of other topics.

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How to Study for a Mathematics Degree by Lara Alcock

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How to Study for a Mathematics Degree by Lara Alcock

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A useful guide for anyone wishing to pursue mathematics beyond A-level.

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science & mathematics: textbooks & study guides

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mathematics - study and teaching (higher)

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mathematics - study and teaching (higher)

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science & mathematics: textbooks & study guides

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Buy How to Study for a Mathematics Degree by Alcock, Lara (ISBN: 9780199661329) from Amazon's Book Store. Everyday low prices and free delivery on eligible orders.

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Calculus: Early Transcendentals (Latest Edition) by James Stewart

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Calculus: Early Transcendentals (Latest Edition) by James Stewart

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This is the definitive calculus textbook. According to the description on Amazon, it 'provides you with the strongest foundation for a STEM future'. I still use this book for my own mathematical projects.

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Calculus: Early Transcendentals, Metric Edition

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Buy Calculus: Early Transcendentals, Metric Edition 9 by Stewart, James, Watson, Saleem, Clegg, Daniel K. (ISBN: 9780357113516) from Amazon's Book Store. Everyday low prices and free delivery on eligible orders.

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An Introduction to Mathematical Reasoning by Peter Eccles

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An Introduction to Mathematical Reasoning by Peter Eccles

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Peter Eccles is a British mathematician and emeritus professor of mathematics at the University of Manchester. I found his book really helpful in my first year as an undergraduate at the U of M.

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an introduction to mathematical reasoning: numbers

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science & mathematics: textbooks & study guides

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science & mathematics: textbooks & study guides

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An Introduction to Mathematical Reasoning: Numbers, Sets and Functions

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Buy An Introduction to Mathematical Reasoning: Numbers, Sets and Functions by Eccles, Peter J. (ISBN: 0884494921894) from Amazon's Book Store. Everyday low prices and free delivery on eligible orders.