We all love music and enjoy it without being musicians. We all appreciate beautiful paintings but may have little artistic talent. We all delight in great literature without being accomplished writers. It is the same with mathematics: we can enjoy the elegance of brilliant logical arguments and appreciate the beauty of mathematical structures and symmetries without being skilled creators of new theorems. In this course, I will deliver an expository treatment of several delightful topics in mathematics. Their history will be presented and their importance in the modern world illustrated by applications in engineering, technology, astronomy, finance, music and the visual arts.
Mathematics pervades the modern world. It underlies technological advances and governs the social networks and systems that are crucial in our world. Our future wellbeing depends on the application of mathematics. While we may never acquire advanced technical skills in mathematics, it is very valuable and empowering to have a general appreciation of the subject.
The emphasis will be on giving a broad qualitative exposition of the key results without becoming embroiled in technicalities. Proofs will be presented only where they illustrate crucial concepts like induction and where they are uncomplicated and short.
10 Mondays 7.00pm – 9.00pm
Sept 24, Oct 1, 8, 15, 22, Nov 5, 12, 19, 26, Dec 3
(No Class Bank Holiday Monday Oct 29)
The following is a selection of recommended texts for those interested in reading further around the course content. We advise that you do not buy books in advance of the course as your tutor will discuss the list and suggest the most relevant reading for particular interests. Recommended reading:
- Peter Lynch (2016): That's Maths. Gill Books. A collection of readable articles on all areas of mathematics and its applications. Articles are self-contained, so that they can be read in any order and the contents assimilated in small doses.
- [This book will be available at a discounted price of €10.]
Peter Lynch is Emeritus Professor in the UCD School of Mathematical Sciences. Formerly Deputy Director of Met Eireann, he was Professor of Meteorology from 2004 to 2013. He writes a regular mathematical column in The Irish Times and maintains a mathematical blog, thatsmaths.com. He has a passionate interest in all things mathematical.
- Early History: Archimedes' formulas for the Circle and Sphere.
- The Foundation of Mathematics: elementary set theory.
- The Golden Number in art, technology and the living world.
- Fractals: a new window on the world.
- Maths and Music: the Synergies of Harmony & Rhythm.
- Symmetry: a guiding principle in maths, science and the arts.
- The Music of the Spheres: mathematics in astronomy.
- Topology: going far beyond Euclid.
At the end of this course, a student should be able to:
Appreciate the role of mathematics the modern world.
Have an enhanced perception of and delight in the beauty and elegance of mathematics. Gain greater knowledge, insight and pleasure from reading popular mathematical books. Be able to discuss in general terms, some of the great unsolved problems of mathematics.
Ten two-hour lectures in the Autumn semester.
(To enhance accessability, lectures will be segmented into 20-minute components on mathematical history, theory, applications, problems and diversions).
Additional resources include:
Selected articles from Wikipedia and similar quality websites.
Specially-chosen videos from the Khan Academy, AMS and You-Tube, to be viewed and discussed.
Presentation slides of the lectures, available online.
No formal assessments, but additional reading will be recommended, and topics for independent exploration will be suggested.