This article contains links to materials and extra resources to my Inaugural Professorial Lecture, with the same name, delivered on 17th February 2016 at Ulster University.

- If you have any comments or questions, use the Twitter hashtag #nesssuff and I’ll pick them up later and try to address them. My Twitter ID is @ProfCTurner.
- The Vote of Thanks will be given Sarah Flynn, whose Twitter ID is @sarahjaneflynn.

# Synopsis

**“Necessary and Sufficient: a look at elegance, efficiency and completeness in Engineering and its Mathematics
**

Engineers and Pure Mathematicians have a surprising amount in common, despite working at opposite ends of many problems; one at the totally theoretical end and the other at that of practical realisation, sometimes centuries apart. They both use tools created or designed mainly by other members of their own profession; they both enjoy testing things to destruction in order to explore how they work; and they both enjoy finding solutions to problems that cover all the requirements but which tend to do so in an efficient and elegant way.

This lecture explores how basic concepts that began with natural numbers to count livestock in antiquity eventually gave rise to complex numbers, and how techniques to measure buildings and the movement of the stars evolved into techniques to analyse data in totally new ways.

Some modern applications, ranging from every day examples such as photographs taken by smart-phones through to research applications, will also be considered.

Finally, the lecture will examine the implications for how Engineers can be educated to bring the power of some of humanity’s most beautiful abstract ideas to bear on the practical problems that surround us in everyday life.

# Lecture Slides

(“Director’s cut” and “Commentary/Video” to be uploaded at a later date).

– Videos not embedded, no pauses (~3 MB)

– Full Size Slides with pauses and embedded Video (~52 MB)

For those interested the slides were produced with PDFLaTeX, Beamer and Tikz. Diagrams with plots and positions of complex numbers are all calculated as the PDF is compiled. The presentation was stored in a git repository and a Makefile was used to produce the various versions.

A GitHub repository with some files missing (due to them being University property) is available here. But this does contain all Tikz diagram source code, cow images, and a LaTeX Beamer template aligned to the Faculty template that was produced. Faculty colleagues can request the required University images for their own presentations. The Makefile shows how to create different versions of the talk, with embedded or linked videos, and with or without pauses.

The content of the talk is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

# Extra reading

**Introduction**

**The Evolution of Numbers**

- Lists of Numbers in different languages and alphabets
- The cultures that do and do not have a year zero
- About Hippasus, believed by some to have proved the irrationality of the square root of two and perhaps to have been murdered as a result.
- One nice proof of the irrationality of the square root of two.
- The origin of the margin “joke”.
- Searching for numbers within pi.
- Lewis Carroll and his reputed aversion to complex numbers.
- Phasors (no, not the ones you set to stun).
- Damped Simple Harmonic Motion.

**Circular Functions and Fourier Series**

- The history of trigonometry
- Much more detail on Fourier Series
- The Fourier Transform
- The Discrete Fourier Transform
- An overview of how the DFT works
- The Discrete Cosine Transform, a cousin of DFT is what is used in JPEG
- Video explaining how the DCT used in JPEG works.

# Event Brite

- The lecture was advertised on EventBrite here.

## Leave a Reply