How to Derive a Formula : Volume 2: Further Analytical Skills and Methods for Physical Scientists

Will artificial intelligence make scientific formulae redundant by eventually solving all current and future physical problems? The authors of this book would argue that there is still a vital role for humans to play in making sense of the laws of nature. To derive a formula one follows a series of steps, only the last of which is to check that the result is correct. The book is about unravelling this machinery.

Mathematics is the 'queen of all sciences', but students encounter many obstacles in learning the subject: familiarization with the proofs of hundreds of theorems, mysterious symbols, and technical routines for which the usefulness is not obvious upfront. Learners could lose motivation, not seeing the wood for the trees.

This two-volume book How to Derive a Formula is an attempt to engage learners by presenting mathematical methods in as simple terms as possible, with more of an emphasis on skills as opposed to technical knowledge. Based on intuition and common sense rather than mathematical rigour, it teaches students from scratch using pertinent examples, many taken from across the physical sciences to demonstrate the application of the methods taught.

This book draws on humour and historical facts to provide an interesting new perspective on what a mathematics textbook could be. The two volumes are presented as an ascent to Everest. Volume 1 covered the necessary basics, taking readers from Base Camp to Camps 1 and 2. This volume moves readers from Camp 2 up to Camps 3 and 4, tackling more advanced methods for deriving formulae. Inevitably, Volume 2 requires readers to tackle more challenging terrain than was experienced in Volume 1 and so is targeted at more advanced students.

Alexei Kornyshev, theoretical physicist by background, is an internationally renowned expert in theoretical chemical physics, who over his long scientific career made pioneering contributions to the theory of electrochemical interfaces, solvation, hydration forces, electron and proton transfer in complex environment, fuel cells and supercapacitors, electrowetting, DNA biophysics, physical material science. He has published >350 original papers and > 35 monographic/review articles, many of which are highly cited. His current research lie in the areas of nanophotonics, single-molecule electronics, fundamentals of ionic liquids and their applications, electrochemical metamaterials and meta-devices, molecular genetics.

He received numerous prestigious awards and medals: 2017 Lynde-Bell Award for "outstanding career in the field of ionic systems"; 2010 RSC Interdisciplinary Prize ― for "His many outstanding contributions at the interfaces of chemistry with both physics and with biology"; 2006 Electrochemistry Barker Medal ― for "his pioneering works and outstanding achievements in the application of modern theory of condensed matter to electrochemical systems"; 2003 Schönbein Silver Medal "for his outstanding contributions to understanding of fundamentals of fuel cells"; 2002 Royal Society Wolfson Research Merit Award; 1991 Humboldt Prize in Physical Chemistry and Electrochemistry. He is an elected Foreign Member of Royal Danish Academy of Sciences & Letters and Fellow of four learned societies: IUPAC, Institute of Physics, Royal Society of Chemistry, International Society of Electrochemistry. He is an Honorary Professor of Huazhong University of Science and Technology (China) where he has a group collaborating with him. He is on the Editorial Boards of a number of physical and chemical journals.

Dominic O'Lee got his BSc in Physics in 1994 at the University of Leeds. In 1998 he completed his DPhil in Theoretical Physics at Oxford with Prof. I J R Aitchison. Dominic has worked in different areas of physical sciences, in Canada, Germany and the UK. His research ranges from quantum field theory of superconductors to the statistical mechanics of biopolymers and DNA biophysics. He has published over 40 seminal papers in these areas in physical and chemical journals. He has taught undergraduate and postgraduate students over a range of topics in physics and chemistry at Imperial, at first as a Senior Research Associate and later as an appointed Teaching Fellow. Dominic was a passionate adept of innovative, nontraditional ways of teaching, intent on making complicated things transparent and more obvious to the students. Sadly for many of his colleagues and students who admired his uniquely generous personality and style, after a tragic accident, he had to retire. Thus, having previously worked tirelessly on the preparation of this Volume, he was unable to see it through to completion.