Will artificial intelligence solve all problems, making scientific formulae redundant? The authors of this book would argue that there is still a vital role in formulating them to make sense of the laws of nature. To derive a formula one needs to follow a series of steps; last of all, check that the result is correct, primarily through the analysis of limiting cases. 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. Those interested in the physical sciences could lose motivation, not seeing the wood for the trees.
This two-volume book How to Derive a Formula is an attempt to engage these learners, presenting mathematical methods in as simple as possible terms, with more of an emphasis on skills as opposed to technical knowledge. Based on intuition and common sense rather than mathematical rigor, it teaches students from scratch using pertinent examples, many taken across the physical sciences to demonstrate the application of the taught methods.
This book provides an interesting new perspective of what a mathematics textbook could be, including historical facts and humour to complement the material. The metaphor adopted in both volumes is an ascent to Everest; from the Base Camp to Camp 1, from Camp 1 to Camp 2 (Volume 1); from Camp 2 to Camp 3, from Camp 3 to Camp 4 (Volume 2). Volume 1 was about the necessary basics. Volume 2 proceeds to more advanced and challenging methods for deriving formulae. Inevitably, the formalism of these methods is more involved and challenging for the readers, than in Volume 1. Whereas the approach of Volume 1 is upheld in Volume 2, the latter cannot be expected to be the same 'easy reading'.
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.
