17. The Beauty of Everyday Mathematics by Norbert Herrmann - for those who want to know how much a fizzy drink must be consumed so that the can is the most stable. In Praise of Simple Physics and How to Fall Slower than Gravity are both brilliant and lucid pieces of science writing that we have come to expect from Paul Nahin, exploring the physics of everyday phenomena. One of the latest of his is the book, In Pursuit of Zeta-3, a fascinating account of the enigmas still surrounding the zeta function, Riemann hypothesis and the Euler gamma.
16. Quantum Mechanics by David H McIntyre - a "modern" approach to QM similar to that of Feynman et al, Cohen-Tannoudji et al, J J Sakurai, John Townsend, R Shankar, Englert and J Schwinger. Nice read! A rather unusual presentation of quantum mechanics is found in Malcolm Longair's Quantum Concepts in Physics, which tells a compelling historical story, from Lavoisier and John Dalton discovering how matter may actually be composed of smaller units to Heisenberg's and Dirac's interpretations of quantum mechanics, and is packed with many experimental details and mathematical derivations.
15. Problem-Solving Strategies by Arthur Engel - a great collection of mathematical competition problems grouped into chapters like invariance principle, inequalities, polynomials, etc. Another wonderfully written treatise is Paul Zeitz's The Art and Craft of Problem Solving.
14. The Strangest Man by Graham Farmelo - a biography of P A M Dirac, physics Nobel Prize 1933 for atomic physics and quantum field theory.
13. Gamma, Exploring Euler's Constant by Julian Havil - Gamma is defined as the limit of the sum of 1 + 1/2 + 1/3 +...up to 1/n minus the natural log of n. The book takes the reader on a journey into a tantalizing maze of history and mathematics. The history of mathematics flowed through different countries, personalities, even geniuses. Early mathematics was largely applied mathematics, for the building of towers, and for trading. A distinct development of geometric proofs occurred among the Greeks of whom Euclid and Pythagorus were pre-eminent. There were nascent algebraic uses in geometric calculations and tagging of geometric structures with co-ordinate numbers, and among them the work of Viete stood out for using unknowns in algebraic solutions. Subsequent study by Descartes and Fermat of the forms of geometric loci of algebraic equations gradually ushered in the era of analytical geometry. Although Newton's Principia, of which the first edition appeared in 1687 several decades after the death of Descartes and revised twice subsequently, showed some influence of Descartes whose works Newton admitted he read, geometrical constructions were still largely used for mathematical proof. A good book on exploring Newton's greatest work is Colin Pask's Magnificent Principia. Further, both Newton and Leibniz experimented with a form of infinitesimal geometric argument that eventually led to the formulation of calculus. Newton, Leibniz, Euler, Fermat, Gauss, Lagrange, Laplace, Legendre, Fourier, Galois, Weierstrass, Cauchy, Riemann, Lebesgue, Poincare are among the greatest of mathematicians who have changed our understanding of the world. Other than good general texts like Uta C Merzbach's and Carl B Boyer's A History of Mathematics, as well as the book From Five Fingers to Infinity edited by Frank J Swetz, there are some very well written, even interesting, books on specific periods of the history of mathematics, including Steven G Krantz's An Episodic History of Mathematics, Leo Corry's A Brief History Of Numbers, Avner Ash's and Robert Gross's Summing It Up From One Plus One To Modern Number Theory, Victor Katz's and Karen H Parshall's Taming The Unknown, A History Of Algebra From Antiquity To The Early Twentienth Century, Jeremy Gray's The Real And The Complex: A History Of Analysis In The 19th Century, Gonzalez-Velasco's Journey Through Mathematics and Krantz's and Parks' A Mathematical Odyssey, Journey From The Real To The Complex. An unusual and entertaining way of presenting some of the history of mathematics is Dana Mackenzie's The Universe in Zero Words The Story of Mathematics as Told through Equations.
12. From Falling Bodies to Radio Waves by Emilio Segre - the late Nobel prize physicist Segre chronicles physics and physicists from Galileo, Newton, Faraday, Watts, Maxwell, Boltzmann to Gibbs in an old but still fascinating book.
Nancy Forbes and Basil Mahon have written an engaging book on Faraday, Maxwell, and the Electromagnetic Field: How Two Men Revolutionized Physics.
Carlo Rovelli, in Reality Is Not What It Seems, tells the story of how the scientific understanding of matter developed from the early Greeks (particularly Democritus) to Quantum Gravity. The story of the quantum revolution from Max Planck to the superstring theory is told in 40 lively chapters in Jim Baggott's The Quantum Story.
11. The Theoretical Minimum by Leonard Susskind and George Hrabovsky is a little tour of classical mechanics for the curious-minded that does not shy away from things like Lagrange's and Hamilton's equations. The second volume is devoted to Quantum Mechanics. The third is on classical field theory (which includes electricity and magnetism, and sometimes gravitation and special relativity).
Anthony Zee has written a most iconoclastic physics book in his usual witty and conversational style, Fly by Night Physics, replete with back of the envelope estimates, dimensional reasoning, order of magnitude guesses and intuitive thinking that looks laterally into what really lies behind the equations of physics.
A fascinating account of variational mechanics and the principle of least action, written with an eye to non-physicists, is Jennifer Coopersmith's The Lazy Universe. This is built on the highly regarded Cornelius Lanczos' book and explains where the Hamiltonian comes from and what D'Alembert principle is.
10. Letters to a Young Scientist by emeritus professor of biology at Harvard, Edward Wilson, records his musings and advice on how to teach science to the younger generation.
9. Haken's and Wolf's The Physics of Atoms and Quanta is one of the classic texts for modern physics, written with great elegance and poise, synthesizing both theory and experimental topics into a satisfying whole. Highly recommended.
8. For those who "cannot spend too much time on the subject" stated Albert Einstein, read the 1945 classic The Einstein Theory of Relativity by Lillian R Lieber. Don't assume this is a walk-over; it actually explains in simple language the Riemann tensor with mathematics! Another book with a similar motivation to introduce general relativity to the "mathematically untrained" is Oyvind Gron's and Arne Naess' Einstein's Theory. Recently Sean Carroll has produced another well written book, this time on Einstein's general relativity, aptly called The Biggest Ideas in the Universe. Ta-Pei Cheng has written an interesting physics account, in his book Einstein's Physics, based on Einstein's writings on blackbody radiation, photoelectric effect, quantum statistics, special and general relativity. There are several ways of defining tensors - as a kind of vector product, or as objects that behave in a certain way under co-ordinate transformations or as an abstract geometric mapping "function" that takes in vectors or dual vectors (or forms) and outputs a scalar. Put in a simple way, a tensor is something which has 0, 1, 2 or more directions and a magnitude that is generally related to the directions. A vector in this reckoning is a tensor of rank 1 because it has a direction and a magnitude. A tensor of rank 2 (such as a stress tensor) has 2 directions and a magnitude. For those who may be interested in understanding what a tensor is, consult Gabriel Weinreich's Geometric Vectors, Pavel Grinfeld's Introduction to Tensor Analysis and The Calculus of Moving Surfaces, or Stephenie Frank Singer's Symmetry in Mechanics (one that uses differential geometry in a gentle way for explaining phase space and Hamiltonian mechanics). Heavier stuff are found in V.I. Arnold's classic Mathematical Methods of Classical Mechanics, Jorge Jose's and Eugene Saletan's Classical Dynamics a Contemporary Approach or Spivak's Physics for Mathematicians (Mechanics I).
Advanced discussions on tensor calculus, manifolds, fibre bundles, and how differential topology are used in physics are found in Theodore Frankel's The Geometry of Physics.
7. Enjoy reading John Barrow's 100 Essential Things You Didn't Know You Didn't Know about Maths & The Arts! If you can't figure out why you had to learn mathematics in the past, or even now, you have to read Jordan Ellenberg's captivating prose in How Not To Be Wrong, The Power Of Mathematical Thinking. The back cover says it is "the Freakonomics of maths". Similar in nature to Barrow's and Ellenberg's and as eloquent is Alex Through the Looking Glass, on how mathematics is so intimately related to the world, a book by Alex Bellos.
6. Three fascinating books of similar type: Alfred S Posamentier and Ingmar Lehmann's Magnificent Mistakes in Mathematics, Edward J Barbeau's Mathematical Fallacies, Flaws and Flimflam and Eugene P Northrop's Riddles in Mathematics.
5. If you are fascinated by the question "Does the world embody beautiful ideas?" then read Nobel Physics Prize scientist Frank Wilczek's new book (2015) A Beautiful Question. Another 4 books that explore the big meta-questions about science are: Marcus Du Sautoy's What We Cannot Know (published in the US as The Great Unknown), Max Tegmark's Our Mathematical Universe, Roger Penrose's Fashion, Faith and Fantasy and Sean Carroll's The Big Picture. Talking about symmetry and how important it is in physics, read Anthony Zee's Group Theory In A Nutshell For Physicists and Jakob Schwichtenberg's Physics From Symmetry for lovely if mathematical accounts. In particular, Schwichtenberg showed how we can understand some of the key aspects of particle physics from the Lie algebra of the SO(1,3) Lorentz group.
4. Reminiscent of the 3-volumes Feynman's Lectures on Physics, R Shankar has written a highly readable and enjoyable 2-volumes Fundamentals of Physics I and II, as taught at Yale.
3. There are many books on particle physics pitched at different audiences. A nice overall view is provided by Frank Close, Michael Marten, Christine Sutton, The Particle Odyssey. Another clear non-technical description is M Y Han's, Quarks and Gluons, A century of particle charges. A slightly more mathematical account for the layman is John Iliopoulos, The Origin of Mass, Elementary Particles & Fundamental Symmetries.
A lovely and conversational book on Quantum Field Theory pitched at an advanced popular level with a couple of true-blue equations thrown in (eg. Dirac equation in its unabridged form) is Anthony Zee's Quantum Field Theory as Simply as Possible.
2. A delightful and clear account of how bioluminescence was discovered is found in the 2018 book, Luminous Creatures, The History and Science of Light Production in Living Organisms by Michel Anctil. Naturalists worked to dispel fanciful and mythical ideas of animal light. Dubois became the first scientist in 1887 to discover that 2 biological substances which he called luciferin and luciferase were necessary to produce animal luminescence in-vitro.
1. An autobiography, a book for layman on topology, differential geometry and Calabi-Yau manifolds, and an exciting account of the physics of string theory. This is the book The Shape of Inner Space by Shing-Tung Yau, a professor of mathematics at Harvard since 1987 and a Fields Medallist. If you wanted to know intuitively whether curved spaces can "naturally" exist even when there are no masses or gravity to curve it or about Euler characteristic, Chern classes or Ricci flow, this is the book for you.
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