Downloadable PDF versions of many books can be found by searching “Free PDF xxxx” on Google.
Things To Make And Do In The Fourth Dimension | Matt Parker
A practical and impractical guide to mathematics. Pizza sharing, prime numbers, tieing knots, domino computers and higher dimensions in Parker’s voice.
The Theoretical Minimum: What You Need To Know To Start Doing Physics | Leonard Susskind
A concise summary of mathematical and thinking skills that are not taught at A-level but are essential. Covering ideas such as kinematics, partial differentiation, energy, Hamiltonian Mechanics, Poisson brackets, and planetary orbits.
“What a wonderful and unique resource. For anyone who is determined to learn physics for real, looking beyond conventional popularizations, this is the ideal place to start” – Sean Carroll, Physicist, CalTech
Quantum Mechanics: The Theoretical Minimum | Leonard Susskind & Art Friedman
Excellent introductory for A-level mathematicians and physicists who want to begin to explore quantum mechanics from a quantitative perspective. Mathematical ‘Interludes’ on linear operators, spherical coordinates, and probability give the reader necessary skills to tackle all the basic ideas and start to use Dirac notation.
Solutions for exercises left to the reader can be found here
References are made to ‘The Theoretical Minimum: What You Need To Know To Start Doing Physics’ so I recommend reading it before or alongside.
Guidance for New Undergraduates
How to study for a Mathematics degree | Lara Alcock
“This has lots of good, readable advice for students about to start a
maths degree, based on research evidence and experience of teaching undergraduates,
and you will find it useful to refer back to this book during
the first year of your course.” – Murray Edwards College, Cambridge in Summer Reading for Mathematics
How to think like a mathematician | Kevin Houston
“This has lots of really excellent advice for someone
just starting to study mathematics at university level, including plenty of
exercises. There is a short leaflet online with a few top tips from the book.” – Murray Edwards College, Cambridge in Summer Reading for Mathematics
Mathematics: A very short introduction | Timothy Gowers
“It talks about the differences between school maths
and university maths, and has the merits of being beautifully written and
very readable, while also being short and relatively cheap.” – Murray Edwards College, Cambridge in Summer Reading for Mathematics
How To Read And Do Proofs: An Introduction to Mathematical Thought Processes | Daniel Solow
Readable reference source for learning methods of proof and dictionary for notation. Includes basic logic directionality, contradiction, contrapositive, induction, and methods specific to ‘either/or’ and inequalities. Step by step walkthroughs and plenty of exercises of varying difficulty to consolidate and stretch.