'Extra Maths'

Recommended Reading (University level)

(1) Complex Analysis – An Introduction (Kevin Houston; publisher:  to the power of ” [sic])

(2) "Div, Grad, Curl, and all that (an informal text on vector calculus)" (H.M. Schey; publisher: W.W. Norton)

- avoids non-essential mathematical rigour

- assumes knowledge of vector product, partial derivatives and multiple integrals

(3) “Vector Calculus” (P.C. Matthews; publisher: Springer)

(4) “Dynamics and Relativity” (Stephen Siklos, CU Lecture Notes – Lent term 2011)

(5) “Mechanics” (Smith and Smith; publisher: John Wiley)

(6) "Classical Mechanics" (R.D. Gregory; publisher: CUP)

(7) “Profound Physics”: Profound Physics – For Those Wanting To Learn Physics Profoundly

- website has some free articles on Relativity etc

Pure

Counting Exs 1 2 3 4 5 6 7

Functions & Curve Sketching

Convex & Concave Functions (2 pages; 2/6/23)

Rational Functions (5 pages; 12/7/24)

y squared = f(x) (2 pages; 2/6/23)

Mappings & Functions (3 pages; 2/6/23)

Exponential Functions (2 pages; 2/6/23)

Inverse Functions (3 pages; 2/6/23)

Modulus Function (2 pages; 2/6/23)

Geometry

Shortest distance from Origin to line (9 pages; 5/6/26)

Groups - Part 1 (10 pages; 22/10/16)

Groups - Part 2 (12 pages; 23/10/16)

Groups Exs 1 2 3 4

Linear Interpolation (5 pages; 7/2/16)

Linear Interpolation Exs 1

Matrices

Invariant points & lines - conditions (12 pages; 16/4/20) 

Shears (8 pages; 12/8/18) 

Shears (Exs) (1 page; 4/6/26); Sol'ns (11 pages; 4/6/26)

Eigenvectors (10 pages; 4/9/18)

Eigenvectors & Invariance (6 pages; 16/4/20) 

Eigenvectors (Exs) (4 pages; 4/6/26); Sol'ns (38 pages; 4/6/26)

Numbers

Algebraic & Transcendental Numbers (1 page; 5/6/23)

Number Theory (18 pages; 12/11/24)

Primes - Results (3 pages; 21/5/25)

Parametric equations (7 pages; 5/5/21)

Parametric Eq'ns Exs 1 

Recurrence relations (16 pages; 29/4/25)

Taylor Series (7 pages; 1/6/26)

Series - Results (3 pages; 1/7/26)

Trigonometry

Factor Formulae (1 page; 15/4/21)

t=tan(x/2) substitution (4 pages; 24/3/20)

Mechanics

Circular Motion [Important Ideas] (2 pages; 25/10/20)

Circular Motion - Constant Speed (9 pages; 25/10/20)

Circular Motion - Variable Speed (13 pages; 30/9/15)

Circular Motion Exs 1 2

Frameworks (9 pages; 25/3/21)

Bending moment & shearing force (5 pages; 25/3/21)

Fictitious forces (5 pages; 25/10/20) 

Systems of forces (5 pages; 14/11/18)

Rolling wheel: Friction (14 pages; 31/5/24)

Collisions - reversal of direction (6 pages; 24/6/20) 

Impulses & connected particles (13 pages; 28/8/18) 

Oscillations

Differential equations: Oscillations (11 pages; 29/5/20)

Oscillations Exs 1 2 3 4

Rotating Bodies

Motion of a particle in a rotating frame of reference (27 pages; 29/1/24)

Angular Momentum & Planar Rigid Body Motion (20 pages; 27/11/23)  

Moments of Inertia (7 pages; 1/8/23) 

Rolling wheel - Point on circumference (5 pages; 1/2/21) 

Rolling Wheel - Friction (11 pages; 3/5/23) 

Rotating Bodies Ex 1

Gravitational Potential Energy (3 pages;15/2/19) 

Probability & Statistics

Conditional Probability (2 pages; 1/2/23)

Confidence Intervals - Types (3 pages; 16/4/16)

Geometric & Negative Binomial distributions (5 pages; 11/2/25)

Hypothesis Tests - Types (8 pages; 24/1/20)

Linear Coding (2 pages; 8/7/21)

Normal distribution (9 pages; 21/2/17)

Normal Distribution Exs 1 2

Approximations to Binomial & Poisson (4 pages; 30/1/17)

Probability & Counting Approaches (12 pages; 21/3/24)

Selections (6 pages; 15/3/24)

Probability Exs 1 2

Probability Generating Functions: Ideas & Exs (16 pages; 27/2/25)

Probability Generating Functions: Further Exs (11 pages; 27/2/25)

Sampling (4 pages; 7/8/17)

Uniform distribution (Discrete) (2 pages; 20/3/20)

Uniform Distribution (Discrete) Ex 1

Sample variance (3 pages; 8/7/21)