Basic Maths

Table of contents

1. Logic and proof

   • Logic symbols

2. Sets

   • Set operations

3. Functions

   • Basic definitions

   • Graph

   • Restriction

   • Image

   • Real functions

4. Elementary functions 1

   • Polynomial function

   • Rational functions

   • Exponential function

   • Hyperbolic functions

   • Trigonometric functions

5. 5_composition_and_inverse

   • Injection, Surjection, Bijection

   • Function composition

   • Inverse function

6. 6_elementary_functions_2

   • Roots

   • Logarithmic functions

   • Inverse trigonometric functions

   • Inverse hyperbolic functions

7. Coordinate systems

8. Vectors

References and further reading

Coordinate Systems and Vectors sessions:

• Lecture 1 of the “Mathematics Methods 1” module

A light introduction to topics covered in this section:

• Devlin, K., 2003. Sets, functions, and logic: an introduction to abstract mathematics. CRC Press.

A very novice-friendly book with good visualisations and plenty of exercise problems with solutions:

• Briggs, W.L., Cochran, L., Gillett, B. and Schulz, E.P., 2013. Calculus for scientists and engineers: early transcendentals. Pearson Education.

An extensive collection of problems of all levels:

• Demidovich, B.P. and Baranenkov, G.S., 1964. Problems in mathematical analysis. Peace Publishers.