The essence of mathematics through elementary problems
It is increasingly clear that the shapes of reality – whether of the natural world, or of the built environment – are in some profound sense mathematical. Therefore it would benefit students and educated adults to understand what makes mathematics itself ‘tick’, and to appreciate why its shapes, pat...
| Otros Autores: | , |
|---|---|
| Formato: | Libro electrónico |
| Idioma: | Inglés |
| Publicado: |
Cambridge, UK :
Open Book Publishers
2019
[2019] |
| Colección: | OBP Series in Mathematics
|
| Materias: | |
| Ver en Biblioteca Universitat Ramon Llull: | https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009435733606719 |
Tabla de Contenidos:
- I. Mental Skills
- 1.1 Mental arithmetic and algebra
- 1.2 Direct and inverse procedures
- 1.3 Structural arithmetic
- 1.4 Pythagoras' Theorem
- 1.5 Visualisation
- 1.6 Trigonometry and radians
- 1.7 Regular polygons and regular polyhedra
- 1.8 Chapter 1: Comments and solutions
- II. Arithmetic
- 2.1 Place value and decimals: basic structure
- 2.2 Order and factors
- 2.3 Standard written algorithms
- 2.4 Divisibility tests
- 2.5 Sequences
- 2.6 Commutative, associative and distributive laws
- 2.7 Infinite decimal expansions
- 2.8 The binary numeral system
- 2.9 The Prime Number Theorem
- 2.10 Chapter 2: Comments and solutions
- III. Word Problems
- 3.1 Twenty problems which embody "3 - 1 = 2"
- 3.2 Some classical examples
- 3.3 Speed and acceleration
- 3.4 Hidden connections
- 3.5 Chapter 3: Comments and solutions
- IV. Algebra
- 4.1 Simultaneous linear equations and symmetry
- 4.2 Inequalities and modulus
- 4.3 Factors, roots, polynomials and surds
- 4.4 Complex numbers
- 4.5 Cubic equations
- 4.6 An extra
- 4.7 Chapter 4: Comments and solutions
- V. Geometry
- 5.1 Comparing geometry and arithmetic
- 5.2 Euclidean geometry: a brief summary
- 5.3 Areas, lengths and angles
- 5.4 Regular and semi-regular tilings in the plane
- 5.5 Ruler and compasses constructions for regular polygons
- 5.6 Regular and semi-regular polyhedra
- 5.7 The Sine Rule and the Cosine Rule
- 5.8 Circular arcs and circular sectors
- 5.9 Convexity
- 5.10 Pythagoras' Theorem in three dimensions
- 5.11 Loci and coonic sections
- 5.12 Cubes in higher dimensions
- 5.13 Chapter 5: Comments and solutions
- VI. Infinity: recursions, induction, infinite descent
- 6.1 Proof by mathematical induction I
- 6.2 'Mathematical induction' and 'scientific induction'
- 6.3 Proof by mathematical induction II
- 6.4 Infinite geometric series
- 6.5 Some classical inequalities
- 6.6 The harmonic series
- 6.7 Induction in geometry, combinatorics and number theory
- 6.8 Two problems
- 6.9 Infinite descent
- 6.10 Chapter 6: Comments and solutions
