Basic Mathematics¶
This is my series on Basic Mathematics by Serge Lang.
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YouTube Playlist: https://www.youtube.com/playlist?list=PLMcpDl1Pr-viA25VUkHNmcUkWx9usPgyb
Contents:
- Introduction
- 1.1 The Integers
- 1.2 Rules for Addition
- 1.3 Rules for Multiplication
- 1.4 Even and Odd Integers; Divisibility
- 1.5 Rational Numbers
- 1.6 Multiplicative Inverses
- 2.1 Equations in Two Unknowns
- 2.2 Equations in Three Unknowns
- 3.1 Addition and Multiplication
- Real Numbers: Positivity
- 3.3 Powers and Roots
- 3.4 Inequalities
- 4 Quadratic Equations
- I.1 On Reading Books
- I.2 Logic
- I.3 Sets and Elements
- I.4 Notation
- 5.1 Distance
- 5.2 Angles
- 5.3 The Pythagoras Theorem
- 6.1 Some Standard Mappings of the Plane
- 6.2 Isometries
- 6.3 Composition of Isometries
- 6.4 Inverse of Isometries
- 6.5 Characterization of Isometries
- 6.6 Congruences
- 7.1 Area of a Disc of Radius r
- 7.2 Circumference of a Circle of Radius r
- 8.1 Coordinate Systems
- 8.2 Distance Between Points
- 8.3 Equation of a Circle
- 8.4 Rational Points on a Circle
- 9.1 Dilation and Reflections
- 9.2 Addition, Subtraction, and the Parallelogram Law
- 10.1 Segments
- 10.2 Rays
- 10.3 Lines
- 10.4 Ordinary Equation for a Line
- 11.1 Radian Measure
- 11.2 Sine and Cosine
- 11.3 The Graphs
- 11.4 The Tangent
- 11.5 Addition Formula
- 11.6 Rotations
- 12.1 The Straight Line Again
- 12.2 The Parabola
- 12.3 The Ellipse
- 12.4 The Hyperbola
- 12.5 Rotation of Hyperbolas
- 13.1 Definition of a Function
- 13.2 Polynomial Functions
- 13.3 Graphs of Functions
- 13.4 Expnential Functions
- 13.5 Logarithms
- 14.1 Definition
- 14.2 Formalism of Mappings
- 14.3 Permutations
- 15.1 The Complex Plane
- 15.2 Polar Form
- 16.1 Induction
- 16.2 Summations
- 16.3 Geometric Series
- 17.1 Matrices
- 17.2 Determinants of Order 2
- 17.3 Properties of 2x2 Determinants
- 17.4 Determinants of Order 3
- 17.5 Properties of 3x3 Determinants
- 17.6 Cramer’s Rule
- Review
