Basic Mathematics
=================
This is my series on Basic Mathematics by Serge Lang.
You can support my work by buying this book through this Amazon affiliate
link:
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YouTube Playlist: https://www.youtube.com/playlist?list=PLMcpDl1Pr-viA25VUkHNmcUkWx9usPgyb
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.. toctree::
:maxdepth: 2
:caption: 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
3.2 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
YouTube Playlist: https://www.youtube.com/playlist?list=PLMcpDl1Pr-viA25VUkHNmcUkWx9usPgyb
.. raw:: html
.. toctree::
:maxdepth: 2
:caption: 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
3.2 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