- #1
- 19,480
- 10,173
- Author: Serge Lang
- Title: Basic Mathematics
- Amazon Link: https://www.amazon.com/dp/0387967877/?tag=pfamazon01-20
- Prerequisities: Mathematics before high school
- Level: Motivated high-school students, college students
- Contents: Real numbers, solving equations, logic, geometry, trigonometry, functions, complex numbers, induction, determinants
Table of Contents:
Code:
[LIST]
[*] Algebra
[LIST]
[*] Numbers
[LIST]
[*] The integers
[*] Rules for addition
[*] Rules for multiplication
[*] Even and odd integers; Divisibility
[*] Rational numbers
[*] Multiplicative inverse
[/LIST]
[*] Linear equations
[LIST]
[*] Equations in two unknowns
[*] Equations in three unknowns
[/LIST]
[*] Real numbers
[LIST]
[*] Additions and multiplication
[*] Real numbers: positivity
[*] Powers and roots
[*] Inequalities
[/LIST]
[*] Quadratic equations
[*] On logic and mathematical expressions
[LIST]
[*] On reading books
[*] Logic
[*] Sets and elements
[*] Notation
[/LIST]
[/LIST]
[*] Intuitive Geometry
[LIST]
[*] Distance and Angles
[LIST]
[*] Distance
[*] Angles
[*] The Pythagoras Theorem
[/LIST]
[*] Isometries
[LIST]
[*] Some standard mappings of the plane
[*] Isometries
[*] Composition of Isometries
[*] Inverse of isometries
[*] Characterization of isometries
[*] Congruences
[/LIST]
[*] Area and application
[LIST]
[*] Area of a disc of radius [itex]r[/itex]
[*] Circumference of a circle of radius [itex]r[/itex]
[/LIST]
[/LIST]
[*] Coordinate Geometry
[LIST]
[*] Coordinates and geometry
[LIST]
[*] Coordinate systems
[*] Distance between points
[*] Equation of a circle
[*] Rational points on a circle
[/LIST]
[*] Operations on points
[LIST]
[*] Dilatations and reflections
[*] Addition, subtraction, and the parallelogram law
[/LIST]
[*] Segments, Rays, and Lines
[LIST]
[*] Segments
[*] Rays
[*] Lines
[*] Ordinary Equation for a Line
[/LIST]
[*] Trigonometry
[LIST]
[*] Radian measure
[*] Sine and cosine
[*] The graphs
[*] The tangent
[*] Addition formulas
[*] Rotations
[/LIST]
[*] Some Analytic Geometry
[LIST]
[*] The straight line again
[*] The parabola
[*] The ellipse
[*] The hyperbola
[*] Rotation of hyperbolas
[/LIST]
[/LIST]
[*] Miscellaneous
[LIST]
[*] Functions
[LIST]
[*] Definition of a function
[*] Polynomial functions
[*] Graphs of functions
[*] Exponential function
[*] Logarithms
[/LIST]
[*] Mappings
[LIST]
[*] Definition
[*] Formalism of mappings
[*] Permutations
[/LIST]
[*] Complex Numbers
[LIST]
[*] The complex plane
[*] Polar form
[/LIST]
[*] Induction and Summations
[LIST]
[*] Induction
[*] Summations
[*] Geometric Series
[/LIST]
[*] Determinants
[LIST]
[*] Matrices
[*] Determinants of order [itex]2[/itex]
[*] Properties of [itex]2\times 2[/itex] determinants
[*] Determinants of order [itex]3[/itex]
[*] Properties of [itex]3\times 3[/itex] determinants
[*] Cramer's rule
[/LIST]
[/LIST]
[*] Index
[/LIST]
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