Sets for Mathematics (Book)

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Basic Mathematics
Information
Author	Serge Lang
Language	English
Publisher	Springer
Publication Date	1 July 1988
Pages	496
ISBN-10	0387967877
ISBN-13	978-0387967875

The textbook Basic Mathematics by Serge Lang provides an overview of mathematical topics usually encountered through the end of high school/secondary school, specifically arithmetic, algebra, trigonometry, logic, and geometry. It serves as a solid review no matter how far along one may be in their studies, be it just beginning or returning to strengthen one's foundations.

Reading the Foreword and the Interlude is recommended for those unfamiliar with reading math texts.

Table of Contents

Chapter/Section #	Title	Page #
PART I: ALGEBRA
Chapter 1: Numbers
1	The integers	5
2	Rules for addition	8
3	Rules for multiplication	14
4	Even and odd integers; divisibility	22
5	Rational numbers	26
6	Multiplicative inverses	42
Chapter 2: Linear Equations
1	Equations in two unknowns	53
2	Equations in three unknowns	57
Chapter 3: Real Numbers
1	Addition and multiplication	61
2	Real numbers: positivity	64
3	Powers and roots	70
4	Inequalities	75
Chapter 4: Quadratic Equations
Interlude: On Logic and Mathematical Expressions
1	On reading books	93
2	Logic	94
3	Sets and elements	99
4	Notation	100
PART II: INTUITIVE GEOMETRY
Chapter 5: Distance and Angles
1	Distance	107
2	Angles	110
3	The Pythagoras theorem	120
Chapter 6: Isometries
1	Some standard mappings of the plane	133
2	Isometries	143
3	Composition of isometries	150
4	Inverse of isometries	155
5	Characterization of isometries	163
6	Congruences	166
Chapter 7: Area and Applications
1	Area of a disc of radius r	173
2	Circumference of a circle of radius r	180
PART III: COORDINATE GEOMETRY
Chapter 8: Coordinates and Geometry
1	Coordinate systems	191
2	Distance between points	197
3	Equation of a circle	203
4	Rational points on a circle	206
Chapter 9: Operations on Points
1	Dilations and reflections	213
2	Addition, subtraction, and the parallelogram law	218
Chapter 10: Segments, Rays, and Lines
1	Segments	229
2	Rays	231
3	Lines	236
4	Ordinary equation for a line	246
Chapter 11: Trigonometry
1	Radian measure	249
2	Sine and cosine	252
3	The graphs	264
4	The tangent	266
5	Addition formulas	272
6	Rotations	277
Chapter 12: Some Analytic Geometry
1	The straight line again	281
2	The parabola	291
3	The ellipse	297
4	The hyperbola	300
5	Rotation of hyperbolas	305
PART IV: MISCELLANEOUS
Chapter 13: Functions
1	Definition of a function	313
2	Polynomial functions	318
3	Graphs of functions	330
4	Exponential function	333
5	Logarithms	338
Chapter 14: Mappings
1	Definition	345
2	Formalism of mappings	351
3	Permutations	359
Chapter 15: Complex Numbers
1	The complex plane	375
2	Polar form	380
Chapter 16: Induction and Summations
1	Induction	383
2	Summations	388
3	Geometric series	396
Chapter 17: Determinants
1	Matrices	401
2	Determinants of order 2	406
3	Properties of 2 x 2 determinants	409
4	Determinants of order 3	414
5	Properties of 3 x 3 determinants	418
6	Cramer's Rule	424
Index		429