Sets for Mathematics (Book)
This article is a stub. You can help us by editing this page and expanding it.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.
| Basic Mathematics | |
| |
| Information | |
|---|---|
| Author | Serge Lang |
| Language | English |
| Publisher | Springer |
| Publication Date | 1 July 1988 |
| Pages | 496 |
| ISBN-10 | 0387967877 |
| ISBN-13 | 978-0387967875 |
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 | |