Basic Mathematics

An amazing and easy-to-follow precalculus book, both suited for high-schoolers and undergraduates who are looking to review or expand their knowledge of high-school mathematics. The proofs Lang wrote are simple and straightforward, and the book offers plenty of exercises (albeit, straightforward ones outside of some of the proofs). The book focuses heavily on beginner and informal exposure to the concepts of abstract algebra that pertain to classical non-modern algebra taught in most basic K-12 educations, which I'd assume was intentional given Lang's record.
Overall, I'd say it is one of if not the best early mathematics textbooks you can get your hands on. It's a fun read and is definitely worth the time it takes to complete.

easily method to understanding the math

Indeholder "Acknowledgments", "Forword", "Part I. Algebra", "1. Numbers", " 1. The integers", " 2. Rules for addition", " 3. Rules for multiplication", " 4. Even and odd integers; divisibility", " 5. Rational numbers", " 6. Multiplicative inverses", "2. Linear Equations", " 1. Equations in two unknowns", " 2. Equations in three unknowns", "3. Real Numbers", " 1. Addition and multiplication", " 2. Real numbers: positivity", " 3. Powers and roots", " 4. Inequalities", "4. Quadratic Equations", "Interlude: On Logic and Mathematical Expressions", " 1. On reading books", " 2. Logic", " 3. Sets and elements", " 4. Notation", "Part II. Intuitive geometry", "5. Distance and Angles", " 1. Distance", " 2. Angles", " 3. The Pythagoras theorem", show more "6. Isometries", " 1. Some standard mappings", " 2. Isometries", " 3. Composition of isometries", " 4. Inverse of isometries", " 5. Characteristics of isometries", " 6. Congruences", "7. Area and Applications", " 1. Area of a disc of radius r", " 2. Circumference of a circle of radius r", "Part III. Coordinate geometry", "8. Coordinates and Geometry", " 1. Coordinate systems", " 2. Distance between points", " 3. Equation of a circle", " 4. Rational points on a circle", "9. Operations on Points", " 1. Dilations and reflections", " 2. Addition, subtraction, and the parallelogram law", "10. Segments, Rays, and Lines", " 1. Segments", " 2. Rays", " 3. Lines", " 4. Ordinary equation for a line", "11. Trigonometry", " 1. Radian measure", " 2. Sine and cosine", " 3. The graphs", " 4. The tangent", " 5. Addition formulas", " 6. Rotations", "12. Some Analytic Geometry", " 1. The straight line again", " 2. The parabola", " 3. The ellipse", " 4. The hyperbola", " 5. Rotation of hyperbolas", "Part IV. Miscellaneous", "13. Functions", " 1. Definition of a function", " 2. Polynomial functions", " 3. Graphs of functions", " 4. Exponential function", " 5. Logarithms", "14. Mappings", " 1. Definition", " 2. Formalisms of mappings", " 3. Permutations", "15. Complex Numbers", " 1. The complex plane", " 2. Polar form", "16. Induction and Summations", " 1. Induction", " 2. Summations", " 3. Geometric series", "17. Determinants", " 1. Matrices", " 2. Determinants of order 2", " 3. Properties of 2 x 2 determinants", " 4. Determinants of order 3", " 5. Properties of 3 x 3 determinants", " 6. Cramer's Rule", "Index", "Answers to Selected Exercises".

Hurtig og lige-ud-ad-landevejen gennemgang af noget basalt matematik op til et sted på førsteårs matematik på universitetet. Forfatteren gør en del ud af at skelne mellem fx cirkel og cirkelskive, så den første kan have en længde og den anden et areal. Fint nok, men hvor stor en hjælp er det at kalde det indre af en "circle" for en "disc"? Han har samme forbehold med trekanter, for det ord bruges både om omridset og det indre, men han afstår dog (efter en diskussion om fx at kalde det en trisc) fra at finde på et nyt ord for det indre af en trekant. show less