Modern Number Theory
Modern Number Theory book notes, into 5 chapters.
Modern Number Theory
| Chapter | Title | Description |
|---|---|---|
| 1 | Chapter 1. Foundations of Arithmetic | The natural numbers arise from the basic act of counting. When we count objects in a collection, we assign successive numbers: |
| 2 | Chapter 2. Classical Number Theory | A Diophantine equation is an equation whose solutions are required to be integers. The unknowns are not allowed to range over the real numbers or complex numbers unless... |
| 3 | Chapter 3. Analytic Number Theory | The harmonic series is the infinite series |
| 4 | Chapter 4. Algebraic Number Theory | A field is a number system in which addition, subtraction, multiplication, and division by nonzero elements are always possible. The rational numbers $\mathbb{Q}$, the real... |
| 5 | Chapter 5. Arithmetic Geometry and Modern Directions | Arithmetic geometry studies solutions of polynomial equations by combining algebra, geometry, and number theory. Its basic objects are spaces defined by polynomial equations.... |
| Appendix | Appendix | A set is a collection of objects, called its elements. If $x$ is an element of a set $A$, we write $x \in A$. If $x$ is not an element of $A$, we write $x \notin A$. |