Introduction

https://www.youtube.com/watch?v=04MWqyhD61g&list=PLMcpDl1Pr-viA25VUkHNmcUkWx9usPgyb

This book covers the mathematics you need to know before you go into higher math. By “higher math”, I mean calculus and “beyond” – linear algebra and more advanced topics that are difficult to describe to the budding mathematician.

This is also a great book if you want to get back into mathematics if you used to do it but have forgotten it all.

Serge Lang wrote this textbook to get high school graduates ready to learn math at a college level. At the time, there was a huge difference between what students were taught in High School, such that it was impossible to know which students were ready for higher math and which needed remedial courses.

Theorems are at the heart of this textbook. It is emphasized from the very beginning to the end. There is a heavy emphasis on real numbers, with sufficient detail so as to remind the student that there are different numbers with different properties.