Basic Mathematics

by Serge Lang

This text in basic mathematics is ideal for high school or college students. It provides a firm foundation in basic principles of mathematics and thereby acts as a springboard into calculus, linear algebra and other more advanced topics. The information is clearly presented, and the author develops concepts in such a manner to show how one subject matter can relate and evolve into another.

Genres: Mathematics, Science, Nonfiction, Textbooks, Reference, Computer Science, Education

496 pages, Paperback

First published July 1, 1988

About the author

Serge Lang was an influential mathematician in the field of number theory. Algebra is his most famous book.

Librarian Note: There is more than one author in the GoodReads database with this name. See this thread for more information.

Reviews

[Cario Lam · Rating 5 out of 5]

Serge Lang was a regular guest lecturer at the university I attended. I always enjoyed the lectures. Even though I have been out of college for a number of decades now, I still find myself reading and even re-reading many of his works. This book is one that falls into that category.

[Jace Davies · Rating 5 out of 5]

Elegant and lovely exploration of the fundamentals of the discipline.

[Mohamoud Abdallah]

Numbers

[Acacia · Rating 5 out of 5]

this book paired with velleman's how to prove it has been changing my life especially how i think. its also been amazing since starting my biochem underdrag degree this september!!!! i recommend to everyone and anyone who wants to relearn mathematics/has dyscalculia like i do!

[Isaac · Rating 3 out of 5]

Good as an introductory book (about upper highschool level). Some of the notation is a bit old, but most of it is still up to date.

[Craine · Rating 5 out of 5]

A fantastically well written math book which gives a serious treatment to the foundations of mathematics. Covers more than your typical high school which goes as far as covers elementary topics in linear algebra as well as introducing a heavier leniency on geometry which has sadly been neglected in modern times.

Also covers a philosophical short chapter which addresses learning mathematics and states how hard it is to write an actual math book!
Would recommend to anyone remotely interested in math through serious study.

(Note I don't like the star rating and as such I only rate books based upon one star or five stars corresponding to the in my opinion preferable rating of thumbs up/down. This later rating system encourages in my opinion the degree to which the reader is likely to read a review instead of merely glancing at the number of stars)

[Calvin · Rating 4 out of 5]

A lot of interesting things learnt in this book. Overall, it’s a good book though it is a bit misleading. It’s not basic at all but this book is a good introduction to proofs. I learnt a lot of about proofs and how theorems I take for granted work, including those on determinants, complex numbers, geometry, coordinate systems, etc.

The main content of the book centers on precalculus. This includes:
1) algebra
2) geometry
3) coordinate systems
4) trigonometry
5) complex numbers
6) matrices (determinants)
7) series and summations
8) induction

I studied this book quite quickly, because most of the things I studied I’ve already had a good understanding of them, with the exception of Isometries, which is the most difficult of the bunch. Other than that, it’s a good review and exercise for post-high school maths.

[Kerimcan Ak · Rating 4 out of 5]

This book was beloved when I was in university library with all the stress around me and me neglecting myself from joy of mathematics for years...
After I took this book, I started looking at maths in different light as firs tin my life I was reading a book where mathematics were a subject to learn and not a subject assumed to know and practiced upon, like basically all lublic schools here do.
But I have one complaint:
While this book tells basic concepts, numbers, algebra, equations and squareroots... the geometry section of book is pretty weak. It only tells basic encyclopedic i formation about triangles, circles, other shapes, functions of all these shapes, size and scale then the book ends.

Also if you like this book my next recommendation would be watching courses about linear algebra as they appear more fun to listen after lesrning basic concepts.

[Allan · Rating 5 out of 5]

The best book on elementary mathematics bar none. I try to read this textbook once a year to brush up on the foundations and Serge Lang's style is as appealing every time.

It must be warned that Serge Lang's style is controversial and widely criticized. Lang treats words like they are going extinct and will say only precisely as much as he needs to on a given topic, this can make his texts unapproachable, hard to understand and fleeting. The criticisms are valid, and probably not necessarily criticisms that Lang would disapprove of, he himself admitted that many of the texts were written as a way for himself to learn a given field which is reflected in his texts that often feel more like notes than a comprehensive thesis on a given topic.

To a certain kind of student Lang is indispensable, if you turn out to be that kind of student then Lang is treat.

[Jaden Smallwood · Rating 4 out of 5]

If you’re struggling with math sometimes it is good to get back to the basics. I’ve found myself enjoying math and wanted to work on my foundational skills. This is a good book for that. I struggled through it but so far my understanding of pre-calculus has really improved. My only gripe is sometimes it can be a bit hard to follow along how the conclusion was reached. However, this is probably purposeful to really make you think. I would recommend this to anyone who may be scared of taking a college math course or something cause this will really help.

[Kasparas · Rating 4 out of 5]

As I read the book after I've finished my degree, it wasn't as useful as I would've wanted. Still, I did find his method to view functions as transformations rather appealing and would certainly like to explore it in the future.

[Snorlax · Rating 5 out of 5]

One of the basic book for basic math.
It can be used as a textbook from elementary to middle school.

[Aidan Gibson · Rating 5 out of 5]

A god

[Davidd Silva · Rating 1 out of 5]

From the book: "If you find some mistakes ... write your own book."
And there are too many "this is obvious, you do it."

[Cau Sality · Rating 3 out of 5]

Good

[Nattapon Chotsisuparat · Rating 5 out of 5]

Although the contents covered are elementary, the problem sets can occasionally be very difficult. This book will help you brush up on the fundamentals of mathematics.

[Smilexx · Rating 5 out of 5]

Good book, Its make me raise to new level in my view for math. I like it and I really recommand for anybody to reading the book.

[Samuel · Rating 5 out of 5]

Good review of high school mathematics with emphasis on the practice of proofs

[juca · Rating 5 out of 5]

The best intuitive (but also formal) introduction to university mathematics that I found.

[Lucas Bomfim · Rating 4 out of 5]

Basic Mathematics é um livro de excelentes explicações e "péssimos" exercícios. Os exercícios não servem para aqueles que acabaram de aprender determinado conceito pelo texto, mas para aqueles que já tem familiaridade com este. Ou seja, existe um lapso entre o texto e os exercícios; um serve para absolutos iniciantes; o outro serve para quem já é acostumado a usar a matemática em questão e deseja aprimorar sua técnica, ganhar um novo insight.

Se você é alguém que busca aprender matemática com este livro, leia somente as explicações e busque exercícios em outros lugares. Se você já tem experiência com matemática, pratique os exercícios e guarde o livro como referência para quando precisar lembrar de algo.

Obs: Algumas explicações muito importantes para a matemática não estão no texto, mas nos exercícios: Serge Lang espera que você as prove por si mesmo. Eu considero isto como uma falha.