Basic Mathematics

This is a book that covers high school math as if you were going to major in math in college. It covers everything up to introductory calculus with the exception of sequence and series. There are fantastic chapters on introductory linear algebra, functions, and mappings that teach you the jargon and mindset of a math major in college. Even if you're not a math major or going to major in math, this book is a great, focused approach to 3-4 years of high school math. The problems are a mix of standard calculations, more challenging problems that require the knowledge of multiple chapters, and proofs. The proofs are especially good problems as 1) they are simple and direct and 2) are a good introduction to proofs for higher level math classes because they occur in a variety of chapters that are commonly the same subjects that a proofs class in college would cover. I wish I had this book as a junior in high school. It's a rigorous yet comprehensible review of math that will not only prepare you for calculus, but also higher level math classes in how it gets you to think like a mathemetician. Along with a book like Sheldon Axler's Precalculus (whose problem sets are by far the best for any precalculus textbook), you'll be incredibly well-prepared for calculus.

This book is ultimately for creating a strong foundation for calculus. "Basic" mathematics can be used lightly, as it's still relatively challenging, but by no means difficult. You'll spend time trying to understand proofs (by the way, he doest an excellent job of incoorporating proofs into the learning process, which is extremely necessary if you want to fully understand math) and figuring out some of the more challenging exercise problems, but the book is by no means painful to go through. I'll be a junior in high school next year, and was recommended studying this book by a math professor in Belgium (yes, really). The biggest thing to know about math, at least in the earlier levels, is that it is cumulative. You will be absolutely and forever f'ed if you go into Calculus with hardly any knowledge of algebra. That's why, if you find yourself struggling in math, or need to strengthen your foundations, you need to go throuh this book. It's excellent for self studying, which is what I'm currently doing this summer. When you take this book on at your own pace, and can spend more time on each section as required, and breeze through other sections that you have a firm grasp on, you'll find yourself enjoying the book. Serge Lang was an excellent mathematician (was... only because he is dead) and his books are well written and devoted to helping you understand the material. Remember though, that just because the book claims to be covering basic mathematics, that you won't be challenged. It can be tough, and especially when you're at the high school level, the mathematics won't seem like they're "basic", but more like, "hey, I just learned that last year/this year/whenever." It's ultimately a wonderful book if you're looking to strengthen the foundation of your mathematic ability, and Lang also includes a brief section after the first chapter about how you should logically examine math, which is invaluable. Math, to a lot of people, is pointless and not fun. It's that way because of botched U.S. public education, a lack of good/inspiring math teachers, and partly due to a lack of motivation in students. Pick up this book, maybe make a schedule for it, and just sit down and DO math. After a while, you'll start to see the beauty of something that is so logical and amazing, something that has been the collective work of various genius human minds, collaborating to further mathematics, that you'll pick up a passion for math. Math is almost like a language. You can choose to go through life in ignorance, sitting by and listening to others communicate with eachother, looking on in awe, wondering what beautiful and inspiring things they could be saying, or you can sit down, get to work, and be right there with them, able to communicate in a logical and correct language that governs the universe.

Fantastic read lots to learn.

This is a fantastic "all-in-one" refresher.

I have a popular, highly regarded book on precalc that is much easier to work through. It highlights all of the insights and formulas and shortcuts to make the practice problems as easy as possible. It is about 1000 pages, and covers precalc topics very thoroughly. It is mostly boring, but can be used to help memorize a lot of information rather quickly. Basic Mathematics is different. The author presents some fundamental ideas about a topic, then gives problems that, if worked through with perseverance, will cause breakthrough insights and deeper understanding of the material. Solving these problems feels incredibly satisfying. What is given as an "Important Tip" in my precalc book, may instead be presented as a challenge in this book, a challenge which feels like a mathematical revelation, once solved. Sometimes I'll be working on a problem for hours, not be able to solve it, look up the answer in the back, still not understand, come back to it again and again days or weeks later and still not really understand. I may move on, but I'll come back to it. This book makes me want to understand.

Excelentes condiciones! Estoy a gusto con la compra

I have been going back to relearn math from essentially the ground up before I enter a PhD in computer science. This book does a great job of presenting a rigorous introduction to all the basic concepts that I took for granted in high school. For example, in my school we were just given the Pythagoras theorem and distance formula to memorize, but Lang actually includes the proofs of these. The one thing that really annoyed me were the proofs. The only way I could navigate his proofs was due to my exposure to mathematics in undergrad. Many of the proof techniques that he used seemed arbitrary, and even the solutions to proof problems in the back of the book were arbitrary and ad hoc. There is a little section in the middle of the book about proofs and mathematical logic, but it covers nowhere near the level of proofs that he uses in the text. If this is truly a text on basic mathematics, let it be basic, or fill in the reader on proof techniques.

This really my preferred book about fundamental maths. It gives me the possibility of learning maths taking an intuitive and in-depth approach. Serge Lang, the author, did a really nice job!

Don't bother buying this if you actually want to use it. The typesetting makes it unusable unless you crack the spine. They put a lot of whitespace on the outer edges of the pages, while they should have used it on the inside. Makes for a very unpleasant read.

The content is excellent and even more advanced in some topics than a usual precalculus textbook. However, the book is thick and does not lay flat. Additionally, it would be better if the book layout is square with a wide margin.

beautiful

Para los que quieren una base sólida en matemáticas, empezando desde lo más básico, pero con el rigor y la notación matemática de un libro avanzado. Muy ameno y completo. La edición no es muy bonita pero para un libro técnico me parece bien. Lo recomiendo mucho.

O texto não trás todos conteúdos sobre matemática básica, como por exemplo, combinatória e probabilidade, bem como alguns tópicos sobre geometria de sólidos. Porém, todos os assuntos que o livro trás são expostos de maneira profunda e precisa, como por exemplo, a parametrização racional do círculo unitário, o qual é a ideia elementar por de trás da demonstração da veracidade da Conjectura de Fermat, ou seja, como os números racionais se distribuem no círculo. Acredito que um livro como este é ideal para um país como o Brasil, que possui um ensino médio estagnado, onde muitos assuntos são propostos, porém estudados de forma tangencial, pouco aprofundada. Mas para tal, o populismo educacional e acadêmico deve acabar e focarmos em ambientes mais competitivos.