Basic Mathematics

The best I've seen so far for reviewing basic math.

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.

Great book but a little more assistance with proofs at the start can help.

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

Fantastic read lots to learn.

Overall I'm content with this book, but it has a good number of issues. If you're using it for self study, it can be frustrating because the answers in the back are fairly sparse, and even the ones that do exist have a lot of errors. Answers will be completely wrong, or sometimes swapped (b answers a and vice versa). I think this is unacceptable for a book that was originally published in 1971 and Amazon has this version listed as 1998. They've had plenty of time to fix their errors for a republishing. I used this book to refresh my math knowledge after a decade away from math, and while it did an acceptable job, I did still have to reference other sources a number of times as this book will throw things at you that it hasn't explained. As an example, simplifying roots is never covered, but they do so in their solutions, so you'll have to learn how to do it elsewhere. This one in particular was disappointing to me, because the way exponents and roots are covered in the book was excellent, and it did set me up to understand why it works on a deeper level than any videos/articles I read on it, but it would have been way better to not have to do that.

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.

I didn’t pay attention from gr8-gr10. Though the methods don’t really add up to the way my school teaches math. I did learn a lot. It’s a solid read for maybe a review over the summer or if you need extra help but it shouldn’t be used as the primary teaching method.