Basic Mathematics

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.

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.

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!

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

I love the way this book is written! It really circumvents a lot of the dry technical material that you see in a lot of math textbooks but still gives you the most necessary information. The exercises are great for practicing the skills covered. This book is good to have on reference as well as to use for a prep for higher level math like calculus.

Let’s be honest we all wonder about quality when your spending a chunk of change. This book was brand new and in perfect condition. It’s not an easy book to find.

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.

Never really learned math until studied using this book. Awesome. Serge Lang make everything become simple and intuitive. That is how math really looks like: something that makes sense. That is the feel you will have at the end of each chapter. I highly recomend this book for pretty much anybody. It starts very simple, then go deep on each subject. Go for it. Throw you money at it! You wont regret.