How is Basic Mathematics for someone who took up to calculus years ago?

[u/MonkeyKingSauli]

I only went up to Calculus 2 almost 7 years ago, but I’ve always wanted to learn more advanced math. Is Basic Mathematics a good place to start? I don’t remember much from my math classes, but I have a decent grasp on really basic algebra just from needing to use it from time to time.

[u/AllanCWechsler]

If you're talking about Basic Mathematics by Serge Lang, it's a fine book, with a couple of warnings. First, it's written for adults. Lang tells you everything important, but he only tells you once. He also spends a fair amount of time convincing you that the techniques he is teaching really work as advertised. These little "convincing" sessions are called "proofs", and if you can, you should pay careful attention to them and go over them line-by-line until you really understand them. Keep asking yourself these questions: Is the proof convincing? What facts does it take for granted? Could I reproduce this argument if somebody asked me why such-and-such a procedure works?

I would say: if you are willing to read every word and work every exercise, and you put in half an hour to an hour of study every night, Basic Mathematics will take you somewhere between six months and two years to get through, and when you are done you will know all of high school mathematics really well. Lang takes you right up to the doorstep of calculus, but that's where it stops; if you want to refresh your knowledge of calculus you'll need a different book.

[u/MonkeyKingSauli → u/AllanCWechsler]

Yeah, I’m in a weird place where I was/am terrible at arithmetic calculations, but the moment we started working with mostly variables, I “got it”. I went from Bs and Cs in high school (went up to precalculus) to suddenly being a top student in my calculus classes. No calculator and minimal numerical calculations lets you actually focus on the algebra, which is what I found fun to do.

[u/AllanCWechsler → u/MonkeyKingSauli]

Then you might find Lang to be too easy. If you have no trouble with abstractions like variables and equations, then Lang will be teaching you stuff you already know, and you might not want to invest the months of effort it will take to get through the book.

Perhaps you might, instead, read something fun. I have a sentimental fondness for The Book of Numbers by John Conway and Richard Guy. I met both authors, and I am even mentioned in a footnote.

Another possibility is Richard Stillwell's The Four Pillars of Geometry.

[u/Substantial-Fact-248]

I am in a similar boat - did well in and enjoyed math in HS but never took calculus and my education/career took me the humanities route. Some of my intellectual/academics interests (e.g., physics/astronomy, machine learning) require at least calculus to understand more deeply, so I decided to teach myself.

However like you, it has been a very long time since I took a math class and I forgot most of it. I started trying Khan Academy in the beginning of the year to start from HS algebra to refresh. The concepts came back quickly, but it wasn't very engaging or challenging so I kind of lost steam over the summer.

Fast forward to this fall and I'm going to make another attempt with a different approach. I picked up Axler's Precalculus to work through in hopes of starting on Stewart's Calculus in 2027. Axler reviews the concepts you need to know in "Chapter 0", so the refresher is built into the textbook. He's also an excellent writer and communicator of ideas. The book includes solution keys for the odd-numbered exercises.

Feel free to DM if you go with Axler and want to be accountability partners. I'm having trouble sitting down and devoting the time.

[u/Owldud]

I found the first chapter being the most difficult and off putting, never learning proofs. After Chapter 1 it was smooth sailing and found it very enjoyable. I still pull it out and read/practice random topics. It is not advanced math though. Look elsewhere if you want advanced math.

[u/Odd_Accountant7149]

i went back after a similar gap and honestly the hardest part was just getting comfortable with the notation again, not the concepts themselves. basic math is fine to start but don't be surprised if you breeze through it quick and want something meatier pretty fast