Ask HN: What are the best general math workbooks?
By saying general math in the title I mean all of the following (in American way):
- Algebra 1, 2
- Geometry
- Precalculus
- Calculus 1, 2, 3
- Statistics and Probability
- Discrete Math
- Linear Algebra
- Differential Equations
But especially these two:
- Calculus 1, 2, 3
- Linear algebra
I am currently studying at a non-english university in a technical specialty involving math (Calculus and Linear Algebra, to be exact). Right now the workload is 3-4 hours of classes a week, which is painfully low. And after a second year, apparently even less time will be spent on it. My English is good enough to consume math content, so that's not an issue. As well as explanations: I have already found and used resources (both in English and my mother tongue) to self-study fast enough to submit my homework.
What actually is an issue are workbooks (or exercise books, whatever you call it). All the workbooks by which we study vary in quality and there are library shortages. The authors are almost always dropping easy exercises right after the start of the paragraph in favor of much more complex ones.
Since I can buy books on Amazon or acquire PDFs using other methods I am asking for your advice on picking general math workbooks that fall under all of the following criteria:
1. There is a shit ton of exercises in the book, varying greatly in their complexity. You can't solve the book in a month or two even if you study 24/7. This way it's suitable for spaced repetition.
2. The author does not sacrifice easy stuff for hard stuff and vice versa.
3. The answers are given to all of the exercises, no matter the complexity.
4. The solutions, however, are unnecessary.
5*. The workbook itself may actually be some online platfrom like Grasple. Paul's Online Math Notes https://tutorial.math.lamar.edu He's got a healthy amount of exercises for each topic with worked out solutions, both inside the notes (as examples) and as practice/assignment problems. I've found that his exercises/examples don't pull punches. Oh my god, this took me on a nostalgia trip. I am near tears seeing this site again. I was a terrible CS student in university. I had failed all my classes(Math, Physics, CS) my first semester at engineering school, got placed on probation and ended up dropping out into community college. There I continued to struggle but when I discovered Paul's online notes I started to turn things around eventually getting back into that Engineering school and graduating with a respectable 3.3 GPA(don't look at my disaster of a transcript though). I still wasn't great academically and not putting in 100% effort stand among one of my greatest regrets in life but the feeling of sitting down and studying with friends using Paul's online notes was a memorable moment during my university days. It was a care free world (other than anxiety over test grades) just me, my friends, and Paul's online notes and then going to the local Chinese buffet after all of us passed our midterms with at least a C. I never really felt like I internalized the concepts rather just constantly barely being above water prepping for tests and a school like NJIT is not as kind towards plug and chug learning as community colleges are but still these guides will help you study better and it lead me to better appreciating all of these concepts years down the line even though I didn't fully internalize all of them. My Linear Algebra https://hefferon.net/linearalgebra/index.html comes with lots of exercises in each section, from easy to (a few) pretty hard. There is a book of worked solutions that covers all exercises. It is free so if you download it (and the solutions) and you find that it doesn't suit then no harm done. There is no platform, no way of having the computer check your answers (if that is what you mean). For things like proofs, I don't think the technology can do that at this point. > It is free so if you download it (and the solutions) and you find that it doesn't suit then no harm done. Not entirely free. It does seem to require you to give an email address to OpenIntro. I'm guessing they send a download link there, but the site does promise to spam you, keep your data indefinitely, and share (read sell) it if they decide that doing so furthers "the mission of OpenIntro" Your book has helped me understand determinants so much better than I had before. I really love its progression and depth, and I still have a lot more of it to get through. Thank you for making it easily available. You are welcome. I am glad you find it useful. I am glad to find you here. I did do some practice problems on rusty topics from your textbook 2-3 years ago. Thanks for putting it together I re-learned math via Kahn academy. While I had a good math education, that was two decades prior. My child was starting to study the Calculus AB curriculum, and I wanted to have some basis for helping them (or at least encouraging them). I found I literally had to start with adding/ multiplying fractions. I did get through the Calc, but stopped during that section because of time constraints. But I found the basic math portions of the exercises to be quite helpful and feel like it was a good progression. There are a lot of exercises and it is free. I recently started a degree with Open University in Engineering (a distance learning course that's fully accredited in the UK but works for me as I move around while my wife works as a Postdoc, currently in Palo Alto). The book I've found that covers me from math basics (basically GCSE, so high school Maths) through to the more advanced topics I know I will need is Engineering Mathematics by K. A. Stroud. I'd highly recommend it. It contains a good number of exercises (and all solutions), covers all the topics I need, and progresses at a good pace. You can see the contents here: https://www.bloomsbury.com/us/engineering-mathematics-978135... Fellow Brit! I used KA Stroud (eng maths and advanced eng maths) all the way through my BEng and MSc! I know what you're asking for "sbornik" notebook with all problems to solve. The rough equivalent in the North America market is the Schaum's Outline series. I have two books that satisfy criteria 1 through 4, but they are full textbooks with explanations not just exercises. Lots of exercises though (easy) and lots of problems too (hard). Links in my profile. In the meantime I will share with you the concept maps from the two books, since they might be helpful to "situate" you on the journey towards all these topics: https://minireference.com/static/conceptmaps/math_and_physic... and https://minireference.com/static/conceptmaps/linear_algebra_... Not a traditional paper workbook, but a better web-based alternative is Math Academy: https://mathacademy.com/#courses A fellow hacker with a strong math education background spent most of the last decade building this and it's quite impressive (more exhaustive than anything I've seen). I don't know of a better way to learn math than this. One answer: the Schaum's Outline series. Find the one(s) corresponding to your topic. This is the actual answer to the question OP asked. Most of these other answers are good generic advice, but for somebody wanting "workbook" resources with exercises and answers, Schaum's is the way to go. The publisher of the "for Dummies" series also has workbook type books for many (most?) of the required math subjects here, that are pretty much just exercises and answers. Those and/or the Schaum's books should cover pretty much everything OP is asking about. I concur with this post. Shaum’s outlines are no-nonsense supplements for any math course that isn’t proof-based. I wish someone wrote math books in the style of The Little Schemer. That’s the only style I can follow and be engaged. If anyone knows math books written in this style please let me know! Art of Problem Solving has a great high school math curriculum with exercises. It also has an online math question component called "Alcumus" that you can use as well. Cannot speak highly enough of this recommendation. This will give you a clear picture of your progress and make you confident about the type of problems you can solve. If you're not too concerned about proofs, I can highly recommend K. A. Stroud's 'Engineering Mathematics', and the follow-on text, 'Advanced Engineering Mathematics'. It leads the reader from basic arithmetic all the way up to complex analysis, one exercise at a time. This will take up some space in your home, but there are a ton of used textbooks on Amazon and eBay. The older ones that aren't used anymore are only a few dollars each. The books themselves may only have answers to the odd-numbered questions, but that's still a lot of questions. (Learning how to check your own work is also a good exercise, but if you need something guaranteed to be reliable, you can plug a lot of problems straight into Wolfram Alpha or even a good graphing calculator.) Mathematical Statistics with Application by Mendenhall Scheaffer Wackerly. Works for me, at least #1 #2 criteria are satisfied, critery #3 is satisfied only for numerical tasks. Stewart’s Calculus has an enormous number of exercises. Can't recommend this book enough. Khan Academy fits most of your description. The number of exercises is not unlimited (because that’s an unusual requirement). It could supplement other material if you truly need a huge quantity of exercises. Once you’re into more advanced topics (calculus and above), mit opencourseware is probably the best quality material. Once again, the exercises are the quantity of a typical course. For calculus, I found Thomas' Calculus (https://www.amazon.com/Thomas-Calculus-Early-Transcendentals...) the most helpful. It's a textbook but has a lot of exercises. Advanced Calculus by Woods is an oldie but goodie. Concise, but with a lot of exercises. A pdf can be obtained legally from the Internet Archive:
https://archive.org/details/advancedcalculuswoods We got a few Beast Academy workbooks for my niece for Christmas last year and she loved them. A little lower level than what you are looking for (target ages 6-13), but tons of fun. For probability all the way up to (excluding) measure theory, Grimmett & Stirzaker's "Probability and Random Processes", plus the accompanying "1000 exercises in Probability" for the solutions, should fit your bill perfectly. Essential Calculus Skills Practice Workbook with Full Solutions By Chris McMullen The Art of Problem Solving!!! Cannot recommend highly enough. Comprehensive, rigorous, and well written. Amazing community around them too. Can take you all the way to the IMO, if you want. Yes! The books if I remember correctly are designed around solving a lot of problems first and foremost. Taken from the description of one of their books: "The text is structured to inspire the reader to explore and develop new ideas. Each section starts with problems, giving the student a chance to solve them without help before proceeding. The text then includes solutions to these problems, through which algebraic techniques are taught. Important facts and powerful problem solving approaches are highlighted throughout the text. In addition to the instructional material, the book contains well over 1000 problems." Richard W. Hamming, Applied Mathematics - Methods of Mathematics Applied to Calculus, Probability, and Statistics. I don't know if Schaum's outlines satisfy all your criteria, but some of them are surprisingly good. “The practical man” series. Calculus for the practical man is good. (Hat tip to Feynman for recommending it.) Variations of this exact question are asked so often. Have you tried searching about it?
hn.algolia.com Variations of "How do I learn math?"? Yes, absolutely. Variations of anything math-related but not textbooks or courses? Heck no. It would be foolish of me to ask HN something that is publicly avaliable on the internet. For example, that's how I found out about mathtutordvd.com in a comment thread for a three year old reddit post. I have spend a few evenings looking for information on math workbooks, but there just isn't enough of it. I disagree, what is common are questions or discussions on math books in general which are typically dominated by higher math and material for people already in posession of a stem degree. However many, if not most, math books are not suited for self study. I don't often see discussions on fundamentals or other "unsexy" parts of mathematics. I find OPs question refreshing in a way. Principles of mathematical analysis by rudin Yes!!!!