Book recommendation for Abstract Algebra for self study and beginner

Question

I am currently attending Coursera course named "Intro to mathematical thinking" and i want to do some abstract algebra along with it to test my proof writing. Please suggest easy gentle intro to subject so that i can study in my own.

Thanks

Answer 1

I personally recommend "A Book of Abstract Algebra", https://www.amazon.co.uk/gp/aw/d/0486474178/ref=mp_s_a_1_1?ie=UTF8&qid=1523270468&sr=8-1&pi=AC_SX236_SY340_FMwebp_QL65&keywords=a+book+of+abstract+algebra&dpPl=1&dpID=516WR87HwbL&ref=plSrch.

It is the most gentle introduction I can think of. Later Chapters are more difficult, but the first part is gentle and it is self contained I would say.

Answer 2

'calculus for the ambitious' explains how calculus works from the basics using 'basic' algebra and intuition. https://www.amazon.co.uk/Calculus-Ambitious-T-W-K%C3%B6rner/dp/1107686741

edit: below are some of my recommendations for other resources

there are lots of resources on AOPS (the art of problem solving) you can try out, including problems and book suggestions). The best way to improve is normally my doing questions you find hard and require some thought.

I also have a brilliant subscription, which - you could do the trial and see whether it helps - can be quite good for problem-solving based learning with a variation in difficulty.

Longer-term goals:

STEP (Sixth Term Examination Paper) have good pre-university questions. If you want to attempt these, start with STEP I, as this is a bit easier than STEP II and STEP III. This is the exam used in the UK -where I live- to determine entrance to Cambridge for Maths (the best maths course in the world according to the QS rankings I saw). This is a hard exam, even for questions which require little maths knowledge. My experience with these is that once you understand GCSE level maths in the UK (i.e. age 15/16) you can attempt some questions but not all, and after A-level (age 18) you could attempt them all. The first time you attempt a question like this, it will probably take a while, so persistence is key!

Once you get a bit more experience, it is fun to have a go at some algebraic IMO (International Maths Olympiad) problems. It also could act as a nice mid/long-term goal, to try and do one of them (even if it takes several days' hard thought!).

Links to resources: https://artofproblemsolving.com/store?msclkid=42fcbc06ed6714fdf763e6d5eb8ff346 This has AOPS recommended books https://artofproblemsolving.com/ https://mathsorchard.weebly.com/step-past-papers.html https://brilliant.org/ https://www.imo-official.org/problems.aspx

Good luck and enjoy!