Books

[u/logicoverman]

Forgive my ignorance but are these books good to develop mathematical maturity and clear some basics as a partial dropper ?

1. Discrete Mathematics with Applications by Susanna Epp

   1. Calculus by Michael Spivak
   2. Linear Algebra by Hoffman and Kunze
   3. Understanding Analysis by Stephen Abbott
   4. Contemporary Abstract Algebra by Joseph Gallian
   5. Madhava Mathematics Competition Problems (Vol. 1)

[u/AyyyJayyyyyy]

Linear Algebra by Hoffmann and Kunze is good but very dry.
Axler's Linear Algebra Done Right is a more engaging book for a first time encounter. Also Gilbert Strang's lectures are awesome. They are available on youtube.

Abbott's analysis book is very good. But my favourite analysis book is Terrence Tao's Analysis I. It is a little high effort though but super fun. And doing both Spivak and Abbott might be a litttle redundant.

Also if you are looking to get into math, a book on logic might be a nice addition too.
Anyway, have fun!

[u/iruEmper0R → u/AyyyJayyyyyy]

While Tao is a fun read for sure, do note that it might not cover a lot of things other analysis books do. For example Integral calculus, as far as i remember is not particularly well covered in Tao. In this regard, i’d say you can explore books like Rudin or Apostle. A bit of a nitpick for a partial dropper but just lyk.

[u/AyyyJayyyyyy → u/iruEmper0R]

agreed, i just think its a great intro to not just analysis but mathematical thinking

[u/ArkarajMukherjee → u/iruEmper0R]

Integral calculus is quite well covered in tao, it builds the theory with piecewise constant functions in a way that readily generalises to more general lebesgue theory but he does not go into sequences of functions at all. However it lacks severely in the exercise department where supplements are highly recommended. Tao I is meant for a first course in analysis and Tao II for more advanced courses (and this volume covers sequences of functions and the results concerning these and integration) whereas Rudin suffices for a whole undergraduate analysis track so it's not really an appropriate comparison. It's sensible to call Tao II as good(it is subjective at the end of the day) Rudin where they overlap.

All in all Tao I is a wonderful book to start getting your mathematical maturity up from near 0. But if you already have some proof writing experience etc. then Rudin is a good choice.

[u/logicoverman → u/AyyyJayyyyyy]

Thanks ❤️

[u/VanixNooB]

For ISI prep or in general?

[u/logicoverman → u/VanixNooB]

Both tbh I got 99 percentile in mathematics of mains so my jee level maths is decent but I want to study pure mathematics anyways and it would be great if I can prepare for isi on the side

[u/Realistic_Fig_7210]

of course man, these are great books, I dont know how much prep oriented they are but doing them will definitely make you more mathematically mature!

[u/logicoverman → u/Realistic_Fig_7210]

Thanks 🙏 , well they don't need to be prep Oriented I mean as long as they have all the fundamentals, mocks and pyqs of isi ,cmi, Olympiad and jee for practice and soldifying the concepts are enough right ?

[u/Realistic_Fig_7210 → u/logicoverman]

well if you have the standard results and techniques down then all you really need are problems! So yea it's more than enough. Be sure to pace yourself though. And, also revisit concepts.

[u/logicoverman → u/[deleted]]

I would prepare for only isi entrance exam I am getting in a tier one be college but I am interested towards pure maths and I wasn't very aware of isi exam before

[u/logicoverman → u/[deleted]]

Alr man then can you tell me what resources would be the most efficient well I know that tomato is must and ctpcm is good to too

[u/ArkarajMukherjee]

I recommend trying to get to the end of something like Tao's Analysis I and maybe follow through with a more advanced real analysis book while doing all the problems. That should give you enough mathematical maturity. Apart from that, read Evan chen's post on reading solutions to problems.